Body segment inertial parameters of elite swimmers ... · Body segment inertial parameters of elite...

Body segment inertial parameters of elite swimmers:

analysis using DXA and estimation of errors from

indirect estimation methods

by

Marcel Mourao Rossi

Bachelor in Sports Training

Submitted as partial requirements for the degree of Master of Science

School of Sport Science, Exercise and Health

The University of Western Australia

August 2012

DEDICATION

This thesis and any other future work or achievement is always dedicated to my parents,

Alberto M. Rossi and Sonia M.O.M. Rossi, the most dedicated, nurturing, encouraging and

supportive human beings I could have ever possibly met in life. Dad, mom, God only knows

how hard this journey has been for us and whether it will pay off after all. It’s not the most

important though, I would go through this another thousand times if necessary, as nothing in

life motivates me more to work as hard as necessary to reach for the stars (amongst which

that sky lantern with my name on that dad launched when I was born may be aloft now) than

knowing that by doing so I’ll be your pride and joy. I know I’ve chosen a road in life that does

not allow me to be with you whenever I want or need, but if after every step forward I make I

can safely picture yourselves alongside me, squeezing my shoulders and saying “Attaboy,

that’s my son!”, I’ll know the step was worthwhile indeed. I love you, endlessly.

“Mas o mundo foi rodando

Nas patas do meu cavalo

E já que um dia montei

Agora sou cavaleiro

(Laço firme e braço forte)

Num reino que não tem rei.”

Geraldo Vandré - Disparada

[iii]

ABSTRACT

The present study proposed a new method to compute body segment inertial parameters

(BSIPs) using DXA. This new approach essentially co-registers the areal density data with

grayscale images, which enables a relationship between the pixel colour intensity and the

mass recorded to be established for the referred area. BSIPs could then be calculated for

various segments. Using this method, BSIP were then measured in elite male swimmers,

elite female swimmers and young adult Caucasian males. The study then compared BSIPs

derived from the proposed technique against five previously used indirect BSIP estimation

methods across all three populations.

Ten elite male swimmers, eight elite female swimmers, and ten young adult Caucasian

males had their whole body mass calculated from the relationship found between pixel

colour intensity and areal density. The calculated masses were compared against the

criterion value obtained from the DXA scanner by percentage root mean square error

(%RMSE). Subjects were also scanned with 3D surface scans to enable mapping of key

anthropometric variables necessary for calculation of BSIPs when using the indirect

estimation methods. The mass, centre of mass (COM) and moment of inertia (MOI) about

the sagittal axis of seven body segments (head, trunk, head combined with trunk, upper arm,

forearm, thigh & shank) were computed from the proposed DXA method for each group.

Differences between participant groups were assessed using the analysis of variance

(ANOVA). When applying the five indirect estimation methods to each of the three referred

populations, errors were assessed, using the BSIPs gathered with DXA as criterion, by

calculating the %RMSE and searching for significant differences in absolute percentage

errors for all BSIPs.

Computing BSIPs using the proposed method yielded %RMSE of less than 1.5%. This

agreed with the accuracy of previous DXA BSIP estimation methods. The results also

revealed significant differences in BSIPs between participant groups. Elite female swimmers

reported significantly lower segment masses than male swimmers and untrained males.

iv

Male swimmers recorded greater inertial parameters of the trunk and upper arms than the

other two groups. Using BSIP computed from DXA as a measurement criterion, the analysis

revealed that none of the indirect methods were able to accurately estimate BSIPs in any of

the participant groups, as large errors were observed for each method. Therefore, caution

should be taken when computing BSIPs for elite swimmers using these indirect methods.

Finally, this work demonstrated that DXA can be used to accurately estimate BSIPs, at least

in the frontal plane. With further development, DXA has the potential to provide a full set of

BSIP in all dimensions.

[v]

TABLE OF CONTENTS

Dedication ................................................................................................................................ 2

Abstract ....................................................................................................................................iii

Table of Contents ..................................................................................................................... v

List of Figures ......................................................................................................................... viii

List of Tables ............................................................................................................................ x

Acknowledgements ................................................................................................................xiv

Chapter 1 ........................................................................................................................... 16

Introduction to the Problem .................................................................................................... 16

1.1 Introduction ................................................................................................................. 16

1.2 Statement of the Problem .......................................................................................... 18

1.3 Significance of the Study ............................................................................................ 19

1.4 Research Hypotheses ................................................................................................ 20

1.5 Delimitations and Limitations ..................................................................................... 20

1.5.1 Delimitations ....................................................................................................... 20

1.5.2 Limitations .......................................................................................................... 20

1.6 Definition of Terms ..................................................................................................... 21

1.7 List of Abbreviations ................................................................................................... 22

Chapter 2 ........................................................................................................................... 23

Literature Review ................................................................................................................... 23

2.1 Introduction ................................................................................................................. 23

2.2 Direct Estimation Methods ......................................................................................... 25

2.3 Indirect Estimation Methods ....................................................................................... 31

2.3.1 The Modified Chandler Method .......................................................................... 32

2.3.2 The Yeadon Method ........................................................................................... 33

2.3.3 The Zatsiorsky Simple Regression Method ....................................................... 34

2.3.4 The Zatsiorsky Multiple Regression Method ...................................................... 34

2.3.5 The Zatsiorsky Geometric Method ..................................................................... 35

[vi]

2.4 The DXA Method ........................................................................................................ 36

2.5 Influence of different methods on dynamic analyses ................................................. 39

2.6 Summary .................................................................................................................... 42

Chapter 3 ........................................................................................................................... 43

Methods and Procedures ....................................................................................................... 43

3.1 Participants ................................................................................................................. 43

3.2 Indirect BSIP estimation methods .............................................................................. 44

3.3 Data acquisition Protocol ........................................................................................... 45

3.3.1 Dual-Energy X-Ray Absorptiometry (DXA) ........................................................ 46

3.3.2 Body laser scan .................................................................................................. 47

3.3.3 Anthropometry .................................................................................................... 49

3.4 Biomechanical model ................................................................................................. 50

3.5 Data Processing ......................................................................................................... 50

3.6 Data Analysis ............................................................................................................. 63

Chapter 4 ........................................................................................................................... 64

Results ................................................................................................................................... 64

Chapter 5 ........................................................................................................................... 77

Discussion .............................................................................................................................. 77

Chapter 6 ........................................................................................................................... 82

Summary Conclusion & Recommendations for Future Studies ............................................. 82

6.1 Summary .................................................................................................................... 82

6.2 Conclusion .................................................................................................................. 84

6.3 Recommendations for Future Studies ....................................................................... 84

REferences............................................................................................................................. 85

Appendix A ......................................................................................................................... 93

Consent Form ........................................................................................................................ 93

Consent Form ....................................................................................................................... 94

Appendix B: ........................................................................................................................ 95

Indirect Estimation Methods ................................................................................................... 95

Cadaveric-based geometric method (modified Yeadon (1990)): ........................................... 96

Cadaveric-based regression equation method (modified Chandler et al. (1975)) ............... 105

Gamma-ray-based simple regression method (Zatsiorsky and Seluyanov, 1983) .............. 107

[vii]

Gamma-ray-based multiple regression method (Zatsiorsky and Seluyanov, 1985) ............ 110

Gamma-ray-based geometric method (Zatsiorsky et al., 1990) .......................................... 115

Appendix C: ..................................................................................................................... 118

Anthropometric measures .................................................................................................... 118

Appendix D: ..................................................................................................................... 127

Biomechanical Model ........................................................................................................... 127

Appendix E ....................................................................................................................... 135

Matlab Codes ....................................................................................................................... 135

Convert_dxa_images.m ....................................................................................................... 136

segment_body.m .................................................................................................................. 140

[viii]

LIST OF FIGURES

Figure 3.1: The GE Lunar DXA scanner ................................................................................ 46

Figure 3.2: The Artec LTM

3D scanner. .................................................................................. 47

Figure 3.3: The 3D scan of the participant after the scanning procedure (before post-

process).................................................................................................................................. 49

Figure 3.4: Screenshot of the enCORE® software when the day pass code is used, showing

the two BMD and TISSUE images derived from the respective matrixes. When the mouse is

placed on a given area (red circle), the mass and the coordinates the local mass element

pointed by the arrow are shown on the bottom of the screen (red ellypses). ........................ 52

Figure 3.5: The relationship between the mass element (red rectangle) and the pixels of the

bitmap image; often the mass element contained pixels from the outside of the body or its

borders were not aligned with the pixels. ............................................................................... 54

Figure 3.6: Grayscale images of the BMD and TISSUE compartment matrices created by

the enCORE® software (right and middle, respectively), and the summation of both images.

Red and blue dots correspond to the locations of the mass elements used for the first and

second matrices, respectively. ............................................................................................... 56

Figure 3.7: Binary images of the BMD, TISSUE and whole body mass created to eliminate

noise outside the region of interest. All black pixels have nil mass value. ............................ 57

Figure 3.8: 2D representation of the I_BMD_mass, I_TISSUE_mass, and I_mass_total

matrices (right, middle and left images, respectively) using a colour scale to show the

density of the mass pixels. ..................................................................................................... 58

Figure 3.9: A 3D representation of the I_mass_total matrix. ................................................ 59

Figure 3.10: Representation of the 25 points used to segment the body using the

segment_whole_body.m function. ......................................................................................... 61

Figure 3.11: Output of the segment_whole_body.m function, containing the segmentation

planes in the whole body (left figure, red dashed line), the clicked points that defined the

geometric figure used as frontier to delimit the segments (red dots), and the segment COM

positions. ................................................................................................................................ 62

[ix]

Figure 4.1: Mean Absolute Percentage Error (MAPE) for segment mass (Kg) of the Chandler

(C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and

Zatsiorsky geometric (Z3) estimation methods against DXA, observed for young adult

Caucasian males (Normal), Male swimmers and Female swimmers. ................................... 73

Figure 4.2: Mean Absolute Percentage Error (MAPE) for segment centre of mass position in

the longitudinal axis from the distal end point (COM, cm) of the Chandler (C), Yeadon (Y),

Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky

geometric (Z3) estimation methods against DXA, observed for young adult Caucasian males

(Normal), Male swimmers and Female swimmers. ................................................................ 74

Figure 4.3: Mean Absolute Percentage Error (MAPE) for segment principal moment of

inertia about the sagittal axis (Ixx, Kg�cm2) of the Chandler (C), Yeadon (Y), Zatsiorsky

simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3)

estimation methods against DXA, observed for young adult Caucasian males (Normal), Male

swimmers and Female swimmers. ......................................................................................... 75

Figure A1: The stadium-shape section (left) and the stadium frustum (right) (Yeadon, 1990).

............................................................................................................................................... 96

Figure A2: Representation of the solids for the modified Yeadon’s model. ......................... 100

[x]

LIST OF TABLES

Table 3.1. Mean (SD) of the age (years), height (cm) and weight (Kg) of young adult

Caucasian males in the cohort of the present study (DXA, n=10) and in the studies of

Zatsiorsky et al. (1983, 1985, 1990; n=100) .......................................................................... 43

Table 3.2: Glass marble naming and locations ...................................................................... 46

Table 3.3: 3D scan marker naming convention and locations ............................................... 48

Table 4.1: Minimum error (Emin, Kg), Maximum error (Emin, Kg), Mean Absolute Percentage

Error (MAPE, %) and Percent Root Mean Square (%RMSE) for the bone mineral, tissue and

whole body masses calculated from the respective images. ................................................. 64

Table 4.2: Mean (SD) segment masses (kg) of young adult Caucasian males tested in the

present study (DXA, n=10) and the young adult Caucasian males from Zatsiorsky studies

(Zatsiorsky, n=100). ............................................................................................................... 65

Table 4.3: Mean (SD) segment mass (Kg) calculated for adult Caucasian male (n = 10),

male swimmers (n = 10) and female swimmers (n = 8) using the Chandler model (C),

Yeadon model (Y), Zatsiorsky simple regression model (Z1), Zatsiorsky multiple regression

model (Z2), Zatsiorsky geometric model (Z3,) and the proposed estimation protocol using

DXA (DXA). ............................................................................................................................ 66

Table 4.4: Mean (SD) distance of the centre of mass position in the longitudinal axis from the

distal end point (COM, cm) of adult Caucasian male (n = 10), male swimmers (n = 10) and

female swimmers(n = 8) according to the Chandler (C), Yeadon (Y), Zatsiorsky simple

regression (Z1), Zatsiorsky multiple regression (Z2), Zatsiorsky geometric (Z3) and DXA

estimation methods. ............................................................................................................... 67

Table 4.5: Mean (SD) values for segment principal moment of inertia about the sagittal axis

(Ixx, Kg�cm2) of adult Caucasian male (n = 10), male swimmers (n = 10) and female

swimmers (n = 8) according to the Chandler (C), Yeadon (Y), Zatsiorsky simple regression

(Z1), Zatsiorsky multiple regression (Z2), Zatsiorsky geometric (Z3) and DXA estimation

methods.................................................................................................................................. 68

Table 4.6: Percentage Root Mean Square Error (%RMSE) for segment mass (Kg) of the

Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression

(Z2), and Zatsiorsky geometric (Z3) estimation methods against DXA, observed for adult

Caucasian male (n = 10), male swimmers (n = 10) and female swimmers (n = 8). .............. 70

[xi]

Table 4.7: Percentage Root Mean Square Error (%RMSE) for segment centre of mass

position in the longitudinal axis from the distal end point (COM, cm) of the Chandler (C),

Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and

Zatsiorsky geometric (Z3) estimation methods against DXA, observed for adult Caucasian

male (n = 10), male swimmers (n = 10) and female swimmers (n = 8). ................................ 71

Table 4.8: Percentage Root Mean Square Error (%RMSE) for segment principal moment of

inertia about the sagittal axis (Ixx, Kg�cm2) of the Chandler (C), Yeadon (Y), Zatsiorsky

simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3)

estimation methods against DXA, observed for adult Caucasian male (n = 10), male

swimmers (n = 10) and female swimmers (n = 8). ................................................................. 72

Table A1: Labelling of the solids forming each of the 16 segments, with the respective type

of solid used and density (Kg*l-1

) ........................................................................................... 97

Table A2: Labelling of the sections as bottom (b) or top (t) base of the solids, anthropometric

measures used to determine the parameters r and t for each section and the position relative

to the longitudinal axes of the referred segments .................................................................. 98

Table A3: mass (Kg) and principal moments of inertia (Kg*cm2) equations and average

centre of mass position obtained for the modified study of Chandler et al. (1975).............. 106

Table A4: modified predictors for the non-linear equations for segmental moments of inertia

............................................................................................................................................. 107

Table A5: Coefficients of the linear regression equations to determine the inertial parameters

of the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is

the body weight, X2 is the body height and Y is segment’s mass (M), centre of mass position

on the longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or

transverse (IZ) axes. ............................................................................................................. 108


of the upper limb segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the

body weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on

the longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or



of the lower limb segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the

body weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on

the longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or


[xii]


of the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3 +

B4X4, where X1, X2, X3 and X4 are the most predictive anthropometric measures for each

segment and Y is segment’s mass (M), centre of mass position on the longitudinal axis

(HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.

............................................................................................................................................. 111


of the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3,

where X1, X2 and X3 are the most predictive anthropometric measures for each segment and

Y is segment’s mass (M), centre of mass position on the longitudinal axis (HCM), or moments

of inertia about the sagittal (IX), longitudinal (IY) or transverse (IZ) axes. ............................. 112

Table A10: Coefficients of the linear regression equations to determine the inertial

parameters of the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2 +

B3X3, where X1, X2 and X3 are the most predictive anthropometric measures for each

segment and Y is segment’s mass (M), centre of mass position on the longitudinal axis

(HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.

............................................................................................................................................. 113

Table A11: The most predictable anthropometric measures for each segment to be used in

the multiple linear equations for inertial parameters of the head and trunk segments. ....... 114





Table A14: Anthropometric lengths and girths used to create the geometrical model of the

subject and determine the inertial parameters. The coefficient KB is used to multiply the

anthropometric length to obtain the biomechanical length. ................................................. 115

Table A15: Segment mass coefficients (KM), and the moments of inertia coefficients relative

to the sagittal (KX), longitudinal (KY) and transverse (KZ) axes. ........................................... 117

Table A16: Virtual points created ......................................................................................... 128

Table A17: End points of all segments of the biomechanical model ................................... 129

[xiii]

[xiv]

ACKNOWLEDGEMENTS

As the road to complete my thesis has finally come to its end, I cannot help thinking of those

who had a very meaningful role in this journey. Thus, I would like to express my deep

gratitude to all of you, for all the support, guidance, encouragement, friendship, and (why

not?) criticism. Each of you can claim a little piece of this work!!

To my dear family, the first ones ever to believe in me and in my dreams, for all this years by

my side. Here I am, and wouldn’t be without you. Thanks mom, dad, Andrea, Bruce, Mike,

Aunt Ana, Uncle Antonio, grandma, always in my heart.

To all the great Brazilian friends that never let the distance fade our bond away, who always

ensured I could count on them wherever and whenever I needed. So many to be listed, but

not to be forgotten! Miss you a lot guys!!!

To Yes Australia, for the excellent job and assistance throughout all the process to arrive in

Australia and become an UWA student. Thanks Antonio, Thiago and Rodrigo!

To my supervisors, for all valuable feedback provided with expert knowledge and opinions.

Thank you Profs. Amar El-Sallam, Brian Blanksby, Andrew Lyttle and Nat Benjanuvatra,

your expertise and experience were deeply appreciated and helped me improve as an

academic.

To all the participants, who volunteered and handled the data collection with such good

mood and patience. Thank you swimmers, UWA students and cricket lads!

To all the academics, who helped me so much and allowed me to learn a bit from their

expertise in the area. Thank you Profs Ricardo Barros, Cesar Montagner, Jacque Alderson,

Bruce Elliott, Jim Dowling, Tim Ackland, Michael Rosemberg.

To the friends at SSEH who have helped a lot, without you it would simply not happen.

Thanks Koji, Trenton, Laurence, Christian, Fausto, Luqman, Marius, Sathis, Nev, you are

legend!

To the SSEH staff and technicians, always so kind and helpful. Thanks Inga (mother figure

#1), Margareth, Barbara, and Jarrid!

To the Uniswim staff, for all the friendship and empathy!! Thanks Suzette (mother figure #2),

Julia, Michelle, Taku, Susan (mother figure #3), Shan, Julie, Mel, and Daniel for being

alongside on the pool deck!!

[xv]

To Swimming, that tailored the man who I am and still provide me with the values to become

even better, and the courage to pursuit my dreams. Thank you so much, it is more than a

pleasure living for you!

Finally, if you feel you had a meaningful role in this journey but did not see your name listed

here, please do not get mad at me! You know, a bunch of neurons had been burned, and my

memory is not the same after this thesis. I might have forgotten to include your name here,

but not your contribution, so thank you so much _____________, and sorry for my goldfish

memory!!!

[16]

Chapter 1

INTRODUCTION TO THE PROBLEM

1.1 Introduction

Achieving accurate body segment inertial parameters (BSIPs) is important in human motion

analysis. The inertial parameters are segment mass, centre of mass (COM) and principal

moments of inertia (MOI) about the longitudinal, sagittal and transverse axes passing

through the COM; and are needed in inverse dynamic modelling to obtain kinetic information

around joints. Several BSIP estimation methods, classified as either direct (i.e., BSIPs

measured directly from cadavers or using medical imaging technology in living subjects) or

indirect (i.e., BSIPs are estimated based on specific anthropometric values) have been

proposed.

The earlier BSIP estimations in living subjects resulted from modelling direct measurements

of cadavers (Chandler et al., 1975; Clauser, McConville, and Young, 1969; Dempster,

1955). Analysis was limited to only a few cadavers who were elderly Caucasian males.

Hence, extrapolating their results to other populations, especially elite athletes, is restrictive.

Also, factors such as fluid and tissue loss in segmentation, and different properties of living

and deceased tissue, can affect the accuracy of the derived BSIP information (Durkin,

2008).

The development of medical imaging technologies such as gamma-ray scanning (Zatsiorsky

and Seluyanov, 1983; Zatsiorsky, Seluyanov, and Chugunova, 1990), computed

tomography imaging (Ackland, Henson, and Bailey, 1988; Huang and Suarez, 1983), and

magnetic resonance imaging (Cheng et al., 2000; Martin et al., 1989; Mungiole and Martin,

[17]

1990), have enabled direct measurement of BSIPs on living humans. Despite their accuracy,

they are expensive, labour intensive during data processing, not widely accessible and/or

expose subjects to high doses of radiation. Hence, they are not widely used.

Indirect methods estimate BSIPs based on the relationship between anthropometric

variables and the desired inertial parameters. As a subject’s anthropometry can be gathered

quickly, at minimal cost, free of radiation, and without the need of expensive equipment and

facilities, indirect methods are used more than direct estimations. Indirect methods are

classified into regression equations which use anthropometric data to predict the BSIPs

(Chandler et al., 1975; Dempster, 1955; Durkin and Dowling, 2003; Zatsiorsky and

Seluyanov, 1983, 1985); and geometric models which create and use geometric figure

templates for the segments from the anthropometry. Thus, the BSIPs are calculated using

geometric formulae (Durkin and Dowling, 2006; Hanavan Jr, 1964; Yeadon, 1990; Zatsiorsky

et al., 1990). Despite the advantages, the indirect estimations found large errors when

applied to a population having different physical characteristics from those for whom the

methods were devised; and did not provide accurate subject-specific BSIP data (Durkin and

Dowling, 2003). Therefore, it could be expected that indirect estimation methods are

unsuitable for computing BSIPs in elite athletes (e.g., swimmers), due to the different

anatomies of these populations (Olds and Tomkinson, 2009). However, this hypothesis

remains untested.

Dual-energy X-ray absorptiometry (DXA) technology is used mainly to determine bone

mineral density and body composition in vivo (Ellis, 2000; Fuller, Laskey, and Elia, 1992;

Haarbo et al., 1991; Laskey, 1996; Mazess et al., 1990). More recently, it has been used to

estimate segment mass, COM position in the frontal plane, and MOI about the sagittal axis

(Durkin, Dowling, and Andrews, 2002; Ganley and Powers, 2004a; Wicke and Dumas,

2008). Using DXA is accurate, non-invasive, costs less, emits lower radiation exposure, and

requires less time for each analysis than the gamma-ray scanning and other imaging

methods (Durkin et al., 2002; Ganley and Powers, 2004b; Wicke and Dumas, 2008).

Therefore, the purpose of this project was to investigate the validity of five currently used

BSIP estimation methods by comparing the resultant BSIPs of three unique participant

[18]

groups to those derived from the newly proposed direct DXA method. The sample groups

were male and female elite swimmers, and 10 healthy, young adult males who were

anthropometrically similar to those examined by Zatsiorsky and colleagues (Zatsiorsky and

Seluyanov, 1983, 1985; Zatsiorsky et al., 1990).

1.2 Statement of the Problem

The aim of this study was to examine the validity of BSIPs calculated from five regularly

used indirect estimation techniques by comparing them against BSIPs gathered using the

propose DXA method in elite swimmers (10 males and 8 females); and a group of 10 healthy

young adult Caucasian males who were selected to match subjects of Zatsiorsky et al.

(Zatsiorsky, 1983; Zatsiorsky and Seluyanov, 1985; Zatsiorsky et al., 1990).

More specifically, a series of studies will be conducted to:

• Determine whether the BSIPs from the DXA method devised for this study were as

accurate as other methods reporting DXA findings (Durkin et al., 2002; Ganley and

Powers, 2004a; Wicke and Dumas, 2008);

• Determine whether there were significant differences in BSIPs between elite male

swimmers, elite female swimmers and young adult Caucasian males;

• Examine 5 different indirect BSIP estimation models with similar segmentation

protocols to compare with the new DXA method. They are:

1) The Modified Chandler method: used simple linear relationship between the

whole body weight and the segment masses, the COM position as a fixed

proportion of the segment’s length (Chandler et al., 1975), and the non-linear

equations from Yeadon and Morlock (1989) were used to calculate the MOI

about the sagittal axis (Ixx).

2) The Yeadon method is a geometric method using cylindrical and stadium-

shaped solids to represent body segments (Yeadon, 1990). To calculate BSIPs,

the geometrical representations are assigned a density value based on the

findings of Dempster (Dempster, 1955). Small adaptations to the geometric

figures were made to ensure whenever possible that the body could be

[19]

segmented the same way as in other estimation models. Thus, the number of

anthropometric measurement is minimised.

3) The Zatsiorsky Simple Regression Method (1983) (Z1) only uses the whole

body mass and height as predictors for all BSIPs.

4) The Zatsiorsky Multiple Regression Model (1985) (Z2) uses a set of up to 4

specific anthropometric data for each segment as predictors in linear equations.

5) The Zatsiorsky Geometrical Model (1990) (Z3) assumes each segment as a

circular cylinder and uses a segment-specific, quasi-density value calculated to

minimise the difference between the cylinder and the real segment volumes.

• Compute the errors associated with each of the previously used indirect BSIP

estimation methods when applied to elite male and female swimmers, by means of

root mean square error;

• Determine whether significant differences occur in absolute errors of indirect BSIP

estimation methods; when applied to elite male swimmers, elite female swimmers,

and young adult Caucasian males;

1.3 Significance of the Study

There is a paucity of literature investigating the validity of indirect BSIP estimation methods

drawn from specific populations, especially from elite athletes. Sports analyses demand

great precision, particularly at the elite level where .01 s or miniscule technique alterations

can be the difference between winning and losing. Therefore, they must be highly valid and

accurate when assessing athletes’ performances. A lack of accuracy in determining BSIPs

may jeopardise an analysis and render it useless.

This study introduced a new approach that has the potential for development for extraction

of accurate and subject specific BSIPs. The proposed techniques addressed, in part, some

the limitations associated with the other indirect methods. This study was the first to quantify

errors associated with using indirect BSIP estimation methods for elite athletes. The

outcomes of this study may assist in future development of a full three-dimensional BSIP

measurement technique.

[20]

1.4 Research Hypotheses

• There would be significant differences in the BSIPs between the three groups (elite

male swimmers x elite female swimmers x Caucasian males).

• Errors associated with each of the different indirect estimation methods would vary

with different participant groups, particularly those with different anthropometric

profile to the samples used in their original development. Hence, there would be a

significant participant groups by methods interaction in BSIP estimation errors.

• Errors associated with indirect BSIP methods would be greater in specialised

populations (elite male & female swimmers) than adult Caucasian males.

Currently, the magnitude of such inaccuracies has not been explored for an elite

swimmer population.

1.5 Delimitations and Limitations

1.5.1 Delimitations

• Competitive swimmers participants were limited to athletes who had achieved at

least one qualifying standard for entry into the Australian Championships from

swimming clubs within the Perth metropolitan area of Western Australia (10 males &

8 females).

• The ten young, healthy, adult Caucasian males participants were required to have a

similar anthropometric profile to the cohort used by Zatsiorsky et al. (Zatsiorsky and


1.5.2 Limitations

• Currently, one cannot definitively determine the validity of the new DXA direct BSIP

estimations, because there are no true criterion measures of the inertial parameters

in vivo (Mungiole and Martin, 1990). Thus, its assessment must be based on

[21]

comparisons with other estimation procedures and the sensitivity of the inertial

parameters to those methods.

• The study did not attempt to validate the new DXA direct estimation method in vitro,

which could provide greater insight regarding its effectiveness. But, this in vitro

approach should be viewed with caution, as errors in the criteria measures were

also reported (Dowling, Durkin, and Andrews, 2006).

1.6 Definition of Terms

• Body segment inertial parameters: measures of the body segment’s resistance to a

change in its linear and angular velocity.

• Principal Moments of Inertia: moments of inertia about the principal axes of the

body.

• Direct body segment inertial parameter estimation methods: methods that enable

each of the inertial parameters to be measured directly.

• Indirect body segment inertial parameter estimation methods: mathematical models

that use other anthropometric measures and their relationship with the inertial

parameters to compute the latter.

• Pixel: the smallest element of a picture represented on the screen.

• Areal density: the mass per unit area of a two-dimensional object.

• Mass element: the rectangular area unit to which a mass value is addressed during

the DXA scan.

• Pixel element: the image pixel with a singular mass value associated after the co-

registration of the areal density matrix data from the DXA scan with the grayscale

image.

[22]

1.7 List of Abbreviations

• DXA: Dual Energy X-Ray Absorptiometry.

• COM: centre of mass.

• MOI: principal moment of inertia.

• Ixx: principal moment of inertia about the sagittal axis.

• Iyy: principal moment of inertia about the longitudinal axis.

• Izz: principal moment of inertia about the transverse axis.

• %RMSE: percentage root mean square error.

• MAPE: mean absolute percentage error.

• ANOVA: analysis of variance.

• SPANOVA: split plot analysis of variance.

[23]

Chapter 2

LITERATURE REVIEW

2.1 Introduction

Biomechanical analyses of human motion use inverse and forward dynamic analyses as

standard tools. Both techniques rely on body segment inertial parameter (BSIP) data such

as the mass, position of the centre of mass (COM) relative to the segment’s length; and the

principal moments of inertia (MOIs) about axes passing through the COM, as input to

calculate the resultant joint forces and moments.

Several techniques were developed to calculate BSIPs. Initially, cadaver specimens were

used to obtain BSIPs directly and, from these, predictive equations were devised and

translated to data from living subjects (Chandler et al., 1975; Clauser et al., 1969; Dempster,

1955). Direct estimation techniques for living subjects also were devised (Drillis and Contini,

1964, 1966), including the use of medical imaging techniques (Durkin et al., 2002; Huang

and Suarez, 1983; Martin et al., 1989; Zatsiorsky, 1983) being the most accurate and

reliable means to obtain subject-specific BSIP data (Durkin, 2008).

As access to the costly instrumentation required for these methods is restrictive, indirect

estimation methods such as calculating BSIPs from subject anthropometry are more

commonly used. Indirect estimation methods extrapolate the relationship between some

anthropometric measures and BSIPs computed from cadavers or living subjects (Durkin and

Dowling, 2003; Zatsiorsky and Seluyanov, 1985); or some modelling techniques are applied

(Durkin and Dowling, 2006; Hanavan Jr, 1964; Zatsiorsky et al., 1990) to the subjects being

analysed. Five of these techniques yield all BSIPs for all body segments and are used

[24]

regularly. Of these five, two were developed from cadaver data (Chandler et al., 1975;

Yeadon, 1990) and three used data collected from living subjects (Zatsiorsky, 1983;

Zatsiorsky and Seluyanov, 1985; Zatsiorsky et al., 1990).

The Modified Chandler Method used simple linear relationship between the whole body

weight and the segment masses, a fixed ratio between the distance from the COM to the

proximal joint relative to the segment’s longitudinal axis (Chandler et al., 1975), and non-

linear equations to compute MOI from measures of segment’s length, width and breadth

(Yeadon and Morlock, 1989).

The Yeadon Method is a geometric method that uses cylindrical and stadium-shaped solids

to represent body segments (Yeadon, 1990). To calculate BSIPs, the geometric

representations were assigned a density value based on the findings of Dempster

(Dempster, 1955). Small adaptations to the geometric figures were made to ensure

whenever possible that the body could be segmented in the same manner as in the other

estimation models. Hence, the number of anthropometric measurements is minimised.

The Zatsiorsky Simple Regression Model (Zatsiorsky and Seluyanov, 1983), the

Zatsiorsky Multiple Regression Model (Zatsiorsky and Seluyanov, 1985) and the Zatsiorsky

Geometrical Model (Zatsiorsky et al., 1990) were developed from measurements collected

from the same 100 adult Caucasian male subjects. The Zatsiorsky Simple Regression

Method (Z1) only uses the whole body mass and height as predictors for all BSIPs.

The Zatsiorsky Multiple Regression Method (Z2) uses a set of specific anthropometric

data (up to 4 measures) for each segment as predictors in linear equations.

The Zatsiorsky Geometrical Method (Z3) assumes each segment as a circular cylinder

and uses a segment-specific quasi-density value, calculated to minimise the difference

between the cylinder and the real segment volumes. A series of kinanthropometric

measures was carried out for all subjects according to the specifications of each study.

However, these techniques might not yield sufficiently accurate results, or be capable of

accounting for morphological differences between subjects. Given the importance of

[25]

accurate BSIP information, the limitations of the previous direct methods must be overcome

so BSIPs of individual subjects can be assessed directly.

2.2 Direct Estimation Methods

Direct BSIPs result from methods enabling direct estimation of the mass, COM position and

MOIs (or the radii of gyration, as the moments of inertia are proportional to the segment’s

mass) of previously defined body segments. They are classified as in vitro (cadaveric) or in

vivo (living subjects), and used to provide individual test scores or to calculate measurement

averages and variations of data drawn from specific populations, which can then be

extrapolated to others in similar populations.

The three most referenced research papers investigating human BSIPs using cadaver

samples were performed at the Wright Paterson USA Air Force Base. The cadavers used by

Dempster (1955) were of eight male war veterans aged 51-83 years old. The limbs were

separated at each of the main joints; and the trunk was divided into neck, shoulder, thorax

and abdomino-pelvis segments. The study provided mass, COM position, volume, density

and MOI about the transverse axis of the segments. The second study was of 13 adult male

cadavers each dissected into 14 segments to provide weight, volume and COM positions

(Clauser et al., 1969). Also, the cadavers were dissected to provide the densities of muscle

(1.08 g/cm3), fat (0.96 g/cm

3), cortical bone (1.8 g/cm

3) and cancellous bone (1.1 g/cm

3)

tissues. Thirdly, Chandler et al. (1975) used six adult male cadavers to obtain mass, COM

position, and the principal MOIs about the three orthogonal axes of the 14 segments (head,

trunk, upper arms, forearms, hands, thighs, shanks & feet).

Direct BSIP estimations from cadavers is the only way to physically separate the body

segments and gather inertial parameters using proper tools such as a balance to measure

mass of a segment. Therefore, in vitro direct BSIP estimations often are used to validate

other estimation procedures, especially in vivo direct methods. Yet, the values obtained,

depend upon the accuracy and reliability of how the measurements were taken; so, results

should be used with caution. For example, Dowling, Durkin and Andrews (2006) studied the

uncertainty/error of the pendulum model used to calculate the moments of inertia of cadaver

[26]

segments, and found them to be subject to errors in the period of oscillation. They also

demonstrated that the uncertainty was reduced to < 3% when the suspension axis was

positioned at a distance from the COM equal to the radius of gyration, rather than at the

proximal site as in previous studies.

Although BSIPs of cadavers can be calculated directly, in vitro methods have limitations to

be considered, such as availability of cadavers, the complexity, cost, time required for the

procedures, and difficulty in obtaining specimens from specific populations. The loss of fluid

and tissue during the segmentation process also should be accounted for as a source of

error. Some procedures have used frozen specimens to avoid this problem, but freezing can

alter the volume of the segment and, subsequently, the calculated moments of inertia

(Durkin, 2008).

Hence, results from a few Caucasian elderly males cannot be extrapolated to other groups

with confidence (Dempster, 1955). Also, pooling data does not account for variations in

segmentation protocols (Durkin, 2008); any differences in tissue properties between living

and dead subjects; or whether the preservation technique influences BSIPs (Pearsall, Reid,

and Livingston, 1996; Pearsall and Reid, 1994). For example, Pearsall et al. (1996) stated

that in-vitro lung tissue density was at least double that of in vivo. This could help to explain

the overestimated trunk mass when cadavers are compared with living subjects. Hence,

extrapolating values from cadaver studies to living subjects, regardless of the approach used

(see indirect BSIP estimation methods), may not be sufficiently accurate.

To overcome the limitations of in vitro methods for estimating BSIP of living subjects, non-

invasive in vivo approaches such as water immersion, photogrammetry, weighing in various

positions, quick release and compound pendulum (Contini, 1972; Drillis and Contini, 1964;

Durkin, 2008; Zatsiorsky et al., 1990) were proposed to enable computation of subject-

specific BSIP data. Water immersion was used originally to measure segment volumes of

either living or cadaver subjects (Clauser et al., 1969; Drillis and Contini, 1964). When

assuming that density is uniform across segments, and its value is known, water immersion

could calculate COM position and MOIs of the segment in vivo (Drillis and Contini, 1964;

Zatsiorsky et al., 1990). However, Drillis and Contini (1966) only used this method to

[27]

estimate BSIPs of the limbs as they were unable to overcome the difficulties in measuring

trunk and head BSIPs with this method. Photogrammetry can obtain volumes of irregularly

shaped segments by using one (mono-photogrammetry) or two cameras (stereo-

photogrammetry). The principle resembles aerial photos of a terrain with applied contour

levels. The volume of each slice (i.e. the portion between successive contour levels) is

calculated with a polar planimeter on the photograph. Thus, the sum of the volume of every

slice equals the volume of the segment (Drillis and Contini, 1964). Then, the same

assumptions used for water immersion regarding the density properties of the segments, are

applied to calculate the BSIP values. Weighing in changing positions is limited in that it

does not allow the calculation of all BSIPs. It only enables one to calculate either the

segment’s COM position when segment’s mass is known, or the segment’s mass when the

segment’s COM position is known (Pataky, Zatsiorsky, and Challis, 2003). The subject lies

on a force plate and moves one segment at a time to adopt a number of positions. For each

position, the centre of pressure displacement is recorded and used to estimate the mass, or

COM position, of the moving segment. According to Pataky, Zatsiorsky and Challis (2003),

it can be assumed that the COM position varies little between individuals. Moreover, when

used in association with either water immersion or photogrammetry (i.e. assuming uniform

density for the segments), it could provide more accurate values of the segment masses for

a single individual without relying on cadaver data (Drillis and Contini, 1964; Pataky et al.,

2003). The quick release method is used exclusively to obtain the MOIs of the segments

(Drillis and Contini, 1964; Zatsiorsky et al., 1990). It is based on Newton’s Law of Rotation

which states that- “the angular acceleration of a body is proportional to the torque applied to

it, and the MOI is the proportionality constant”. Hence, one applies a known force at a given

distance from the segment’s proximal joint, and measures the angular acceleration of the

segment by optical or electrical means to obtain the MOI (Drillis and Contini, 1964).

Calculating MOI in this way does not assume that the density of the segment is uniform;

rather, it assumes no friction at the proximal joint and no antagonistic muscular tension

during the procedure (Zatsiorsky et al., 1990). The compound pendulum method enables

calculation of the MOIs and the COM position of a segment (Drillis and Contini, 1964). Two

approaches can be adopted. Firstly, the segment can be treated as a compound pendulum

[28]

oscillating about its proximal joint in a set of trials that includes oscillation of the segment

alone, or with known weights attached at known positions. The second approach uses a

plaster model of the segment that swings about a fixed point. While both approaches

assume no muscular action or friction at the joints (Zatsiorsky et al., 1990), the first approach

has the advantage of allowing BSIPs to be calculated without assuming that the segment

has a uniform density. On the other hand, the second approach assumes uniform density of

the segment, and overlaps the joint properties and muscle action issues.

Although these in vivo methods provide individual values for BSIPs and are non-invasive,

the non-invasive component requires researchers to make some assumptions that could

jeopardise the accuracy of the results. The most common is assuming uniform density of the

body segment. Ackland, Henson and Bailey (1988) demonstrated marked variations in

cross-section density of the human leg along its length. But, they also found it contributed

less for inaccuracies in MOI measurements than estimations of a segment’s volume. While

assuming uniform density may not significantly influence the BSIP accuracy for the limbs,

this is not so for the trunk segment, where discrepancies were found between the centre of

volume and the centre of mass (Pearsall et al., 1996). When assuming uniform density, the

calculated BSIPs of a living person could be subject to errors from differences in body

composition and mass distribution, between the subject and the specimen used in the in

vitro study; and/or the possible differences between living and dead tissues properties

(Durkin, 2008; Mungiole and Martin, 1990; Pearsall et al., 1996; Pearsall and Reid, 1994).

The quick release and compounding-pendulum segment methods are the only ones not

assuming uniform density. However, their accuracy is compromised due to assuming

frictionless joints and zero muscular tension. Drillis and Contini (1966) combined the five

methods, trying to provide BSIP values for individuals without relying on cadaver data.

However, they noted that the accuracy of results still depends upon the assumptions

associated with each method. Also, to subject research participants through all of these

methods to obtain individual BSIPs is highly time consuming and not practical.

More recently, imaging methods, such as gamma-ray scanning (Zatsiorsky, 1983; Zatsiorsky

and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990), computerised tomography (CT)

[29]

(Ackland et al., 1988; Henson, Ackland, and Fox, 1987; Huang and Suarez, 1983; Pearsall

et al., 1996), magnetic resonance imaging (MRI) (Cheng et al., 2000; Martin et al., 1989;

Mungiole and Martin, 1990) have been explored as tools to directly obtain BSIPs.

The first BSIP study using a gamma-ray mass scan was based on the gamma-radiation

beam losing energy when it passes through a material layer (Zatsiorsky and Seluyanov,

1983; Zatsiorsky et al., 1990). The subject lies on a table and is scanned by an emitter

above, and a collimated detector below, the table. The output is the surface density (i.e.

mass per surface unit, expressed as g/cm2). In theory, when the surface density is the sole

output, it only allows an estimation of a segment’s mass, the 2D coordinates of COM (in the

frontal plane) and the MOI around the antero-posterior axis (Durkin et al., 2002; Wicke and

Dumas, 2008). To obtain COM position in the antero-posterior direction, and the MOIs

around the longitudinal and transverse axes, Zatsiorsky and Seluyanov (1983) adopted an

average body density of 1 g/cm3. They integrated this density value with the mass of every

finite surface area unit (pixel, with rectangular shape) to reconstruct the volume (height),

known as parallelpiped, for each pixel. Therefore, the whole body volume was divided into

several parallelepipeds with known dimensions and uniform density (Zatsiorsky et al., 1990).

Using this technique, they collected BSIPs from 100 Caucasian men, mostly college

students. The study provided means and standard deviations for mass; positions of COM

over the longitudinal axis; and the radii of gyration about the three axes for each of the

following segments: feet, shanks, thighs, hands, forearms, upper arms, lower torso, middle

torso, upper torso, and head (with neck). These data formed the basis for several other

studies to develop indirect BSIP estimation models (De Leva, 1996; Zatsiorsky and


While gamma-ray scanning could provide subject-specific BSIP data, it has some limitations.

Because gamma-rays are ionising radiation, they are biologically hazardous with scanning

exposing subjects to a relatively high dose of radiation (Durkin, 2008; Martin et al., 1989;

Mungiole and Martin, 1990). Secondly, it assumes uniform segment density at 1 g/cm3,

whereas densities have been shown to vary across segments of a subject, and especially

for the trunk where lungs and other internal organs lie (Pearsall et al., 1996; Wicke and

[30]

Dumas, 2010; Wicke, Dumas, and Costigan, 2008; Wicke, Dumas, and Costigan, 2009).

Tissue density is also expected to vary between subjects due to variations in body

composition and proportionality. Hence, this technique could possibly under/overestimate

the segment volume which, in turn, under/overestimate the MOIs. But, gamma ray scanning

could provide direct estimation of BSIPs with sufficient accuracy relatively simply, when

compared with the other non-imaging direct estimation methods. To date, only a few studies

have used this technique, and all come from the same research group (De Leva, 1996;

Zatsiorsky, 1983; Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990).

To overcome the uniform and arbitrarily-set densities for body segments, other technologies

have been used. Computerised tomography (CT) provides 3D estimations of the internal

structures of the body through a series of X-ray tomograms taken parallel to the transverse

plane, and created by computer processing. Each tomogram enables one to identify bone,

muscle and fat tissues, to each of which an empirical density is assigned to compute the

mass of the tomogram. After obtaining mass density and geometric characteristics of each

tomogram, the inertial parameters of each tomogram, regarding its thickness according to

the CT machine specifications, can be obtained. Data from the tomograms are then

combined to estimate the total segment inertial parameters (Huang and Suarez, 1983;

Pearsall et al., 1996). Therefore, CT scanning is a powerful tool for accurately estimating

density of the body tissues and their distribution throughout the various segments (Ackland

et al., 1988; Huang and Suarez, 1983; Pearsall et al., 1996). Yet, despite some advantages,

CT exposes subjects to higher doses of radiation than gamma ray scanning. Thus, that

could limit its usage to only a few body parts (Erdmann, 1997).

An alternative technology is magnetic resonance imaging (MRI). As with CT, the MRI also

yields a series of tomograms perpendicular to the longitudinal axis of the body to enable

BSIPs to be estimated. However, MRI can provide images with greater resolution than CT

(Martin et al., 1989; Mungiole and Martin, 1990) and, because it uses a large magnetic field

to generate the scanned image, there are no radiation risks. When the body is placed in a

magnetic field, the hydrogen nuclei, which are abundant in all tissues, have a specific

orientation of their magnetic moments (dipole) for a given tissue (Martin et al., 1989). A

[31]

tomogram is then created at the plane where the magnetic field passes, and the brightness

of the image is related to the orientation of the hydrogen magnetic dipole.

Both CT and MRI methods share a similar disadvantage of being labour intensive during the

data processing stage. The procedures used to estimate the inertial parameters of each

slice of the body are demanding as digitisation of every tomogram is required. The time

spent on digitising all tomograms could decrease with future advances in imaging software

that allows recognition of the tissues in the image by shape and pixel intensities (Martin et

al., 1989). Another common disadvantage of CT and MRI is that they do not directly

measure tissue density and, therefore, rely on external input. By doing so, it assumes that

tissue densities are uniform throughout the body. However, these vary across specific sites

of the body, and between subjects. It is known that tissue densities can be influenced by

fitness level, age, gender and somatotype. Moreover, different CT or MRI based research

could yield different values of segmental mass and density distribution, depending on which

tissue density values the researchers used. (e.g. tissue densities obtained from embalmed

cadavers) (Pearsall et al., 1996). Another factor affecting the practicality of using CT and

MRI techniques to obtain subject specific BSIPs, is the cost. The cost of CT and MRI scans,

in combination with the time consuming digitisation procedures, can limit the number of

subjects a research study can undertake. This is evident in the fact that the largest cohort

size using CT or MRI was 12 (Mungiole and Martin, 1990).

In brief, medical-image-based BSIP estimation methods are more accurate than non-

medical direct estimation methods, or by extrapolating in vitro values to living subjects.

However, they can be limited by costs, machine access, onerous data processing, and/or

exposure to high doses of radiation.

2.3 Indirect Estimation Methods

Indirect methods for BSIP estimations are based on the relationship between some

anthropometric variables and the desired inertial parameters. As anthropometric variables

can be gathered quickly, at minimal cost, free of radiation, and without the need of

expensive equipment and facilities, these methods have been more widely used.

[32]

Anthropometry can be used as a predictor in either linear or non-linear equations, where the

criterion is an inertial parameter of a determined segment (e.g. regression equation method).

Also, anthropometry can create a simple geometric representation of the body from which

one then assumes the inertial parameters of the geometric figures are the same of the

segments (geometric methods).

2.3.1 The Modified Chandler Method

Chandler et al. (1975) provided linear equations for determining segment mass and the

three principal MOIs. They used body mass or segmental volume as predictors, and the

COM position as a fixed ratio of the distance from the COM to the proximal joint of the

segment and the length of the segment. The equations were computed from measurements

taken from 6 elderly male cadavers. The protocol segmented the body into 14 segments

(head, trunk, upper arms, forearms, hands, thighs, shanks and feet). This was the first

cadaver study to enable full BSIP calculations of living subjects. However, the authors stated

that the equations “are given for the convenience of the reader, but, again, cannot be

considered to reliably estimate population parameters” (Chandler et al., 1975, p. 66).

Therefore, Yeadon and Morlock (1989) proposed a set of non-linear regression equations for

determining segmental MOIs , using the anthropometry and BSIP data from Chandler et al.

(1975). The authors claimed that it might be inappropriate to establish linear relationships

between dimensionally distinct quantities such as MOI (Kg�cm2) and circumference or length

(cm). Furthermore, the theoretical relationships between the three dimensions of an object

(i.e. height, depth and width) and its inertial properties (i.e. mass and the MOIs ) can be

obtained when the characteristics of density distribution are known, which enables them to

be used as a basis for non-linear equations. To validate the approach, data were compared

from the left and right limbs. That is, the right limb was used to derive the equations and the

left limbs were used for cross-validation. Comparisons with the principal MOIs were

measured with a pendulum model and reported an average standard error of 21% for the

linear equations. The average error was 13% for the non-linear equations. When

extrapolating both equations to living subjects, and using the geometric model as criteria

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(Yeadon, 1990), the average percentage residuals for the linear equation were 286%; and

just 20% for the non-linear equations.

2.3.2 The Yeadon Method

Yeadon (1990) proposed a geometric approach that fractionated the segments into solids of

circular (limbs and head) or stadium-shaped (trunk, hands and feet) cross-sections. Forty

solids were created from 95 anthropometric measures (girths, widths and distances between

each section). Here, the stadium cross-sections (a rectangle with an adjoining semicircle at

each side, so the depth equals the diameter of the semi-circle) match the real cross-

sectional areas more closely than the ellipses used previously (Hanavan Jr, 1964; Hatze,

1980; Jensen, 1978). Then, Dempster’s density values (1955) were used to calculate the

inertial parameters of each solid (uniform density). This enabled calculation of inertial

parameters for 11 segments (head + trunk, upper arms, forearms + hands, thighs, shanks

and feet). Even though the trunk was regarded as a unique segment, adoption of

representing it by five solids plus the different density values according to location in the

trunk from Dempster (1955), enabled the separation of the trunk into sub-segments (e.g.,

thorax, abdomen and pelvis). This procedure was simpler than other geometric methods

proposed by Jensen (1978) and Hatze (1980), and produced a maximum error for the total

mass of 2.3%, which was comparable to the other two methods (Hatze, 1980; Jensen,

1978).

The Yeadon Method (Yeadon, 1990), as with most of the geometric methods, relies on

assuming uniform density of the modelled segment. But, subjects from different populations

have revealed differences in segmental densities, especially when comparing athletes from

different sports, or versus a non-athletic population (Kerr and Stewart, 2009). Therefore, the

average density value obtained from studies with subjects of similar body composition, age,

gender and ethnicity should be chosen to avoid errors when using geometrical models. For

instance, Wicke and Dumas (2010) found an average density value for the lower trunk from

Dempster (1955) was overestimated when applied to their 24 male and 25 female college-

aged participants.

[34]

The geometric models vary with the complexity of the solids adopted as templates for the

limbs. Studies suggest that the more the volume of the solid resembles the actual segment,

the lower are the errors in BSIP calculations. This follows earlier findings that inaccuracies in

volume representation account more for BSIP error than the uniform density assumption

(Ackland et al., 1988; Wicke and Dumas, 2010).

2.3.3 The Zatsiorsky Simple Regression Method

Zatsiorsky and Seluyanov (1983) gathered full BSIPs from 100 young adult Caucasian

males using a gamma-ray scanner and computed individual coefficients for each BSIP in a

set of linear equations that considered whole body weight and height as predictors. The

protocol separated the body into 16 segments (head, upper trunk, middle trunk, lower trunk,

upper arms, forearms, hands, thighs, shanks and feet). Unfortunately, no information was

provided regarding the number of subjects used to devise the equations, or the number of

subjects used in the cross-validation procedure. However, results showed that, when using

only body weight and height as predictors, it is unlikely that the resultant BSIP is accurate.

This is because the formulae provided very low Pearson’s product moment correlation

coefficients, and was especially so for the segmental COM positions (r range 0.25-0.60).

Ratio-based methods use only height or body weight as sole predictors for BSIPs and are

not as accurate as regression equations that use more predictors. This is especially so if

those predictors are restricted to only the segment being analysed because they don’t

account for different proportionalities between subjects (Hatze, 1975). Also, a greater

number of predictors enable the regression equation to better account for variations within

the population from which the equations were derived.

2.3.4 The Zatsiorsky Multiple Regression Method

Multiple regression methods establish linear relationships between a given inertial parameter

and a certain quantity of independent anthropometric variables. Generally, inertial

parameters of a given segment are expected to correlate better with the anthropometry of

that segment, rather than a more global measure such as body weight. Therefore,

Zatsiorsky and Seluyanov (1985) used up to four classes of anthropometric measures (i.e.,

[35]

segment lengths, breadths, girths and diameters) as independent variables from the same

100 young adult Caucasian males analysed with the gamma-ray scanner. These

anthropometric values were derived from the segment of interest. This resulted in stronger

correlations with values gathered via gamma-ray scans than the equation with just body

weight and height as predictors. Moreover, the regression equations derived by Zatsiorsky

and Seluyanov (1985) have achieved the most accurate results when applied to a general

population (de Leva, 1994; Durkin, 2008).

However, the errors can be large when these equations are applied to populations different

from those from which the equations were derived (Durkin and Dowling, 2003). It should be

noted that, if large differences exist within any population, the regression equations also may

yield poor results, and caution is required when estimating BSIPs. The set of predictive

equations also need to acknowledge differences in age, gender, race and morphology.

(Durkin and Dowling, 2003).

2.3.5 The Zatsiorsky Geometric Method

Zatsiorsky et al. (1990) proposed a geometric model for the human body based on living

subject data analysed with a gamma-ray scanner. Each segment was regarded as a cylinder

with a circular base, and the segment’s length and girth were used to calculate the cylinder

volume. To compensate for differences between the actual volume of the segment, and the

volume of its cylindrical representation, a quasi-density value was calculated. Here, the

segment mass was divided by the volume of the representative cylinder, and then

incorporated into the equations.

Zatsiorsky et al. (1990) claimed that this geometric model can estimate the BSIPs of a

population not necessarily matching the anthropometric values found in the cohort from

whom the equations were derived. But, this assumes that the densities of all segments must

remain similar. On the other hand, the authors also noted that results for people with greater

amounts of fat tissue will be less accurate when using their proposed geometric method, and

the same might be true for a population of weightlifters with high muscle mass and low fat

levels, for example.

[36]

2.4 The DXA Method

The dual-energy X-ray absorptiometry (DXA) is the most recent medical-imaging based,

direct BSIP estimation method. It is similar to gamma-ray scanning in that it relies on the

attenuation of radiation beams passing through the body to measure its surface density. The

main difference is that DXA uses two X-ray intensities which allow the measurement of two

compartments separately. These are bone mineral and soft tissue, which includes both fat

mass and lean tissue mass (Ellis, 2000; Laskey, 1996). The mass of these two

compartments is measured at every surface unit (pixel) according to the following formulae

(Laskey, 1996):

�� (Formula 1)

�� (Formula 2)

Where:

• �� and �� are the ratios of attenuated and unnattenuated energies of the low and

high X-ray energies, respectively;

• �� and �� are the ratios of mass attenuation coefficients at the

low and high energies (�� and ��) for soft tissue and bone mineral, respectively.

Initially, DXA was developed to obtain the surface density of the bone minerals at the lumbar

spine, femur and forearm (Ellis, 2000). It was soon discovered that, when the fat-to-lean

tissue ratio is assumed to be constant for a given segment, DXA can estimate the total fat

mass, because the RST calculated is linearly related to the percentage of fat mass in the soft

tissue (Haarbo et al., 1991; Laskey, 1996; Mazess et al., 1990). Body composition data

obtained from DXA also has shown to be accurate and reliable (Ellis, 2000; Fuller et al.,

1992; Haarbo et al., 1991; Laskey, 1996; Mazess et al., 1990; Ogle et al., 1995; St-Onge et

[37]

al., 2004a; St-Onge et al., 2004b; Wang et al., 2004). As the attenuation coefficients of the

high energy beam are proportional to mass (Durkin et al., 2002), DXA also has been

explored as a potential tool for assessment of human BSIPs during the past decade (Durkin

and Dowling, 2006; Durkin and Dowling, 2003; Durkin et al., 2002; Durkin, Dowling, and

Scholtes, 2005; Ganley and Powers, 2004a, 2004b).

An early study using DXA to estimate BSIPs examined the relationship between the high-

energy attenuation coefficients and mass by scanning a book with known dimensions and

mass (Durkin, Dowling & Andrews, (2002). Then, a mass constant was obtained by

summing the attenuation coefficients and dividing it by the whole mass. The relationship was

validated by scanning 11 male subjects and comparing the whole body mass with the

criterion established. Their custom-built software was developed to increase the areal

resolution of the mass data and enhance the bone image. This enabled specific anatomical

landmarks to be located more accurately. The landmarks were used for segmentation of the

body so that BSIPs in the frontal plane of each segment can be calculated. The mean error

for whole body mass was 1.06% (1.32% SD) which indicated greater accuracy than gamma-

ray scanning (Zatsiorsky et al., 1990). Durkin et al. (2002) also analysed the masses, COM

positions, MOIs about COM, and longitudinal lengths of a plastic cylinder and a human

cadaver leg. To accomplish this, criterion value measures were made with a force plate, by

balancing the object on a knife-edge orthogonal to its length; and using the pendulum

technique and a tape measure, respectively. A geometric formula also was used as the

criterion for the MOI of the cylinder. When the results were compared with those criterion

values, DXA data contained less than 3.2% errors for all inertial parameters except for MOI.

The criterion value for the MOI was derived using the pendulum technique, which was

deemed inaccurate as the values from both criterion measures used for the cylinder did not

match. This was because the objects were suspended from their proximal ends, which is a

distance from the COM greater than the radius of gyration, thereby increasing the errors

(Dowling et al., 2006). Wicke and Dumas (2008) improved accuracy of DXA BSIP

estimations when using a more recent fan-beam DXA scanner that also reduced scanning

time.

[38]

Durkin and Dowling (2003) used DXA to examine the differences in BSIPs of four distinct

human populations (adult males, adult females, elderly males and elderly females). The

forearms, hands, feet, lower legs and thighs of 100 subjects representative of the four

groups were analysed with DXA to obtain the respective mass, COM position and MOI in the

frontal plane. Significant differences were found between the four groups, again indicating

that caution should be taken when applying cadaver-based values to any population.

A series of studies by Ganley and Powers (Ganley and Powers, 2004a, 2004b) also

demonstrated significant differences in BSIPs between DXA and the cadaver-based method

of Dempster (1955), regardless of whether the subjects were adults or children (aged 7-13

years). However, Ganley and Powers used a different approach from Durkin and Dowling

(2003; 2006) and Durkin et al. (Durkin and Dowling, 2006; Durkin and Dowling, 2003; Durkin

et al., 2002; Durkin et al., 2005). Ganley and Powers (2004a, 2004b) used 4 cm-thick

continuous slices as the basic mass data unit rather than smaller mass information units of

0.132 cm x 0.132 cm (Durkin et al., 2002).

Wicke et al. (Wicke and Dumas, 2008, 2010; Wicke et al., 2008; Wicke et al., 2009) also

used DXA to estimate BSIPs. They appear to be the only group to use DXA to explore the

inertial characteristics of the trunk. The trunk is the segment with the greatest variability in

density along its longitudinal axis, and inter-individual differences amongst all body

segments (Wicke et al., 2008). Comparisons between the trunk segmental, inertial

parameters gathered with DXA and other indirect estimation methods showed that the latter

had lower accuracy (errors ranging from 10% to 50%) and consistency (Wicke and Dumas,

2008; Wicke et al., 2009). Wicke and Dumas (2010) assessed the trunk segmental inertial

parameters as functions of the density and volume values. These were calculated by

combining the mass distribution profile gathered with DXA and the volumetric profile

gathered with the photogrammetric method as proposed by Jensen (1978). They found that

the inertial parameters were most sensitive to the variations in volume; and the non-uniform

density model provided more accurate results for the lower trunk, compared to when the

trunk segment was assumed to have uniform density.

[39]

In short, DXA can be a viable alternative to the gamma-ray scanner because it exposes

subjects to lower levels of radiation and appears to provide more accurate results. However,

as the scanning principle is the same for both scanners, the current development only allows

estimation of inertial parameters in the frontal plane. This limitation could be overcome by

combining DXA with other imaging methods or modelling techniques (Durkin et al., 2002).

For instance, Zatsiorsky et al. (1990) used the arbitrary value of 1cm/g3. Others have

identified density values for fat, bone mineral and lean tissue to obtained a more realistic

representation of the human body (Ganley and Powers, 2004a, 2004b). The disadvantages

of the empirical density values have been discussed above. In the studies of Durkin et al.

(Durkin and Dowling, 2006; Durkin et al., 2005), the mass distribution across limb segments

was used to create a volumetric representation from which the other moments of inertia can

be calculated. However, validation of the MOI about the transverse axis could only be

carried out for the lower leg, as the segment also was scanned with its sagittal plane parallel

to the scanning table (Durkin and Dowling, 2006). Finally, volumetric information can be

used along with the DXA output by using the photogrammetric method (Jensen, 1978) or,

more recently and accurately, the 3D body scan (Lee et al., 2009).

2.5 Influence of different methods on dynamic analyses

The sensitivity of joint kinetics to variations in BSIPs is seldom explored in solving inverse

dynamics problems. The BSIP error propagation problem is challenging given the difficulty to

establish the magnitude of the maximum error of any inertial parameter. This is so for any

given segment of any subject; and also due to the dependency of the propagated error in the

joint resultant forces and moments of a given analysed motion (Andrews and Mish, 1996).

Andrews and Mish (1996) tested two different approaches for determining the joint resultant

forces and moments due to variations in BSIPs. They simulated the rotation of a shank-plus-

foot rigid segment around the transverse axis of the knee by using the BSIP values from

Clauser et al. (1969). A BSIP error estimation was assumed of ± 5% and, even with a small

segmental acceleration, the maximum errors in knee moment were up to 12%.

[40]

Desjardins, Plamondon and Gagnon (1998) investigated two inverse dynamic models

(bottom-up and top-down), for estimating the net moment at the L5/S1 joint during lifting. It

was found that in the bottom-up approach, the result was influenced mostly by the external

forces applied (i.e., the ground reaction force). The segmental masses contributed the most

to the sensitivity of the top-down inverse dynamics. Therefore, not only is the bottom-up the

most preferred for the referred analysis, but also it is expected that open-chain activities, or

those where applied external forces cannot be accurately measured, may be more sensitive

to errors in BSIP calculations. Similar findings were observed by Lariviere and Gagnon

(1999).

The influence of the type of movement being analysed and subject characteristics in the

propagation of BSIP errors also can be verified in different velocity gaits. For instance, the

influence of BSIP in walking gait was explored in adults (Ganley and Powers, 2004b; Rao et

al., 2006) and children (Ganley and Powers, 2004a). Ganley and Powers (2004b) compared

the net joint moments in walking gaits of adults when using BSIPs derived from DXA, with

those having used cadaver data. The significant difference between the two sets of BSIPs

had little influence on the calculated moments during the stance phase where the ground

reaction forces exerted greater influence. However, during the swing phase, the inertial

values dominated the moment calculations. Similarly, Rao et al. (2006) found maximal

variation in peak flexion/extension moments at the hip during the swing phase (20%) for a

similar cohort. The BSIP estimation methods provided deviations ranging from 9% to 60%.

Ganley and Powers (2004a) also verified significant differences in BSIP estimation when

using DXA or cadaver values in a population of children ranging from 7 to 13 years old.

Conversely, the influence of different BSIP values on joint moment calculation seems to be

negligible for a group of children.

Sheets, Corazza and Andriacchi (2010) used the abovementioned method when comparing

BSIPs with the regression equations of Dempster (1955) and Clauser et al. (1969); and the

influence of different BSIPs and body mass index values on the hip and knee net moments

during a running swing phase. Given the high linear and angular accelerations of the shanks

during the swing phase, differences in shank inertial parameters had a large influence on

[41]

moment values at the knee which, in turn, also influenced the hip moment as the inverse

dynamics chain progressed upwards. They found that the BSIPs have the largest effect on

kinetic analyses in situations involving subjects with high limb masses or body mass indices;

and movements with high segment accelerations, especially at joints farther along the kinetic

chain.

Kwon (1996) analysed the influence of different sets of BSIPs on the body angular

momentum of airborne movements performed by gymnasts. The estimation methods were

derived from cadaver (Chandler et al., 1975), gamma-ray scanner (Zatsiorsky and

Seluyanov, 1983, 1985; Zatsiorsky et al., 1990) and geometric studies (Hanavan Jr, 1964;

Yeadon, 1990). These were used in the 3D analyses of nine somersaults with full-twist,

horizontal-bar dismounts performed by three collegiate male gymnasts. This was to compute

the whole body angular momentum. The author found that the magnitude of the angular

momentum was affected by the different BSIP estimation methods. However, similar

fluctuations in the angular momentum during airborne movements were observed (i.e., no

estimation method yielded lowest fluctuations in angular momentum during the airborne

manoeuvres, as when in theory the angular momentum is meant to be constant).

In a following study, Kwon (2001) investigated the effect of the BSIP estimation method on

the accuracy of the experimental simulation of complex airborne movements. The

applicability of different methods was assessed along with the sensitivity analysis to identify

the different BSIPs, and segments responsible for inter-method differences in the simulation

accuracy. The same estimation methods were used as in(Kwon, 1996). The accuracy of the

experimental simulation was significantly affected by the different methods, largely being the

mass items, and the trunk and lower limb segments were more responsible for the variability

than other inertial parameters and segments, respectively. More importantly, the estimation

methods which better accounted for differences between subjects enabled the more

accurate simulation. In this study, the geometric models and the cadaver-based stepwise

regression methods were superior to the other methods on the accuracy of more complex

airborne movements.

[42]

Therefore, the extent to which the BSIPs can affect the accuracy of dynamic analyses

depends on the task characteristics. These could include whether it involves rapid

linear/angular movements of the segments, is an open-chain or closed-chain analysis, or the

external forces exert greater or lesser influence than the BSIPs on the kinetic calculations.

Whenever the kinetic analysis of a movement is likely to be affected by the BSIP used, one

must ensure that the estimation method resembles as closely as possible the morphological

characteristics of the segments (i.e., the volume and the mass distribution properties of the

segments) to minimise the errors when estimating the inertial properties. The greater the

ability of the estimation method to yield subject-specific BSIP data, the greater the chances

are of completing accurate dynamic analyses.

2.6 Summary

In summary, several approaches have been proposed above to determine the inertial

properties of human body segments. They can be measured directly (with medical-imaging

technologies the preferred approach) or indirectly through mathematical models devised

from certain specific groups of subjects.

This review has demonstrated that the populations previously assessed and validated using

the most common BSIP estimation methods are representative of only a few groups within

any community. Data for specific populations, by gender and activity levels and type, such

as from elite athletes, is lacking. Therefore, greater clarification is required in several sports

to ascertain the extent to which performance analyses can be affected by inaccurate BSIPs.

A first step towards this clarification is to study some commonly used methods and compare

how DXA rates with those methods for immediate use. Then, the most effective method

could be adopted until a non-medical imaging process is developed which avoids onerous

calculations, high radiation, high cost, is reliable and valid, safe and accessible.

[43]

Chapter 3

METHODS AND PROCEDURES

3.1 Participants

Twenty-eight participants were recruited for this study. Ten experienced competitive male

swimmers (age 26.17 ± 3.96 yrs, height 186.43 ± 8.67 cm, weight 81.16 ± 9.30 kg) and 8

experienced female competitive swimmers (age 21.13 ± 5.85 yrs, height 173.38 ± 6.96 cm,

weight 61.69 ± 5.47 kg) were recruited from swimming clubs in the Perth,Western Australia.

Only swimmers who had qualified for Australian National Championships were selected. In

addition, a group of 10 healthy, young adult Caucasian males were recruited from students

in the School of Sport Science, Exercise and Health at The University of Western Australia.

The latter had similar anthropometric profiles to subjects in the studies by Zatsiorsky et al.

(Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990), as seen in Table 3.1.

Table 3.1. Mean (SD) of the age (years), height (cm) and weight (Kg) of young adult Caucasian

males in the cohort of the present study (DXA, n=10) and in the studies of Zatsiorsky et al.

(1983, 1985, 1990; n=100)

Cohort Age Height Weight

DXA (n=10) 22.5 (4.8) 177.2 (8.0) 74.9 (8.7)

Zatsiorsky et al.

(n=100)

23.8 (6.2) 174.1 (6.2) 73.0 (9.1)

Approval was obtained from The University of Western Australia Human Research Ethics

Committee. Information regarding the procedures and possible risks was distributed to all

participants, who completed a written informed consent form prior to testing (Appendix A).

[44]

3.2 Indirect BSIP estimation methods

The BSIPs derived from the proposed DXA method were compared with those gathered

from five different indirect BSIP estimation methods. Two methods were based on data from

cadavers (Chandler et al., 1975; Yeadon, 1990) and the three others were based on data

from living human subjects (Zatsiorsky, 1983; Zatsiorsky and Seluyanov, 1985; Zatsiorsky et

al., 1990). These methods were chosen because they are commonly used in biomechanical

analyses, and they provide moments of inertia in all of the orthogonal planes.

Five different indirect BSIP estimation models with similar segmentation protocols were

chosen to be compared with the new DXA method. They are:

1) The Modified Chandler method (C) used simple linear relationships between the whole

body weight and the segment masses, a fixed ratio between the distance from the COM to

the proximal joint relative to the segment’s longitudinal axis (Chandler et al., 1975), and non-

linear equations to compute MOIs from measures of segment lengths, widths and breadths

(Yeadon and Morlock, 1989);

2) The Modified Yeadon method (Y) is a geometric method that uses cylindrical and

stadium-shaped solids to represent body segments. A density value based on the findings of

Dempster (1955) is assigned to each solid to calculate the mass and the MOI of the

segment;

3) Zatsiorsky Simple Regression model (Z1) only uses the whole body mass and height as

predictors for all BSIPs (Zatsiorsky and Seluyanov, 1983);

4) The Zatsiorsky Multiple Regression Model (Z2) uses a set of specific anthropometric data

(up to 4 measures) for each segment as predictors in linear equations (Zatsiorsky and

Seluyanov, 1985);

5) The Zatsiorsky Geometrical Model (Z3) assumes each segment as a circular cylinder and

uses a segment-specific quasi-density value, calculated to minimise the difference between

the cylinder and the real segment volumes (Zatsiorsky et al., 1990).

[45]

In the original work of Chandler et al. (1975), the whole body weight is used as the only

predictor in simple linear equations to calculate the segment masses and MOI. However, as

inaccurate results were expected when computing MOIs from these equations, the non-

linear equations from Yeadon and Morlock (1989) were used, as they were devised using

the same cadavers as Chandler et al. (1975). Small adaptations to the geometric figures of

the original Yeadon (1990) method were made to ensure, whenever possible, that the body

could be segmented in the same manner as in the other estimation models. Thus, the

number of anthropometric measures is minimised. The Zatsiorsky Simple Regression Model

(Zatsiorsky and Seluyanov, 1983), the Zatsiorsky Multiple Regression Model (Zatsiorsky and

Seluyanov, 1985) and the Zatsiorsky Geometrical Model (Zatsiorsky et al., 1990) were

developed from measuring the same 100 adult Caucasian male samples.

Whenever necessary, estimation methods were modified to minimise variations due to

different segmentation protocols; and to facilitate using anthropometric measures derived

from a standardised protocol established by the International Society for Advancement of

Kinanthropometry (ISAK) (Olds and Tomkinson, 2009). A brief explanation of each method

and modifications applied are outlined in Appendix B.

3.3 Data acquisition Protocol

Participants underwent a full body DXA scan and a full body 3D surface scan, at the School

of Sport Science, Exercise and Health (SSEH). For both tests, participants wore Fédération

Internationale de Natation (FINA) approved swimsuits and swimming caps. Participants had

22 spherical markers (20mm diameter) made from glass marbles attached to specific body

landmarks prior to the above scans (Table 3.2). These markers were placed so as to

appear outside the boundary of the body on the DXA output image. Glass was chosen as

the material for markers because its density was vastly different from bone mineral and other

body tissues (approximately 3g/cm3). Therefore, it could be identified easily on the DXA

output image.

[46]

Table 3.2: Glass marble naming and locations

Segment / Joint Label Location

Head L/R FHD Front head marker

Shoulder joint L/R ACR The midpoint on the acromion process lateral ridge

Elbow joint L/R MEL Medial epicondyle of the humerus

L/R LEL Lateral epicondyle of the humerus

Wrist joint L/R AMWR Anterior mid-stylion

L/R PMWR Posterior mid-stylion

Trunk L/R ICP Tubercle of the iliac crest

Knee joint L/R MKN Medial epicondyle of the femur

L/R LKN Lateral epicondyle of the femur

Ankle joint L/R MAN Medial malleolus of the tibia

L/R LAN Lateral malleolus of the tibia

3.3.1 Dual-Energy X-Ray Absorptiometry (DXA)

The DXA scanner was the GE Lunar (Figure 3.1). In brief, the DXA scanner projects two X-

ray beams of different intensities onto the subject’s body. Based on the attenuation of the

energies as they pass through the body, the scanner can evaluate the areal density (i.e.,

mass per area unit at the frontal plane) and the mass associated to each compartment (i.e.,

bone mineral, lean tissue and fat tissue).

Figure 3.1: The GE Lunar DXA scanner

[47]

The subjects assumed a supine lying position with the feet placed at shoulder-width apart,

and the forearms in a neutral position of mid-pronation/supination. Then, the sagittal plane

could be assumed to be parallel to the scan table and the subjects fitting within the 60-cm

wide scanning area. The whole body was scanned once in a process taking around 5

minutes and exposed the subject to a radiation dose of ~0.8 µSv.

3.3.2 Body laser scan

An Artec LTM

3D scanner (Artec, TDSL) was used to create the surface scan of the

participants (Figure 3.2). It consisted of a light projector which emitted a mesh of dots onto

the body surface, and a video camera to capture images of the projected dots (3D frames).

Both the camera and projector were calibrated relative to each other (raster-stereography).

According to the manufacturer, the scanner has a 3D resolution of up to 1.0 mm; 3D point

accuracy of up to 0.2 mm; and a maximal capture rate of 15 frames per second. The Artec

3D Scanner v0.6 software was used to operate the scanner, and capture and process the

scanned data.

Figure 3.2: The Artec L

TM 3D scanner.

[48]

Prior to scanning, 28 additional spherical wooden markers (20 mm diameter) were

strategically placed on the body (Table 3.3). These markers combined with the marble

markers to create the anatomical coordinate system (ACS) for each body segment.

Participants were scanned while standing in the anatomical position, except for the slightly

abducted shoulders and more neutral forearm and hand position having the palms facing

inwards (Figure 3.3). To avoid excessive sway during scanning, subjects looked at a fixed

point on the wall ahead, and rested their fingers on two nearby tripods. The first scanning

phase covered the head, trunk and upper limbs; and the second, the lower limbs.

Table 3.3: 3D scan marker naming convention and locations

Segment / Joint Label Location

Head L/R BHD Back head marker

Shoulder joint L/R Acr1 Acromion triad: posterior marker

L/R Acr2 Acromion triad: central-medial marker

L/R Acr3 Acromion triad: posterior marker

The rigid bar between Acr1 and Acr3 runs parallel with the

lateral ridge of the acromion

Wrist joint L/R MWR Styloid process of the ulna

L/R LWR Styloid process of the radius

Hand L/R Hand1 2nd

carpo-metacarpal joint

L/R Hand2 5th

carpo-metacarpal joint

L/R Hand3 Head of the 3rd

metacarpal

Trunk C7 Spinous process of the 7th

cervical vertebra

IJ Deepest point of the incisura jugularis (suprasternale)

XP Xiphoid process

Nav Navel

L/R ASIS Anterior superior iliac spine

L/R PSIS Posterior superior iliac spine

Foot L/R Foot1 Calcaneus

L/R Foot2 Head of the 1st metatarsal

L/R Foot3 Head of the 5th

metatarsal

[49]

Figure 3.3: The 3D scan of the participant after the scanning procedure (before post-process)

The post-processing was also conducted using the Artec 3D Scanner v0.6 software. The

software enabled finer alignment of the 3D frames, smoothness of the surface, filling the

surface holes, discarding of unwanted objects and the creation of the single polygonal 3D

model of the whole body (i.e., representation of the body surface using a triangulation grid).

Each subject required approximately 5h to create the final 3D scan.

3.3.3 Anthropometry

Heights, lengths, breadths and girths were taken from all subjects’ 3D scans for input into

the equations of the indirect BSIP estimation methods. Anthropometry gathered from 3D

scans was shown to have high validity and reproducibility (Lu and Wang, 2008). When

possible, measures followed the definitions set by the International Society for Advancement

of Kinanthropometry (ISAK); and the Laboratory Standards Assistance Scheme of the

Australian Sports Commission (Olds and Tomkinson, 2009). In some cases, additional

measures were required to comply with a specific BSIP method (i.e., those not listed in the

ISAK protocol). The body landmarks, girths, lengths and breadths, as well as the results of

the concurrent validity tests, are found in Appendix C.

[50]

3.4 Biomechanical model

A 16-segment biomechanical model (head, upper trunk, middle trunk, lower trunk, upper

arms, forearms, hands, thighs, shanks and feet) was devised so all BSIP estimation

methods could be easily fitted to the model. A model of every subject was created using the

3D coordinates of the markers obtained with the Artec 3D Scanner v0.6 software.

The ACS of the upper and lower limb segments were created from the recommendations of

the International Society of Biomechanics (Lu and Wang, 2008; Wu et al., 2005). The ankle,

wrist and shoulder (glenohumeral) joint centres were determined according to the UWA

biomechanical model (Besier et al., 2003; Campbell et al., 2009; Chin et al., 2010). The

elbow and knee joint centres were defined as midway between the medial and the lateral

epicondyles, of the humerus and the femur, respectively. Regression equations proposed

by Harrington et al. (1999) were used for the hip joint centre. A whole trunk coordinate

system was created after de Leva (1996). The long axis of the whole trunk was used as the

long axes of the three sub-segments of the trunk, and also for the head segment. For details

of all anatomical-landmark-based ACS, see Appendix D.

3.5 Data Processing

Previous studies used the linear relationship between the attenuation coefficients of the high

energy beams, and each were recorded in rectangular elements that formed the scan area

matrix, and the mass of a given phantom (Durkin et al., 2002; Wicke and Dumas, 2008).

This was done because the company supplying the scanner and the analysis software

preferred not to provide access to the code enabling calculation of the mass for each

rectangular element (Jim Dowling, personal correspondence). Hence, the raw data was

accessed using an ACSII code de-compiler.

The unique aspect of this study was that mass data were extracted directly from the generic

DXA enCORE® software (version 8.50.093, GE Healthcare, 2004). In order to access raw

data from the DXA generic software, enCORE®, a day-pass licence was required from the

manufacturer. Hence, an agreement was made between The University of Western Australia

and the Healthcare Division of General Electric Company (GEHC) acknowledging that data

[51]

would be used for internal and non-commercial research purposes only. First, contact was

made with the Australia/New Zealand Lunar Product Manager of the GE Healthcare

Systems, who informed the University that an agreement had to be drawn up. Then, contact

was established directly with the Global Research Manager and the Chief Scientist of the

GEHC, with whom the details of the research and details of the licence agreement were

discussed directly.

After approximately four months of interaction with GEHC representatives, the company

kindly supplied a password that would enable the enCORE® software to display two different

data matrices. The first matrix provided mass data for the bone mineral compartment (BMD).

The second provided mass data for the tissue compartment (TISSUE), which consisted of

extracellular fluids and solids, total body water, intracellular solids and fat (St-Onge et al.,

2004a). Each matrix was divided into rectangular elements with dimensions of 0.51 cm x

1.54 cm in the transverse (x) and longitudinal (y) directions, respectively, and referred to as

mass elements. Hence, each element represents a section within the entire scanned area,

and the summation of both matrices provided the whole body mass.

The day-pass licence enabled the enCORE® software to show the coordinates and mass

value of each mass element on the bottom of the screen when the mouse cursor is over an

area of the scan image (Fig 3.4). This worked for both the BMD and the TISSUE images.

However, the enCORE® software (version 8.50.093, GE Healthcare, 2004) did not allow any

of the data matrices to be exported and saved in any other formats for further processing. To

extract mass data manually by moving the mouse cursor from one mass element to the next,

and then record the values externally, was not practical. Therefore, data from the two

matrices were co-registered with their respective grayscale images (8-bits bitmap files,

resolution of 72 DPI) exported by the scanner software (Figure 3.4) using a code written in

Matlab® (Ver. 7.8.0.347). As the images that were created were based on the coefficients of

attenuation measured, it made sense that there should be a linear relationship between the

shade of a given pixel of the image and the areal density of the region represented by the

pixel (i.e., the whiter the shade of the pixel, the greater the amount of mass referred to that

area). Therefore, a Matlab code was created (convert_dxa_images.m, Appendix E) to

[52]

compute the mass distribution of the scanned area using the intensity colour of every pixel in

the grayscale image. As input, this used the BMD and TISSUE images; the dimensions of

the scanning area; the number of mass elements of both matrices and two arrays - one of

which was for the BMD data and another for the TISSUE data, and each containing the

coordinates and the associated mass (in grams) of 15 random mass elements. The following

steps were conducted by the code for both BMD and TISSUE matrices:

Figure 3.4: Screenshot of the enCORE® software when the day pass code is used, showing the

two BMD and TISSUE images derived from the respective matrixes. When the mouse is placed

on a given area (red circle), the mass and the coordinates the local mass element pointed by

the arrow are shown on the bottom of the screen (red ellipses).

1) The grayscale images were scaled to the same size of the scanning area. Each

pixel in the image then represented an area of 0.23 x 0.23 cm. Therefore, this also

enhanced the areal resolution of the mass data.

[53]

2) Then, the image data was co-registered with the raw data such that each mass

element was represented by a group of image pixels in the same area (Figure 3.5).

The colour intensity of each pixel is represented by integer values ranging from 0

(black) to 255 (white) and the relationship between the colour intensity (integer

value) and the mass of the pixel area was assumed to be linear. The summation of

the integer values of all pixels representing the mass element is directly proportional

to the mass of the referred mass element. This relationship is then found using the

following formula:

�� · ∑ ��, (Formula 1)

Where mel is the mass of a mass element, Ii,j is the gray intensity of a pixel within the

mass element and kel is a constant calculated for each mass element and further

used to calculate the mass value associated with a representative pixel (mass pixel)

by multiplying it by its gray intensity.

[54]

Figure 3.5: The relationship between the mass element (red rectangle) and the pixels of the

bitmap image; often the mass element contained pixels from the outside of the body or its

borders were not aligned with the pixels.

3) It is important to note from Figure 3.5 that the mass elements were not necessarily

represented by integer pixels (i.e., the borders of the pixels and the referred mass

element may not be aligned). Therefore, the relationship between the summation of

the integer values and the mass value of the mass element may be over or under

estimated. To minimise those errors, the step 2) was performed for 15 different

mass elements that had mass pixels computed from the calculated kel constants.

[55]

The mass elements were selected from all segments, and from areas associated to

pixels with varying intensity, trying to cover the greatest range of the colour

spectrum as possible (Figure 3.6). The colour intensity and singular mass of all

those mass pixels, were then used as input and output, respectively, to compute a

final polynomial of degree 1 through a least squares sense:

��, � ( · ��, ) * (Formula 2)

Where mi,j is the mass associated to a pixel in the bitmap image, and α and β are

two real constants.

4) Finally, the two images (BMD and TISSUE) are linearly mapped using Formula (2)

and summed to compute the mass distribution of the whole body in a higher

resolution than the two matrices representing the raw data (Figure 3.6).

5) To eliminate noise from the areas outside the body, binary images for each matrix

were created and used as masks (i.e., the pixels that had a black color in the

referred mask were given a nil mass value). A global threshold was computed such

that all pixels referred to the outside of the body were addressed as black, whereas

the pixels referred to the body mass values were addressed as white (Figure 3.7).

The noise-free matrixes contained all mass pixels for the bone mineral

(I_BMD_mass), tissue compartments (I_TISSUE_mass), and the total body

(I_mass_total=I_BMD_mass + I_TISSUE_mass), to be then used to calculate the

BSIPs (Figures 3.8 and 3.9).

[56]

Figure 3.6: Grayscale images of the BMD and TISSUE compartment matrices created by the enCORE® software (right and middle, respectively), and the

summation of both images. Red and blue dots correspond to the locations of the mass elements used for the first and second matrices, respectively.

[57]

Figure 3.7: Binary images of the BMD, TISSUE and whole body mass created to eliminate noise outside the region of interest. All black pixels have nil mass value.

[58]

Figure 3.8: 2D representation of the I_BMD_mass, I_TISSUE_mass, and I_mass_total matrices (right, middle and left images, respectively) using a colour scale to

show the density of the mass pixels.

[59]

Figure 3.9: A 3D representation of the I_mass_total matrix.

[60]

Validation of the method was carried out by comparing the whole body mass, tissue mass

and bone mineral mass values calculated by the enCORE® software; and those calculated

by summing all pixel masses for the 28 subjects. The minimum (Emin) and maximum (Emax)

errors expressed in kilograms (Kg) were computed using the enCORE® values as criteria.

The mean absolute percentage errors (MAPE) and the percentage root mean square errors

(%RMSE), were calculated as:

-./0 � ∑ 1|�3��|�3 4 5 6��7 (Formula 3)

%�-90 � :∑;�3<��3 =>7 5 100 (Formula 4)

Where MR and MM are the real mass value from the scanner and summing all pixel masses,

and N is the number of subjects.

Another Matlab code (segment_whole_body.m, Appendix E) was created to divide the scan

image into a 16-segment model (head, upper trunk, middle trunk, lower trunk, upper arm,

forearm, hands, thighs, shanks and feet); and calculate the mass (MS, Kg), COM (cm) lying

on the longitudinal axis of the segment (as a distance from the distal end point of the

segment) and the principal MOI about the sagittal axis (Ixx, Kg�cm2, assuming all sagittal

axes were perpendicular to the scanning plane) of each segment. The segmentation

protocol used was the same adopted in the study of Zatsiorsky and Seluyanov (1983). This

function used body landmark coordinates as input to determine the joint centres and

sectioning planes (Figure 3.10). Those coordinates were entered when clicking on the bone

landmarks viewed in the BMD image. Extra clicked points also were used to define vertices

of a geometric figure within which the segment was placed; and, outside which, all the mass

pixels were excluded from the calculations (Figure 3.11). Coordinates of the elbow, wrist,

knee and ankle joint centres were calculated as described previously (Appendix D). The

same points used to define those joint centres also defined the segmentation plane

(perpendicular to the scanning plane). The shoulder and hip joint centres were obtained by

[61]

clicking on the regions of the BMD image that represented the centres of the heads of the

humerus and femur. The segmentation plane of the shoulder was defined by the line linking

the acromion landmark to the armpit. The segmentation plane of the hip was defined by a

line passing over the hip joint centre with an angle of 37º to the longitudinal axis of the trunk

(i.e., line linking the midpoint between the hips and the midpoint between the shoulders).

1 & 2: Left and Right Acromion

3 & 4: Left and Right Armpit

5: C7

6 & 7: Left and Right Shoulder Joint Centre

8 & 12: Left and Right Lateral Epicondyle

9 & 13: Left and Right Medial Epicondyle

10 & 14: Left and Right Posterior Mid Wrist

11 & 15: Left and Right Anterior Mid Wrist

16 & 17: Left and Right Hip Joint Centre

18 & 22: Left and Right Lateral Tibial Condyle

19 & 23: Left and Right Medial Tibial Condyle

20 & 24: Left and Right Lateral Malleolus

21 & 25: Left and Right Medial Malleolus

Figure 3.10: Representation of the 25 points used to segment the body using the

segment_whole_body.m function.

[62]

Figure 3.11: Output of the segment_whole_body.m function, containing the segmentation planes in the whole body (left figure, red dashed line), the clicked points

that defined the geometric figure used as frontier to delimit the segments (red dots), and the segment COM positions.

[63]

The MS, COM and Ixx were computed for each segment using the following equations

(Durkin et al., 2002):

-� � ∑ � (Formula 5)

DE- � F∑ GH��∑ IH�� J (Formula 6)

�KK � ∑ �LM (Formula 7)

Where x and y are the coordinates of the pixel mass, m is the mass value of each pixel

mass, and r is the distance from the pixel mass to the COM of the segment (radius of

gyration).

3.6 Data Analysis

The mean percentage error was calculated between each indirect estimation method and

the DXA/3D surface scan method – the criterion - for each subject group. A 5 X 3 (indirect

estimation method X subject group) mixed-model analysis of variance (SPANOVA, α=0.05)

of the percentage errors was conducted for each segment and for each inertial parameter.

This was followed by a Tukey-HSD post-hoc analysis to determine any differences between

estimation methods, between swimmers and normal Caucasian males, and possible

interaction factors. It was hypothesised that any errors found for the two groups of swimmers

would be significantly greater than those found in the cohort resembling the studies by

Zatsiorsky et al. (Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990), regardless

of segment or inertial parameters.

[64]

Chapter 4

RESULTS

The errors associated with using the proposed DXA methods are reported in Table 4.1.

While large MAPE and %RMSE could be observed for the bone mineral mass, it had little

influence on total mass prediction But, in contrast, tissue mass was able to be estimated

with marginal errors.

Table 4.1: Minimum error (Emin, Kg), Maximum error (Emin, Kg), Mean Absolute Percentage Error

(MAPE, %) and Percent Root Mean Square (%RMSE) for the bone mineral, tissue and whole

body masses calculated from the respective images.

Compartment Emin (Kg) Emax (Kg) MAPE %RMSE

Bone mineral 0.04 0.60 9.32% 10.55%

Tissue 0.09 1.72 1.09% 1.27%

Total 0.01 2.12 1.18% 1.45%

Table 4.2 shows the means and standard deviations (SD) for segment masses calculated by

using DXA for the 10 young adult males who resembled subjects analysed by Zatsiorsky

and Seluyanov (1983). These results were compared with the segment masses of the

subjects in Zatsiorsky and Seluyanov (Zatsiorsky and Seluyanov, 1983). The ‘Zatsiorsky’

studies (Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990) presented segment

length as distances between bony landmarks rather than between joint centres. Moreover,

rather than the absolute value of the MOI or the radii of gyrations, they presented the radii

of gyration as percentages of the segmental lengths. Therefore, similar comparisons for

COM and MOI are not provided as the values could not be computed in the same way. A

series of one-sample t-tests was used to determine whether segment masses from of the

[65]

participants were different to those found in the ‘Zatsiorsky’ studies (Zatsiorsky and

Seluyanov, 1983, 1985; Zatsiorsky et al., 1990). Only the head (t = −0.20, p = 0.84) and

forearm (t = 0.51, p = 0.61) segments showed non-significant differences.

Table 4.2: Mean (SD) segment masses (kg) of young adult Caucasian males tested in the

present study (DXA, n=10) and the young adult Caucasian males from Zatsiorsky studies

(Zatsiorsky, n=100).The (*) indicates the segments for which the differences were significant

(p<0.05)

Mass

Segment DXA Zatsiorsky

Head 4.99 (0.50) 5.02 (0.39)

Trunk* 34.08 (2.57) 31.77 (3.24)

Upper arm* 2.30 (0.33) 1.98 (0.32)

Forearm 1.20 (0.16) 1.18 (0.16)

Thigh* 9.69 (1.15) 10.36 (1.57)

Shank* 3.46 (0.44) 3.16 (0.44)

* Significant differences between DXA and Zatsiorsky (p<0.05)

Tables 4.3, 4.4 and 4.5 show the means and SD for mass, COM and Ixx for each of the

estimation methods and subject groups. Despite some variations, comparisons between the

mean values obtained from DXA and the other estimation methods did not reveal them to be

statistically significance (p >.05)

[66]

Table 4.3: Mean (SD) segment mass (Kg) calculated for adult Caucasian male (n = 10), male

swimmers (n = 10) and female swimmers (n = 8) using the Chandler model (C), Yeadon model

(Y), Zatsiorsky simple regression model (Z1), Zatsiorsky multiple regression model (Z2),

Zatsiorsky geometric model (Z3,) and the proposed estimation protocol using DXA (DXA).

Estimation Method

Segment Group C Y Z1 Z2 Z3 DXA

Head Adult male 4.34 4.96 5.13 6.07 5.74 4.99

(0.22) (0.92) (0.23) (0.76) (0.76) (0.50)

Male swimmers 4.54 5.04 5.35 6.37 5.71 5.18

(0.29) (0.65) (0.26) (0.67) (0.68) (0.37)

Female swimmers 3.92 3.79 4.85 5.66 4.91 4.40

(0.16) (0.53) (0.18) (0.35) (0.58) (0.30)

Trunk Adult male 39.72 34.10 33.02 36.05 32.07 34.08

(3.64) (3.29) (2.95) (3.07) (2.61) (2.57)

Male swimmers 43.04 38.91 35.55 37.68 36.52 39.14

(4.89) (4.46) (4.20) (3.72) (3.96) (4.02)

Female swimmers 32.80 27.48 26.71 31.52 26.02 28.45

(2.58) (2.54) (2.03) (2.70) (2.43) (2.09)

Head + Trunk Adult male 44.06 39.06 38.15 42.12 37.81 39.07

(3.86) (4.00) (3.16) (3.46) (3.20) (2.97)

Male swimmers 47.57 43.95 40.91 44.05 42.23 44.32

(5.18) (5.06) (4.44) (3.92) (4.35) (4.34)

Female swimmers 36.72 31.27 31.57 37.18 30.93 32.85

(2.74) (2.94) (2.19) (2.84) (2.65) (2.28)

Upper arm Adult male 2.09 2.41 2.06 2.54 2.25 2.30

(0.14) (0.38) (0.18) (0.29) (0.37) (0.33)

Male swimmers 2.21 2.87 2.23 2.85 2.55 2.61

(0.19) (0.46) (0.25) (0.30) (0.41) (0.42)

Female swimmers 1.84 2.08 1.68 2.27 1.78 1.91

(0.09) (0.22) (0.13) (0.19) (0.20) (0.19)

Forearm Adult male 1.27 1.26 1.21 1.35 1.20 1.20

(0.12) (0.20) (0.09) (0.17) (0.26) (0.16)

Male swimmers 1.37 1.42 1.30 1.48 1.32 1.31

(0.16) (0.26) (0.12) (0.24) (0.25) (0.20)

Female swimmers 1.05 1.04 1.03 1.15 0.92 0.90

(0.08) (0.16) (0.06) (0.16) (0.13) (0.11)

Thigh Adult male 9.70 9.69 10.90 10.34 10.90 9.69

(1.81) (1.22) (1.07) (1.01) (1.36) (1.15)

Male swimmers 10.49 10.23 11.92 10.70 11.06 9.65

(1.96) (1.30) (1.40) (1.15) (1.30) (1.45)

Female swimmers 8.06 8.83 8.94 9.03 9.68 8.11

(1.72) (0.86) (0.77) (0.76) (1.01) (0.63)

Shank Adult male 3.12 4.03 3.30 3.61 3.39 3.46

(0.28) (0.55) (0.33) (0.43) (0.48) (0.44)

Male swimmers 3.37 4.32 3.63 3.81 3.56 3.58

(0.37) (0.62) (0.40) (0.45) (0.61) (0.51)

Female swimmers 2.58 3.31 2.79 3.00 2.60 2.92

(0.19) (0.44) (0.24) (0.36) (0.43) (0.33)

[67]

Table 4.4: Mean (SD) distance of the centre of mass position in the longitudinal axis from the

distal end point (COM, cm) of adult Caucasian male (n = 10), male swimmers (n = 10) and female

swimmers(n = 8) according to the Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1),

Zatsiorsky multiple regression (Z2), Zatsiorsky geometric (Z3) and DXA estimation methods.

Estimation Method


Head Adult male 11.91 11.81 11.88 14.77 12.05 11.32

(0.86) (1.20) (1.68) (1.31) (0.87) (0.88)

Male swimmers 13.04 11.94 13.98 15.48 13.19 11.57

(0.72) (0.86) (1.42) (1.80) (0.73) (0.55)

Female swimmers 12.01 11.14 12.12 15.15 12.15 11.69

(0.86) (0.92) (1.80) (0.54) (0.87) (0.31)

Trunk Adult male 35.70 27.29 26.18 28.42 28.36 27.96

(0.92) (0.83) (0.55) (1.32) (0.73) (1.08)

Male swimmers 37.89 30.27 28.47 31.94 30.11 30.81

(1.32) (0.99) (1.21) (1.11) (1.05) (0.89)

Female swimmers 34.47 26.48 24.78 27.16 27.39 27.02

(1.62) (1.13) (1.38) (1.13) (1.29) (0.89)

Head + Trunk Adult male 39.10 32.71 32.12 34.87 34.73 33.74

(0.87) (1.23) (0.65) (1.71) (0.97) (1.27)

Male swimmers 41.44 35.27 34.72 38.55 36.20 36.39

(1.30) (1.15) (1.18) (1.44) (0.97) (0.99)

Female swimmers 38.09 31.44 31.51 33.92 33.91 33.06

(1.63) (1.32) (1.51) (1.15) (1.40) (0.89)

Upper arm Adult male 14.68 15.78 16.19 13.26 12.56 15.28

(0.85) (0.94) (1.59) (0.72) (0.73) (0.82)

Male swimmers 15.76 17.20 17.74 14.10 13.48 16.18

(1.19) (1.20) (1.88) (1.04) (1.02) (1.43)

Female swimmers 14.68 16.02 16.79 13.38 12.56 15.26

(0.73) (0.74) (1.20) (0.64) (0.63) (0.52)


(1.16) (1.29) (1.58) (0.82) (1.08) (1.23)

Male swimmers 15.77 15.49 11.86 10.46 14.65 16.46

(1.32) (1.28) (1.85) (0.92) (1.23) (1.51)

Female swimmers 14.47 14.10 10.22 9.43 13.44 14.86

(0.97) (0.89) (1.33) (0.72) (0.90) (1.01)

Thigh Adult male 26.38 24.06 19.21 22.23 25.74 24.42

(1.92) (1.75) (2.08) (2.38) (1.88) (1.75)

Male swimmers 27.21 24.84 19.23 23.13 26.55 24.80

(2.15) (1.96) (2.59) (2.42) (2.10) (2.20)

Female swimmers 26.19 24.51 19.91 22.39 25.56 23.85

(1.59) (1.61) (1.92) (2.32) (1.55) (1.35)

Shank Adult male 24.36 24.09 25.38 26.34 23.01 24.49

(1.74) (1.75) (2.17) (1.81) (1.65) (1.75)

Male swimmers 25.74 25.50 26.81 27.82 24.32 25.72

(1.91) (2.19) (2.56) (2.12) (1.80) (2.23)

Female swimmers 23.72 23.28 24.32 25.48 22.40 23.66

(1.72) (1.64) (2.24) (1.69) (1.62) (1.56)

[68]

Table 4.5: Mean (SD) values for segment principal moment of inertia about the sagittal axis (Ixx,

Kg��cm2) of adult Caucasian male (n = 10), male swimmers (n = 10) and female swimmers (n = 8)

according to the Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky

multiple regression (Z2), Zatsiorsky geometric (Z3) and DXA estimation methods.

Estimation Method


Head Adult male 248.95 226.92 280.09 400.67 366.98 233.51

(69.14) (71.57) (19.65) (84.37) (84.27) (46.15)

Male swimmers 290.75 230.10 299.95 441.04 372.79 253.81

(61.00) (54.30) (22.06) (93.48) (94.18) (29.45)

Female

swimmers

226.96 141.22 259.11 379.78 309.98 197.83

(25.79) (40.58) (15.72) (33.37) (63.34) (19.44)

Trunk Adult male 16595.16 14500.71 13523.39 16840.92 13142.09 13239.06

(2574.00) (1886.73) (1473.89) (1598.89) (1762.19) (1838.08)

Male swimmers 20323.68 20276.15 16550.85 21742.87 17157.06 17958.63

Female

swimmers

(4132.74) (3149.84) (2460.68) (2860.52) (2750.40) (2773.83)

12013.65 10937.66 9868.27 13467.26 10095.63 10727.80

(2221.96) (1724.73) (1101.34) (1916.16) (1533.64) (1552.61)

Head +

Trunk

Adult male 21522.06 22757.78 22446.33 27679.62 22118.59 21122.58

(2883.82) (3520.69) (2496.32) (3254.45) (2989.02) (2917.95)

Male swimmers 26263.57 29055.61 27355.76 33511.44 27530.55 27197.73

Female

swimmers

(4647.40) (4717.17) (3299.51) (4081.15) (3883.40) (3870.66)

16262.99 16725.16 17968.52 23286.48 17373.26 17510.21

(2454.89) (2783.86) (1660.50) (2839.84) (2225.34) (2253.45)

Upper

arm

Adult male 167.92 194.90 135.71 205.55 133.72 161.64

(42.42) (48.10) (21.56) (28.37) (30.94) (35.41)

Male swimmers 230.29 266.42 157.93 241.06 166.40 207.70

Female

swimmers

(63.78) (75.58) (24.67) (34.00) (49.98) (65.86)

142.30 167.27 109.70 186.09 98.50 125.88

(27.14) (32.75) (16.86) (20.74) (17.29) (18.88)


(17.31) (18.52) (8.77) (18.64) (23.62) (19.20)

Male swimmers 70.52 86.30 77.16 92.46 79.11 75.81

Female

swimmers

(23.18) (28.89) (10.75) (23.84) (27.19) (23.61)

42.22 53.24 54.79 64.25 45.92 44.62

(11.75) (16.11) (6.52) (16.40) (12.25) (12.25)

Thigh Adult male 2072.24 1538.01 2148.83 1617.71 1866.66 1531.03

(592.00) (427.61) (346.60) (302.58) (404.13) (368.93)

Male swimmers 2315.68 1721.38 2500.23 1741.60 1975.19 1552.45

Female

swimmers

(583.40) (445.80) (410.82) (361.78) (417.61) (450.55)

1778.59 1356.51 1666.21 1308.98 1601.63 1177.87

(357.03) (259.67) (263.92) (210.22) (250.00) (185.44)

Shank Adult male 518.60 633.37 418.36 457.95 494.11 449.14

(147.73) (183.73) (80.15) (107.78) (147.19) (122.80)

Male swimmers 619.18 759.39 501.79 527.34 575.65 516.44

Female

swimmers

(165.06) (208.23) (89.44) (103.06) (157.39) (139.82)

395.90 489.37 333.59 375.94 363.23 361.52

(101.27) (124.04) (64.00) (102.64) (112.17) (98.24)

[69]

The ANOVA revealed significant differences in the BSIP data between groups except for the

head COM (F(2,25) = 0.80, p = .46) and thigh COM (F(2,53) = 1.21, p = 0.31). Female

swimmers had significantly lower mass values than the other two groups for all segments

(head: F(2,25) = 8.90; trunk: F(2,25) = 27.03; head plus trunk: F(2,25) = 25.68; upper arm:

F(2,53) = 19.27; forearm: F(2,53) = 28.91; thigh: F(2,53) = 10.41; shank: F(2,53) = 10.87),

forearm Ixx (F(2,53) = 11.64) and thigh Ixx (F(2,53) = 5.78). Male swimmers had

significantly greater values than the other two groups for all parameters of the trunk (mass:

F(2,25) = 27.06; COM: F(2,25) = 39.27; Ixx: F(2,25) = 26.49), head + trunk (mass: F(2,25) =

25.68; COM: F(2,25) = 25.19; Ixx: F(2,25) = 22.13), and upper arm (mass: F(2,53) = 19.27;

COM: F(2,53) = 5.08; Ixx: F(2,53) = 14.14), and the Male swimmers also had significantly

larger forearm COM value (F(2,53) = 7.43), greater head Ixx (F(2,25) = 5.94), shank COM

value (F(2,53) = 5.46) and shank Ixx (F(2,53) = 7.04) than female swimmers.

The %RMSE of mass, COM and Ixx of each indirect estimation method against DXA, for

each group of subjects, are presented in Tables 4.6, 4.7 and 4.8, respectively. Overall, the

Ixx values are the least accurate inertial parameter, while estimation of the COM produced

least amount of errors, when using any indirect estimation methods.

The error assessment of all indirect BSIP methods according to subject group is presented

by plotting the MAPE for the mass (Figure 4.1), COM (Figure 4.2) and Ixx (Figure 4.3)

[70]

Table 4.6: Percentage Root Mean Square Error (%RMSE) for segment mass (Kg) of the Chandler

(C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and

Zatsiorsky geometric (Z3) estimation methods against DXA, observed for adult Caucasian male

(n = 10), male swimmers (n = 10) and female swimmers (n = 8).

Estimation Method

Segment Group C Y Z1 Z2 Z3

Head Adult male 13.97 12.99 8.37 23.69 17.44

Male swimmers 12.66 7.83 4.68 25.47 14.50

Female swimmers 11.50 15.50 12.06 30.36 14.76

Trunk Adult male 16.69 4.94 3.87 8.57 6.49

Male swimmers 10.60 3.00 9.99 5.17 7.06

Female swimmers 15.75 4.69 6.72 11.20 9.41

Head + Trunk Adult male 13.04 5.20 3.32 9.46 4.10

Male swimmers 7.99 3.18 8.40 2.80 4.96

Female swimmers 12.20 5.82 4.61 13.31 6.57

Upper arm Adult male 13.47 9.80 13.04 13.58 7.58

Male swimmers 16.88 13.02 15.40 13.87 6.31

Female swimmers 8.20 12.08 13.38 20.27 8.71

Forearm Adult male 11.20 12.93 9.24 16.90 15.79

Male swimmers 9.60 12.40 7.74 15.65 9.24

Female swimmers 19.57 16.95 17.46 28.36 7.27

Thigh Adult male 16.45 4.42 13.53 10.47 13.89

Male swimmers 19.81 7.27 24.92 13.48 16.61

Female swimmers 19.36 10.40 10.97 13.23 20.42

Shank Adult male 12.32 17.01 8.78 6.81 5.65

Male swimmers 7.50 21.13 6.50 8.42 5.60

Female swimmers 13.24 17.82 8.62 10.64 17.24

[71]

Table 4.7: Percentage Root Mean Square Error (%RMSE) for segment centre of mass position in

the longitudinal axis from the distal end point (COM, cm) of the Chandler (C), Yeadon (Y),

Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky

geometric (Z3) estimation methods against DXA, observed for adult Caucasian male (n = 10),

male swimmers (n = 10) and female swimmers (n = 8).

Estimation Method


Head Adult male 10.86 11.74 15.73 32.62 11.65

Male swimmers 14.27 8.26 23.71 38.04 15.50

Female swimmers 8.11 9.02 15.31 30.49 8.68

Trunk Adult male 28.06 3.09 7.35 3.45 3.45

Male swimmers 23.10 2.24 8.48 4.42 2.98

Female swimmers 27.74 3.17 8.92 3.04 2.88


Male swimmers 14.02 3.20 5.41 6.68 1.98

Female swimmers 15.43 5.53 5.58 3.70 3.87


Male swimmers 3.61 7.28 10.42 12.95 16.72

Female swimmers 5.14 6.17 11.87 12.70 17.92


Male swimmers 5.07 6.29 28.85 36.48 11.26

Female swimmers 3.43 5.80 31.83 36.56 9.74

Thigh Adult male 8.52 2.71 21.86 10.34 6.09

Male swimmers 10.16 2.48 23.24 7.85 7.61

Female swimmers 10.02 3.62 17.36 8.49 7.43

Shank Adult male 1.66 2.36 4.38 7.81 6.21

Male swimmers 2.40 1.83 5.74 8.76 5.81

Female swimmers 2.41 2.67 4.44 7.77 5.80

[72]

Table 4.8: Percentage Root Mean Square Error (%RMSE) for segment principal moment of

inertia about the sagittal axis (Ixx, Kg��cm2) of the Chandler (C), Yeadon (Y), Zatsiorsky simple

regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3) estimation

methods against DXA, observed for adult Caucasian male (n = 10), male swimmers (n = 10) and

female swimmers (n = 8).

Estimation Method


Head Adult male 19.25 24.24 29.84 76.86 59.87

Male swimmers 26.00 18.75 20.48 82.82 57.48

Female swimmers 23.13 32.63 33.96 97.50 63.43

Trunk Adult male 29.33 12.82 6.20 29.07 6.07

Male swimmers 15.24 13.85 11.10 22.63 6.74

Female swimmers 15.98 7.61 9.19 27.19 9.14


Male swimmers 7.29 9.23 5.06 24.49 4.30

Female swimmers 9.60 9.49 6.70 33.84 6.03


Male swimmers 18.28 33.55 24.16 30.99 20.43

Female swimmers 18.46 36.61 15.14 50.81 22.51


Male swimmers 12.00 17.53 23.05 27.41 13.84

Female swimmers 10.17 22.63 33.80 46.85 12.59

Thigh Adult male 37.23 9.05 45.54 17.91 27.39

Male swimmers 52.30 14.85 72.90 21.23 34.25

Female swimmers 52.33 17.58 42.55 19.81 40.20

Shank Adult male 16.30 41.24 13.40 8.35 12.30

Male swimmers 22.96 49.55 11.89 10.82 16.74

Female swimmers 19.09 40.95 16.25 19.87 25.35

Figure 4.1: Mean Absolute Percentage Error (MAPE) for segment mass (Kg) of the Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple

regression (Z2), and Zatsiorsky geometric (Z3) estimation methods against DXA, observed for young adult Caucasian males (Normal), Male swimmers and Female

swimmers.

Figure 4.2: Mean Absolute Percentage Error (MAPE) for segment centre of mass position in the longitudinal axis from the distal end point (COM, cm) of the

Chandler (C), Yeadon (Y), Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3) estimation methods against DXA,

observed for young adult Caucasian males (Normal), Male swimmers and Female swimmers.

Figure 4.3: Mean Absolute Percentage Error (MAPE) for segment principal moment of inertia about the sagittal axis (Ixx, Kg��cm2) of the Chandler (C), Yeadon (Y),

Zatsiorsky simple regression (Z1), Zatsiorsky multiple regression (Z2), and Zatsiorsky geometric (Z3) estimation methods against DXA, observed for young adult

Caucasian males (Normal), Male swimmers and Female swimmers.

[76]

The SPANOVAs showed significant interactions between the estimation method and subject

groups for all segment masses, except for the head (trunk mass: F(6.99,87.41) = 5.15; head

+ trunk mass: F(7.03,87.91) = 8.42; upper arm mass: F(3.69,97.76) = 3.10; forearm mass:

F(4.71,124.90) = 3.78; thigh mass: F(5.83,154.44) = 8.72; shank mass: F(5.94,157.31) =

4.16). The thigh was the only segment where significant interaction between the estimation

method and subject groups was observed for COM (F(3.17,84.11) = 4.39). Only for the head

and the head + trunk segments no significant interactions occurred between the estimation

method and subject groups for segment Ixx, (trunk Ixx: F(5.72,71.47) = 3.32; upper arm Ixx:

F(4.41,116.98) = 4.43; forearm Ixx: F(5.99,158.76) = 4.25; thigh Ixx: F(5.31,140.63) = 6.92;

shank Ixx: F(5.82,154.33) = 2.19).

The SPANOVAs also showed significant differences (p < 0.05) in absolute errors between

estimation methods for all BSIPs, whereas significant differences between subject groups

were found for trunk mass (F(2,25) = 15.17), head + trunk mass (F(2,25) = 33.50), forearm

mass (F(2,53) = 6.80), thigh mass (F(2,53) = 6.80), head and trunk Ixx (F(2,25) = 3.48),

upper arm Ixx (F(2,53) = 4.58), forearm Ixx (F(2,53) = 4.40) and thigh Ixx (F(2,53) = 7.00).

The Tukey HSD post hoc test indicated significantly greater errors in female swimmers than

the other two groups for trunk mass, head and trunk mass, and forearm mass (p<0.05). The

female swimmers also recorded greater errors than male swimmers for forearm Ixx and

significantly greater errors than normal male subjects for upper arm Ixx (p<0.05). Normal

male subjects revealed significantly lower errors than male and female swimmers for head +

trunk mass, and thigh mass (p<0.05). Normal male subjects also exhibited significantly lower

errors in thigh Ixx than male swimmers, and tended towards demonstrating (p = 0.056) lower

errors than female swimmers. Although significant differences were found between groups

for the head + trunk Ixx, the Tukey HSD did not indicate which pair (s) was (were)

significantly different.

[77]

Chapter 5

DISCUSSION

The primary aim of this study was to validate the proposed method of extracting BSIP data

from DXA scans. The DXA results also were compared with five other regularly used indirect

methods in samples of 10 elite male and 8 elite female swimmers, and 10 normal adult

Caucasian males. The DXA relies on the relationships between the attenuation coefficients

of the high energy beams and the mass of a given phantom to predict the mass of the

scanned object (Durkin et al., 2002). A unique feature of the method developed for this study

is that mass value for each unit area (mass element) could be extracted directly, thanks to

the day-pass licence authorisation from the manufacturer, Healthcare Division of General

Electric Company (GEHC). Their enCORE® software also exports two bitmap images to

graphically illustrate mass distribution within the scanned area. Because the software did

not allow mass element data to be exported into any other formats, it was necessary to

establish the relationship between mass elements and the pixel intensity of the scan images.

The comparison between segment mass calculated from pixel colour-mass relationship and

the mass calculated for the two compartments (BM mass and tissue mass) by the enCORE®

software revealed a similar level of accuracy as previously (Durkin et al., 2002). The lower

accuracy of the bone mineral mass seems to result from inadequate threshold values used

to create the binary images of the bone mineral images. When comparing both the noise

and noise-free images, it seems that some bone information may have been lost. Also, the

edges of a number of flat bones did not line up with the edges of the rectangular mass

elements (Wicke and Dumas, 2008). This could have contributed to the incorrect bone mass

values for the pixels closest to the boundaries of those bones.

[78]

The present study also demonstrated that BSIP profiles of elite swimmers are quite different

from those of untrained Caucasian adults (Tables 4.3, 4.4 and 4.5). Durkin and Dowling

(2003) warned that caution is urged when the population investigated is not reasonably

matched with the population from which the equations were devised. If using the proposed

DXA method as the ‘gold-standard’, the indirect BSIP estimations in the non-athlete group

consistently produced errors (Tables 4.6, 4.7 & 4.8). Figure 4.1 illustrates that none of the 5

indirect estimation methods consistently reported MAPEs less than 5%. This was even

though the characteristics of this group were approximately similar to the Zatsiorsky and

Seluyanov sample (Zatsiorsky and Seluyanov, 1983, 1985) with whom they were compared.

The accuracy of any given indirect estimation method relies on its ability to replicate the

subject-specific body morphology and body composition. Early studies in kinanthropometry

revealed differences in absolute and relative body size, somatotype and body composition,

between elite swimmers and the normal population (Ackland, Elliott, and Bloomfield, 2009).

Carter and Ackland (Carter and Ackland, 1994) also reported variations between genders

and swim events, for different strokes and different distances, even within an elite swimming

population. Therefore, it might be expected that equations using just the whole body mass,

or mass and stature (C and Z1), would showed greater MAPE values or differences in

MAPE between groups. Even the Z2 model, which used the most number of anthropometric

variables as predictors for inertial parameters of a given segment, reported errors > 20% and

varied greatly between groups. The geometric models (Y and Z3) seemed to generate less

error in general, and were more consistent between groups. However, none of the latter

consistently performed better than the others. Even though Y appeared to resemble the

geometric shape of the body better than Z3, using uniform segment densities gathered from

cadavers might have contributed to the errors found. The Z3 method proposed using a

quasi-density value to compensate for differences between the actual segment volume, and

its cylindrical representation. But, this approach was not enough to provide low and

consistent levels of MAPE between the groups for all segments, and especially was more

evident for the lower limbs. For most of the body segments, results of this study reject the

hypothesis that the indirect methods would produce significantly lower errors for the

untrained adult group than the two athlete groups. The hypothesis was based on the

[79]

premise that the indirect method would only be accurate for subjects with similar

anthropometric profile to the population which the method was developed from. The normal

young adults tested in this study closely resembled the population from Zatsiorsky’s

methods (Z1, Z2 and Z3) (Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990).

However, errors in the BSIPs estimated for this group using Z1, Z2 and Z3 did not produce

consistently less errors than other techniques. Reduced errors were only found for the thigh

and head + trunk segments. Durkin and Dowling (2003) also found similar %RMSE in young

adult males which indicated that not even the apparent anatomical similarities minimised the

errors yielded by those methods.

Analysing the COM of thigh segment revealed a significant interaction between estimation

method and subject group, yet no significant differences were found between groups. Good

consistency can be observed when plotting the MAPE for COM (Figure 4.2), as the three

groups recorded similarly low errors for most COM and estimation methods. Nevertheless,

no estimation method found MAPE to be less than 5% for all COMs and all groups. The Y

method was the only one not showing errors greater than 15% at least once. Also, the

greatest %RMSE for Y was 11.74% (Table 4.7), which was for the head segment of the

untrained subjects. This indicated that the uniform density assumption and the geometrical

solids that were used, enabled fairly accurate results for the COM. The two methods, C and

Z3, used a fixed proportion between COM distance from distal endpoint and segment length.

The first was Chandler which performed poorly for the head, trunk, and sum of head and

trunk. Perhaps this could be partially explained by the different segmentation protocol used

by Chandler et al. (1975). For instance, once elderly cadavers are used, there needs to be

some consideration of the ageing effect over the spine. Over the years, the spine tends to

shorten its longitudinal length due to disc flattening when losing the nucleus pulposus, a jelly

like substance in the middle of the spinal disc. Thus, the resultant, reduced trunk length

might have induced errors when being compared with younger subjects whose spines had

not yet been affected in this way. On the other hand, the Z3 method used adjusted positions

for the COM relative to the joint centres (De Leva, 1996) rather than the anatomical

landmarks. However, rather than using the same cohort as in the studies of Zatsiorsky and

colleagues (Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990), some

[80]

adjustments were carried out using anthropometric data from other Caucasian ethnic

groups, which certainly added errors to the adjustment. The other two methods (Z1 and Z2)

demonstrated considerably large errors for the head, forearm and thigh COMs, although little

difference between groups were observed.

Not surprisingly, the largest percentage errors (MAPE and %RMSE) were found for Ixx

(Figure 4.3): even though it is not dependent upon the mass and COM values for its

calculation. However, the Ixx is physically related to those two inertial parameters. As

happened with the mass values, significant interactions between the estimation method and

subject group were found for most of segment Ixxs; except for the head, and the head +

trunk segment. The Ixx of all limb segments of female swimmers seemed to be affected

more than in the other two groups. Even though it was hypothesised to occur, it was only

with the thigh segment that there was a trend towards significantly lower percentage errors

for the normal subjects when compared to the two groups of swimmers. But, the %RMSE

was inferior to 10% only for the Y method (Table 4.8). Nevertheless, with %RMSE of up to

50% for each of the estimation methods, regardless of subject group, for at least one

segment (Table 4.8), it is clear that indirect estimation methods should be avoided when

applied to a population of different morphology and body composition.

Despite the accuracy, easy access, low radiation exposure and easier data processing than

required for other medical imaging technologies, calculating BSIPs using DXA is not widely

practised. One limitation is that one might not gain access to the raw data from the scan

because manufacturers need to protect their intellectual property. Another problem is that

had to be resolved was the inability to establish a relationship between the binary files and

channels of data with the mass of the scanned object/subject (Jim Dowling, personal

correspondence). The scan area may not be compatible for elite swimmers or athletes from

other sports who are generally much taller and larger than the normal population. The scan

used in this study was 59.75cm x 197cm; whereas the dimensions were 59.4cm x 192.7cm

in studies that used the Hologic QDR-1000/W model (Hologic Inc., Bedford, MA, USA)

(Durkin and Dowling, 2006; Durkin and Dowling, 2003; Durkin et al., 2002; Durkin et al.,

2005). However, the major limitation of the method is the 2D characteristics of DXA scan,

[81]

which do not enable calculation of the COM position in the sagittal plane, or the principal

moments of inertia about the longitudinal and transverse axes (Durkin et al., 2002; Ganley

and Powers, 2004b; Wicke and Dumas, 2008). Therefore, kinetic analyses in sporting

manoeuvres that are typically three-dimensional (e.g., swimming) cannot rely on data

extracted from DXA without incorporating modelling techniques. Several modelling

technique approaches can be performed, as proposed in previous studies (Durkin and

Dowling, 2006; Durkin et al., 2005; Lee et al., 2009; Wicke et al., 2008; Wicke et al., 2009).

Finally, it can be argued that the influence of errors in BSIP calculations depends on the

nature of the movement being analysed. Factors such as whether the task involves rapid

linear/angular movements of the segments, is an open-chain or closed-chain analysis, or

whether external forces exert greater or lesser influence than the BSIP method used, will

determine the level of accuracy in the joint forces and moments that are calculated.

However, this study demonstrated that using an indirect estimation method can lead to

grossly inaccurate BSIPs. The recent advances in kinematic analysis systems have resulted

in greater validity, reproducibility, and also flexibility with regard to the environment in which

the assessment is required. It seems counter-intuitive to then ignore the potential errors

from using inappropriate BSIP data. However, extracting full body 3D BSIP from DXA

requires further development before it can be readily used.

[82]

Chapter 6

SUMMARY CONCLUSION &

RECOMMENDATIONS FOR FUTURE

STUDIES

6.1 Summary

This study proposed a new method to compute body segment inertial parameters (BSIPs)

via DXA. This was done by co-registering the areal density data with grayscale images,

thereby enabling the relationship between the pixel colour intensity and the mass recorded

for the referred area to be established. BSIPs were then calculated for elite male swimmers,

elite female swimmers and young adult Caucasian males using DXA scans. Thirdly, and

using the DXA method as criterion, the study assessed the errors in BSIP estimations that

could arise when using five different indirect BSIP estimation methods for these three

populations.

Eight elite female swimmers, 10 elite male swimmers, and 10 young adult Caucasian males

had their whole body mass calculated from the relationship found between pixel colour

intensity and areal density. The values were compared against the criterion value obtained

from the DXA scanner when used to calculate body composition by %RMSE. Subjects also

were scanned with 3D surface scans to compute the anthropometry necessary to calculate

the BSIPs when using the indirect estimation methods. The mass, COM and MOI about the

sagittal axis of seven body segments (head, trunk, head + trunk, upper arm, forearm, thigh,

and shank) were computed from the proposed DXA for each group. Differences were

[83]

assessed using analysis of variance (ANOVA). When applying the five indirect estimation

methods to each of the three referred populations, errors were assessed using the BSIPs

gathered with DXA as criterion, by calculating the %RMSE and searching for significant

differences in absolute percentage errors for all BSIPs.

Computing BSIPs using the DXA scanner by establishing the relationship between the areal

density of the full body scan, and the colour intensity of the pixels from the grayscale images

of the scan, resulted in %RMSE errors of less than 1.5%. This agreed with the accuracy of

previous DXA BSIP estimation methods. Using the proposed DXA method, significant

differences in BSIPs were observed when comparing 10 young adult Caucasian males, 10

elite male swimmers, and 8 elite female swimmers. Elite female swimmers reported

significantly lower segment masses than the other two groups. The male swimmers

recorded greater inertial parameters of the trunk and upper arms than the other two groups.

Also, when using DXA as a criterion against the BSIPs computed for the three populations

when using the five indirect estimation methods, the %RMSE and the comparisons between

absolute percentage error of each indirect method for each group revealed that no BSIP

indirect estimation method performed best for all groups, in segments or BSIPs; as large

errors were observed for each method. Therefore, caution should be taken when computing

BSIPs for elite swimmers and the DXA method should be used when accessible.

Using the proposed DXA method, significant differences in BSIP were observed when

comparing 10 young adult Caucasian males, 10 elite male swimmers, and 8 elite female

swimmers. Elite female swimmers have significantly lower segment masses than the other

two groups, whereas male swimmers have greater inertial parameters of the trunk and upper

arms than the other two groups.

When using DXA as a criterion against the BSIP computed for the three populations using

the five indirect estimation methods, the %RMSE and the comparisons between MAPE of

each indirect method for each group revealed that no BSIP indirect estimation method

performed best for all groups, segments or BSIP, as large errors were observed for each

method. Therefore, caution should be taken when computing BSIP for elite swimmers, and

the DXA method should be used when accessible.

[84]

6.2 Conclusion

Based on the results obtained in this study, it can be concluded that:

• The method developed in this study to compute BSIP from DXA was deemed highly

accurate as errors in whole body mass were inferior to 1.5%;

• A population of elite swimmers have significantly different BSIPs when compared

with young adult Caucasian male;

• Elite male swimmers also have significantly different BSIP when compared to elite

female swimmers;

• None of the 5 proposed indirect BSIP estimation methods emerged to be better than

others in providing accurate BSIPs for any of the subject groups. This was true

even for the BSIPs of untrained participants via Z1, Z2 and Z3.

• While it was generally assumed that the indirect estimation methods would produce

least errors when they are used to estimate BSIPs in subjects that are similar to the

samples used to develop the methods, this study found large errors for the non-

swimming group when using the three methods developed by Zatsiorsky et al.

(Zatsiorsky and Seluyanov, 1983, 1985; Zatsiorsky et al., 1990) which indicated

large individual differences within the group;

6.3 Recommendations for Future Studies

It is recommended that future studies should:

• Investigate the BSIP errors yielded by indirect BSIPs when applied to other elite

sportsmen populations, or outliers in physique types (eg. obese, elderly, etc);

• Investigate the influence of inaccurate BSIPs in dynamic analyses of elite athletes;

• Develop methods to compute full BSIP data by combining DXA with modelling or

other imaging techniques;

[85]

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[93]

Appendix AAppendix AAppendix AAppendix A

CONSENT FORM

[94]

Consent Form

I (the participant) have read the information provided and any questions I have asked have

been answered to my satisfaction. I agree to participate in this activity, realising that I may

withdraw at any time without reason and without prejudice.

I understand that all identifiable information that I provide is treated as strictly confidential

and will not be released by the investigator in any form that may identify me. The only

exception to this principle of confidentiality is if documents are required by law.

I have been advised as to what data is being collected, the purpose for collecting the data,

and what will be done with the data upon completion of the research.

I agree that research data gathered for the study may be published provided my name or

other identifying information is not used.

____________________________________ __________

Participant Date

____________________________________ __________

Researcher Date

Approval to conduct this research has been provided by The University of Western Australia,

in accordance with its ethics review and approval procedures. Any person considering

participation in this research project, or agreeing to participate, may raise any questions or

issues with the researchers at any time.

In addition, any person not satisfied with the response of researchers may raise ethics

issues or concerns, and may make any complaints about this research project by contacting

the Human Research Ethics Office at The University of Western Australia on (08) 6488 3703

or by emailing to [email protected].

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and/or Participant Consent Form relating to this research project.

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CRICOS Provider Code: 00126G

[95]

Appendix B:Appendix B:Appendix B:Appendix B:

INDIRECT ESTIMATION METHODS

[96]

This appendix explains each indirect BSIP used to be compared against the new DXA/3D

surface scan method. All models are breathily explained, along with all anthropometric

measures needed and the equations used to obtain the inertial parameters.

Cadaveric-based geometric method (modified Yeadon (1990)):

The method proposed by Yeadon (1990) was slightly modified to minimise the amount of

measures to be taken and to ensure that most of the measures were in accordance with the

ISAK 2001 protocol (Olds and Tomkinson, 2009).

Geometric solids

The modified version contains a total of 19 different solids. They are classified as

hemispheres, circular cylinders, conical frusta, stadium frusta and complex frusta (stadium-

shaped bottom based with circular top base). These solids are created through sections

perpendicular to the longitudinal axis of the segment (the longitudinal axis passes in the

centre of the section), which can be either circular or stadium-shaped (Fig. 1).

Figure A1: The stadium-shape section (left) and the stadium frustum (right) (Yeadon, 1990).

The circular section has a radius r defined by the girth:

π2girth

r =

The stadium section can be classified as a rectangle of width 2t and depth 2r with an

adjacent semi-circle of radius r at each side (fig 1). The parameters t and r can be defined

through the girth, breadth and/or depth as follow:

[97]

( )( ) 242

2 depthbreadthgirthr =

−−

=π

( )( )

( )242

depthbreadthgirthbreadtht

−=

−−

=π

π

The parameters t and r, along with the height of the solid (distance between the top and

bottom sections) and the density provided for each segment by Dempster (1955) are then

used to calculate the inertial properties of each solid. All anthropometry and heights are

measured in cm. Then, these solids combined form a 16-segment model (head, upper trunk,

middle trunk, lower trunk, upper arms, forearms, hands, thighs, shanks, and feet).

Table A1: Labelling of the solids forming each of the 16 segments, with the respective type of

solid used and density (Kg*l-1

)

Segment Solid Type Density

Head H1 Hemisphere 1.11

H2 Conical Frustum 1.11

H3 Circular cylinder 1.11

Upper Trunk T1 Complex frustum 1.04

T2 Stadium Frustum 0.92

T3 Stadium Frustum 0.92

Middle Trunk T4 Stadium Frustum 1.01

Lower Trunk T5 Stadium Frustum 1.01

Upper Arm U1 Conical Frustum 1.07

U2 Conical Frustum 1.07

Forearm F1 Conical Frustum 1.13

F2 Complex frustum 1.13

Hand Ha1 Stadium Frustum 1.16

Ha2 Stadium Frustum 1.16

Thigh Th1 Conical Frustum 1.05

Th2 Conical Frustum 1.05

Th3 Conical Frustum 1.05

Shank S1 Conical Frustum 1.09

S2 Conical Frustum 1.09

Foot Foot Complex frustum 1.10

Head and trunk:

The head segment comprises two solids at the level of the cranium (H1 and H2) and another

for the neck (H3). H1 is the only hemisphere used in the whole model, whereas H2 is an

inverted conical frustum (top base larger than bottom one) and H3 is a circular cylinder.

[98]

The trunk suffered the greatest amount of modifications when compared to the original

model (Yeadon, 1990). The upper trunk is subdivided into T1 (complex frustum), T2 and T3

(stadium frusta). T4 (stadium frustum) represents the middle trunk and T5 represents the

lower trunk. This modified model of the trunk enabled a better representation of the upper

trunk specially for the swimmers and also enabled its segmentation into the three sub-

segments, using the same protocol proposed by Zatsiorsky and Seluyanov (1983).

Table A2: Labelling of the sections as bottom (b) or top (t) base of the solids, anthropometric

measures used to determine the parameters r and t for each section and the position relative

to the longitudinal axes of the referred segments

Section Shape Anthropometry Level

H1(b)=H2(t) Circular Head Girth Glabella

H2(b)=H3(t) Circular Head Girth Chin/neck junction

H3(b)=T1(t) Circular Neck Girth C7

T1(b)=T2(t) Stadium Suprasternale depth

Biacromial breadth

Suprasternale

T2(b)=T3(t) Stadium Chest girth

Transverse chest breadth

Mesosternale

T3(b)=T4(t) Stadium Lower chest girth

Lower chest breadth

Xyphoid process

T4(b)=T5(t) Stadium Waist girth

Waist breadth

Navel

T5(b) Stadium Gluteal girth

Bitrochanterion breadth

Hip joint centre

U1(t) Circular Proximal upper arm girth Shoulder joint centre

U1(b)=U2(t) Circular Arm girth relaxed Mid-distance between shoulder and

elbow joint centres

U2(b)=F1(t) Circular Elbow joint centre girth Elbow joint centre

F1(b)=F2(t) Circular Forearm girth Forearm girth

F2(b)=Ha1(t) Stadium Wrist girth

Wrist breadth

Wrist joint centre

Ha1(b)=Ha2(t) Stadium Hand girth

Hand breadth

Distal point of the third metacarpal

Ha2(b) Stadium Palm girth

Palm breadth

Distal point of the middle finger

Th1(t) Circular Gluteal girth

Bitrochanterion breadth

(same r value as T5(b))

Hip joint centre

Th1(b)=Th2(t) Circular Thigh girth Thigh girth

Th2(b)=Th3(t) Circular Mid-thigh girth Mid-thigh girth

Th3(b)=S1(t) Circular Knee joint centre girth Knee joint centre

S1(b)=S2(t) Circular Calf girth Calf girth

S2(b)=Foot(t) Circular Ankle joint centre girth Ankle joint centre

Foot(b) Stadium Ball of the foot girth

Ball of the foot breadth

Distal point of second toe

[99]

Upper limbs:

The upper arm comprises two conical frusta, U1 and U2. For the forearm, the distal solid

was a conical frustum, whereas the distal solid was a complex frustum, with circular section

at the level of maximum forearm girth and stadium section at the wrist joint centre.

The hand was modified from the original (Yeadon, 1990) as it comprises two frusta, Ha1 and

Ha2. Even though the bottom base for Ha2 was calculated using the anthropometric

measures at the level of the third metacarpal, its location is at the level of the distal point of

the middle finger.

Lower limbs:

The thigh comprises three circular frusta (Th1, Th2, and Th3). The top circular section of

Th1 is calculated using the same anthropometric measures of the bottom stadium section of

T5, as the parameter r for the stadium section is the same for the circular section. The shank

comprises two conical frusta (S1 and S2).

The foot comprises only one complex frustum (Foot), with a distal stadium-shape section

and a proximal circular section. Even though the stadium section is calculated at the level of

the ball of the foot, its level is at the distal point of the distal phalange of the second toe.

[100]

Figure A2: Representation of the solids for the modified Yeadon’s model.

Calculation of each solid’s inertial properties

Five different solids are used: hemisphere, circular cylinder, conical frustum and stadium-

shape frustum and specifically for the distal forearm solids and feet, a frustum with stadium-

shape bottom section and circular top section is also calculated. For all formulas, the

parameters r and t are used along with the height (h) and density (D). The density value is

specific for each segment, obtained from the study of Dempster (1955) and presented in

Table A1. The inertial properties are then defined as mass (M), centre of mass position

along the longitudinal axis (HCM) and the principal moments of inertia about the sagittal (IX),

longitudinal (IY) and transverse (IZ) axes.

Hemisphere:

Only adopted for the H1 (head).

[101]

3

3

2rDM ⋅⋅⋅= π

(Formula A1)

rH CM ⋅=8

3, from the circular face (Formula A2)

2

320

83rMII ZX ⋅⋅==

(Formula A3)

2

5

2rMIY ⋅⋅=

(Formula A4)

Cylinder:

Adopted for the H3 solid (head).

hrDM ⋅⋅⋅=2

π (Formula A )

2

hH CM =

(Formula A6)

22

12

1

4

1hMrMII ZX ⋅⋅+⋅⋅==

(Formula A7)

2

2

1rMIY ⋅⋅=

(Formula A8)

Conical Frustum:

Adopted for H2, U1, U2 (upper arm), F1 (forearm), Th1, Th2, Th3 (thigh), S1 and S2

(shank).

( )2

110

2

03

1rrrrDhM ++= π

(Formula A 9)

( )( )2

110

2

0

2

110

2

0

4

32

rrrr

rrrrhHCM

++

++=

(Formula A10)

[102]

( ) ( )( )2

1

2

010

4

1

4

0

3

10

2

1

2

01

3

0

2

110

2

0

2

20

3632

rrrr

rrrrrrrrrrrrhMII ZX

++

+++++++==

π

(Formula A11)

( )( )2

1

2

010

4

1

4

0

3

10

2

1

2

01

3

0

10

3

rrrr

rrrrrrrrMIY

++

++++=

π (Formula A12)

Stadium Frustum:

Adopted for T2, T3, T4, T5 (trunk), Ha1 and Ha2 (hand). T1 (trunk, F2 (forearm) and Foot

are a special frusta that has a stadium-shape bottom section and a circular top section.

Therefore, in order to calculate their inertial properties, the same formula used for the

stadium frustum is applied, but using the parameter t for the top section as equal to 0.

If a solid is regarded as a series of parallel slices of infinitesimal thickness orthogonal to the

longitudinal (Y) axis, the inertial parameters can be calculated according to the formulas:

∫ ⋅⋅⋅=

1

0

dyAhDM

(Formula A13)

∫ ⋅⋅⋅⋅

=

1

0

2

dyAyM

hDHCM

(Formula A 14)

2

1

0

23

1

0

CMXX HMdyAyhDdyJhDI ⋅−⋅⋅⋅⋅+⋅⋅⋅= ∫∫ (Formula A15)

∫ ⋅⋅⋅=

1

0

dyJhDI YY

(Formula A16)

2

1

0

23

1

0

CMZZ HMdyAyhDdyJhDI ⋅−⋅⋅⋅⋅+⋅⋅⋅= ∫∫

(Formula A17)

[103]

Where JX, JY and JZ are the second moments of area about the xslice, yslice and zslice axes of a

slice (stadium shape), respectively, and thus the integrals ∫ ⋅

1

0

dyJ X , ∫ ⋅

1

0

dyJY , and

∫ ⋅

1

0

dyJ Z are the respective summation of the second moments of area of all slices for each

axis. The theorem of parallel axes is used to calculate (i) the summation of each slice’s

second moment of area about the xsolid and zsolid axes of the solid coordinate system (insert

figure) through the integral ∫1

0

2 Adyy , where y is the normalized distance ( 10 ≤≤ y ) of the

slice from the plane xz and A is the area of the slice in function of the distance, and (ii) the

moment of inertia of the whole solid about the respective xCM and zCM axes passing through

the centre of mass of the solid.

In order to simplify the calculation of all integrals, Yeadon (1990) used the parameters r0 and

t0 for the lower bounding stadium and r1 and t1 for the upper bounding stadium (Fig. 2).

Thus, the parameters a and b are calculated as:

( )0

01

rrr

a−

= (Formula A18)

( )0

01

ttt

b−

= (Formula A19)

The following functions are then defined through the equations:

( ) ( ) bababaF ⋅⋅++⋅+=

3

1

2

11,1

(Formula A20)

( ) ( ) bababaF ⋅⋅++⋅+=

4

1

3

1

2

1,2

(Formula A21)

( ) ( ) bababaF ⋅⋅++⋅+=

5

1

4

1

3

1,3

(Formula A22)

[104]

( ) ( ) ( ) ( ) ( )32

5

13

4

13

2

11,4 abbabbabbabaF ++⋅++⋅++⋅+=

(Formula A23)

( ) ( ) ( ) ( ) ( )2222

5

1

2

14

3

11,5 babaabbabababaF ++⋅+++⋅+++=

(Formula A24)

Therefore, all the previous integrals can be calculated as:

( ) ( )[ ]aaFrbaFtrhDM ,1,14000

⋅⋅+⋅⋅⋅⋅= π

(Formula A25)

( ) ( )[ ]M

aaFrbaFtrhDHCM

,2,242

0002 ⋅⋅+⋅⋅⋅⋅⋅=

π

(Formula A 26)

( ) ( ) ( ) ( )∫ ⋅⋅⋅+⋅⋅+⋅⋅⋅+⋅⋅⋅=

1

0

4

00

3

0

2

0

2

0

3

00,4

4

1,4

3

8,5,4

3

4aaFrabFtrbaFtrbaFtrdJ yX ππ

(Formula A27)

( ) ( ) ( ) ( )aaFrabFtrbaFtrbaFtrdyJY ,42

1,44,5,4

3

4 4

00

3

0

2

0

2

0

3

00

1

0

⋅⋅⋅+⋅⋅+⋅⋅⋅+⋅⋅⋅=∫ ππ

(Formula A28)

( ) ( )aaFrbaFtrdyJ Z ,44

1,4

3

4 4

0

3

00

1

0

⋅⋅⋅+⋅⋅⋅=∫ π

(Formula A29)

( ) ( )aaFrbaFtrAdyy ,3,342

000

1

0

2⋅⋅+⋅⋅⋅=∫ π

(Formula A30)

[105]

Cadaveric-based regression equation method (modified Chandler et al.

(1975))

The cadaver-based method by Chandler et al. (1975) provided simple equations for

segment’s mass and principal moments of inertia using either whole body mass (BW) or

segment’s volume as predictors, along with the average centre of mass position on the

longitudinal axis. Rather than using the BW as predictors to the principal moments of inertia,

the non-linear equations proposed in the study of Yeadon and Morlock (1989) will be

applied, as they were devised from the same cadaveric cohort used in the study of Chandler

et al. (1975).

Apart from the trunk segment (which was not subdivided for this method), the non-linear

equations only used the anatomical length and mean girth ((p1 + p2)/2 when using two girths,

or (p1 + 2p2 + p3)/4 when using three girths) of the segments as predictors. For the trunk, the

anatomical length, mean girth ((p1 + 2p2 + p3)/4) and breadth ((w1 + 2w2 + w3)/4) were used

as predictors (table A2).

In order to suit the method to the biomechanical model used in the study (Appendix D), the

head and trunk centre of mass positions and moments of inertia equations were recalculated

as new coordinate systems were created and different predictors for the moments of inertia

equations were used (table A4).

[106]

Table A3: mass (Kg) and principal moments of inertia (Kg*cm2) equations and average centre of

mass position obtained for the modified study of Chandler et al. (1975).

Segment Mass Centre of Mass Moments of Inertia (10-6

)

Head 0.032BW + 1.906 61.19% IX = IZ = 6M IY +2.19p

2h

3

IY = 1.315p4h

Trunk 0.532BW – 0.706 49.4% IX = dwh[58.66w2 + 92.63h

2]

Iy = dwh[86.67d2 + 58.66w

2]

IZ = dwh[86.67d2 + 92.63h

2]

Right upper arm 0.016BW + 0.809 48.65% IX = IZ = 6M IY + 6.11p

2h

3

IY = 0.979p4h

Right forearm 0.020BW – 0.218 58.76% IX = IZ = 6M IY + 4.98p

2h

3

IY = 0.81p4h

Right hand 0.007BW - 0.030 44.75% IX = IZ = 6M IY + 7.68p

2h

3

IY = 1.309p4h

Left upper arm 0.022BW + 0.485 49.42% IX = IZ = 6M IY + 6.11p

2h

3

IY = 0.979p4h

Left forearm 0.013BW + 0.246 58.41% IX = IZ = 6M IY + 4.98p

2h

3

IY = 0.81p4h

Left hand 0.005BW + 0.076 40.84% IX = IZ = 6M IY + 7.68p

2h

3

IY = 1.309p4h

Right thigh 0.126BW + 1.688 61.19% IX = IZ = 6M IY + 8.12p

2h

3

IY = 1.593p4h

Right shank 0.038BW + 0.179 57.59% IX = IZ = 6M IY + 5.73p

2h

3

IY = 0.853p4h

Right foot 0.008BW + 0.343 43.74% IX = IZ = 6M IY + 3.72p

2h

3

IY = 1.001p4h

Left thigh 0.127BW - 1.511 60.51% IX = IZ = 6M IY + 8.12p

2h

3

IY = 1.593p4h

Left shank 0.044BW – 0.178 58.66% IX = IZ = 6M IY + 5.73p

2h

3

IY = 0.853p4h

Left foot 0.009BW + 0.253 43.92% IX = IZ = 6M IY + 3.72p

2h

3

IY = 1.001p4h

[107]

Table A4: modified predictors for the non-linear equations for segmental moments of inertia

Segment Predictor Definition

head h Stature - C7 height

p Head girth

trunk h C7 height – trochanterion height

p1 Chest girth

w1 Transverse chest breadth

p2 Waist girth

w2 Waist breadth

p3 Gluteal girth

w3 Bitrochanterion breadth

Gamma-ray-based simple regression method (Zatsiorsky and

Seluyanov, 1983)

Zatsiorsky and Seluyanov (1983) presented a set of linear equations using only the whole

body mass and height as predictors for all BSIP. Those equations were devised from a

cohort of 100 male Caucasian men analysed with the gamma-ray scanner.

[108]

Table A5: Coefficients of the linear regression equations to determine the inertial parameters of

the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the

body weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on the

longitudinal axis (HCM), or moments of inertia about the sagittal (IX), longitudinal (IY) or

transverse (IZ) axes.

Inertial

Parameters

Coefficients for the multiple regression

Segment B0 B1 B2

Head M 1.296 0.0171 0.0143

HCM 8.357 -0.0025 0.023

IXX -78 1.171 1.519

IYY 61.6 1.72 0.0814

IZZ -112 1.43 1.73

Upper Trunk M 8.2144 0.1862 -0.0584

HCM 3.32 0.0076 0.047

IXX 81.2 36.73 -5.97

IYY 561 36.03 -9.98

IZZ 367 18.3 -5.73

Middle Trunk M 7.181 0.2234 -0.0663

HCM 1.398 0.0058 0.045

IXX 618.5 39.8 -12.87

IYY 1501 43.14 -19.8

IZZ 263 26.7 -8

Lower Trunk M -7.498 0.0976 0.04896

HCM 1.182 0.0018 0.0434

IXX -1568 12 7.741

IYY -775 14.7 1.685

IZZ -934 11.8 3.44

[109]


the upper limb segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the body

weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on the



Inertial

Parameters


Segment B0 B1 B2

Upper Arm M 0.25 0.03012 -0.0027

HCM 1.67 0.03 0.054

IXX -250.7 1.56 1.512

IYY -16.9 0.662 0.035

IZZ -232 1.525 1.343

Forearm M 0.3185 0.01445 -0.00114

HCM 0.192 -0.028 0.093

IXX -64 0.95 0.34

IYY 5.66 0.306 -0.088

IZZ -67.9 0.855 0.376

Hand M -0.1165 0.0036 0.00175

HCM 4.11 0.026 0.033

IXX -19.5 0.17 0.116

IYY -6.26 0.0762 0.0347

IZZ -13.68 0.088 0.092

[110]


the lower limb segments. Equations in the form of Y = B0 + B1X1 + B2X2, where X1 is the body

weight, X2 is the body height and Y is segment’s mass (M), centre of mass position on the



Inertial

Parameters


Segment B0 B1 B2

Thigh M -2.649 0.1463 0.0137

HCM -2.42 0.038 0.135

IXX -3557 31.7 18.61

IYY -13.5 11.3 -2.28

IZZ -3690 32.02 19.24

Shank M -1.592 0.0362 0.0121

HCM -6.05 -0.039 0.142

IXX -1105 4.59 6.63

IYY -70.5 1.134 0.3

IZZ -1152 4.594 6.815

Foot M -0.829 0.0077 0.0073

HCM 3.767 0.065 0.033

IXX -100 0.48 0.626

IYY -15.48 0.144 0.088

IZZ -97.09 0.414 0.614

Gamma-ray-based multiple regression method (Zatsiorsky and

Seluyanov, 1985)

Using the same cohort of the previous study (1983) Zatsiorsky and Seluyanov devised linear

equations with the most predictable anthropometric measures, as they were mostly taken

from the same segment whose inertial parameters were calculated. Total body fat (in Kg)

was also included in some segments’ equations, and was measured using the DXA scan.

Four predictors were used for the head and trunk segments, whereas for all limb segments

only three predictors were used.

[111]


the head and trunk segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3 + B4X4,

where X1, X2, X3 and X4 are the most predictive anthropometric measures for each segment and

Y is segment’s mass (M), centre of mass position on the longitudinal axis (HCM), or moments of

inertia about the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.

Inertial

Parameters


Segment B0 B1 B2 B3 B4

Head M -7.385 0.146 0.071 0.0356 0.199

HCM 0.21 0.503 0.027 0.043 -0.158

IXX -987 23.74 3.97 3.46 18.58

IYY -721 7.36 6.14 2.28 18.25

IZZ -983 19.9 8.43 3.22 10.2

Upper Trunk M -18.91 0.421 0.199 0.078 0.065

HCM -2.854 0.567 0.0067 0.0321 0.0152

IXX -5175 105.4 45.8 4.01 8.65

IYY -4149 54.8 43.7 8.88 9.63

IZZ -2650 65.6 17.12 5.84 9.8

Middle Trunk M -13.62 0.444 0.195 -0.017 0.0887

HCM -0.742 0.485 0.0007 -0.002 0.001

IXX -3271 76.7 30.3 10.2 18.3

IYY -2657 43 33.3 1.6 20.6

IZZ -2354 65.3 21.5 -2.3 10.57

Lower Trunk M -15.18 0.182 0.243 0.0216 0

HCM 0.205 0.064 0.134 -0.08 0

IXX -2354 22.6 34.37 4.41 0

IYY -2009 20.1 24.9 11.2 0

IZZ -1816 18 23.6 7.29 0

[112]


the upper limb segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3, where X1, X2 and

X3 are the most predictive anthropometric measures for each segment and Y is segment’s

mass (M), centre of mass position on the longitudinal axis (HCM), or moments of inertia about

the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.

Inertial

Parameters


Segment B0 B1 B2 B3

Upper Arm M -2.58 0.0471 0.104 0.0651

HCM -2.004 0.566 0.056 -0.016

IXX -359 10.2 6.4 8.5

IYY -106 0.4 3.8 4.5

IZZ -331 10.3 5.5 5.6

Forearm M -2.04 0.05 -0.0049 0.087

HCM 0.732 0.588 -0.0857 -0.0187

IXX -229 7.12 -0.049 5.066

IYY -39.2 0.56 -0.972 1.996

IZZ -220 7.06 -0.082 4.544

Hand M -0.594 0.941 0.035 0.029

HCM -3.055 0.596 0.264 0.091

IXX -41.05 2.29 1.62 1.27

IYY -14.9 0.596 -0.814 0.818

IZZ -26.6 1.818 -1.083 0.527

[113]


of the lower limb segments. Equations in the form of Y = B0 + B1X1 + B2X2 + B3X3, where X1, X2

and X3 are the most predictive anthropometric measures for each segment and Y is segment’s

mass (M), centre of mass position on the longitudinal axis (HCM), or moments of inertia about

the sagittal (IX), longitudinal (IY) or transverse (IZ) axes.

Inertial

Parameters


Segment B0 B1 B2 B3

Thigh M -17.819 0.153 0.23 0.367

HCM -3.655 0.478 -0.07 0.088

IXX -6729 87.8 50.3 75.3

IYY -1173 4.06 6 26.8

IZZ -6774 88.4 38.6 78

Shank M -6.017 0.0675 0.0145 0.205

HCM 0.0937 0.396 0.064 -0.041

IXX -1437 28.64 3.202 21.6

IYY -194.8 0.214 -3.64 8.9

IZZ -1489 28.97 6.48 21.5

Foot M -0.6286 0.066 -0.0136 0.0048

HCM -1.267 0.519 0.176 0.061

IXX -91.17 5.25 0.335 0.386

IYY -11.9 0.771 0.047 0.243

IZZ -89.1 4.788 0.477 0.271

[114]

Table A11: The most predictable anthropometric measures for each segment to be used in the

multiple linear equations for inertial parameters of the head and trunk segments.

Segment Variables

Head X1 = head length (stature – C7 height), cm

X2 = head girth, cm

X3 = RSTR>M , where

D1 = head girth, cm

D2 = neck girth, cm

X4 = diameter of the head (head girth/π), cm

Upper Trunk X1 = upper trunk length (C7 height – xyphoid process height), cm

X2 = chest girth, cm

X3 = transverse chest breadth, cm

X4 = fat, Kg

Middle Trunk X1 = length of the middle trunk (xyphoid process height – navel height),

cm

X2 = waist girth, cm

X3 = bitrochanterion breadth, cm

X4 = fat, Kg

Lower Trunk X1 =gluteal girth, cm

X2 =bispinal breadth, cm

X3 = fat, Kg



Segment Variables

Upper arm X1 = upper arm length*0.73, cm

X2 = arm girth relaxed, cm

X3 = RSTR>M , where

D1 = lower diameter of the upper arm (elbow girth/π), cm

D2 = lower diameter of the forearm (wrist girth/π), cm

Forearm X1 = forearm length, cm

X2 = hand breadth, cm

X3 =RSTR>TRUM , where

D1 = wrist girth, cm

D2 = forearm girth, cm

D3 = elbow girth, cm

Hand X1 = hand length, cm

X2 = hand breadth, cm

X3 = RSTR>M , where

D1 = hand girth, cm

D2 = wrist girth, cm



[115]

Segment Variables

Thigh X1= thigh length, cm

X2= knee diameter (knee girth/π) , cm

X3 = RSTR>TRUM , where

D1 = knee girth, cm

D2 = mid-thigh girth, cm

D3 = thigh girth, cm

Shank X1= leg length, cm

X2= ankle diameter (ankle girth/π) , cm

X3 = RSTR>TRUM , where

D1 = knee girth, cm

D2 = ankle girth, cm

D3 = calf girth, cm

Foot X1= foot length, cm

X2= foot breadth, cm

X3= fat, Kg

Gamma-ray-based geometric method (Zatsiorsky et al., 1990)

Zatsiorsky, Seluyanov and Chugunova developed the geometrical model from the same

cohort of the foremost gamma-ray study (1983) aiming to provide BSIP to populations of

distinct characteristics of those analysed with the gamma-ray scanner. Each segment is

regarded as a circular cylinder, and therefore its mass is calculated using its girth (G) and

biomechanical length (L, the anthropometric length multiplied by a coefficient KB provided):

π4

2GLK

M D ⋅⋅=

(Formula A31)

Where KD is the quasidensity of the segment, calculated from the average mass of the

segment of the analysed cohort measured with the gamma-ray scanner divided by the

average quasivolume (cylinder volume). The segment mass coefficient (Ki=KD/4π) is then

provided by the authors. A coefficient for correction is also calculated as the ratio between

the summations of all calculated segment masses and the whole body weight to minimize

discrepancies.

Table A14: Anthropometric lengths and girths used to create the geometrical model of the

subject and determine the inertial parameters. The coefficient KB is used to multiply the

[116]

anthropometric length to obtain the biomechanical length.

Segment KB Length Girth

Head 0.76 Head length (stature - C7 height) Head girth

Upper trunk 1.456 Upper trunk length (C7 height - xyphoid process

height)

Chest girth

Middle trunk 1.035 Middle trunk length (xyphoid process height -

navel height)

Waist girth

Lower trunk 2.305 Middle trunk length (xyphoid process height -

midASIS height)

Gluteal girth

Upper arm 0.73 Upper arm length Arm girth relaxed

Forearm 1 Forearm length Forearm girth

Hand 1 Hand length Hand girth

Thigh 1.083 Thigh length Thigh girth

Shank 1 Leg length Calf girth

Foot 1 Foot length Foot girth

Then, the principal moments of inertia are calculated as follows:

2MLKI XX = (Formula A32)

2MCKI YY = (Formula A33)

2MLKI ZZ = (Formula A34)

Where KX, KY, and KZ are the moments of inertia coefficients for the sagittal, longitudinal and

transverse axes, respectively. Given the different orientation of the foot segment, the

squared circumference is used in the equation to determine IX; conversely, the squared

length is used in the equation to determine IY.

[117]

Table A15: Segment mass coefficients (KM), and the moments of inertia coefficients relative to

the sagittal (KX), longitudinal (KY) and transverse (KZ) axes.

Segment Km��10-5

KX��10-2

KY��10-2

KZ��10-2

Head 6.37 8.68 1.25 9.38

Upper Trunk 5.72 21.83 1.35 9.35

Middle Trunk 8.49 20.65 1.43 12.6

Lower Trunk 3.6 10.9 0.76 8.92

Upper Arm 9.67 10.81 2.06 9.71

Forearm 6.26 7.55 1.51 7.03

Hand 5.54 6.65 2.29 4.86

Thigh 6.64 7.18 1.33 7.18

Shank 5.85 8.77 1.44 8.44

Foot 6.14 1.6 7.86 7.14

The study also provided the centre of mass position as the average values of the analysed

cohort. However, the authors used anatomical landmarks rather than the joint centres as

reference for locating the centre of mass and defining segment’s length, and therefore the

adjustments to the centre of mass position proposed by de Leva (1996) were used instead.

The centre of mass position for the head and the upper trunk were adjusted so the projection

of C7 onto the longitudinal axis was used as endpoint between the head and upper trunk.

Therefore, the centre of mass position for the head was 49.98% and for the upper trunk was

49.34%.

[118]

Appendix C:Appendix C:Appendix C:Appendix C:

ANTHROPOMETRIC MEASURES

[119]

Most of the measures are defined according to the ISAK 2001 protocol (Olds and

Tomkinson, 2009). Whenever a measure is not defined by the protocol, its explanation is

given by the study that used it.

All measures except the thigh length were taken from the 3D surface scan of the subject.

The thigh length was obtained from the DXA image, which allowed the visualization of the

throcanter and the lateral epicondyle of the femur. Breadths, girths and lengths were

calculated using the Artec Studio software, whereas the heights were calculated using the

MeshLab, as a Global Coordinate System (GCS) with a sagittal plane at the level of the floor

needed to be created.

For the modified Yeadon methods and the moments of inertia calculated for the modified

Chandler method, anatomical lengths were also used. These lengths are the distance

between two joint centres or end points.

Heights and Lengths:

Stature: the linear distance from the floor level to the subject’s vertex, measured with a

stadiometer. Used in all BSIP estimation methods.

C7 height: the linear distance from the floor level to the subject’s C7 vertebra, measured

with a stadiometer. It is not an ISAK anthropometric measure. Used in the Zatsiorsky

(multiple regression) and Chandler methods.

Suprasternale height: the linear distance from the floor level to the subject’s suprasternale,

measured with a stadiometer. It is not an ISAK anthropometric measure. Used in the

Zatsiorsky (geometrical) method.

Xiphoid process height: the linear distance from the floor level to the subject’s xiphoid

process, measured with a stadiometer. It is not an ISAK anthropometric measure. Used in

the Zatsiorsky (multiple regression and geometrical) methods.

[120]

Navel height: the linear distance from the floor level to the subject’s navel, measured with a

stadiometer. It is not an ISAK anthropometric measure. Used in the Zatsiorsky (multiple

regression and geometrical) methods.

Mid ASIS height: the linear distance from the floor level to the midpoint of the subject’s

anterior superior iliac spine (ASIS), measured with a stadiometer. It is not an ISAK

anthropometric measure. Used in the Zatsiorsky (geometric) method.

Trochanterion height: the linear distance from the floor level to the trochanterion,

measured with a stadiometer while subject maintains an upright stance with feet together.

Used in the Chandler method.

Acromiale – Radiale length (upper arm length): the linear distance from the acromiale to

the radiale, measured with a segmometer. With the right forearm pronated, anchor the end

pointer to the acromiale and move the housing pointer to the radiale. Used in the Zatsiorsky

(multiple regression and geometrical) methods.

Radiale – Stylion length (forearm length): the linear distance from the radiale to the

stylion, to the radiale measured with a segmometer. With the subject standing up, anchor

the end pointer to the radiale and move the housing pointer to the stylion. Used in the

Zatsiorsky (multiple regression and geometrical) methods.

Midstylion – Dactylion length (hand length): the linear distance from the midstylion to the

dactylion, measured with a segmometer. Anchor the end pointer at the midstylion mark and

move the housing pointer to the dactylion. Used in the Zatsiorsky (multiple regression and

geometrical) methods.

Trochanterion – Tibiale laterale length (thigh length): the linear distance from the

trochanter to the tibiale laterale, measured with a segmometer. The subject stands with feet

together and arms folded across the chest. Anchor the end pointer at the trochanter mark

and move the housing pointer to the tibialle laterale. Used in the Zatsiorsky (multiple


[121]

Tibiale mediale-sphyrion tibiale length (leg length): the linear distance from the tibiale

mediale to the sphyrion tibiale, measured with a segmometer. The subject is seated with the

right ankle resting on the left knee. Anchor the end pointer at the tibiale mediale mark and

move the housing pointer to the sphyrion tibiale mark. Used in the Zatsiorsky (multiple


Foot length: the distance from the heel to the distal point of the distal phalang of the second

toe, measured with a calliper. Used in the Zatsiorsky (multiple regression and geometrical)

methods.

Breadths and depths:

Suprasternale depth: the linear distance between the suprasternale and the spinous

process of the vertebra at the horizontal level of the suprasternale, measured with a sliding

calliper. Subject is in a sitting position with hands resting on the thighs. It is not an ISAK

measure. Used in the Yeadon method.

Biacromial breadth: the distance between the most lateral points on the acromion process,

measured with a sliding calliper. Measures are taken behind the subject who holds and

upright stance, with the calliper branches angled at approximately 30o pointing upwards.

Used in the Yeadon method.

Transverse chest breadth: the distance between the most lateral aspects of the torax

when the top of the body of the sliding calliper is positioned at the level of the mesosternale,

and branches angled 30o downwards. Used in the Zatsiorsky (multiple regression) and

Yeadon methods.

Lower chest breadth: the distance between the most lateral aspects of the torax when the

top of the body of the sliding calliper is positioned at the level of the xiphoid process, and

branches angled 30o downwards. It is not an ISAK measure. Used in the Yeadon method.

Waist breadth: the distance between the most lateral aspects of the torax when the top of

the body of the sliding calliper is positioned at the level of the navel. It is not an ISAK

measure. Used in the Yeadon method.

[122]

Bispinal breadth: the distance between the left and right anterior superior iliac spines,

measured with a calliper with branches angled 45o upwards. Subject stands with arms

across the chest. Used in the Zatsiorsky (multiple regression) method.

Bitrochanterion breadth: the distance between the greatest posterior protuberance of the

buttocks, measured with a sliding calliper. It is not an ISAK measure. Used in the Yeadon

method.

Wrist breadth: the distance between the styloid processes of the ulna and the radio,

measured with a segmometer. It is not an ISAK measure. Used in the Yeadon method.

Hand breadth: measured with the calliper perpendicular to the longitudinal axis of the hand

and one branch at the first metacarpal-phalangeal joint (base of the thumb). It is not an ISAK

measure. Used in the Zatsiorsky (multiple regression) and Yeadon methods.

Palm breadth: measured at the level of the second to fourth metacarpal-phalangeal joints

with a sliding calliper. It is not an ISAK measure. Used in the and Yeadon method.

Ball of the foot breadth: measured at the level of the metatarsal-phalangeal joints (I to V)

with a sliding calliper. It is not an ISAK measure. Used in the Zatsiorsky (multiple regression)

and Yeadon methods.

Girths:

Head girth: measured with an anthropometric tape at the level of the glabella. Subject

seated and head in the Frankfort plane. Used in the Zatsiorsky (multiple regression and

geometric), Chandler and Yeadon methods.

Neck girth: measured with an anthropometric tape at the level immediately superior to the

thyroid cartilage. Subject seated and head in the Frankfort plane. Used in the Zatsiorsky

(multiple regression) and Yeadon methods.

Chest girth: measured with an anthropometric tape at the level of the mesosternale.

Subject raises the arms and following lowers them as the measurement is taken. Used in the

Zatsiorsky (multiple regression and geometric) and Yeadon methods.

[123]

Lower chest girth: measured with an anthropometric tape at the level of the xiphoid

process. Subject raises the arms and following lowers them as the measurement is taken. It

is not an ISAK measure. Used in the Yeadon method.

Waist girth: measured with an anthropometric tape at the level of the navel. Subject folds

the arms while measured. Used in the Zatsiorsky (multiple regression and geometric) and

Yeadon methods.

Gluteal girth: measured with an anthropometric tape at the level of the trochanter (greatest

posterior protuberance of the buttocks). Subject stands erect with feet together and gluteal

muscles relaxed. Used in the Zatsiorsky (multiple regression and geometric) and Yeadon

methods.

Proximal upper arm girth: measured at the highest up the upper arm as possible. Subject

adducts the arm without raising the scapula. It is not an ISAK measure. Used in the

Hanavan, Zatsiorsky (multiple regressin) and Yeadon methods.

Arm girth relaxed: measured with an anthropometric tape at the level of the midacromiale-

radiale. The subject assumes a relaxed position with the arm hanging by the side. Used in

the Zatsiorsky (multiple regression and geometric) and Yeadon methods.

Elbow joint centre girth: measured with an anthropometric tape at the level of the knee

joint centre. Subject maintains the elbow fully extended. It is not an ISAK measure. Used in

the Hanavan, Zatsiorsky (multiple regression) and Yeadon methods.

Forearm girth: measured with an anthropometric tape at the maximum girth of the forearm

distal to the humeral epicondyles. Used in the Zatsiorsky (multiple regression and geometric)

and Yeadon methods.

Wrist girth: the minimum writ girth distal to the styloid processes, measured with an

anthropometric tape. Subject maintains the forearm supinated and the hand relaxed. Used in

the Hanavan, Zatsiorsky (multiple regression and geometric) and Yeadon methods.

[124]

Hand girth: measured with an anthropometric tape at the level of the first metacarpal-

phalangeal joint (base of the thumb). Subject maintains fingers extended and together. It is

not an ISAK measure. Used in the Zatsiorsky (multiple regression) and Yeadon methods.

Palm girth: measured with an anthropometric tape at the level of the distal points of the four

last metacarpals. Subject maintains fingers extended and together. It is not an ISAK

measure. Used in the Hanavan and Yeadon methods.

Thigh girth: measured roughly 2 cm below the gluteal fold with an anthropometric tape.

Subject stands erect with the feet slightly apart, the tapes is passed around the leg and slipe

up using a cross-handed technique to a horizontal position. Used in the Hanavan, Zatsiorsky

(multiple regression) and Yeadon methods.

Midthigh girth: measured at the level of the midtrochanterion-tibiale laterale landmark with

an anthropometric tape. Subject stands erect with the feet slightly apart, the tapes is passed

around the leg and slipe up using a cross-handed technique to a horizontal position. Used in

the Zatsiorsky (multiple regression) and Yeadon methods.

Knee joint centre girth: measured at the level of the two epicondyles with an

anthropometric tape. Subject stands erect with the feet slightly apart, the tapes is passed

around the leg and slipe up using a cross-handed technique to a horizontal position. It is not

an ISAK measure. Used in the Hanavan, Zatsiorsky (multiple regression) and Yeadon

methods.

Calf girth: measured at the medial calf skinfold site level with an anthropometric tape.

Subject stands on a box with weight distributed evenly. Used in the Zatsiorsky (multiple

regression) and Yeadon methods.

Ankle girth: the minimum girth of the ankle superior to the sphyrion tibiale. Subject stands

on a box with weight distributed evenly. Used in the Hanavan, Zatsiorsky (multiple

regression) and Yeadon methods.

Ball of foot girth: measured at the level of the metatarsal-phalangeal joints (I to V) with an

anthropometric tape. It is not an ISAK measure. Used in the Yeadon method.

[125]

Landmarks:

Acromiale: the point at the most superior and lateral border of the acromion process when

the subject stands erect with arms relaxed and hanging vertically;

Radiale: the point at the most proximal and lateral border of the head of the radius;

Midacromiale-radiale: the point equidistant from the acromiale and radiale landmarks;

Stylion: the most distal point on the lateral margin of the styloid process of the radius;

Mesosternale: the midpoint of the corpus sterni at the level of the centre of the articulation

of the fourth rib with the sternum;

Iliocristale: the point on the iliac crest where a line drawn from the midaxilla (middle of the

armpit), on the longitudinal axis of the body, meets the ilium;

Iliac crest skinfold site: the site at the centre of the skinfold raised immediately above the

iliocristale;

Iliopsinale: the most inferior or undermost part of the tip of the anterior superior iliac spinale

(ASIS);

Trochanterion: the most superior aspect of the greater trochanter of the femur;

Tibiale laterale: the most superior aspect on the lateral border of the head of the tibia;

Midtrochanterion-tibiale laterale: the point equidistant from the trochanterion and the

tibiale laterale;

Tibiale mediale: the most proximal aspect on the border of the head of the tibia;

Sphyrion tibiale: the most distal tip of the medial malleolus of the tibia;

Akropodion: the most anterior point of the foot, which may be the first or second digit;

Anterior patella: the most anterior and superior margin of the anterior surface of the patella

when the subject is seated and the knee bent at a right angle;

[126]

Dactylon: the tip of the middle (third) finger;

Glabella: midpoint between the brow ridges;

Gluteal fold: the crease at the junction of the gluteal region and the posterior thigh;

Inguinal fold: the crease at the angle of the trunk and the anterior thigh;

Orbitale: the lower bony margin of the eye socket;

Pternion: the most posterior point of the calcaneus;

Tragion: the notch superior to the tragus of the ear;

Vertex: the most superior point on the skull when the head is held in the Frankfort plane

(i.e., when the orbitale and the tragion are horizontally aligned).

[127]

AppendixAppendixAppendixAppendix DDDD::::

BIOMECHANICAL MODEL

[128]

Virtual points

Prior to the creation of the ACSs, some virtual points had to be created using mathematical

procedures and the locations of the markers. Those points can be end points or auxiliary

points conveniently used during the creation of the ACSs.

Table A16: Virtual points created

Segment

/ Joint

Point

Label

Anatomical / extended

name

Location

Head VertexEP Vertex end point Projection of the highest point on the top of

the head onto the straight line defined by

MidHJC and MidSJC

Trunk MidSJC Shoulder midpoint Midpoint between the two SJC

MidHJC Hip midpoint Midpoint between the two HJC

C7EP Cervicale end point Projection of C7 on the straight line defined by

MidHJC and MidSJC

XPEP Xiphoid process end point Projection of XP on the straight line defined

by MidHJC and MidSJC

NavEP Navel end point Projection of Nav on the straight line defined

by MidHJC and MidSJC

AMP Anterior mid-pelvis Midpoint between the two ASIS

PMP Posterior mid-pelvis Midpoint between the two PSIS

Hand L/R IIIEP Third phalange end point The projection of the most distal point of the

hand, on the tip of the third distal phalange,

onto the straight line defined by the ipsi-lateral

EJC and WJC

Foot L/R IIEP Second phalange end

point

The most distal point of the foot, lying on the

tip of the second distal phalange

Shoulder SGCP Shoulder girdle central

point

Midpoint between IJ and C7

L/R AcrLR Acromion triad: lateral

ridge

Midpoint between Acr1 and Acr3

L/R SJC Shoulder joint centre Regression equations (Campbell et al., 2009),

with position relative to the acromion

coordinate system (AcrCS):

x = 96.2 – 0.302 x (IJ – C7mm) – 0.364 x

height (cm) + 0.385 x mass (kg)

y = –66.32 + 0.30 x (IJ – C7mm) – 0.432 x

mass (Kg)

z = 66.468 – 0.531 x (AcrLR – SGCPmm) –

0.364 x height (cm) + 0.385 x mass (Kg)

Elbow L/R EJC Elbow joint centre Midpoint between MEL and LEL

Wrist L/R WJC Wrist joint centre Midpoint between MWR and LWR

Hip L/R HJC Hip joint centre Regression equations (Harrington et al.,

2007), with position relative to the pelvis

coordinate system(PeCS):

x = 9.9 – 0.24 x (AMP –PMPmm)

y = –7.1 + 0.16 x (L ASIS – R ASISmm) –

0.04 x (ASIS – MAN)

z = 7.9 + 0.28 x (AMP – PMPmm) – 0.16 x (L

[129]

ASIS – R ASIS)

Knee L/R KJC Knee joint centre Midpoint between MEL and LEL

Ankle L/R AJC Ankle joint centre Midpoint between MAN and LAN

A proximal and a distal end point is created for each segment to define their anatomical

length and thereby the position of the CM lying on each longitudinal axis (Table A17). The

biomechanical model has six pairs of joint centres (shoulders, elbows, wrists, hips, knees

and ankles joint centres). Given the complexity of the vertebral joints, the end points of the

head and the sub-segments of the trunk are not true joints.

Table A17: End points of all segments of the biomechanical model

Segment Proximal end point Distal end point

Head VertexEP C7EP

Upper trunk C7EP XPEP

Middle trunk XPEP NavEP

Lower trunk NavEP MidHJC

Upper arm SJC EJC

Forearm EJC WJC

Hand WJC IIIEP

Thigh HJC KJC

Shank KJC AJC

foot Foot 1 IIEP

Biomechanical model

The biomechanical model adopted consists of 16 segments (head, upper trunk, middle

trunk, lower trunk, upper arms, forearms, hands, thighs, shanks and feet), to which

anatomical coordinate systems were assigned based on the markers positions and virtual

points created. The model is based on the UWA model (Besier et al., 2003; Campbell et al.,

2009; Chin et al., 2010; Lloyd, Alderson, and Elliott, 2000) with slight modifications so all

BSIP estimation methods can be applied to it.

Head Coordinate System (HCS – HX , H

Y , HZ )

HO : The origin is located at the C7EP;

[130]

The sagittal (H

X ), longitudinal (H

Y ) and transverse (HZ ) axes of the HCS have the same

directions of the respective axes of the trunk coordinate system (TCS) when the anatomical

position is maintained.

Trunk Coordinate System (TCS – TX, TY

, TZ)

The TCS is used to create the coordinate systems of the sub-segments of the trunk (upper

trunk, middle trunk and lower trunk) and head, as all these segments have coordinate

systems with the same orientation in space. Also, it is used for the modified version of

Chandler et al. (1975), as it only uses the whole trunk segment.

TO : The origin is located at the MidHJC;

TY : The line pointing proximally from the DEP to the MidSJC (unit vector

MidHJCMidSJC

MidHJCMidSJCj

−

−=

r)

TX : The line orthogonal to TrY and to the line linking both HJCs (unit vector

LHJCRHJC

LHJCRHJCji

−

−×=

rr)

TZ: The line orthogonal to a plane containing TrX

and TrY (unit vector

jikrrr

×=)

Upper Trunk (UPTC), Middle Trunk (MTCS) and Lower Trunk (LTCS) Coordinate

Systems:

The axes of each sub-segment of the trunk have the same respective directions of the TCS.

UTO : The origin is located at the XPEP;

MTO : The origin is located at the NavEP;

LTO : The origin is located at the MidHJC;

[131]

Upper arm Coordinate System (UCS – UX

, UY

, UZ)

UO : The origin is located at the EJC;

UY : line pointing proximally from the EJC to the SJC (unit vector EJCSJC

EJCSJCj

−

−=

r);

UX : The line orthogonal to UY and to the line linking MEL and LEL (unit vector

RMELRLEL

RMELRLELji

−

−×=

rr) for the right upper arm;

LLELLMEL

LLELLMELji

−

−×=

rr for the left

upper arm);

UZ: The line orthogonal to a plane containing UX

and UY (unit vector jik

rrr×= )

Forearm Coordinate System (FCS – FX

, FY

, FZ)

FO : The origin is located at the WJC;

FY : line pointing proximally from the WJC to the EJC (unit vector WJCEJC

WJCEJCj

−

−=

r);

FX : The line orthogonal to FY and to the line linking MWR and LWR (unit vector

RMWRRLWR

RMWRRLWRji

−

−×=

rr) for the right forearm;

LLWRLMWR

LLWRLMWRji

−

−×=

rr for the left

forearm);

FZ: The line orthogonal to a plane containing FX

and FY (unit vector

jikrrr

×=)

Hand Coordinate System (HaCS – HaX

, HaY

, HaZ)

The HaCS has the same position and orientation of the FCS when the anatomical position is

maintained.

[132]

Thigh Coordinate System (ThCS – ThX

, ThY

, ThZ )

ThO : The origin is located at the KJC;

ThY : The line pointing proximally from the KJC to the HJC (unit vector KJCHJC

KJCHJCj

−

−=

r)

ThX : The line orthogonal to the ThY line and the line linking the MKN and the LKN (unit

vector RMKNRLKN

RMKNRLKNji

−

−×=

rr for the right thigh;

LLKNLMKN

LLKNLMKNji

−

−×=

rr for the left

thigh);

ThZ: The line orthogonal to a plane containing ThX

and ThY (unit vector jik

rrr×= )

Lower leg Coordinate System (LCS – LX

, LY

, LZ)

LO : The origin is located at the AJC;

LY : The line pointing proximally from the AJC to the KJC (unit vector AJCKJC

AJCKJCj

−

−=

r)

LX : The line orthogonal to the LY line and the line linking the MAN and the LAN (unit

vector RMANRLAN

RMANRLANji

−

−×=

rr for the right lower leg;

LLANLMKAN

LLANLMKANji

−

−×=

rr for

the left lower leg);

LZ: The line orthogonal to a plane containing LX

and LY (unit vector

jikrrr

×=)

Foot Coordinate System (FootCS – FootX

, FootY

, FootZ)

FootO : The origin is located at Foot 1 (marker located at the calcaneous)

[133]

To calculate the unit vectors of the anatomical coordinate system, the vectors V1 and V2

had to be defined as follows:

121

FOOTFOOTV −=

132

FOOTFOOTV −=

FootY : The line perpendicular to both V1 and V2 pointing cranially (unit vector

12

12

VV

VVj

×

×=

r

for the right foot;

21

21

VV

VVj

×

×=

rfor the left foot)

FootZ : The line orthogonal to the line linking FOOT1 and IIEP pointing forward and the LY

(unit vector jFOOTIIEP

FOOTIIEPk

rr×

−

−=

1

1

FootX : The line pointing distally from Foot1 to the IIEP (unit vector kjirrr

×= )

Acromion Coordinate System (AcrCS - System AcrX

, AcrY

, AcrZ)

The AcrCS is created uniquely to define the SJC from the regression equations (Campbell et

al., 2009).

AcrO : The origin is located at the AcrLR

AcrX : The line defined by the points Acr1 and Acr3, pointing anteriorly (unit vector

13

13

AcrAcr

AcrAcri

−

−=

r)

AcrY : The line perpendicular to a plane containing Acr1, Acr2 and Acr3 (unit vector

2

2

AcrAcrLR

AcrAcrLRji

−

−×=

rr)

[134]

AcrZ: The line orthogonal to a plane containing LlX

and LlY (unit vector jik

rrr×= )

Pelvis Coordinate System (PeCS – PeX

, PeY

, PeZ)

Similarly to the AcrCS, the PeCS is only created to determine the HJC from the regression

equations used (Thorpe and Steel, 1999).

PeO : The origin is located at the AMP

PeZ : The line linking both ASISs, from left to right (unit vector LASISRASIS

LASISRASISk

−

−=

r);

PeY : defined by the vector resulting from the cross product of the vectors

PMPRASISV −=1

r and PMPLASISV −=

2

r whose common origin is the PMP and the

(unit vector

21

21

VV

VVj rr

rrr

×

×= )

PeX : The line parallel to the line lying in the plane defined by the two ASISs and the PMP,

orthogonal to PeZ , and pointing anteriorly (unit vector kjirrr

×= )

[135]

Appendix EAppendix EAppendix EAppendix E

MATLAB CODES

[136]

Convert_dxa_images.m

function [I_TISSUE_mass,I_BMD_mass,I_mass_total,total_mass,

total_mass_com,total_mass_com_cm,... TISSUE_mass,TISSUE_mass_com,TISSUE_mass_com_cm,... BMD_mass,BMD_mass_com, BMD_mass_com_cm,I_for_part_segementation]

= convert_dxa_images(I1,I2,BMD,TISSUE,DXA_WH)

% Copyright : This code is written by Marcel Rossi

([email protected]) and Amar El-Sallam

([email protected]) % The University of Western Australia. The code is part

of Marcel's Master degree and % may be used, modified and distributed for research

purposes with % acknowledgment of the authors/publications and

inclusion this copyright information. % % Disclaimer : This code is provided as is without any warranty.

%folder_name = 'D:\Marcel\data\montana'; Wp=DXA_WH(1); W=DXA_WH(2); Hp=DXA_WH(3); H=DXA_WH(4);

dW=W/Wp; dH=H/Hp;

[M,N]= size(I1); mass_scale = H/N*W/M;

rx = N/W*dW; ry = 5*M/H*dH;

Mass1=BMD(1:3:end)*mass_scale; X1=(BMD(2:3:end)+1)*rx; Y1=(BMD(3:3:end)+1)*ry;

X1r=round(X1); Y1r=round(Y1); I1_temp=[];

for n=1:length(X1r) I1_temp = [I1_temp I1(Y1r(n), X1r(n))]; end I1_temp =double(I1_temp);

P1=polyfit(I1_temp,Mass1,1);

level1 = graythresh(I1); BW1 = im2bw(I1,level1/2); %BW1(660:750,110:140)=0; % this is to remove the steel calib cube %I11 = double(I1').*double(BW1');

I11 = double(I1).*double(BW1);

[137]

%I_BMD_mass = polyval(P1,double(I11(:))); %I_BMD_mass = vec2mat(I_BMD_mass,N);

I_BMD_mass = I11*mean(Mass1(:))/mean(I1_temp(:)); clear I11;

Mass2=TISSUE(1:3:end)*mass_scale; X2=(TISSUE(2:3:end)+1)*rx; Y2=(TISSUE(3:3:end)+1)*ry;

X2r=round(X2); Y2r=round(Y2); I2_temp=[]; for n=1:length(X2r) I2_temp = [I2_temp I2(Y2r(n), X2r(n))]; end I2_temp =double(I2_temp);

%P2=polyfit(I2_temp,Mass2,1);

level2 = graythresh(I2); BW2 = im2bw(I2,level2/2); %BW2(660:750,110:140)=0; %I22 = double(I2').*double(BW2'); I22 = double(I2).*double(BW2); %I22=I2; %I_TISSUE_mass = polyval(P2,double(I22(:))); %I_TISSUE_mass = vec2mat(I_TISSUE_mass,N);

I_TISSUE_mass = I22*mean(Mass2(:))/mean(I2_temp(:)); clear I22;

I_total = I1+I2; I_for_part_segementation =I_total;

I_mass_total = I_BMD_mass+I_TISSUE_mass;

[M,N]= size(I_mass_total);

total_mass = sum(I_mass_total(:)); TISSUE_mass = sum(I_TISSUE_mass(:)); BMD_mass = sum(I_BMD_mass(:));

[x,y]=meshgrid(1:M,1:N); x=x(:); y=y(:);

total_mass_com(1)=0; total_mass_com(2)=0; TISSUE_mass_com(1)=0; TISSUE_mass_com(2)=0; BMD_mass_com(1)=0; BMD_mass_com(2)=0;

[138]

for n=1:length(x) total_mass_com(1)= total_mass_com(1)+

I_mass_total(x(n),y(n))*x(n);

total_mass_com(2)=total_mass_com(2)+I_mass_total(x(n),y(n))*y(n);

TISSUE_mass_com(1)=TISSUE_mass_com(1)+I_TISSUE_mass(x(n),y(n))*x(n);

TISSUE_mass_com(2)=TISSUE_mass_com(2)+I_TISSUE_mass(x(n),y(n))*y(n); BMD_mass_com(1)=BMD_mass_com(1)+I_BMD_mass(x(n),y(n))*x(n); BMD_mass_com(2)=BMD_mass_com(2)+I_BMD_mass(x(n),y(n))*y(n); end total_mass_com = total_mass_com/total_mass; TISSUE_mass_com=TISSUE_mass_com/TISSUE_mass; BMD_mass_com=BMD_mass_com/BMD_mass;

total_mass_com_cm(1) = total_mass_com(1)*W/N; total_mass_com_cm(2) = total_mass_com(2)*H/M;

TISSUE_mass_com_cm(1) = TISSUE_mass_com(1)*W/N; TISSUE_mass_com_cm(2) = TISSUE_mass_com(2)*H/M;

BMD_mass_com_cm(1) = BMD_mass_com(1)*W/N; BMD_mass_com_cm(2) = BMD_mass_com(2)*H/M;

%% figure('units','normalized','outerposition',[0 0 1 1]) subplot(1,3,1) imshow(I1) hold on plot(X1,Y1,'r*') title('BMD Mass in pixels') xlabel('pixel index') ylabel('pixel index')

hold off

subplot(1,3,2) imshow(I2) hold on plot(X2,Y2,'b*') title('TISSUE Mass in pixels') xlabel('pixel index') ylabel('pixel index') hold off axis image

subplot(1,3,3) imshow(I_total) title('TOTAL Mass in pixels') xlabel('pixel index') ylabel('pixel index') axis image %% figure('units','normalized','outerposition',[0 0 1 1]) subplot(1,3,1) imshow(BW1)

[139]

title('BMD noise removal Mask') xlabel('pixel index') ylabel('pixel index') axis image

subplot(1,3,2) imshow(BW2) %axis(AXIS) title('TISSUE noise removal mask') xlabel('pixel index') ylabel('pixel index') axis image

subplot(1,3,3) imshow(BW1+BW2) title('TOTAL Mass noise removal mask') xlabel('pixel index') ylabel('pixel index') axis image %% Image to Mass figure('units','normalized','outerposition',[0 0 1 1]) subplot(1,3,1) imagesc(I_BMD_mass) title('BMD True Mass') xlabel('pixel index') ylabel('pixel index') hold on plot(BMD_mass_com(2),BMD_mass_com(1),'k+','markersize',10) plot(BMD_mass_com(2),BMD_mass_com(1),'kO','markersize',10) hold off axis image

subplot(1,3,2) imagesc(I_TISSUE_mass) %axis(AXIS) title('TISSUE True Mass') xlabel('pixel index') ylabel('pixel index') hold on plot(TISSUE_mass_com(2),TISSUE_mass_com(1),'k+','markersize',10) plot(TISSUE_mass_com(2),TISSUE_mass_com(1),'kO','markersize',10) hold off axis image

subplot(1,3,3) imagesc(I_mass_total) title('TOTAL True Mass') xlabel('pixel index') ylabel('pixel index') hold on plot(total_mass_com(2),total_mass_com(1),'k+','markersize',10) plot(total_mass_com(2),total_mass_com(1),'kO','markersize',10) hold off axis image %% figure('units','normalized','outerposition',[0 0 1 1]) [X,Y]=meshgrid(1:N,1:M); X=X*W/N; Y=Y*H/M; mesh(X,Y,I_mass_total)

[140]

title('Total mass represented as depth') %xlabel('cm') %ylabel('cm') zlabel('mass') axis tight

%% return figure('units','normalized','outerposition',[0 0 1 1]) I1t=imresize(I_BMD_mass,W/N); imagesc(I1t)

segment_body.m

function [cropped_part, part_mass, part_com,

part_com_cm,part_com_cm_l, part_com_ratio,Im] =

segment_body_2(I_for_part_segementation,I_mass_total,DXA_WH,x,y,PEP,

DEP)

% Copyright : This code is written by Marcel Rossi

([email protected]) and Amar El-Sallam

([email protected]) % The University of Western Australia. The code is part

of Marcel's Master degree and % may be used, modified and distributed for research

purposes with % acknowledgment of the authors/publications and

inclusion this copyright information. % % Disclaimer : This code is provided as is without any warranty.

W=DXA_WH(2); H=DXA_WH(4);

[M,N]=size(I_for_part_segementation);

%xo = [PEP(1); DEP(1)]; %yo = [PEP(2), DEP(2)];

cropped_part=I_mass_total;

mask = poly2mask(x,y,M,N); cropped_part(~mask)=0;

part_mass = sum(cropped_part(:));

[x,y]=meshgrid(1:M,1:N); x=x(:); y=y(:);

com(1)=0; com(2)=0;

for n=1:length(x) com(1)= com(1) + cropped_part(x(n),y(n))*x(n); com(2)=com(2) + cropped_part(x(n),y(n))*y(n);

[141]

end

part_com = com/part_mass;

part_com_cm(1) = part_com(1)*W/N; part_com_cm(2) = part_com(2)*H/M;

part_com_cm_t(1) = (part_com(1)-DEP(2))*W/N; part_com_cm_t(2) = (part_com(2)-DEP(1))*H/M;

part_com_cm_l=norm(part_com_cm_t);

[x,y]=find(cropped_part>0);

%figure('units','normalized','outerposition',[0 0 1 1]) %imagesc(I_for_part_segementation) %hold on %plot(y,x,'w*') %axis image %hold off

Im = 0; for n=1:length(x) rsqr = (x(n)*W/N - part_com_cm(1))^2 + (y(n)*H/M -

part_com_cm(2))^2; Im = Im + cropped_part(x(n),y(n))/1000*rsqr; end

V1(1)=part_com(1)-DEP(2); V1(2)=part_com(2)-DEP(1);

V2(1)=PEP(2)-DEP(2); V2(2)=PEP(1)-DEP(1); V2=V2/norm(V2);

V3(1)=PEP(2)-DEP(2); V3(2)=PEP(1)-DEP(1);

part_com_ratio=100*dot(V1,V2)/norm(V3); %%

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