Quantification of motor patterns inparkinsonian gait

Luisa Fernanda Cardenas Martınez

Cim@Lab Research GroupUniversidad Nacional de Colombia

School of Medicine

Bogota, Colombia

2016

Quantification of motor patterns inparkinsonian gait

Luisa Fernanda Cardenas Martınez

Thesis presented as partial requirement for the degree of:

Master in Biomedical Engineering

Advisor:

Eduardo Romero Castro. MD. Ph.D.

Research Area:

Human Gait Analysis, Movement Analysis

Cim@Lab Research Group

Universidad Nacional de Colombia

School of Medicine

Bogota, Colombia

2016

“Sabemos lo que somos, pero no lo que podemos ser”

William Shakespeare

Acknowledgments

To my family, for their unconditional support, love and motivation to keep going.

To the professor Eduardo, for giving me the chance to do something different, and for pushing

me to think in a different way

To Fabio Martinez, for taking the challenge of teaching engineering concepts to physios. for

the great patience and his friendship.

To “el flaco” and “Truji”, for being the best psychologists, comedians,....in general the best

friends .

And to Cim@lab, for every day in the lab, that allows me to learn .

vi

Abstract

Worldwide Parkinson’s disease (PD) is the second most common neurodegenerative dis-

ease with around 6.3 million cases diagnosed. This disease is characterized by a progressive

disorder of the nervous system, mainly manifested in gait and postural control impairment

that alter the functional independence in patients. Gait analysis becomes as an important

tool to determine the severity of disease as well as to orient the diagnosis. Nevertheless, such

analysis is currently highly dependent on the physician expertise as to detect some subtle

characteristic movements of the disease. Physical gait models arise as a powerful alternative

to reduce the variability in movement analysis. These models allow to emulate the progres-

sion and performance of gait patterns in different disease stages, providing information for

the selection of appropriate treatments. This thesis presents a physical model that integrates

the estimation of the center of gravity (CoG) trajectory based on trunk kinematics, and the

quantification of the symptoms severity for different PD stages. A physical gait model is

herein emulated by using a double inverted pendulum for the leg swinging and a damper-

spring System (SDP) to recreates the double support phase. This model is then adjusted

to follow a particular CoG learned for each stage. The evaluation of the CoG estimations

performed by trunk patterns was performed by comparing the resulting trajectories with

actual ones learned from subjects in stages 2, 3, and 4, achieving a correlation coefficient

of 0.88, 0.92 and 0.86, respectively. The parameters from the model were adjusted to gen-

erate similar trajectories to the ones previously estimated. The frechet distance between

the trajectories generated by the model and the CoG estimation is 0.07, 0.09, 0.29 for each

stage.

Keywords: Parkinson’s disease, Pathologic gait patterns, Gait modelling, trunk

bending patterns.

vii

Resumen

A nivel mundial, la enfermedad de parkinson (EP) es la segunda enfermedad degenerativa

mas comun, con cerca de 6.3 millones de casos diagnosticados. Esta enfermedad se carac-

teriza por un desorden progresivo del sistema nervioso que se manifiesta principalmente en

alteraciones de la marcha y del control postural que limita la independencia funcional de

los pacientes. El analisis de los patrones en la marcha se ha convertido en una herramienta

util para determinar la severidad de la enfermedad, ası como para orientar el diagnostico.

Sin embargo, este analisis es altamente dependiente de la experticia del evaluador, especial-

mente para la deteccion de algunos movimientos sutiles caracterısticos de la enfermedad. Los

modelos fısicos emergen como una alternativa sobresaliente para disminuir la variabilidad

en el analisis de movimiento. Los modelos permiten emular la progresion y los patrones de

la marcha en diferentes momentos de las enfermedades, proporcionando informacion para

la seleccion de tratamientos adecuados. Esta tesis presenta un modelo fısico que integra

la estimacion de la trayectoria del centro de gravedad (CoG) basada en la cinematica del

tronco y la cuantificacion de la severidad de los sıntomas en los diferentes estadıos de la EP.

El modelo fısico propuesto utiliza un doble pendulo invertido para la fase de apoyo simple

y un sistema resorte-amortiguador para la fase de doble apoyo. Este modelo es ajustado

para seguir un CoG especıfico, definido para cada uno de los estadios. La evaluacion de la

estimacion del CoG realizada por los patrones de tronco se realizo comparando las trayec-

torias resultantes con trayectorias aprendidas de sujetos en estadios 2, 3 y 4. Se obtuvo un

coeficiente de correlacion para la estimacion del CoG de 0.88, 0.92 y 0.86, respectivamente.

Los parametros del modelo fısico se ajustaron para generar trayectorias cercanas a los CoG

estimados anteriormente, obteniendo una distancia de frechet entre las curvas generadas por

el modelo y la trayectoria estimada del CoG de 0.07, 0.09, 0.29.

Palabras claves: Enfermedad de parkinson, Patrones de marcha patologicos,

Modelamiento de la marcha, Inclinacion de tronco.

Contents

Acknowledgments v

Abstract vi

1 Theoretical Framework 2

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Balance assessment in Parkinsonian gait . . . . . . . . . . . . . . . . 3

1.1.2 Quantification and gait modeling . . . . . . . . . . . . . . . . . . . . 3

2 Fusing trunk bending patterns 6

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Proposed Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 The Physical Gait model . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.2 Learning a CoG from trunk bending patterns . . . . . . . . . . . . . 9

2.2.3 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Evaluation and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Quantification of gait patterns 14

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 The CoM trajectory and its incidence in the evaluation of PD progression . . 16

3.2.1 The role of Physical Gait models at simulating pathological patterns 16

3.2.2 Damper-Spring Pendulum (SDP) . . . . . . . . . . . . . . . . . . . . 17

3.2.3 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Conclusions and Perspectives 22

1 Theoretical Framework

1.1 Introduction

Parkinson’s disease (PD) has been diagnosed in around of 6.3 million people worldwide

[17, 38], representing a major public health challenge. This disease nowadays implies one of

the most high healthcare expenses because of the reduction of productivity, drug treatment,

the outpatient care, among others [50]. PD is characterized by the lost of dopamine neuro-

transmitter that affects the connection of brain areas located in the basal ganglia, producing

inability to control and coordinate movements [42, 58]. In fact, the effect of the decreas-

ing of dopamine concentration in around of 60 − 70 % can be observed as resting tremor,

rigidity, bradykinesia and balance impairment [7, 33]. Hence, the PD diagnosis is based on

the analysis of the sum up of symptoms as the reduction of the frequency and amplitude of

spontaneous movements, as well as, postural instability during positions against gravity.

Classically, the motor changes produced by PD progression have been evaluated by clinical

rating scales as the Hoehn and Yahr staging [3]. This scale defines the motor decline by

setting five broad categories that highlight the characteristics of movement alteration with

the major impact in the performance of daily living activities. In the initial stage the motor

impairment appear focally in one limb while for the second stage is defined for bilateral

impairment [61]. The third and fourth stages are characterized by moderate and severe

affectation of balance. In the advanced five stage the motor impairments alter the gait

performance and it is necessary a external aid. The assessment of PD progression with this

scale allows to register only coarse motor changes [70, 43], limiting the analysis of motor

patterns among the stages and introducing a natural inter and intra observer variability.

Consequently, Gait analysis has been an important tool in the assessment of motor patterns

in PD progression. In such case, a set of locomotion features such as, swing time, stride

time, and left/right asymmetry, are coded to describe a particular gait PD pattern [4].

This evaluation is commonly carried out by observing the locomotion of a patient during

a short period of time and namely under very restrictive scenarios, i.e., reduced space.

These conditions limit the detection of subtle motion changes, specially in a large number of

patterns[52]. One of main drawback in human gait analysis is that only consider local and

independent patterns of the lower limb dynamics. Additionally, such analysis ignores the

interaction with the other parts of the body as axial structures (trunk) which can be useful

to determine balance and equilibrium status or other associated impairments.

1.1 Introduction 3

1.1.1 Balance assessment in Parkinsonian gait

The CoG response during time is associated to the alternated pendular movement of the

lower limbs, being the main pattern studied in gait analysis. Despite of the importance of

lower limbs to produce motion, current analysis omit the force interaction produced by the

central and upper part of the body. In fact, under the control loop to maintain a stable and

efficient gait, the upper body play a fundamental role because the trunk muscles minimize

the movement produced by the lower limbs, stabilizing the spine and the head [9]. Some

authors have shown that this trunk activation anticipates imbalance due to gait performance

and stabilizes spine segments in a top/down manner(from cervical to lumbar spine)[54].

The balance impairment, defined mainly as the losing of muscles strength in trunk, alters

the ability to maintain the body’s equilibrium under static and dynamic conditions. This

alteration constitutes the cardinal motor symptom in PD, namely present in populations with

the faster evolution and lower response to the pharmacological treatment [19]. This balance

lost is progressive altered and increase the risk of falling [51], and reduce the quality of life

[2, 62]. Trunk bending observations such as forward trunk inclination, lateral bending and the

pelvic obliquity are essential patterns that allows to characterize balance state and coarsely

determine intervention strategies [26, 65],[8],[66]. Currently, such patterns are measured in

sagittal and coronal plane under specific tasks like sitting or standing to assess postural

instability in PD [1]. However, these preliminary studies lost important correlation of such

patterns with lower limbs variables during gait, for instance, the dynamic stabilization cost

by abnormal behaviors of the trunk [68].

1.1.2 Quantification and gait modeling

The relationship between trunk bending patterns and lower limbs kinematics allows for

instance the understanding of the coordinated actions between the stabilization produced in

axial body segments and the dynamics of distal body parts. To describe these axial and distal

patterns during gait, there is available diverse kind of information such as kinematic, that

register the body segments motion in space, kinetic, that quantify the relations between

action-reaction forces, moments and powers of each body segment and muscle activation

variables that evaluate the electrical muscle activity[11]. These evaluations produce several

data from different structures that have to be compared and correlated to obtain useful

information to take actions in clinical practice. However, as it is a demanding task, it is not

usually consider to plan treatments or register results. Then, the assessment of gait patterns

falls in the expertise of the physician when observing patient’s walk. Human gait models

emerge as an option to obtain reproducible and objective information that might predict

and emulate the patient patterns, supporting thereby diagnosis and gathering together the

elements to properly follow up the disease evolution.

Many gait models with different complexity levels have been introduced in the literature,

4 1 Theoretical Framework

some of the more complex are neuromuscular models that are based on the concept of a

central pattern generator(CPG) responsible for the generation and control movement. This

concept motivate the emulation of human neural circuits that can produce rhythmic pat-

terns of neural activity without receiving rhythmic inputs[32]. Although some applications

in dynamic simulators uses this concept for biomedical problems, the concept of the CPG

in human locomotion is a matter of discussion. On the other hand, Musculoskeletal com-

puter models consider the musculoskeletal system as complex mesh of muscles and bone

segments, and take into account physical aspects such as muscle tension and parameters

that represent muscle properties (length, strength), obtained experimentally from dynamic

electromyography and the measured torque[14, 31]. These models require many real data

and expert knowledge to tune manually a large number of parameters, limiting their use in

routine clinical practice.

The most basic gait models are dedicated to describe the global body dynamics by using

physical representations such as a pendulum model or a mass-spring systems [34]. The

pendulum-gait model built from stiff-legged [40] simulates the center of mass (CoM) trajec-

tory during a period of the stance limb, allowing to establish a basic energy transfer analysis

during motion. This model is a very basic representation which misses the leg description and

only involves a structural rigid representation. A complementary mechanism that represents

the lower limb structure as a coupled pendulum has been also proposed [21], but under the

strong assumption that the human locomotion only depends on some basic mass and length

relationships. Alternatively, motion models based on spring-mass systems have been also

used for representing the gait but only when particular patterns are described, such as the

heel strike and the double support phase [40, 25]. Geyer et al [24, 37] proposed a structural

gait model including a pendular system, coupled to a spring mass and a radial structure that

reduces the friction during movement, allowing to analyze how the speed variation during

normal gait affects the leg stiffness. This simple model properly fitted the walking in young

and old people, observing that stiffness and damping may increase with the speed, but with

greater variations in older people [30].

This thesis has contributed to the construction of a computational model to quantify motor

patterns in parkinsonian gait, using complementary information from the upper part of the

body. It provides information that allows the analysis, interpretation and visualization of gait

disturbances in the progression on PD. As a first step, the strategy consists in introducing

trunk bending information to changes in the CoG trajectory, see chapter 2. A contribution

weight was obtained from a linear combination of three trunk patterns for the estimation of

the CoG in each PD stage. Afterwards, this CoG trajectory is tracked by a physical gait

model in the whole gait cycle, where, the model parameters (k and b) are used to aid the

clinician to quantitatively describe this pathology, see chapter 3. The physical gait model

consist in coupling two different systems, the double inverted pendulum that emulates the

leg swinging for the single support phase and a damper-spring System (SDP) that recreates

1.1 Introduction 5

both legs in contact with the ground for the double phase. The model parameters obtained

show discriminating results among the stages and have a physiological representation.

2 Simulation of parkinsonian gait by

fusing trunk learned patterns and a

lower limb first order model

Presented on the “10th International Symposium on Medical Information Processing and

Analysis” SIPAIM 2014, October 2014

Parkinson’s disease is a neurodegenerative disorder that progressively affects the movement.

Gait analysis is therefore crucial to determine a disease degree as well as to orient the

diagnosis. However, gait examination is completely subjective and therefore prone to errors

or misinterpretations, even with a great expertise. In addition, the conventional evaluation

follows up general gait variables, which amounts to ignore subtle changes that definitely

can modify the history of the treatment. This work presents a functional gait model that

simulates the center of gravity trajectory (CoG) for different parkinson disease stages. This

model mimics the gait trajectory by coupling two models: a double pendulum (single stance

phase) and a spring-mass model (double stance). Realistic simulations for different parkinson

disease stages are then obtained by integrating to the model a set of trunk bending patterns,

learned from real patients. The proposed model was compared with the CoG of real parkinson

gaits in stages 2, 3, 4 achieving a correlation coefficient of 0.88, 0.92 and 0.86, respectively.

2.1 Introduction 7

2.1 Introduction

Parkinson’s disease (PD) is a neurodegenerative disorder that affects more than 6.3 million

of people worldwide[29]. A main clinical manifestation of this disease is the alteration of

gait patterns, namely: shuffling steps, reduced walking speed and loss of balance. This last

alteration is produced by the poor response of certain muscles and the deficient coordination

between the structural system and neuromotor commands, leading to an alteration of the

posture when the trunk bends forward. Normal and pathological gaits include complex inter-

actions between the neuromuscular, the musculo-tendinous and the osteoarticular systems

[18],[27]. In spite of this complexity, the following up and prognosis of parkinson disease

are limited by the physician experience, introducing the consequent inherent inter-expert

variability [69]. Hence, reliable, efficient and reproducible physical gait models are required

to quantify the disease and improve the treatment planning of parkinson disease.

Many models have been proposed in diverse areas[47],[13] to describe normal gait patterns.

In general physical representation are used to represent the dynamic of musculoskeletal

structure and a coupling control that emulate the neuromotor commands [59],[63]. However

, these models are limited to simple and restrictive representations of normal trajectories

that do not include abnormal or pathological patterns. An usual gait model is the coupled

pendulum system which mimics the single stance phase but misses important gait phases such

as the heel strike and the double stance phase [21]. The mass-spring system has simulated

human movements such as running, but under some restrictions w.r.t to real gait patterns

[55]. Complementary approaches [48] couple pendulum and physical models to represent

normal and pathological movements. Nevertheless this gait model learns only from lower

limb patterns, ignoring important motion features of the parkinson disease like the trunk

bending.

The main contribution of this work is a coupled physical gait model that learns trunk bend-

ing patterns and simulates different stages of the parkinson disease. The proposed model

mimics the single stance phase with an oscillating trajectory represented as a coupled dou-

ble pendulum while the double stance phase is approximated by a spring mass system. The

parameters of the double stance phase are learned from a set of trunk bending patterns.

2.2 Proposed Approach

The pipeline of the proposed approach is illustrated in Figure 2-1. The single stance is

represented by a coupled-pendulum model while the double stance is simulated as a spring

mass system. Then, the parameters of the model are learned from a linear combination of

trunk bending patterns.

8 2 Fusing trunk bending patterns

Figure 2-1: Proposal Method Pipeline

2.2.1 The Physical Gait model

The gait Cycle is composed of two phases: The single support, which constitutes the 70-

80% of the cycle, and the double support that constitutes about 20-30%. In this work, a

lower limb gait model [48] fully describes the gait cycle during the single support using a

coupled pendulum trajectory and a spring-mass system during the double stance. These

representations are as follows:

The Single Stance Phase: a pendular CoG trajectory

During the single gait stance, a fixed limb supports the body while the other limb swings

forward, using the hip as a fix pivot . A coupled double pendulum system simulates such

movement, See figure 2-1(a), i.e., the mass m, representing the lower limbs, moves forward

a mass M , the upper part, producing the illustrated oscillatory CoG trajectory. The gait

model corresponds to a coupled system of two non-linear differential equations:

β(1 − cosφ)(3θ − φ) − β sinφ(φ2 − 2θφ) + (g sin θ

l)(β(sin(θ − φ) − 1)) = 0

θ(β(1 − cosφ)) − βφ+ βθ2 sinφ+ (βg

l) sin(θ − φ) = 0 (2-1)

where β = m/M , θ is the angle of the stance leg at the particular time t with respect to the

slope and φ is the angle between the stance leg, l is the leg length and g is gravity.

2.2 Proposed Approach 9

The Double stance phase

During the double stance, a forward momentum of the body is produced when the limb

contacts the ground. In this phase, the hip is initially flexed, facilitating the propulsion of

the (opposite) fixed limb (toe-off). The equation is:

Mx = llx− lr(d− x)

My = lry + lry − gM (2-2)

where g is the gravity,d is the inter-leg distance, x and y are the positions in x and y planes,

ll and lr are the left and right legs, respectively and their length changes are:

ll = k(l0√

x2 + y2 − 1)

lr = k(l0√

(d− x)2 + y2 − 1) (2-3)

where k is the spring constant that determines the change of the leg length during the double

support, modeling certain parkinson patterns, for instance, the speed and step length.

2.2.2 Learning a CoG from trunk bending patterns

The balance impairment, a main PD sign, is produced by a progressive weakness of some

postural muscles, debilitating postural adjustments [60] . In consequence, the trunk bending

results a compensation mechanism to maintain the equilibrium and an important sign to

characterize parkinson disease stages [46, 44, 36]. By calculating the trunk bending, it is

possible to follow the progressive muscle imbalance that generates a lateral deviation and

furthermore, to describe the imbalance of the lower limbs by the pelvis obliquity. The

herein proposed work achieves much more accurate PD simulations by introducing trunk

bending information. For doing so, the trunk forward inclination (TFI) x1,t, the trunk

lateral bending(TLB) x2,t, the pelvis obliquity (PO) x3,t were captured and delineated from

the sagittal and coronal views as suggested in [20, 41].

Then, the CoG trajectory was estimated as a linear combination of the three trunk trajec-

tories: CoG(t) =∑

i=1...3Wi,txi,t, where Wi,t is a contribution weight. The estimated CoGCoG(t), for the different PD stages, is then used as a ground truth to map the different CoG

trajectories described by the physical model. A newton-raphson method was used to find the

k parameter describing the most similar CoG w.r.t the learned CoG(t) for the different PD

stages. The similarity between the CoG curves was computed as a simple euclidean metric

of both trajectories, during a gait cycle.

10 2 Fusing trunk bending patterns

2.2.3 Dataset

Data used in this work include a total of 24 patients diagnosed with PD in stages 2, 3

and 4 [53]. These patients were captured in the gait laboratory of Universidad Nacional de

Colombia, under a plug in gait Vicon protocol. For each patient, it was recorded a gait cycle

from IEEE cameras (320 × 240 and 30 fps) in sagittal and coronal planes. Patients signed

an informed consent previously approved by ethics committee of the school of medicine of

Universidad Nacional de Colombia according to the Declaration of Helsinki.

StagesNumber of

AgeVideos

PD 2 6 64.6 ± 7.44

PD 3 7 65.5 ± 5.5

PD 4 4 70.2 ± 8.92

Table 2-1: Dataset characteristics

2.3 Evaluation and Results

The trunk learned parameters by PD stages, are shown in figure 2-2. Evaluation was carried

out by comparing the estimated CoG trajectory w.r.t the average of real CoG trajectories in

the different stages. The model uses the trunk patterns to match a specific CoG trajectory.

The learned k parameters for the model are reported in table 2-2. This k parameter increases

for advanced levels of PD, following the stretch of the limbs and emulating the stiffness and

slow motion of the PD.

PD Stages PD 2 PD 3 PD4

K value estimated 136.2 ± 60.6 197.6 ± 65.1 280 ± 28.28

Table 2-2: Values of constant k estimated by stages

Quantitative evaluation was performed using a standard correlation coefficient between the

estimated CoG and the averaged real trajectories, i.e., the ground truth. The correlation

coefficient measures the trend of two signals and globally estimates their similarity. In Figure

2-3, it is illustrated in blue, the estimated CoG, and in black, the ground truth during a

gait cycle for different PD stages.

2.4 Conclusions 11

Figure 2-2: Trunk learned Parameters by stages

In table 2-3, it was reported the PD correlation for the different stages, showing in average

an 0.891 with a standard deviation of 0.0293. The results obtained in this preliminary work

suggest the model is capable of simulating complex trajectories that may characterize the

disease with only two parameters.

PD Stages PD 2 PD 3 PD 4

Coefficient Correlation 0.8839 0.9242 0.8672

Table 2-3: Correlation coefficient of the COG estimation from trunk data vs real data

2.4 Conclusions

This paper presents a novel approach that simulates the center of gravity trajectory (CoG)

for different parkinson disease stages. The whole strategy consists in estimating the CoG

12 2 Fusing trunk bending patterns

Figure 2-3: Comparison of CoG trajectories between the mean curve estimated from trunk

data and real trajectories obtained from videos

2.4 Conclusions 13

by integrating a set of trunk bending patterns learned from real patients with a very simple

lower limb model. The gait results characterized with a minimal number of parameters that

are entailed with physical meaning and can be used to interpret and correlate different stages

of this complex disease.

3 Quantifying the parkinson’s disease

progression by simulating gait patterns

Presented on the “11th International Symposium on Medical Information Processing and

Analysis” SIPAIM 2015, November 2015

Modern rehabilitation protocols of most neurodegenerative diseases, in particular the Parkin-

son Disease, rely on a clinical analysis of gait patterns. Currently, such analysis is highly

dependent on both the examiner expertise and the type of evaluation. Development of eval-

uation methods with objective measures is then crucial. Physical models arise as a powerful

alternative to quantify movement patterns and to emulate the progression and performance of

specific treatments. This work introduces a novel quantification of the Parkinson disease pro-

gression using a physical model that accurately represents the main gait biomarker, the body

Center of Gravity (CoG). The model tracks the whole gait cycle by a coupled double inverted

pendulum that emulates the leg swinging for the single support phase and by a damper-spring

System (SDP) that recreates both legs in contact with the ground for the double phase. The

patterns generated by the proposed model are compared with actual ones learned from 24 sub-

jects in stages 2,3, and 4. The evaluation performed demonstrates a better performance of

the proposed model when compared with a baseline model(SP) composed of a coupled double

pendulum and a mass-spring system[48]. The Frechet distance measured differences between

model estimations and real trajectories, showing for stages 2, 3 and 4 distances of 0.137,

0.155, 0.38 for the baseline and 0.07, 0.09, 0.29 for the proposed method.

3.1 Introduction 15

3.1 Introduction

Parkinson disease (PD) affects around 6.3 million people worldwide[29]. This pathology is

mainly characterized by movement alterations such as loss of gait automaticity and postural

imbalance [64]. The analysis of the Parkinson gait pursuits the disease characterization and

the follow up of the disease progression[57]. However, this evaluation is highly dependent

on the physician expertise, with the consequent inter and intra observer variability. Fur-

thermore, in practice, the time devoted to clinical examination usually results too short as

to detect subtle motion changes that might be determinant with respect to the disease pro-

gression [52]. Standardization of a particular evaluation requires the development of metrics

that allow an accurate and reproducible comparison between different gaits, a difficult task

when the correspondence between several patterns must be temporal.

Physical gait models emerge as reliable and reproducible methods that can be used as metrics

since they achieve an accurate description of a set of kinematic patterns during locomotion.

The physical models facilitate visualization of biomarkers like the center of gravity, an im-

portant parameter hardly estimated when physicians perform an observational evaluation.

In the literature, many gait models with different complexity levels have been introduced.

Some complex models predict muscle-tendon forces as well as their contribution to joint

accelerations [28]. A main drawback with these models, is that they require an exhaustive

tuning of a large number of parameters as well as prior expert Knowledge e.g. three dimen-

sional bone surface geometry and muscle geometry [45]. This process is highly dependent on

the expert knowledge, while the obtained information is specific for pathology and motion

patterns. On the other hand, low complexity models represent the gait dynamics with global

relationships between very simplified body structures [34] as the inverted pendulum system

[21], still limited when emulating only the simple gait stance. Attempting some improve-

ment for describing the gait, previous works have coupled soft tissue representations to the

inverted pendulum, extending the emulation to the double support phase. These models

have been useful when a general gait description is required, e.g. Geyer et al [24, 37] pro-

posed a pendulum system coupled to a spring mass and a radial foot structure that simulates

the speed variation during normal gait. Afterwards, Hong et al [30] observed the spring-like

leg dynamics in two different age groups, obtaining a different stiffness in both groups. A

spring-mass system coupled to a pendulum, was evaluated in normal and pathological gaits

[48], obtaining different rigidity parameters in normal, PD and crouch gait. These meth-

ods however have been limited to explain normal dynamic patterns, or barely a difference

between normal and pathological stages, but still too far from emulating different PD stages.

This work introduces a novel physical model that determines different PD stages by simu-

lating the gait patterns during a whole gait cycle. The model represents the single stance

phase with a double inverted pendulum while the double stance phase is approximated by

a damper-spring mass system. This paper is organized as follows. Section 2 describes the

proposed method and section 3 presents the results and conclusions.

16 3 Quantification of gait patterns

3.2 The CoM trajectory and its incidence in the

evaluation of PD progression

The CoG is the main gait biomarker, it summarizes main interactions among the body

segments, the external forces and the central neuro-commands[16, 49, 56]. Figure 3-1a

shows the CoG ground truth during a single gait cycle, composed of two steps, one per leg.

Each step starts by the double support phase (DS) followed by the single support(SS) period.

During the DS, the CoG slightly falls down and returns to the initial position, swinging the

body weight from back to front. In the next SS phase, the leg from behind generates a

propulsive force that facilitates the leg elevation and the forward CoG displacement. This

leg then starts the forward swing, that ends when the foot touches the floor.

When compared with normal trajectories, the Parkinson CoG shows a limited vertical dis-

placement for both phases of the cycle. According to Chastan et al[10], this alteration may

be caused by a diminished postural stabilization control and an increased body verticality.

Furthermore, vertical displacement and step duration is asymmetrically observed for both

sides [6]. Hence, the progressive PD motor impairments such as tremor, slowness of move-

ment, stiffness, and balance alterations [67],[39] produce a mark in the CoG trajectory that

become more evident as long as the pathology progresses, see figure 3-1b.

The CoG trajectories in PD were obtained from the analysis of a parkinsonian gait dataset.

An expert tracked the CoG by the sacral marker method[22] and the x, y coordinates were

obtained using an open source video analysis software [12]. The CoG trajectory depends on

the patient height and is expressed as a percentage. The trajectories are normalized in a

range between -1 to 1.

The present work quantifies the PD stages by simulating the CoG using a physical gait

model. For doing so, real CoG trajectories by stages were obtained from a Parkinsonian gait

dataset, and the proposed spring-damper pendulum estimates the CoG trajectories. Finally

the Frechet distance evaluates the similarity between real and the estimated curves.

3.2.1 The role of Physical Gait models at simulating pathological

patterns

Structural physical gait models have emerged as descriptor of the walking dynamic by sim-

ulating the CoG trajectory with known relationships among masses and lengths, describing

motion by simple numerical and deterministic relationships. The main advantage of these

models is that they use few parameters to describe the complex dynamics and establish nat-

ural relationships among multiple displacements and forces. The most basic and important

gait model is the inverted pendulum model[21], a simple mechanical system that represents

the swing of one leg over the other, supporting the entire body weight, representing only the

single support phase. However, subsequent works have used additional systems that comple-

ment the double support phase representation that is missing in the previous approach, e.g.

3.2 The CoM trajectory and its incidence in the evaluation of PD progression 17

(a) Ground truth of normal CoG

trajectory[35].

DS: double support, SS:single

support

(b) Mean curve of the CoG trajectory

in PD

different stages.(PD2,PD3,PD4:

PD stage 2,3 and 4)

Figure 3-1: CoG trajectory in normal and PD

Mass-spring models. These models were initially used to describe hopping and bouncing like

gait models[15],but, Geyer et al [24] in 2006 evidenced that compliant legs in a spring-mass

model, are essential to obtain the basic walking mechanics.

3.2.2 Damper-Spring Pendulum (SDP)

Figure 3-2: Spring-Damper Pendulum model

This model fully describes the center of gravity trajectory during a gait cycle. In the single

support phase, a fixed limb supports the body weight while the other limb swings forward,

using as pivot the mass(M) that represents the hip and the upper part of the body, see figure

3-2. The CoG dynamic in this walking phase is then represented as an oscillatory trajectory

described by a system of two non-linear differential equations as:

β(1 − cosφ)(3θ − φ) − β sinφ(φ2 − 2θφ) + (g sin θ

l)(β(sin(θ − φ) − 1)) = 0

18 3 Quantification of gait patterns

θ(β(1 − cosφ)) − βφ+ βθ2 sinφ+ (βg

l) sin(θ − φ) = 0 (3-1)

where β = m/M , θ is the angle of the stance leg at the particular time t with respect to the

slope and φ is the angle between the stance leg, l is the leg length and g is gravity.

The double stance is represented by a damper-spring mass system. In this phase, the dy-

namic can be understood as the complex interaction of forces produced by passive elements

e.g. tendon, aponeurosis and active elements such as the muscles. From the muscle mod-

elling standpoint, Hill [5] proposed an analogy of these elements with components such as

springs and dampers. The passive elements show elastic characteristics as springs, and with

respect to the active elements, when muscles shorten they spend some of their active force

in overcoming an inherent resistance[23], a similar scenario to what is observed when a pis-

ton shock must be absorbed (damper). In this model, the spring generates the oscillatory

CoG behavior and the damper restrains the excessive CoG motion. The heel strike and the

propulsive action of the opposite limb produces a forward body momentum. The damper-

spring complex represents the leg and receives the body weight, compressed during the first

half of the double stance phase and rebounded during the second half. The equations of

motion for this phase are:

Mx− bx− llx+ lr(d− x) = 0

My − by − lly + lry = Mg (3-2)

where g is the gravity,d is the inter-leg distance, x and y are the positions in x and y planes,

b is the damper constant, ll and lr are the left and right legs, respectively and their length

changes are:

ll = k(l0√

x2 + y2 − 1)

lr = k(l0√

(d− x)2 + y2 − 1) (3-3)

k expresses the spring stiffness, which, determines the change of the leg length during the

double support.

3.2.3 Experimental setup

Data used in this work includes a total of 24 patients diagnosed with PD in stages 2, 3 and 4,

the number of patients by group are 11, 9 and 4 respectively. These patients were captured

in the gait laboratory of Universidad Nacional de Colombia, under a plug in gait Vicon

protocol. For each patient, 6 gait cycles were recorded using IEEE cameras (320 × 240 and

30 fps) in the sagittal plane. Patients signed an informed consent previously approved by

ethics committee of the school of medicine of Universidad Nacional de Colombia, according

to the Helsinki Declaration.

3.3 Results 19

3.3 Results

The evaluation was carried out by the difference of the mean of the CoG estimated from

the model proposed w.r.t the mean of the real curves obtained for each of the PD stages.

Figure 3-3 shows the graphical results per stage, the blue line is the real trajectory and the

red dotted line is the estimation from the model. In stage 2, see figure 3-3a, the estimation

of the model is close to the real trajectory and the slight decrease in the amplitude during

the second part of the gait cycle is properly approximated by the model. In stage 3, see

figure 3-3b this effect is even more evident, the amplitude asymmetry is reproduced by the

model, and also a phase shift in the second half of the gait cycle produced by the earlier

presentation of the CoG ascent during the second cycle half. The real trajectory shows that

one step covers more percentage of the GC than the other. Finally in stage 4, see figure

3-3c, it is observed a larger difference compared with previous stages, however as in PD2,

the SDP model shows a slight amplitude improvement, especially during the double support

phase (0-15 and 50-65 % of GC). In this stage the estimation is a challenge, as the trajectory

does not show a strong periodic and sinusoidal form as for the previous stages.

(a) PD Stage 2 (b) PD Stage 3

(c) PD Stage 4

Figure 3-3: Real CoG trajectories Vs CoG estimation from SP and SDP model for different

PD stages

Quantitative evaluation was performed using the Frechet distance (FD) between the aver-

20 3 Quantification of gait patterns

aged real trajectories, and the estimation of the CoG achieved by the SDP and the baseline

method (SP)[48]. The FD measures the length of the shortest path between two points that

are simultaneously moving through the two curves. The more similar are the two curves,

the smaller the distance and therefore the close to zero they are.

The table 3-1 reported the PD Frechet distance for the different stages. For PD2, the FD in

general shows a difference between the models estimation, having a 0.137 for SP and 0.07 for

SDP. For PD3, SP is 0.155 and SDP is 0.93. In stage 4, as it was expected the FD present

the highest values, having for SP 0.38 and for SDP 0.29. In all stages the FD shows an

performance increase of the SDP when compared to SP for the CoG estimation in different

PD stages. These preliminary results support the role of the spring-damper in the physical

models to simulate pathological gait patterns.

Table 3-1: Frechet distance for spring pendulum and spring damper pendulum pendulum

in the CoG estimation

PD 2 PD 3 PD 4

SP 0.137 0.155 0.38

SDP 0.07 0.09 0.29

Finally table 3-2 shows the parameter values obtained to estimate the CoG in DSP model.

The k and b parameters reflect in a general way the changes produced during the progression

of this pathology. In the model the k value is higher as the disease progresses, and at the same

time b value shows a greatest value in the highest stage that can be interpreted physiologically

as the resistance increment when a movement is produced.

Table 3-2: k and b parameters estimated by stages (SDP)

PD 2 PD 3 PD 4

k 130 135 161.6

b 0.73 1.75 1.83

3.4 Conclusions

This paper presents an performance analysis of the SDP gait model when simulating the

center of gravity trajectory (CoG) for different stages of Parkinson’s disease. Based on the

results obtained with the Frechet distance, in general shows discriminating results, giving to

3.4 Conclusions 21

the SDP a better performance in the 3 stages when it is compared with a baseline method.

Graphical analysis shows the capability of SDP to approximate real trajectories when it

presents amplitude asymmetries. Stage 4 presents the lower similarity results by large CoG

disturbances. Finally, the model parameters (k and b) have a physiological representation

and the value obtained might effectively aid the clinician to quantitatively describe this

pathology .

4 Conclusions and Perspectives

Conclusions

This thesis has explored the problem to quantify gait motor patterns in PD progression in-

cluding new source of information from the upper body. A main contribution has introduced

the trunk bending information to changes in the CoG trajectory, that can be used as a basis

in physical gait models for the simulation and quantification of gait patterns. The integration

of trunk kinematics with gait patterns as the CoG is essential to understand gait alterations,

especially in PD where balance disorders have major impact on functional independence. Ad-

ditionally, the refinement of physical gait models allows an accurate quantitative description

of the disease with physiological interpretability that can support clinicians in the assess-

ment of PD progression and therapeutic interventions. In this research was observed an

inherent problem of Parkinson’s Disease, the high variability between the patients produced

by the underlying motor alterations and compensation mechanisms, what makes modeling a

complex process, but necessary for the disease understanding. Finally, this work contributed

to the building of a dataset of parkinsonian gait that can be useful in the ongoing research

in this field of knowledge.

Perspectives

For health professionals, the possibility of obtaining quantitative and complementary infor-

mation about the patients, refines the medical decision making, resulting in more accurate

treatments that impact directly on the patient quality of-life. Further studies should be

undertaken to achieve the objective of constructing computational methods for the quantifi-

cation of motor patterns in clinical areas and to become an accessible tool in the medical

consultation and rehabilitation fields. The development of this tools will assess the objec-

tively comparison of the information inter e intra patient enabling the better understanding

of the natural history of the disease and the development of strategies to treat the disease

symptoms. Further researches can taking into account issues as: Larger number of subjects,

specially from the first and fourth PD stages, the development of more robust computa-

tional models, that do not require large infrastructure or complex equipments and the the

preparation of these tools for implementation.

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