2006_Pain_Challis_JB.pdf

ARTICLE IN PRESS

Journal of Biomechanics 39 (2006) 119–124

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The inﬂuence of soft tissue movement on ground reaction forces,

joint torques and joint reaction forces in drop landings

Matthew T.G. Pain a, ,John H. Challis b

a School of Sport & Exercise Sciences, Loughborough University, Loughborough, Leics LE11 3TU, UK

b Biomechanics Laboratory, The Pennsylvania State University, University Park, PA 16802-3408, USA

Accepted 28 October 2004

Abstract

The aim of this study was to determine the effects that soft tissue motion has on ground reaction forces,joint torques and joint

reaction forces in drop landings. To this end a four body-segment wobbling mass model was developed to reproduce the vertical

ground reaction force curve for the ﬁrst 100 ms of landing. Particular attention was paid to the passive impact phase,while selecting

most model parameters a priori,thus permitting examination of the rigid body assumption on system kinetics. A two-dimensional

wobbling mass model was developed in DADS (version 9.00,CADSI) to simulate landing from a drop of 43 cm. Subject-speciﬁc

inertia parameters were calculated for both the rigid links and the wobbling masses. The magnitude and frequency response of the

soft tissue of the subject to impulsive loading was measured and used as a criterion for assessing the wobbling mass motion. The

model successfully reproduced the vertical ground reaction force for the ﬁrst 100 ms of the landing with a peak vertical ground

reaction force error of 1.2% and root mean square errors of 5% for the ﬁrst 15 ms and 12% for the ﬁrst 40 ms. The resultant joint

forces and torques were lower for the wobbling mass model compared with a rigid body model,up to nearly 50% lower,indicating

the important contribution of the wobbling masses on reducing system loading.

Keywords: Wobbling mass; Soft tissue; Joint torque; Forward dynamics; Landings

1. Introduction

often associated with injuries or discomfort ( Nigg and

Bobbert,1990 ). As modeling these activities is one of

the few methods of obtaining joint loading information

it may be very important that the model can account

for soft tissue motion and the kinetic effects it has on

the body.

Models which accommodate some force interactions

within a body segment have received limited attention

( Minetti and Belli,1994 ; Cole et al.,1996 ; Gruber et al.,

1998 ; Wright et al.,1998 ; Nigg and Liu,1999 ; Liu and

Nigg,2000 ). Typically in these models segments are

separated into two elements: a rigid component,and a

soft tissue component—the wobbling mass. Minetti and

Belli (1994) and Wright et al. (1998) only included a

single wobbling mass to represent the visceral mass.

Nigg and Liu (1999) and Liu and Nigg’s (2000) model of

the impact phase of running considered vertical motion

To try and circumvent the many problems associated

with internal force measurement in man,inverse

dynamics and computer modeling are commonly used.

Biomechanical whole body models are normally com-

posed of rigid segments linked by simple kinematic

connections (e.g. Bobbert and van Soest,1994 ; Gerritsen

et al.,1996 ). However,the segments of the human body

are not rigid and such an assumption can lead to

substantial errors in both inverse and direct dynamics

analyses,especially those associated with high accelera-

tions and impulsive loading. These types of activity are

Corresponding author. Tel.:+44(0)1509 226327;

fax: +44(0)1509 223971.

E-mail address: m.t.g.pain@lboro.ac.uk (M.T.G. Pain).

doi:10.1016/j.jbiomech.2004.10.036

120

ARTICLE IN PRESS

M.T.G. Pain, J.H. Challis / Journal of Biomechanics 39 (2006) 119–124

only. The model represented the body as two segments

(upper and lower body) each consisting of rigid and

wobbling masses connected with springs and dampers.

Gruber et al. (1998) used a two-dimensional,three

segment wobbling mass model to recreate the vertical

ground reaction force for a subject landing from a drop.

They showed that ground reaction forces and joint

torques and forces were markedly different for their

wobbling mass model and an equivalent rigid body

model when simulating the same landing from a drop.

However,a large number of model parameters,includ-

ing mass distributions between segment rigid and

wobbling mass elements were optimized to achieve a

ground reaction force match between model and

experimental data. The distributions of segmental mass

between skeletal and soft tissue components were well

beyond the ranges indicated from dissection (e.g. Clarys

et al.,1984 ). Model joint torques were zero until 5 ms

after impact,but inverse dynamics analysis of landings

show signiﬁcant joint torques prior to impact ( Bobbert

et al.,1992 ). Pain and Challis (2004) demonstrated the

sensitivity of such wobbling mass models to their model

parameters and showed that compensating errors could

account for anomalies such as these.

Cole et al. (1996) produced a two-dimensional,four

segment wobbling mass model to examine joint loading

during impact in running. In this model the mass of the

bone and soft tissue were calculated from the tissue

distributions in Clarys and Marfell-Jones (1986) . The

soft tissue elements were point masses constricted to

move along the line of action of the muscle–tendon unit

and had a moment of inertia of zero. The soft issue

motion being restricted to one line of action and having

no moment of inertia would greatly reduce the kinetic

contributions of this element. As the soft tissue would be

the dominant contributor to the inertial properties of

the segment,and as soft tissue motions have been

recorded in all three planes ( Reinschmidt,1996 ),these

assumptions may limit this model’s ability to examine

soft tissue motion affects.

Previous studies have shown the potential inﬂuence of

the wobbling masses on system kinetics,but these studies

have suffered from a variety of deﬁciencies. These

deﬁciencies include unrealistic model parameters,con-

strained wobbling mass motion,and joint torque patterns

which are not observed experimentally. The aim of this

study was to determine the effects that soft tissue motion

have on ground reaction forces,joint torques and joint

reaction forces in drop landings. To this end a four body-

segment wobbling mass model was developed to repro-

duce the vertical ground reaction force curve for the ﬁrst

100 ms of landing. Particular attention was paid to the

passive impact phase,(occurring in the ﬁrst 50 ms, Nigg,

1986 ),while selecting most model parameters a priori,

thus permitting examination of the rigid body assumption

on system kinetics.

2. Methods

Measurements were performed on an experimental

subject performing drop landings,and a model was

developed to simulate these landings.

The subject was a male,age 27 years,height 1.75 m,

mass 85 kg,body fat 10% of total body mass,who had

provided informed consent. The subject performed two

two-footed landings from a drop height of 0.43 m,

making initial contact with the heels. The subject had

reﬂective markers on the lateral second metatarsal,the

lateral malleolus,the heel,the center of rotation of

the knee,the greater trochanter,and the shoulder. The

drops were performed barefooted and the arms were

squeezed tight across the chest to minimize arm motion.

Force plate data (Bertec,N50601,Type 4080s) were

recorded at 1200 Hz,and the marker motion data were

recorded at 240 Hz (Pro-Reﬂex,Qualisys,Sweden).

During these landings segment orientations at impact

differed by less than 11,and peak ground reaction forces

by less than 6%. Therefore,initial segment orientations

for the model at contact were the mean data from these

two trials.

It was not feasible to measure soft tissue motion

during the landings,therefore to obtain representative

data soft tissue motion was measured during controlled

impacts,using the methods presented in Pain and

Challis (2002) . The subject was positioned so that he

could strike a force plate with a vertical downward

stamping motion with the knee ﬂexed at 901 and that

allowed the motion of an array of 28 markers on the

posterior aspect of the shank to be recorded at 240 Hz,

the shank test. The stamping motion was performed

such that a rigid beam with a padded surface provided

support for the thigh at impact. Six trials were

performed. The process was repeated with the marker

array on the anterior aspect of the left thigh with the leg

straight,the thigh test,and the upper body and other leg

were supported at impact. From these data mean

marker array motion was determined,and the magni-

tude and frequency content of the experimental soft

tissue motion computed for the passive impact phase for

later comparisons with the model.

A two-dimensional model, Fig. 1 ,consisting of four

rigid links (bone) connected with revolute joints,

controlled by revolute spring–damper actuators,had

wobbling masses (soft tissue) attached to the shank,

thigh and torso bones with translational spring–dam-

pers ( Pain and Challis,2001 ). The ground–heel interface

was represented by a non-linear spring–damper system

described in Pain and Challis (2001) . The model was

developed in DADS (version 9.00,CADSI) to simulate

landing from a drop of 43 cm. Simulations could also be

run with the model as a rigid body model by ﬁxing

together the centers of mass of the bone and the soft

tissue for each body segment using rigid joints.

ARTICLE IN PRESS

M.T.G. Pain, J.H. Challis / Journal of Biomechanics 39 (2006) 119–124

121

Fig. 1. Schematic of the four body-segment wobbling mass model just

before impact. Inner solid segments represent the rigid skeleton. The

outer line segments represent the wobbling mass material.

tissue mounted markers can differ by up to 101

( Reinschmidt,1996 ). Due to the paradoxical problem

of determining bone orientation from surface markers

during impacts the parameters for the torque generators

were determined so that both the bone and soft tissue

segments of the model were within one degree of the

subjects body segment angles at 40 ms after impact.

All angles were measured with reference to the

vertical,with clockwise rotations positive. On the

subject angles were deﬁned with respect to the vertical

and the line joining the joint centers. In the model

angles were deﬁned with respect to the vertical and the

midline of the bone or soft tissue segments. These model

values were then used in the ﬁnal version of the

wobbling mass model. During this phase of model

parameter identiﬁcation the stiffness and damping of

the spring–dampers,which connect the soft tissues to

the rigid body,were constrained so that the bone and

soft tissue segments remained within one degree of

each other. The torque generators at the joints,the

revolute spring–dampers,provided joint torques at the

instant of impact.

The ﬁnal model adjustments were the stiffness and

damping of the spring–dampers,which effectively

connect the soft tissues to the rigid body. The tendon

properties were altered by up to one order of magnitude

( Pain and Challis,2004 ) to produce a vertical ground

reaction force that matched the subject’s. The veracity

of these changes was assessed by comparing the motion

of the wobbling masses in the model to the measured

soft tissue motion on the subject during the shank and

thigh impact experiments.

Body segment inertial parameters for the subject’s

segment mass and location of the center of mass were

calculated using the equations of Zatsiorsky et al.

(1990) . Lower limb segment moments of inertia were

calculated using the equations of Challis (1996) . The

mass of the shank and thigh were divided for each

segment into a bone mass and soft tissue mass by

modeling them as a cylinder and a tube,respectively.

The cadaver data of Clarys and Marfell-Jones (1986)

and Clarys et al. (1984) were used for the relative masses

and density of the rigid and wobbling components. The

radii of the cylinder and the tube were systematically

adjusted so that the total mass and moment of inertia of

the two geometric solids corresponded to the subject’s

anthropometry. The upper body was modeled as one

body composed of rigid and wobbling mass compo-

nents. The mass distributions of these segments was

based on the data of Clarys et al. (1984) and Clarys and

Marfell-Jones (1986) . The rigid component was modeled

as a series of cylinders,each with different densities,

representing the pelvis,spinal column,and the head to

calculate the moments of inertia of the trunk skeleton.

The soft tissue of the trunk was modeled as a tube

surrounding the bone of the trunk,and the arms were

modeled as a cylinder held across the chest to represent

the arms crossed in front of the chest.

In free fall immediately before contact soft tissue

motion is minimal,as indicated by the invariant area of

four additional markers placed on the bellies of the

muscles of the thigh and shank. However,during

impacts segment motion determined by bone and soft

3. Results

The model parameters and initial conditions are

presented in the Tables 1–3 . Table 1 presents the subject

speciﬁc bone and soft tissue inertial parameters. The

subject’s body segment angles at impact and 40 ms after

impact are presented in Table 2 ,the model had the same

segment angles at impact and attempted to reproduce

the same joint angles 40 ms after impact. The model had

variable joint torques throughout the impacts these were

produced by rotational spring–damper actuators at the

joints,their model parameters are described in Table 3 .

Soft tissue motion was measured during controlled

impacts by the subject,and was quantiﬁed by the

magnitude of marker motion and frequency content of

that motion. The experimental and simulation marker

motions and frequency contents compared very favor-

ably ( Table 4 ). For the six trials of shank test the mean

peak vertical ground reaction force was 4615

340 N,

502 N,these forces were for

one leg only. For the experimental two-footed impacts,

the peak vertical ground reaction force was 13675 N.

and for the thigh test 6113

ARTICLE IN PRESS

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M.T.G. Pain, J.H. Challis / Journal of Biomechanics 39 (2006) 119–124

Table 1

The inertia parameters for the bone and soft tissue calculated for the subject

Body segment

Segment type

Mass (kg)

Moment of inertia

(kg m 2 )

Segment length

(cm)

Center of mass above

midpoint (cm)

Foot

Whole

2.20

3.42 10 3

26.5

0.60

Shank

Bone

2.68

3.80 10 3

41.0

2.75

Soft tissue

5.56

0.0132

41.0

2.75

Thigh

Bone

4.30

0.0570

42.5

2.85

Soft tissue

13.42

0.240

42.5

2.85

Trunk

Bone

6.20

0.447

86.3

10.0

Soft tissue

53.40

1.44

86.3

10.0

N.B. The foot,shank and thigh data are for the pair.

Table 2

Subject body segment orientations at impact and 40 ms after impact

for the two drop landings

15000

Foot

Shank

Thigh

Trunk

Initial angle (deg)

92 175

165

Angle at 40 ms (deg) 88 172

147

149

10000

N.B. Angles are measured with reference to the vertical,positive is

clockwise.

Table 3

Model joint rotational stiffness and damping model coefﬁcients

5000

Ankle

Knee

Hip

Stiffness (N/1)

Damping (N.s/1)

0.50

0.35

0.30

0 10 20 30 40 50 60 70 80 90 100 110

Table 4

Comparison of magnitude and frequency content of experimental soft

tissue motion and model soft tissue motion

Time (ms)

Fig. 2. Vertical ground reaction force curves for the two empirical

trials (dotted line and dashed line) and the wobbling mass model (solid

line).

Shank

Thigh

Magnitude

(cm)

Peak

frequencies

(Hz)

Magnitude

(cm)

Peak

frequencies

(Hz)

bodyweights,and for the subject 16.4 bodyweights.

During these simulations,the maximum difference in

orientation between the bone segment and the soft tissue

segment in the model was up to 11 in the shank,and 4.51

in the thigh. For example the orientations of the bone

segments were re-examined at 40 ms after impact for the

wobbling mass model,the angles were 911, 1711,

1501,and 1511 for the foot,shank,thigh,and trunk,

respectively. These values correspond well with the

experimental data ( Table 2 ). The difference between the

models trunk orientation and the experimental data was

no greater than 21 throughout the simulated motion.

Peak joint torques and forces were much greater for

the rigid body model compared with the wobbling mass

model ( Table 5 ). The orientation of the bone segments

differed by less than 21 between the wobbling mass and

the rigid body models. With a fully rigid model the peak

Experimental 1.8 7 0.2

14,28,50

3.2 7 0.9

14,18

Model

1.4

12,24,39

2.8

15,20

N.B. For experimental values this is the mean marker motion across

markers. For the model it is the relative motion of the center of mass of

the bone and soft tissue for each body segment.

Given the model parameters,the ﬁrst 100 ms of an

impact from a 0.43 m drop were simulated. The model

reproduced the experimental vertical GRF for the ﬁrst

15 ms of the landing within 5% and the ﬁrst 40 ms

within 12% ( Fig. 2 ). Between 40 and 80 ms it reproduced

the shape of the curve well and key values such as the

descending shoulder were close to experimental values.

The peak GRF for the wobbling mass model was 16.2

ARTICLE IN PRESS

M.T.G. Pain, J.H. Challis / Journal of Biomechanics 39 (2006) 119–124

123

Table 5

Comparisons between the peak joint torques and forces for the

wobbling mass and rigid body models

kinematics the peak vertical ground reaction forces were

16.4,16.2,and 40.5 bodyweights,for the subject,

wobbling mass model,and rigid body model. Similarly

resultant joint moments were much greater for the rigid

body model compared with the wobbling mass model

( Table 5 ). These results provide evidence of the

important role of soft tissue motion in reducing joints

loads for this task. The task selected here parallels that

used by Gruber et al. (1998) ,and reﬂects a condition

which can occur during landings from a jump,especially

somersaults,and provides links to running where most

impacts are via the heel. Further studies should examine

if these phenomena exist for other activities involving

impacts,for example walking and running.

Comparing the joint torques and forces between the

wobbling mass model and a rigid body model show

the same overall trend as in Gruber et al. (1998) . The

wobbling mass model decreased forces and torques at

the joints. However,here the change was not as drastic

as seen in Gruber et al. (1998) where hip torques varied

by almost an order of magnitude. The results in Gruber

et al. (1998) can be attributed to erroneous timing of the

activation of the torque actuators in their wobbling

mass model.

Sensitivity analyses of the results demonstrate that the

trunk wobbling mass was almost solely responsible for

the peak in the vertical ground reaction force at 80 ms.

The model was weakest in its representation of the

trunk,as there was no impact data to separately

determine the magnitude and frequency response of

the torso as there was for the shank and thigh. It is

feasible that the viscera and musculature of the trunk

are acting over different time scales. Unfortunately no

information is available on the response of the viscera to

an impulsive load. Minetti and Belli (1994) measured

visceral motion but this was for a forced oscillation and

the period of oscillation of the viscera was 5 Hz. The

trunk soft tissue mass is undoubtedly a major con-

tributor to the ground reaction force in latter stages of

the impact. However,its contribution in this study was

not so great that it could be justiﬁed to have a model

which only had one wobbling mass element which is

associated with the trunk segment,for example as used

in Wright et al. (1998) .

Using experimental segment orientation data for

model initial conditions and evaluation is paradoxical.

The soft tissue motion obscures the bone motion and

accurate measurements of bone motion are not practic-

able. However,in the free fall phase of the drop this

motion is minimal,providing conﬁdence in the experi-

mental data used for the initial conditions. Segment

orientations 40 ms into the landing were compared

between the model and subject,and were within 31.

These angles were obtained from surface marker data

and so were inﬂuenced by soft tissue motion. The bone

segment orientations and the subject body segment

Joint

Wobbling mass model

Rigid body model

Torque

(Nm)

Vertical

force (N)

Torque

(Nm)

Vertical

force (N)

Ankle 228

11080

370

17140

Knee

267

7720

500

13280

Hip

240

5100

460

7700

vertical ground reaction force increased to 40.5 body-

weights,compared with 16.2 bodyweights for the

wobbling mass model. With rigid legs,and only a

wobbling mass for the trunk,similar to Wright et al.

(1998) ,the peak vertical ground reaction force was 31.4

bodyweights.

4. Discussion

The aim of this study was to develop a four body-

segment wobbling mass model to simulate landing from

a drop,so that the inﬂuence of the rigid body

assumption on system kinetics could be examined. To

produce the model as many model parameters as

possible were determined prior to the simulations,

speciﬁcally

The segment inertial parameters were calculated to

match the subject.

Partitioning of segment mass to rigid and wobbling

mass components was based on cadaver data ( Clarys

et al.,1984 ; Clarys and Marfell-Jones,1986 ).

A heel pad model was adopted ( Pain and Challis

2001 ).

Initial conﬁguration and velocity of the model at

impact were determined from subject kinematics.

The remaining model parameters were those for the

rotational spring–damper actuators,and the stiffness,

and damping of the spring–dampers connecting the rigid

and wobbling masses. An independent test of soft tissue

motion compared very favorably with the model

produced motion ( Table 4 ),providing a level of

conﬁdence in the model parameters.

The model was successful in reproducing the vertical

ground reaction force curve for the passive impact

period,the ﬁrst 40 ms. The overall shape of the curve

matches well up to 100 ms,and the force values of the

peak and descending shoulder are very similar. With a

rigid body model the system kinematics were similar to

the experimental subject’s; the differences were within

the anticipated experimental error in measurements of

the segment orientations. Despite these similarities in the

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