Deterministic Modelling Biomechanic

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Use of deterministic models in sportsand exercise biomechanics researchJohn W. Chow a & Duane V. Knudson ba Center for Neuroscience and Neurological Recovery, MethodistRehabilitation Center , Jackson, Mississippi, USAb Department of Health and Human Performance , Texas StateUniversity , San Marcos, Texas, USAPublished online: 09 Aug 2011.

To cite this article: John W. Chow & Duane V. Knudson (2011) Use of deterministic modelsin sports and exercise biomechanics research, Sports Biomechanics, 10:3, 219-233, DOI:10.1080/14763141.2011.592212

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Use of deterministic models in sports and exercisebiomechanics research

JOHN W. CHOW1 & DUANE V. KNUDSON2

1Center for Neuroscience and Neurological Recovery, Methodist Rehabilitation Center, Jackson,

Mississippi, USA, and 2Department of Health and Human Performance, Texas State University, San

Marcos, Texas, USA

(Received 14 October 2010; accepted 20 May 2011)

AbstractA deterministic model is a modeling paradigm that determines the relationships between a movementoutcome measure and the biomechanical factors that produce such a measure. This review provides anoverview of the use of deterministic models in biomechanics research, a historical summary of thisresearch, and an analysis of the advantages and disadvantages of using deterministic models. Thedeterministic model approach has been utilized in technique analysis over the last three decades,especially in swimming, athletics field events, and gymnastics. In addition to their applications in sportsand exercise biomechanics, deterministic models have been applied successfully in research on selectedmotor skills. The advantage of the deterministic model approach is that it helps to avoid selectingperformance or injury variables arbitrarily and to provide the necessary theoretical basis for examiningthe relative importance of various factors that influence the outcome of a movement task. Severaldisadvantages of deterministic models, such as the use of subjective measures for the performanceoutcome, were discussed. It is recommended that exercise and sports biomechanics scholars shouldconsider using deterministic models to help identify meaningful dependent variables in their studies.

Keywords: Exercise science, mechanical analysis, performance analysis, quantitative analysis, researchmethodology

Introduction

Advances in computers, transducers, and imaging technologyhavemade it easier andquicker to

collect biomechanics data. Several reviews of these methods in sports biomechanics and their

potential have been reported (Bartlett, 1997; Lees, 2002; Yeadon & Challis, 1994). However,

the increase in the number of laboratories and research reports in sports biomechanics over the

last two decades has not resulted in substantial improvements in the theoretical bases or

frameworks used in sports biomechanics research.

Exercise and sports biomechanics research is a growing field and the expanding body of

research reports fit the chaos in the brickyard perspective (Forscher, 1963) of modern

scientific inquiry, where the danger of an increasing number of less than meaningful

observations are being reported in the literature is a real possibility. Hudson (1997) has

ISSN 1476-3141 print/ISSN 1752-6116 online q 2011 Taylor & Francis

DOI: 10.1080/14763141.2011.592212

Correspondence: John W. Chow, Ph.D., Center for Neuroscience and Neurological Recovery, Methodist Rehabilitation Center,

1350 East Woodrow Wilson Drive, Jackson, MS 39216, USA, E-mail: [email protected]

Sports Biomechanics

September 2011; 10(3): 219233

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noted how our students and colleagues often consider sports biomechanics an atheoretical

and irrelevant discipline. Knudson (2005) reported that fewer than 20% of the papers

published in two applied biomechanics serials could be rated highly on rationale, theory and

statistical analysis. The common use of many statistical tests on many dependent variables in

most exercise and sports biomechanics research reports inflates the experiment-wise type I

error rate (Knudson, 2009) and prevents us from understanding which effects are truly

statistically significant and which are likely to be type I errors.

In many fields of study, a model (a graphical or mathematical description of a system or

process) can be used as a basis for theoretical or empirical understanding of that system or

process. Deterministic models serve such purposes in biomechanics, and their use could

help to promote the use of theoretical models in sports and exercise biomechanics research.

Concise overviews of deterministic models have been given in several review articles

(Glazier, 2010; Lees, 1999, 2002) and textbooks (Bartlett, 1999; Hay & Reid, 1988). This

paper presents a comprehensive narrative review synthesizing the use of deterministic

models in sports biomechanics. First we define deterministic models and summarize their

use in biomechanics. The advantages and disadvantages of this approach are reviewed, and

we conclude with the potential application of these models in research and with athletes.

The deterministic model

A deterministic model is a modeling paradigm that determines the relationships between a

movement outcome measure and the biomechanical factors that produce such a measure

(Hay & Reid, 1988). A block diagram is often used to provide an overview of the

relationship. For example, the goal of a 100-m dash is for a sprinter to complete the distance

of 100m (Figure 1) in the shortest amount of time. This time is determined by the average

speed and the distance covered (a constant in this case) (t D/Savg). The average speed isfurther determined by the athletes average stride length and stride frequency (Savg SLavg SFavg). When necessary, the average flight and support times can be included asfactors that produce the average stride frequency. Stride frequency is determined as the

reciprocal of stride time, which is the sum of the flight and support times during a single

stride. Also, the average stride length can be divided into three shorter distances the

takeoff, flight, and landing distances (Hay, 1993).

Dr. James G. Hay is inarguably the pioneer of deterministic model use in biomechanical

analyses. While working on his dissertation on high jumping (Hay, 1967), he was having

trouble keeping the roles of the variables (performance parameters of high jumping) clear in

his mind, and started to draw block diagrams to clarify things. Hays initial problems with

these block diagrams revolved around causality, inclusion and redundancy. He became

aware that, in some cases, he was leaving an important factor out of a block diagram while in

other cases, he was including factors that were redundant for example, the horizontal

velocity of takeoff, the vertical velocity of takeoff and the angle of takeoff. This eventually led

him to identify a basic mechanical equation that linked the variable in one box to the

variables in the boxes linked to it from below. With this approach, the relationships in Hays

block diagrams were all-inclusive and non-redundant, and all the relationships involved were

causal in nature (Dr. J. Hay, personal communication, May 5, 2001).

According to Hay (1984), a deterministic model should have two distinguishing features.

First, the model is made up of mechanical quantities or appropriate combinations of

mechanical quantities. Secondly, all the factors included at one level of the model must

completely determine the factors included at the next highest level. It is this second feature

that leads us to refer to these types of models as deterministic models. Some authors (e.g.

J.W. Chow & D.V. Knudson220

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Bartlett, 1999; Lees, 2002) refer to these models as hierarchical models. It is worth noting

that the deterministic approach defined here is not the same as the deterministic models in

mathematical modeling. A deterministic model in mathematical modeling is a direct

mathematical representation of phenomena that occur in deterministic, continuous, or

discrete patterns (Kleinstreuer, 1997).

Hay extended the application of the deterministic model by using correlation analysis to

document the strength of association between the movement goal and the subsequent factors

in the model. He and his students illustrated this with papers on the limiting factors of

vertical jumping (Hay et al., 1976, 1978, 1981). These studies were some of the first to use

partial correlation and multiple regression to account for intercorrelations between variables

and identify biomechanical variables with unique associations with performance. The

deterministic model combined with the large sample of subjects allowed the identification of

key joint torques contributing to jump height. Hip extensor torques early in propulsion

and shoulder extensor torques near take-off were identified as significant determinants.

Figure 1. Model for the 100-m dash and illustration of selected kinematic characteristics of a running stride.

Use of deterministic models 221

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The mechanisms of these benefits have recently been confirmed by experimental and

simulation studies (Cheng et al., 2008; Domire & Challis, 2010; Feltner et al., 1999).

Replication of correlational studies or experimental/modeling verification is important

because causation cannot be inferred from correlations and cross-validation of these

associations is necessary.

Development of deterministic models

The steps in the development of a deterministic model are described in detail by Hay and

Reid (1988). Briefly, the first step is to identify the primary goal, result/outcome of the

performance to be investigated. The outcome of a performance can be an objective measure

(e.g. distance, height, time, etc.) or a subjective measure (e.g. points awarded in gymnastic

and diving competition). The next step is to identify those factors that produce the result. As

stated earlier, the factors included in the model should normally be mechanical quantities

wherever possible and each factor should be completely determined by those factors that are

linked to it from below.

It should be emphasized that it is possible to develop more than one model for movement

tasks of similar results. The discus throwmodels with the speed of release of the discus as the

performance result developed by Hay and Yu (1995) and Chow and Mindock (1999) can be

used to illustrate this point. In the second level of the model used by Hay and Yu (Figure 2), a

thrower loses distance if the discus is released inside the throwing circle and vice versa. In the

third level, the flight distance is determined by factors governing the trajectory of a projectile.

In the next level, Hay and Yu considered the speed of the discus at the instant of release to be

the sum of changes in the speed of the discus during different phases of a throw. As a result,

the terminal factors (boxes at the ends of the various paths) of the model are the distance loss,

Figure 2. Model for the discus throw used by Hay and Yu (adapted from Hay & Yu, 1995).


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angle and height of release, aerodynamic distance, and the changes in discus speed during

different phases of a discus throw.

The model developed by Chow and Mindock (1999) focused on the kinematic

characteristics of upper body segments during throws performed by wheelchair athletes

(Figure 3). The first three levels of the model are similar to those of Hay and Yu (1995), while

the rest of the model is formed by repeated applications of several equations relating

kinematics of distal endpoint to proximal endpoint of a segment of the throwing arm. The

terminal factors of the model can be categorized into three groups: (1) the characteristics of

the discus at the instant of release, (2) the characteristics of different upper body segments at

the instant of release, and (3) the characteristics of different segments during the forward

Figure 3. Model for the wheelchair discus throw used by Chow and Mindock (1999).


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swing. Apart from the common finding that the speed of release is the most influential

determinant of the distance of the throw, there are differences in influential variables between

able-bodied and disabled discus throwers. Hay and Yu (1995) demonstrated the importance

of achieving a large gain in the speed of the discus during the second double support phase in

elite able-bodied discus throwers, while Chow and Mindock (1999) found the shoulder

girdle movement during the forward swing to be the important determinant of both medical

classification and throw distance of wheelchair athletes. Although the movement tasks of

able-bodied and wheelchair discus throws are not exactly the same, the segmental approach

used in wheelchair discus can by applied in future research to the delivery phase of the able-

bodied discus throw.

Use of deterministic models in biomechanics

Over the years the utility of a deterministic model approach in biomechanical research has

been illustrated in several sports, especially in swimming, athletics field events, and

gymnastics. A concise summary of this research is presented in Table I.

Use of deterministic models has clarified key performance parameters in swimming starts

and strokes. In competitive swimming the average speed (S) is the product of the average

stroke frequency (SF ) and average stroke length (SL) and the relationships between these

parameters have been investigated using swimmers of different performance levels. Craig

and Pendergast (1979) asked college swimmers to swim at different speeds and found that

increased S toward the maximum was achieved by a combination of increasing SF and

decreasing SL in all of the four competitive strokes. In a group of 168 untrained high school

students, improvement in breaststroke S after six weeks (three times/week) of training

depended upon an increase of SL, rather than SF (Saito, 1982). Based on data collected at

the 1982 British Commonwealth Games, Pai et al. (1984) concluded that elite swimmers

achieved very similar S with very different combinations of SL and SF. With the aid of a

deterministic model Grimston and Hay (1986) identify 21 anthropometric variables relevant

to success in swimming and tried to relate these variables to the freestyle swim performance

of college swimmers. The axilla cross-sectional area, a variable that could be substantially

affected by training, was found to have the largest influence on both SL and SF.

Using the total starting time (sum of block, flight, and water times) as the performance

goal of the hands-between-the feet grab starting technique, Guimaraes and Hay (1985)

tested 24 male high school swimmers and identified several mechanical characteristics that

contribute to a faster start. McLean et al. (2000) adapted the model by Guimaraes and Hay

(1985) to compare the kinematics of three types of relay start one or two-step approach,

and a no-step start. Their findings suggested that step starts offered some performance

improvements over the no-step start.

Deterministic models have been successfully used in the study of jumps and throws in

track and field athletics. Using the deterministic model approach Hay and colleagues

(1985a, 1985b, 1986) successfully identified mechanical characteristics that are significantly

related to the official distances of long and triple jumps of elite jumpers. Chow and Hay

(2005) developed a model of the last support phase of the long jump and used it to examine

the interacting roles played by the approach velocity, the explosive strength (represented by

vertical ground reaction force), and the change in angular momentum about a transverse axis

through the jumpers centre of mass during the last support phase of the long jump, using a

computer simulation technique. The results indicated that approach velocity and vertical

ground reaction force are not independent factors in determining jump distance, and the

jump distance was over-estimated if the change in angular momentum was not considered in


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TableI.Summary

ofresearcharticlesusingthedeterministicmodelapproach.

Reference

Subjects

Perform

ance

result

Terminalfactors

Statistical

approach

Key

findings

Hayetal.(1976)

213M

Verticaljump

height

Jointanglesandkinem

atics

ofcenterof

gravity(C

G)andlimbsegments

Partial

CORR&

REG

Theactionsofhead,trunk,andarm

s

contributedsignificantlyto

thevari-

ationsin

CG

elevationfrom

takeoffto

peakofflight.

Hayetal.(1978)

213M

Verticaljump

height

Jointangularim

pulses

Partial

CORR

Torques

attheshoulder,hip,andknee

weresignificantcontributorsto

jumpheightandcontributionsvaried

acrossphases.

Craig&Pendergast(1979)

63M,47F

Averagesw

im-

mingspeed(S)

Averagestrokelength

(SL)andstroke

frequency

(SF)

t-test

WithinsubjectSincreasedasaresultof

increasingSFanddecreasingSL.

Hayetal.(1981)

194M

Verticaljump

height

Meanjointtorques

REG

Ten

shoulder,hip,knee,andankle

torques

weresignificantcontributorsto

jumpheightandcontributionsvaried

acrossphases

Saito(1982)

168M

high

schoolstudents

Sofbreast-

stroke

SLandSF

t-test

Improvem

entin

Safter

sixweeksof

training(3x/week)wasdueto

an

increase

inSF,rather

thanin

SL.

Paietal.(1984)

64M,46F

Soffourcom-

petitivestrokes

SLandSF

CORR&

REG

Swasnotsignificantlycorrelatedwith

either

SLorSF.Elitesw

immersused

differentcombinationsofSLandSFto

achieve

afairlyconstantS.

Guim

araes

&Hay(1985)

24M

high

schoolsw

im-

mers

Swim

grab

starttime

CG

kinem

atics

andkineticvariables

determinetheblock,flight,&water

times

CORR&

REG

Forafaster

startsw

immersshould

(a)

moveCG

fastforward

onblock,(b)

maxim

izebackward

forcebyfeet,&(c)

maxim

izeforcebyhandsinforward

and

upward

direction.

Hay&Miller(1985a),Hay

etal.(1986)

12M

&12F

elitelongjum-

pers

Long

jumpdistance

Velocities

attakeoffandtouchdownof

thelastfourstrides

oftheapproach

and

thevelocity

andangleattakeoff

CORR

Confirm

ingthedominantrolesofthe

horizontalvelocityoftheapproach,the

horizontalandresultantvelocities

at

takeoff,andtheflightdistance.Other

factorscloselyrelatedto

the

jumpdistance

wereidentified.


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TableIcontinued

Reference

Subjects

Perform

ance

result

Terminalfactors

Statistical

approach

Key

findings

Hay&Miller(1985b)

12M

elitetriple

jumpers

Triple

jumpdistance

Velocitiesattakeoffandtouchdownand

times

offlightandsupportforthethree

phasesofthetriplejump

CORR

Themore

thejumpersresources

are

expended

priorto

thejumpphase

and

themore

verticaltheeffortattakeoff

intothejump,thebetterthefinalresult.

Grimston&Hay(1986)

12M

college

swim

mers

Averagesw

im-

mingspeed(S)

SLandSF.Adeterministicmodelwith

swim

timeastheresultwasusedto

identifyanthropometricvariablesrel-

evantto

successin

swim

ming

Partial

CORR&

REG

Theanthropometricvariables

accountedfor89%

(SL),41%

(SF),

and17%

(S)ofthevariancesin

the

measuredcharacteristics

oftheir

strokes.AlthoughSislittleinfluenced

bythephysique,thecombinationofSL

andSFusedto

attain

agiven

Sisvery

much

afunctionofsw

immersphysi-

que.

Wilsonetal.(1987)

24M

&10F

Skatingsprint

speed

Stridelength,stridefrequency,body

segmentanglesandrangeofmotion

duringsinglesupport

CORR&

REG

Sprintskatingspeedisassociatedwitha

longstridelength

andalargesingle-

supportdistance.

Takei(1988;1989;1990;

1992;1998),Takei&Kim

(1990),Takeietal.(1992;

2000;2003)

Ranged

from

24

to122M/F

worldclass

gymnasts

Gymnastic

vault:point

awarded

by

judges

Linearandangularmotionofthe

gymnastin

preflight,postflight,andthe

executionduringthevault

CORR

Mechanicalfactorsassociatedwith

judgesscoreswereidentified

for

differenttypes

ofvaults.

Gervais(1994)

1gymnast

Gymnastic

vault:judges

score

Tim

eonhorse,timeofpostflight,CG

locationandvelocities

postflight,and

pre-andpost-flightangularmomentum

values

CORR

Theresultsdem

onstratedthatthe

optimizationapproach

developed

could

produce

aviablepredictionofan

individualsoptimalperform

ance

ofa

handspring11 2frontsaltolonghorse

vault.

Hay&Yu(1995)

14M

&15F

Discusthrow

distance

Changes

inthespeedofthediscus(Ds)

duringdifferentphases,speed,angle,

andheightofrelease

CORR

Dsduringtheseconddoublesupport

phase

andthespeedofrelease

are

influentialdeterminantofthethrow

distance

Dixon&Kerwin

(1998)

3F

Maxim

um

Achillesten-

donforce

Componentsofgroundreactionforce

(GRF)andcenterofpressure,and

digitized

marker

location

ANOVA

Thefindingthatincreasedheelliftsmay

increase

maxim

um

Achillestendon

forcesuggestedthatcautionisadvised

intheroutineuse

ofthisintervention.


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TableIcontinued

Reference

Subjects

Perform

ance

result

Terminalfactors

Statistical

approach

Key

findings

Chow&Mindock

(1999),

Chowetal.(2000;2003b)

1417M

wheelchairath-

letes

Discus,shot

put,&javelin

measureddis-

tance

Kinem

atics

oftheim

plementand

differentupper

bodysegmentsatthe

instantofrelease,andkinem

atics

of

differentsegmentsduringthedelivery

CORR

Inadditionto

thespeedofthe

implementatrelease,im

portantdeter-

minantsofmedicalclassificationand

measureddistance

wereidentified

for

each

fieldevent.

McL

eanetal.(2000)

10M

college

swim

mers

Swim

start

time

Speed,angle,andbodypositionat

takeoff,takeoffandentryheights,and

airbornebodymomentofinertiaand

angularmomentum

ANOVA

Comparedwithno-stepstarts,

increasedhorizontaltakeoffvelocity,

decreasedverticaltakeoffvelocity,

increasedtakeoffheight,steeper

entry

angleandorientationwerefoundin

step

starts.

Powers&Harrison(2002)

8show-jumping

horses

CG

path

duringflight

CGvelocitiesattakeoffandlandingand

CG

elevationduringflight

ANOVA

Theriderseffectonjumpinghorseswas

primarilydueto

behavioralchanges

in

horsesmotion,rather

thaninertial

effects.

Chowetal.(2003a)

4M,4F,pro-

fessionalplayers

Balllocationat

landingfora

tennisserve

Kinem

atics

ofballtoss,pre-andpost-

impactballandracquetvelocities

Wilcoxon

From1stto2ndserveplayerstossed

the

ballcloserto

thebodyandim

parted

spinontheballbychangingtheracquet

verticalandlateralvelocities.

Chow&Hay(2005)

NA(computer

simulation)

Long

jumpdistance

Approach

velocity,verticalGRF

(VGRF),andchangein

angular

momentum

duringtakeoff

NA

Sensitivityanalysisrevealedthat

approach

velocity

andVGRFare

not

independentfactorsin

determiningthe

jumpdistance.

Leighetal.(2008)

51M,53F

Discusthrow

distance

Hip-shoulder

andshoulder-arm

separ-

ation,trunkforward-backward

tilt,

throwing-arm

elevationangles,and

throwingprocedure

phase

times

CORR&

REG

Fem

alethrowersuse

amore

sophisti-

catedtechniquethanmalethrowers.

Malethrowersmay

place

more

reliance

onphysicalstrength

toachieve

long

distances.

Abbreviations:M:male,F:female,CORR:correlationanalysis,REG:regressionanalysis,ANOVA:analysisofvariance,NA:notapplicable.


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the analysis. In addition to horizontal jumps, Hay and Yu (1995) developed a model to

analyse discus throws performed by elite able-bodied athletes (Figure 2). In separate studies

Chow and colleagues (Chow et al., 2000, 2003b; Chow & Mindock, 1999) applied a

stationary throw model to the analyses of shot put, discus throw and javelin throw

performance of wheelchair throwers of different medical classifications (Figure 3).

The models used in Takeis studies on gymnastic vaults are good examples of models that

use subjective measures for the performance outcome (Figure 4). Takei and colleagues have

used deterministic models to guide their biomechanical analyses of several gymnastic vaults

performed by elite gymnasts (Takei, 1988, 1989, 1990, 1992, 1998; Takei & Kim, 1990;

Takei et al., 1992, 2000, 2003). Figure 4 shows a typical model used by Takei. Studies using

these models and correlation analysis have documented influential performance variables in

gymnastic vaults and key techniques that are significantly associated with successful

performance (points awarded by judges). Instead of statistical approaches commonly used

by others, Gervais (1994) utilized the evaluation scheme (point deductions) of a vault in

conjunction with a deterministic model to set up an optimization process for predicting the

optimal performance of a gymnastic vault. The predicted optimal performance was found to

display greater virtuosity in postflight height, distance and angular momentum when

compared with the individuals best trial performance.

Other sports skills studied using the deterministic model approach are roller skating

(Wilson et al., 1987), horse jumping (Powers & Harrison, 1999, 2002) and tennis serve

(Chow et al., 2003a). Deterministic models were also used in reviews analyzing the slalom in

alpine skiing (Bober, 1996) and rowing (Soper & Hume, 2004), and physical training for

increasing vertical jump height (Ham et al., 2007).

Deterministic models can be adapted to a goal to minimize the exposure to a mechanical

variable that is hypothesized to be the primary cause of injury. Dixon and Kerwin (1998)

Figure 4. Model showing preflight factors causally related to the official score of a handspring vault (adapted from

Takei, 1989).


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reported one of the few studies that have explicitly taken advantage of deterministic models

to study influential factors related to injury. It is possible that the use of deterministic

models in conjunction with multivariate statistical analysis can identify factors and their

strength of association with injury rates.

Use of deterministic models has found its way into other exercise and sports science

research utilizing biomechanical data. Although no block diagrams were used, three studies

on the acquisition of motor skills have used deterministic models (Heise & Cornwell, 1997;

Schneider et al., 1989; Yoshida et al., 2004). Schneider et al. (1989) examined the net joint

moments at the upper extremity joints during a maximum speed hand movement, in a

vertical plane up and around a barrier to a target. Their model focused on the three

components of the net joint moment: gravitation, interactive and generalized muscle

moments. Their results supported Bernsteins (1967) hypothesis that practice alters motor

coordination among muscular and passive joint moments. Using the same mathematical

procedures Heise and Cornwell (1997) and Yoshida et al. (2004) tried to determine, for a

planar multi-joint throwing skill and a target reaching task respectively, whether the relative

contributions of the components of the net joint moment at the elbow and shoulder change

after an intervention. With practice, subjects in the Heise and Cornwell (1997) study could

throw further. However, the relative contribution of net joint moment components remained

unchanged. Results from Yoshida et al. (2004) suggest that rapid aiming movements are

controlled through a reciprocal interplay between intersegmental dynamics during the

acceleration phase and error corrections. It is clear that deterministic models have been

useful in conducting biomechanical research on a wide variety of human movements. It

should also be mentioned that some studies used the deterministic modeling approach but

the approach was not explicitly stated [e.g., Yu et al. (2006) and Zablotny et al. (2003)].

Extension of deterministic models to qualitative biomechanics

Besides their utility in planning and analyzing biomechanical data in research, Hay also

advocated that deterministic models be used as a basis for qualitative analysis of sports

skills (Hay, 1984; Hay & Reid, 1988). There is strong logical support for this position

because these models enable coaches to focus on important biomechanical variables that

directly affect the movement goal. Some coaches are not educated in exercise and sports

science and rely on passed-down craft knowledge of sports techniques. Qualitative analysis

of technique decisions on meaningful biomechanical factors that directly affect

performance is important, so use of deterministic models to guide qualitative analysis

could be an improvement on traditional error detection and correction based on unverified

technique beliefs.

The utilization of deterministic models as a guide for qualitative analysis, however, has not

been tested by research and deterministic models are only one of several approaches

(Knudson & Morrison, 2002). Hudson (1997) has been critical of any qualitative analysis

model that does not focus the attention of the analyst and athlete on kinematic variables that

are visually observable and potentially meaningful in modifying technique, while others

encourage use of deterministic models and kinetic variables in qualitative analysis (Sanders,

2004). There has been limited and fragmented research on the interdisciplinary skill of

qualitative analysis of human movement (Knudson & Morrison, 2002), so there is a lack of

evidence as to which approach to qualitative analysis is best or the efficacy of biomechanical

data in improving sport performance (Lees, 1999). There is a need for research comparing

the use of deterministic models of qualitative analysis with other models of qualitative

analysis.


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Advantages and disadvantages

The primary advantage of using deterministic models is to help to avoid selecting

performance variables arbitrarily (the trial and error approach). The deterministic model

approach is a more objective approach to identifying factors that affect the outcome of a

performance. If done correctly, this ensures that no major factor that determines the

outcome is overlooked and that nothing is included unnecessarily (Hay, 1984). Use of

deterministic models in biomechanical research could reduce the problems caused by

numerous dependent variables noted earlier.

Another advantage of the deterministic models is that it can be used to provide a theoretical

basis (mechanical relationships) for statistical modeling (Bartlett, 1999). For example,

referring to the model depicted in Figure 3, the significant correlations between the range of

motion and average angular velocity of the shoulder girdle during the forward swing and the

measureddistance (r $ 0.72) of throwers allowed the investigators to affirm the significance ofshoulder girdle movement in wheelchair discus throw (Chow &Mindock, 1999).

It is not uncommon to see many factors and levels of factors in a well-developed model.

A major concern when using such a model for statistical modeling is the sample size and

assumptions of the statistics used. A reasonably large sample of subjects and trials is needed

in order to come up with an acceptable power value. For example, to allow a reliable

multiple linear regression analysis and to overcome problems of colinearity, Hay et al.

(1981) tested 194 subjects for the purpose of identifying limiting factors of vertical

jumping. Partial correlation and multiple regression analyses should be used to define the

variables that are meaningful in predicting the goal of the movement, thereby eliminating

variables that are intercorrelated or not truly influential. Care must also be taken to ensure

and report that the scatterplots do not violate assumptions of linearity and random error, so

that the strength of the correlations and regression equations accurately model the data.

Subjectivity in selecting the number of levels and variables in a deterministic model can be

a disadvantage at times. For example, increasing the number of variables expands the study,

but imposes greater demands on sample size and interpretation. In any event, it is

recommended that researchers should strive to minimize the number of variables involved

and statistical tests performed to maximize the power of their analysis.

Summary

The deterministic model approach provides a strong theoretical or mechanical basis for

examining the relative importance of various factors that influence the outcome of a

movement task. These models have been used successfully in research on a wide variety of

motor skills in the last four decades. Studies using deterministic models in biomechanics and

motor behaviour illustrate their utility in identifying critical mechanical parameters in

humanmovement. The use of correlation and regression analyses to document the size of the

association of variables influencing movement is an important step in planning prospective

studies to apply biomechanics to improve movement performance or reduce injury risk.

Despite the success of these models in a wide variety of biomechanics research, most of the

scholars using deterministic models have links to Dr. Hay and his students. This somewhat

limited use of deterministic models in research may be because many associate deterministic

models with qualitative biomechanical analysis advocated by Hays classic texts (Hay, 1993;

Hay & Reid, 1988). While deterministic models logically have the potential to improve

qualitative analysis, biomechanics scholars are encouraged to use deterministic models to

improve the focus and impact of their research.


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It is likely that greater use of deterministic models in planning biomechanics research can

help reduce some of the problems in the literature related to numerous and likely

meaningless dependent variables (Hudson, 1997; Knudson, 2005, 2009). Research can then

be focused on variables with a strong theoretical or mechanistic connection to performance

as well as risk of injury.

We recommend that sports biomechanics scholars consider using deterministic models to

help identify meaningful dependent variables in their studies, and build mechanistic or

theoretical linkages related to the independent variables being studied. When correlation and

regression analyses are used in conjunction with a deterministic model, care must be take to

sample a well-defined population of subjects adequately in order to document the magnitude

of influence of the factors on performance or potential injury. For scholars interested in the

application of biomechanical theory and principles, research comparing deterministic

models of qualitative analysis with other models would be beneficial to the field.

Acknowledgements

The preparation of this review was supported in part by the Wilson Research Foundation

(Jackson, Mississippi, USA).

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Deterministic Modelling Biomechanic

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