COMPUTATIONAL MUSCLE REFLEX MODEL OF WHEELCHAIR

USERS TRAVELING IN MOTOR VEHICLES

Evaluation of the Motion and the Myoelectric Potential of People with Disabilities

Junichi Takano, Shigeru Aomura

System design, Tokyo Metropolitan University, Hino, Tokyo, Japan

Emiko Kikuchi

Health Science, Tokyo Metropolitan University, Tokyo, Japan

Keywords:

Muscle reﬂection model, Wheelchair, Seatbelt, People with disabilities.

Abstract:

In this study, a human motion computer model in a wheelchair was developed to evaluate the effectiveness of

a seatbelt for people with disabilities traveling in a motor vehicle. The human model was composed of two

rigid links and three masses. This model was characterized with muscle reﬂection deﬁned by Hill’s equation.

A sudden stop experiment by using a carriage on which a wheelchair was ﬁxed with a subject was performed

to obtain the human muscle parameters and to evaluate the model. Volunteer subjects including people with

disabilities participated in the experiment. The motion and muscle activity of a subject wearing a seatbelt were

simulated by this model. The muscle reﬂection of people with disabilities was stronger than that of normal

people in the case of not using a seatbelt, but in the case of using a seatbelt the muscle reﬂection of people with

disabilities was similarly weak with normal people. The result of computer simulation showed that a seatbelt

is more important for people with disabilities than for normal people.

1 INTRODUCTION

Wheelchair users traveling in motor vehicles have

been increasing dramatically. There is a need to im-

prove the safety standards for transporting wheelchair

users (ANSI/RESNA, 2002) (W.E.Fisher, 1987). The

authors carried out a questionnaire for wheelchair

users who frequently traveled in motor vehicles. The

results showed that even though they used seatbelts,

they still felt a strong insecurity during sudden car

stops (Aomura, 2007). The motion of people with

disabilities at a sudden stop should be examined more

in detail.

Computer models are quite effective and widely used

in order to simulate the human motions (Bertocci,

2001) (Bertocci, 2000), by many researchers. In re-

cent years, human motion models have been used

in simulations for crash experiments. For example,

Bertocci (Bertocci, 1999) has used a dynamic lumped

mass crash simulator to develop a model of a re-

strained occupant subjected to a 20g/30mph frontal

motor vehicle crash. And Moorcroft (Mooreroft,

1999) demonstrated that motor vehicle crashes could

be simulated with the use of MADYMO, a program

designed speciﬁcally for occupant safety analysis.

However, the model that can simulate the motion of

people with disabilities has not been developed. The

goal of this study is to make a computer model which

can simulate the motion of people with disabilities

supported by a seatbelt.

In this study, a rigid link model of a human body sit-

ting in a wheelchair was designed with muscle reﬂec-

tion characteristics to demonstrate the motion of peo-

ple with disabilities. Although normal people gen-

erally show a similar muscle reﬂection pattern, the

muscle reﬂection pattern of people with disabilities

depends on the extent of each disorder. Therefore, the

experiment was carried out on two hemiplegia sub-

jects and a quadpledia subject.

As a result, the motion of subject with disabilities

could be simulated by using muscle parameters and

this computer model was a useful tool to evaluate the

motion of wheelchair users with a seatbelt.

Takano J., Aomura S. and Kikuchi E. (2009).

COMPUTATIONAL MUSCLE REFLEX MODEL OF WHEELCHAIR USERS TRAVELING IN MOTOR VEHICLES - Evaluation of the Motion and the

Myoelectric Potential of People with Disabilities.

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 80-86

DOI: 10.5220/0001537900800086

 SciTePress

2 PHYSICAL MODEL

2.1 Rigid Link Model

A two dimensional rigid link model sitting in a

wheelchair is shown in Fig.1. This model is a three

degrees of freedom and composed of a head, a trunk

and a hip. A center of gravity for the head and trunk

is located in the center of each rigid body. A dy-

namic equation for the rigid link model is given in

equation(1).

k1 L1

c1 L2

㱔1

㱔2

Figure 1: Schematic image of a human rigid link model

ﬁxed by a seatbelt in the wheelchair.



q(t)



¨q(t) +C



q(t), ˙q(t)





q(t), A

(t)



= M



q(t), ˙q(t), a(t)



(1)

Input is the surface acceleration A

and outputs

are the horizontal displacement of lumbar spine x and

the angle of cervical and trunk θ

, θ

, C is the term

of the mass of each part and velocity of angle, D is

the term of the moment of inertia of each link, S is the

term of the tension of shoulder and waist of a seatbelt,

M is the torque of each joint generated by a muscle ac-

tivity. M is composed of an active and passive muscle

activity. a is the myoelectric potential.

2.2 The Model of a Seatbelt and the

Friction Force of a Seating Surface

For this study, the seatbelt made by synthetic ﬁbers

of polyamide was used. The seatbelt is called energy

absorbing webbing. The overhead view of the cross

section of a human body with a seatbelt is shown in

Fig.2. A human body was ﬁxed by the seatbelt with

tension S. The tension of the seatbelt S works on the

shoulder and the waist. The tension of the seatbelt is

given by Nakajima’s equation as follows.

= 2S

(1− exp(

−2x

)) (2)

where L

is the length of a seatbelt, S

is the maxi-

mum tension of a seatbelt and ε

is the strain amount

of a seatbelt.

The hip sinks down and moves forward when a

motor vehicle stops causing friction force between hip

and seating surface. The motion in the horizontal di-

rection is affected by friction force. Fig.2 shows the

frictional force between seating surface and hips. It is

difﬁcult to measure friction force by the experiment.

In this study, the friction force was calculated by using

the Kaminishi’s (Uenishi, 2005) equation(3) of static

analysis.

F f

= 0.4S

(3)

Seatbelt

Human body

fF 2=

Seatbelt

Human body

fF 2=

Reaction forceBelt

Body

;Frictional force

Reaction forceBelt

Body

;Frictional force

Figure 2: The overhead view of cross section diagram of a

human body with a seatbelt and frictional force of seating

surface.

2.3 The Muscle Activity Model

There are many reports about muscle activity. For

example, Hase carried out a computer simulation of

the human movement by using a musculo-skeletal

model (Hase, 2002). In this study, the muscle reﬂec-

tion results were obtained by using the Hill’s equation

to express the motion of people with disabilities. A

force of muscle contraction f is described by Hill’s

Eq.(4).

f = aF(l,V) (4)

Where l is the length of muscle, V is the contrac-

tion rate and a is the myoelectric potential. When the

length of muscle and the contractile rate is known, the

muscle tension force F

max

can be calculated.

max







(B−0.3V)

B+V

(l) if (V > 0)

(

−1.3V

+ 1)F

(l) if (

−B

< V < 0)

(

1.3

+ 1)F

(l) if (V <

−B

)

(5)

(l) =



F[1− K

− l)] if (l < l

)

F[1− K

(l − l

)] if (l > l

)

(6)

Where l

is the initial length of each muscle,

F is the

maximum muscle force of isometric contraction, B is

COMPUTATIONAL MUSCLE REFLEX MODEL OF WHEELCHAIR USERS TRAVELING IN MOTOR VEHICLES -

Evaluation of the Motion and the Myoelectric Potential of People with Disabilities

Figure 3: A muscle model of a sternocleidomastoid and a

splenius.

the parameter of each muscle, K

and K

are the con-

stant. The sternocleidomastoid muscle, the splenius

muscle, the abdominal muscle and the back muscles

are used to return the body to its original position.

The length of extensor and ﬂexor muscles are shown

in Fig.3.

2.4 The Model of Myoelectric Potential

The myoelectric potential is the electrical manifesta-

tion of the neuromuscular movement associated with

a contracting muscle. It is an exceedingly compli-

cated signal which is affected by the anatomical and

physiological properties of muscles (Luca, 1979).

In this study, it was assumed that the myoelectric po-

tential would be greater when the angular displace-

ment θ, the angular velocity

θ of subjects and the ac-

celeration A

of the carriage device were stronger.

The myoelectric potential is given by following equa-

tion.

a = 1− exp



−



kθ(t − τ) + b

θ(t − τ)+

(t − τ) + a

}] (7)

where k, b and c are the human muscle parameters,

τ is the time lag and a

is the steady state myoelectric

potential.

2.5 The Passive Torque

In this study, a passive torque on ligament and soft

tissue was described by Yamazaki’s passive muscle

model (Ogihara, 2000) and given in Eq.(8).

= p

exp p

(θ− p

) − p

exp p

− θ) + q

θ (8)

where q is the viscosity resistance, p

are the co-

efﬁcients that detemines angle when elasticity resis-

tance increases. p

are the coefﬁcients that deter-

mines elastic constant when ligament and soft tissue

become stiff. p

are the coefﬁcients which de-

scribes nonlinearity of an elastic resistance.

3 CRASH EXPERIMENT

3.1 The Method of Experiment

In this study, two experiments were performed. The

purpose of the ﬁrst experiment was to determine the

muscle parameters of a subject. The purpose of the

second experiment was to evaluate the motion of the

subjects and the model.

A carriage experiment device was used instead of a

motor vehicle. The carriage experiment device is

shown in Fig.4. The forward crash can simulate a sud-

den stop. A wheelchair (JIS T 9201) was attached to

a metal structure which was harnessed to the carriage

device.

Figure 4: A wheelchair ﬁxed on a carriage experiment de-

vice instead of a motor vehicle.

The acceleration of the carriage device was

measured to compare with that of a car. Fig.5 shows

the comparison of seating face acceleration between

the carriage device and a car. The carriage device

can be used instead of a motor vehicle because the

maximum acceleration and convergence time of the

carriage device matched that of a car.

A normal subject (aged 24), right and left hemi-

plegia subjects by bleeding in the brain (aged 55, 59)

and a quadriplegia subject by a cerebral palsy (aged

29) participated in the experiment. All subjects were

male. The disabled subjects were selected from many

volunteers through the cooperation of a welfare orga-

nization. All subjects signed informed consent forms.

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

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Figure 5: Comparison of seating surface acceleration of a

car and a carriage device.

The sudden stop experiment was carried out and the

seating surface acceleration was measured by an ac-

celerometer. A tensimeter was attached to the seatbelt

to measure the tension of the seatbelt. The trunk an-

gle, the cervical angle were measured by a goniome-

ter. The myoelectric potential of the sternocleidomas-

toid, the splenius, the abdominal and the muscle of

the back were measured by a myoelectric potential

sensor. Myoelectric potential sensors were attached

to the sternocleidomastoid, the splenius, the abdomi-

nal and the back muscles. To measure the sternoclei-

domastoid muscle, a myoelectric sensor was attached

between the sternoclavicularis and mastoid. To mea-

sure the splenius muscle, a myoelectric sensor was

attached one centimeter away from the ﬁfth cervical

vertebra. To measure the abdominal muscle, a my-

oelectric sensor was attached three centimeters away

from the navel. To measure the back muscle, a my-

oelectric sensor was attached three centimeters away

from the ﬁfth lumbar vertebra. Fig.6 shows the loca-

tion to attach the myoelectric sensors and goniome-

ters.

4 SIMULATION

4.1 Method

The muscle and physical parameters are need to be

determined in the muscle reﬂection model. The ﬁrst

crash experiment was performed at a low acceleration

to obtain the human muscle parameters. Both the ex-

periment and the simulation results of the myoelectric

potential were matched to determine the human mus-

cle parameters(k, b,c, a

in Eq(7)). In addition to de-

termining the muscle parameter, another crash experi-

ment was performed at a high acceleration in order to

evaluate muscle reﬂection model. The human phys-

ical parameters(height, weight) were measured. The

trunk and cervical angle were simulated by Runge-

Kutta method which based on parameters obtained.

Input was the seating surface acceleration (A

) and

(a)

(b)

(c)

(c)Accelerometer(b)Myoelectricsensor(a)Goniometer

(a)

(b)

(c)

(c)Accelerometer(b)Myoelectricsensor(a)Goniometer

Figure 6: Location to attach the myoelectric sensors, ac-

celerometers and goniometers.

outputs were the trunk and cervical angle and the my-

oelectric potential of measuring part.

4.2 Result

The relationship between simulation and experimen-

tal results of the trunk angle without/with seatbelt

is shown in Fig.7 and Fig.8. The relationship be-

tween simulation and experimental results of the my-

oelectric potential of the back without/with seatbelt is

shown in Fig.9 and Fig.10. Fig.7(a), (b), (c) and (d)

show that the trunk angle increases around 400ms and

returns to 0 degree. And, Fig.8(a’), (b’), (c’) and (d’)

show that trunk angle doesn’t incline. Therefore, the

simulation results of trunk angle without/with seat-

belt are similar to the experiment results in every sub-

ject. Fig.9(a), (b), (c) and (d) and Fig.10(a’), (b’),

(c’) and (d’) show that the simulation and experimen-

tal results of myoelectric potential increase around

400ms and return to 0 degree. And the peak time

of both results of myoelectric potential is matched.

Therefore, the motion and the muscle reﬂection of

disabled subjects could be simulated by the muscle

reﬂection model without/with seatbelt. And Fig.9(c),

(d) and Fig.10(c’), (d’) show that the muscle reﬂec-

tion of right/left hemiplegia subjects without seatbelt

is larger than that of using seatbelt.

COMPUTATIONAL MUSCLE REFLEX MODEL OF WHEELCHAIR USERS TRAVELING IN MOTOR VEHICLES -

Evaluation of the Motion and the Myoelectric Potential of People with Disabilities

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㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋

Figure 7: Comparison of the result of computer simulation

with crash experiment in measuring of trunk angle without

seatbelt.

4.3 The Calculation of the Seatbelt

Tension

The tension of a seatbelt and horizontal displacement

of the subjects were simulated in order to evaluate the

effectiveness of a seatbelt when the car stops sud-

denly. The acceleration change by sudden stop of

the carriage device in the experiment is shown in

Fig.11(a). The comparison of the tension of the seat-

belt between simulation and experiment is shown in

Fig.11(b).

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㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋

Figure 8: Comparison of the result of computer simula-

tion with crash experiment in measuring of trunk angle with

seatbelt.

Although Fig.11(b) indicated that the maximum ten-

sion of the simulation matched that of the experiment,

the simulation result increased sharply around 400ms.

This indicated that the simulation result didn’t take

time lag into account until the seatbelt started to pull

the human body.

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

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㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋

Figure 9: Comparison of the result of computer simulation

with crash experiment in measuring of myoelectric potential

of the back without seatbelt.

5 DISCUSSION

Fig.7 and Fig.8 show that the trunk angle of each

subject without seatbelt increases more than that of

each subject with seatbelt, because the seatbelt works

effectively. Fig.10(a’) shows that the normal sub-

ject uses his muscle to control his trunk angle when

he is wearing a seatbelt. Fig.9(b), (c) and (d) and

Fig.10(b’), (c’) and (d’) show that the muscle reﬂec-

tion of disabled subjects with seatbelt is stronger than

that without seatbelt. This indicated that the trunk an-

gle of disabled subjects is restored by the seatbelt in-

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㪇㪌㪇㪇㪈㪇㪇㪇㪈㪌㪇㪇㪉㪇㪇㪇

㪫㫀㫄㪼㩿㫄㫊㪀

㩼㪤㪭㪚

㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅

㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋

㩿㪹㩾㪀㪨㫌㪸㪻㫉㫀㫇㫃㪼㪾㫀㪸

㪇

㪇㪅㪉

㪇㪅㪋

㪇㪅㪍

㪇㪅㪏

㪈

㪇㪌㪇㪇㪈㪇㪇㪇㪈㪌㪇㪇㪉㪇㪇㪇

㪫㫀㫄㪼㩿㫄㫊㪀

㩼㪤㪭㪚

㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅

㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋

㩿㪺㩾㪀㪩㫀㪾㪿㫋㩷㪿㪼㫄㫀㫇㫃㪼㪾㫀㪸

㪇

㪇㪅㪉

㪇㪅㪋

㪇㪅㪍

㪇㪅㪏

㪈

㪇㪌㪇㪇㪈㪇㪇㪇㪈㪌㪇㪇㪉㪇㪇㪇

㪫㫀㫄㪼㩿㫄㫊㪀

㩼㪤㪭㪚

㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅

㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋

㩿㪻㩾㪀㪣㪼㪽㫋㩷㪿㪼㫄㫀㫇㫃㪼㪾㫀㪸

㪇

㪇㪅㪉

㪇㪅㪋

㪇㪅㪍

㪇㪅㪏

㪈

㪇㪌㪇㪇㪈㪇㪇㪇㪈㪌㪇㪇㪉㪇㪇㪇

㪫㫀㫄㪼㩿㫄㫊㪀

㩼㪤㪭㪚

㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅

㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋

Figure 10: Comparison of the result of computer simulation

with crash experiment in measuring of myoelectric potential

of the back with seatbelt.

stead of muscle reﬂection. When disabled subjects

don’t wear seatbelt, they need to use their muscles

more than normal subject. Therefore using a seatbelt

is more important for people with disabilities than in

the case of normal people.

Next, the simulation results are focused. The motion

and the muscle reﬂection pattern in each subject are

similar. The experiment results can be simulated by

the model based on muscle reﬂection. The muscle

reﬂection of people with disabilities responds more

strongly than that of normal people in the case without

a seatbelt. Therefore, people with disabilities experi-

COMPUTATIONAL MUSCLE REFLEX MODEL OF WHEELCHAIR USERS TRAVELING IN MOTOR VEHICLES -

Evaluation of the Motion and the Myoelectric Potential of People with Disabilities

㩿㪸㪀㪫㪿㪼㩷㪸㪺㪺㪼㫃㪼㫉㪸㫋㫀㫆㫅㩷㫆㪽㩷㫋㪿㪼㩷㪺㪸㫉㫉㫀㪸㪾㪼㩷㪻㪼㫍㫀㪺㪼

㪄㪉㪇

㪄㪈㪌

㪄㪈㪇

㪄㪌

㪇

㪌

㪇㪌㪇㪇㪈㪇㪇㪇㪈㪌㪇㪇㪉㪇㪇㪇

㪫㫀㫄㪼㩿㫄㫊㪀

㪘㪺㪺㪼㫃㪼㫉㪸㫋㫀㫆㫅㩿㫄㪆㫊

㪉

㪀

㩿㪹㪀㪫㪿㪼㩷㫋㪼㫅㫊㫀㫆㫅㩷㫆㪽㩷㫋㪿㪼㩷㫊㪼㪸㫋㪹㪼㫃㫋

㪇

㪌㪇㪇

㪈㪇㪇㪇

㪇㪌㪇㪇㪈㪇㪇㪇㪈㪌㪇㪇㪉㪇㪇㪇

㪫㫀㫄㪼㩿㫄㫊㪀

㪝㫆㫉㪺㪼㩿㪥㪀

㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅

㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋

Figure 11: The comparison of the tension of a seatbelt of

simulation and experiment result.

ence stronger physical burden than others do. Even

though a serious trafﬁc accident doesn’t occur, a seat-

belt is a useful tool for wheelchair users because it

helps to control their movement instead of using their

muscles while traveling in a motor vehicle.

6 CONCLUSIONS

In this study, a human motion model in a wheelchair

traveling in a motor vehicle was developed. The

model was expressed the motion of subjects with dis-

abilities by using muscle parameters of each subject.

The motion of subjects with disabilities can almost be

simulated by this model. The simulation results show

that the a seatbelt help to control the motion and the

muscle activity of subjects with disabilities. However,

the seatbelt and muscle reﬂection model couldn’t sim-

ulate accurately. The results show that disabled peo-

ple need to wear a seatbelt more than in the case of

normal people.

In the future, relationship between myoelectric poten-

tial and muscle force will be investigated by funda-

mental experiments, improvement of myoelectric po-

tential’s equation and optimal calculation of muscle

parameters in order to make safety guideline which

are acceptable for people with disabilities.

ACKNOWLEDGEMENTS

This work is supported by Mr.Shigeki Abe, Life sup-

port co ltd. and this work was supported by the Grant-

in-Aid for Scientiﬁc Research (B) from the Japan So-

ciety for the Promotion of Science.

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