A 3D PHYSICS-BASED MODEL TO SIMULATE NORMAL

AND PATHOLOGICAL GAIT PATTERNS

Christian Cifuentes, Fabio Mart

ınez and Eduardo Romero

BioIngenium Research Group, Universidad Nacional de Colombia, Bogot

a, Colombia

Keywords:

Physics-based Modeling, Human Gait Animation, Motion Analysis, Rehabilitation Engineering.

Abstract:

This article presents a novel 3D physics-based human gait model that allows to quantify and simulate the

dynamic patterns of normal and pathological movements in the sagittal and coronal views, using an enhanced

inverted pendulum approach. The method outperforms the classic planar representations that do not consider

important gait phases like the double stance phase and the heelstrike, crucial in proper gait descriptions on

clinical routine. The model was assessed by simulating gait cycles and comparing the obtained trajectories

with actual normal and pathological gait data. Results showed that the normal and pathological kinematic

patterns generated by our model are highly similar to the actual data, obtaining an accuracy of about 87%.

1 INTRODUCTION

The gait is one of the most broadly studied motion

in very different domains such as medicine, anima-

tion or robotic (Xiang et al., 2010). This move-

ment is the result of complex interactions between

several sub-systems, which work together to gener-

ate the body dynamics that underlies the bipedal dis-

placement (Gage, 2004). This human gait patterns

are frequently disturbed in many types of patholo-

gies. In the clinical routine, a physician or rehabili-

tation expert searches pathological gait patterns (ac-

cording to her/his expertise), supporting the decision

on some statistical tests of the acquired data and in-

troducing thereby an inevitable expert-dependent bias

(Delp et al., 2007).

In addition, traditional methodologies to capture

gait patterns are very invasive and alter the natural

gait gestures which also are contaminated by cap-

ture noise. Therefore, development of gait models

achieving an accurate quantitative movement descrip-

tion has become a priority to support the physician

decisions (Fregly, 2008; Kuo and Donelan, 2010).

This work introduces a novel 3D human gait

model that generates the dynamic gait patterns in the

sagittal and coronal views observed in a clinical gait

analysis using a physics-based approach . It pro-

vides high ﬂexibility, generating a large number of

walking patterns using only a complete CoG trajec-

tory representation and the heel trajectory data ob-

taining normal and pathological gait patterns, for in-

stance the dynamics of a typical cerebral palsy gait

(Crouch gait), changing a few set of parameters. This

simple mechanic gait representation simulates the en-

ergy accumulation of different anatomical elements,

responsible for most non linear gait patterns: it uses

a double-inverted pendulum system to simulate the

single stance CoG trajectory, while the double stance

CoG trajectory is simulated by a double spring-mass

system, in both sagittal and coronal views. The ob-

tained trajectory feeds a human like-structure, which

is animated using a learned heel trajectory and a clas-

sical inverse kinematic to calculate the dynamic pat-

terns. The rest of the paper is organized as follows:

Section Related Works review similar approaches re-

lated with the model of human gait, section Materials

and Methods introduces our model, section Results

demostrates the effectiveness of the model. The last

section presents the conclusion and future works.

2 RELATED WORKS

Several models have been previously proposed for

simulating the human gait, among which the physics-

based models obtain realistics and natural representa-

tions of the human Center of Gravity (CoG).(Xiang

et al., 2010). Likewise, they properly describe the

gait from an energy standpoint, simulating the change

from the kinematic to potential energy during the gait

cycle and taking into account the movement depende-

197

Cifuentes C., Martínez F. and Romero E..

A 3D PHYSICS-BASED MODEL TO SIMULATE NORMAL AND PATHOLOGICAL GAIT PATTERNS.

DOI: 10.5220/0003862701970201

In Proceedings of the International Conference on Computer Graphics Theory and Applications (GRAPP-2012), pages 197-201

ISBN: 978-989-8565-02-0

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

nce on some external interactions (Xiang et al., 2010).

One of the well known models was proposed by Gar-

cia et al. (Garcia et al., 1998) based on the passive

dynamic theory of McGeer (Garcia et al., 1998): a

double articulated pendulum system for which feet

are relatively small with respect to the trunk and the

heelstrike follows a very restrictive rule. This gait de-

scription is still limited because about a 30 % of the

gait cycle that corresponds to a double stance phase,

is completely eliminated and the CoG displacement

in the lateral axis (Y ) is not considered at all. Other

approaches included the inverted pendulum represen-

tation to describe the lateral and frontal CoG motion,

but not its vertical displacement, which is assumed

constant (Komura et al., 2004).

Other recent approaches are based on optimization

techniques and control-based models. The optimiza-

tion methods include a large number of degrees-of-

freedom for producing optimal motions while joint

force proﬁles remain subjected to a large number of

constraints(Delp et al., 2007; Fregly, 2008; Xiang

et al., 2010). These methods require relatively few

data to simulate simple human structures and pre-

dict new motions, very useful in computer graph-

ics, robotics and animation applications.The control-

based models have been commonly used on robotics

and biomechanics for designing the real-time control

in biped walking prototipes (Trifonov and Hashimoto,

2008). The main advantage of these methods is that

they approximate the actual human control systems,

allowing to simulate both normal and pathological

gaits. The neuromotor system simulation allows the

analysis of some neurological pathologies (Komura

et al., 2004), while this is computationally more ef-

ﬁcient than the optimization-based models. Never-

theless these methods are computationally expensive

and require speciﬁc knowlegde of the problem (Xiang

et al., 2010) whereby these strategies are highly sub-

jective(Xiang et al., 2010), and also require a large

group of experimental data to generate natural mo-

tions. This last drawback has highly limited its appli-

cation in clinical gait analysis because of the speciﬁc

requirements to obtain a stable and natural motion.

3 MATERIALS AND METHODS

The gait model herein proposed fully describes a

3D CoG trajectory of normal and pathological gaits.

The whole model is built upon simple mechanical

relationships, approximating the 3D CoG displace-

ment with a double-inverted pendulum for the sim-

ple stance phase, and a double spring-mass system

for the double stance. Using this physics-based repre-

sentation, we can animate an human leg structure and

simulate normal and pathological kinematic patterns.

The kinematic patterns for each case was calculated

with a classic method of inverse-kinematic, using the

CoG trajectory obtained and a learned heel trajectory

taken from some gait laboratory’s data as illustrated

in ﬁgure 1.

3.1 Sagital CoG Description

As a ﬁrst step, the CoG sagittal trajectory was com-

puted using a physics-based gait representation. The

single stance phase (one foot supporting the body)

was represented as a double-inverted pendulum. This

representation is based on the passive dynamic (Gar-

cia et al., 1998). This model is formulated as a pair of

coupled nonlinear equations: β(1 −cos φ)(3

θ −

φ) −

βsinφ(

−2θ

φ)+(

gsinθ

)(β(sin(θ −φ)−1)) = 0 and

θ(β(1−cosφ))−β

φ+β

sinφ +(

βg

)sin(θ −φ) = 0,

where β = m/M , m is the mass of each foot and

M is the body mass, θ is the angle of the support-

ing leg at a particular time t and φ is the angle be-

tween both legs. When the leg stance has been ac-

complished, the heelstrike is represented by the non

linear ruleφ(t) −2θ(t) = 0. This phase is character-

ized by the hip and knee moments generated within

this interval, important biomarkers in many abnormal

movements.

On the other hand, the double stance phase, which

starts just after the heel strike, was represented as a

double spring-mass system. This physical formula-

tion introduces attenuation as it is usually observed

in an actual CoG trajectory because of the knee rota-

tion, but it also involves an intrinsic representation of

the muscles acting during this phase. This represen-

tation is given by the following equations (Blickhan,

1989): m ¨x = Px −Q(d −x) and m ¨y = Py + Qy −mg,

where P = k(

√

−1), Q = k(

√

(d−x)

−1), m

is the body mass, x and y are the sagittal and frontal

displacement respectively, d in the step length, k is

the spring constant, l

is the spring lengh at rest and g

is the gravity constant (9.81). This physic-based rep-

resentation describes completely the CoG trajectory

and allows to have the ﬂexibility needed to generate

different kind of gaits, i.e., pathological gaits.

3.2 Coronal CoG Trajectory

A main contribution of this work is a 3D gait repre-

sentation that allows to accurately mimic pathological

motions like the pelvic balancing (Garcia et al., 1998).

The CoG trajectory in the coronal view was simu-

lated using the inverted-pendulum approach. First, we

GRAPP 2012 - International Conference on Computer Graphics Theory and Applications

198

Figure 1: Overview of our proposal. Firstly, it is computed independently the CoG trajectory in both sagittal and coronal

views. Then we built up an articulated structure and simulate the human gait using the CoG and a learned heel trajectory

using a classical inverse kinematic approach.

calculated independently the CoG motion in both the

x −z and the y −z planes (Komura et al., 2004). The

CoG trajectory was modeled by a simple inverted pen-

dulum represented by the following equation: ¨y =

Where z

is the CoG heigh at time i (same time

for the sagittal view) and g is the gravity constant

(g = 9.81) (Komura et al., 2004). Given the initial

conditions, the CoG trajectory can be described by

the following equation: y = y

cosh

+ ˙y

T sinh

Where y

and ˙y

are the initial conditions and T =

Finally, a complete 3D CoG trajectory was ob-

tained calculating independently both the sagittal and

frontal CoG trajectories.

3.3 3D Human Model Representation

This model not only describes the gait in terms

of energy, but it also introduces a ﬂexion-

extension/adduction-abduction limb description

as well as a pelvic obliquity that modify the model

dynamics. The kinematic simulation is herein carried

out using a classical inverse-kinematic method whose

resultant trajectory animates a human-like leg struc-

ture, composed of seven articulated rigid segments as

illustrated in Figure 1.

3.4 Pathological Gait Simulation

The main advantage of our proposed 3D human rep-

resentation is that it allows to simulate many kind of

movements patterns in both sagittal and coronal views

by only tuning the parameters k (the elasticity con-

stant) and d (the step length). With little change in

these parameters it is possible to simulate the CoG

changes observed in some pathological gaits and to

obtain the knee rotation and the CoG attenuation that

characterizes some pathological movements. Setting

the k ∼ 400 and d ∼ 0.7, a normal gait is simulated,

but if the k value is increased and/or the d constant is

decreased, a pathological gait, for instance the crouch

gait

that characterizes the motion of several cerebral

palsy patients (Gage, 2004) is simulated.

4 RESULTS

The evaluation was initially carried out by comparing

the CoG trajectory generated by our model with the

actual one observed from normal gait trajectories as

shown in the ﬁgure 2.

Figure 2: Calculated CoG trajectory in sagittal (top) and

coronal view (bottom).

For both sagittal and coronal views, we calculated

the correlation coefﬁcient to establish the degree of

similarity between both actual and simulated CoG tra-

jectories. The results shows that the correlation coef-

ﬁcient in the sagittal view is 0.85 ±0.056 and for the

coronal view is 0.97 ±0.013.

4.1 Simulating Normal Gait Patterns

As a second evaluation, we compared the estimated

obtained gait kinematic patterns with ground truth tra-

jectories that were obtained from normal patients, as

reported in the literature (Gage, 2004), composed of

sagittal and coronal patterns of a gait cycle.

This kind of gait is characterized by an exaggerated

knee ﬂexion.

A 3D PHYSICS-BASED MODEL TO SIMULATE NORMAL AND PATHOLOGICAL GAIT PATTERNS

199

As in the previous subsection we calculated the

correlation coefﬁcient to establish the degree of simi-

larity between both trajectories, the patterns obtained

by our method and the average of each actual normal

pattern(table 1).

Table 1: This table shows the correlation factor calculated

between both actual and simulated kinematic patterns.

Sagittal View R. Hip Flex. 0.974 ± 0.016

R. Knee Flex. 0.71 ± 0.021

L. Hip Flex. 0.968 ± 0.016

L. Knee Flex. 0.71 ± 0.021

Coronal View R. Hip Add. 0.918 ± 0.013

L. Hip Add. 0.891 ± 0.013

Pelvic Obliq. 0.876 ± 0.02

4.2 Evaluation for an Actual Pathology

As previously mentioned, one of the main advantages

of our model is the possibility of representing patho-

logical gaits by only tuning some parameters of the

spring-mass model: The elasticity constant k and the

step length d. A crouch gait pattern was simulated by

simply increasing the k constant and decreasing the

d constant for both frontal and coronal views, as is

comment in the section 3 and as shown in ﬁgures 3

and 4.

Figure 3: Simulation (top) and generated pathological pat-

terns (bottom) in the sagittal view.

Figure 4: Simulation (top) and generated pathological pat-

terns (bottom) in the coronal view.

The correlation coefﬁcient was calculated to com-

pare the similarity between the patterns obtained and

the average of the actual data. The results are shown

in the table 2.

Table 2: This table shows the correlation factor calculated

between both actual and simulated kinematic patterns.

Sagittal View R. Hip Flex. 0.9514 ± 0.012

R. Knee Flex. 0.8638 ± 0.1101

L. Hip Flex. 0.9529 ± 0.00098

L. Knee Flex. 0.8810 ± 0.0425

Coronal View R. Hip Add. 0.9188 ± 0.023

L. Hip Add. 0.891 ± 0.023

5 CONCLUSIONS

This work has introduced a mechanical gait model

which is able to mimic pathological patterns, speciﬁ-

cally a gait crouch which is characteristic of the cere-

bral palsy. This kind of models is a potential useful

tool for the physician understands the nature of a par-

ticular pattern during the gait. This kind of adapted

designs in addition can be a remarkable aide to simu-

late the evolution of a speciﬁc treatment so that treat-

ment planning is possible.

ACKNOWLEDGEMENTS

This work was partially funded by the project number

14510 of 2011 accepted by the DIB (Direccin de In-

vestigacin sede Bogot) of the National University of

Colombia.

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