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Journal of Biomechanical

Engineering Technical Brief

Computational Modeling of a Dynamic

Knee Simulator for Reproduction

of Knee Loading

Trent M. Guesse-mail: [email protected]

Department of Mechanical Engineering, University of

Missouri-Kansas City, 350F Robert H. Flarsheim

Hall, 5100 Rockhill Road, Kansas City, MO 64110

Phone: 816 235-1252

Lorin P. Maletskye-mail: [email protected]

Department of Mechanical Engineering, The University of

Kansas, 1530 W. 15th

St., 3138 Learned Hall,

Lawrence, KS 66045

Phone: 785 864-2985

As a first step towards reproducing desired three-dimensional joint loading and motion on a dynamic knee simulator, the goal of this study was to develop and verify a three-dimensional compu-

tational model that generated control profiles for the simulator using desired knee loading and motion as model inputs. The de-veloped model was verified by predicting tibio-femoral loading onan instrumented analog knee for given actuator forces and theability to generate simulator control profiles was demonstrated using a three-dimensional walking profile. The model predicted axial tibia loading for a sagittal-plane dual-limb squat within 1%of measured peak loading. Adding out-of-sagittal-plane forces de-creased the accuracy of load prediction. The model generated control profiles to the simulator that produced axial tibia loadingwithin 16% of desired for walking. Discrepancies in predicted and measured quadriceps forces influenced the accuracy of the gener-ated control profiles. Future work will replace the analog knee inboth the model and machine with a prosthetic knee.DOI: 10.1115/1.2073676

Introduction

Dynamic knee simulators attempt to reproduce the estimatedforces, moments, and motions of both the patello-femoral andtibio-femoral joints during dynamic activities. These machineshave been used to evaluate the sagittal plane restraining role of the

anterior cruciate ligament ACL during walking and stair ascent

1, the influence of Q angle on knee kinematics during a squat2, and the affect of posterior cruciate ligament PCL resectionon patello-femoral and tibio-femoral kinematics during a squat3. In addition, a dynamic knee simulator has been used to com-pare joint kinematics of implanted mobile bearing prosthetics andfixed implants to original intact cadaver knees 4.

A variety of methods have been employed to reproduce theloading and motion of ambulatory activities on dynamic kneesimulators. Paviovic et al. utilized a plastic knee model whenprogramming their machine to imitate walking. Estimated muscleforces were applied to simulated quadriceps and hamstring actua-tors and then the hip and ankle were iteratively moved until thedesired flexion angle and relative spatial positions were achieved5. McLean and Ahmed imitated walking on their simulator byusing published data of knee flexion, hip and ankle flexion, verti-cal and fore/aft ground reaction, and center of pressure locationunder the foot to calculate the necessary inputs to the actuators of the machine 6,7. A dual-limb knee squat was imitated on theJohn Hopkins Knee Simulator by applying a constant 100-N ver-tical load to a simulated hip and a constant 150 N of force to asimulated hamstring. Flexion angle was then controlled through asimulated quadriceps by linearly extending the actuator at

0.5 mm/s 2–4. A two-dimensional computational model of thePurdue Knee Simulator: Mark II was developed to predict therequired simulator input profiles to produce desired sagittal-planeknee loading 8,9.

This study documents the first step in achieving the overall goal

of reproducing desired three-dimensional net knee loading or mo-tion on a dynamic knee simulator. The overall goal will be accom-plished through development of a computational model that trans-lates three-dimensional net knee loading estimated in a gait lab, orthrough other methods, into control profiles that drive the actua-tors of the dynamic simulator. The specific aims of this studywere: 1 construct a constrained and simplified analog knee in-strumented to measure joint forces, 2 develop a three-dimensional computational model of a dynamic knee simulatorand the analog knee, 3 verify the capability of the computationalmodel to predict knee loading by comparing predicted and mea-sured analog knee forces through squat and laxity tests performedon the simulator, 4 verify the capability of the model to generatecontrol profiles to the controllable axes of the simulator by repro-ducing the loading and motion of a three-dimensional walking

profile on the analog knee.

Materials and Method

Kansas Knee Simulator (KKS). Modeled after the PurdueKnee Simulator: Mark II 8, the Kansas Knee Simulator Fig. 1is a five-axis dynamic simulator designed to reproduce the loadingfrom ambulatory activities using cadaveric knees or total kneeprostheses. Each of the five axes is actuated with a hydrauliccylinder with servo valve control. Both position and force aremeasured at each axis allowing for control in either position orload. The machine includes a femur and tibia that can indepen-dently flex and that are respectively grounded through a hip and

Contributed by the Bioengineering Division of ASME for publication in the J OUR-

NAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Di-vision June 19, 2003; revision received July 25, 2005. Associate Editor: Marcus G.

Pandy.

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wnloaded From: http://www.asmedigitalcollection.asme.org/ on 11/16/2013 Terms of Use: http://asme.org/terms

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ankle sled. The resultant knee loads and motions are reactions toforces applied at the simulated hip and ankle and from a simulatedquadriceps muscle. In general, the simulated quadriceps is used tocontrol femur flexion at the hip and the remaining four actuatorsoperate in load control to apply dynamic loading at the hip andankle.

Computational Model of KKS. A three-dimensional computa-tional model of the KKS was developed in the computer aidedengineering package MSC.ADAMS MSC Software Corporation,Santa Ana, CA. MSC.ADAMS formulates and solves the dy-namic equations of motion for a given system of constraints thatinclude lumped parameter rigid bodies, vector forces, torques,

joints, springs, friction, and contacts. The KKS model Fig. 2 wasintended to provide a computational platform that replicated themotion and loading produced by the hydraulic actuators, mass,and inertia of the machine.

To replicate the proper line of action of the five hydraulic ac-tuators; the basic three-dimensional structures of the machinewere modeled. Four revolute joints and three translational jointswere used to describe the degrees of freedom of the KKS and

vector force elements represented the forces generated by the five

hydraulic cylinders. The mass properties of the rigid bodies werederived from empirical measurements of assembled componentsof the simulator.

Analog Knee. The analog knee included simplified articula-tions and was instrumented to measure tibio-femoral loading. Thetibio-femoral joint was designed as a simple revolute joint and thepatello-femoral joint was designed as a simple pulley mechanismto accommodate loading applied by the quadriceps actuator. Com-pressive forces were measured at four locations, medial and lateraltibia axial compression and medial and lateral posterior force.

The analog knee was designed using a standard computer aideddrafting program and component geometries were imported intothe computational model of the KKS. Three-dimensional deform-able contacts represented the load cells used to measure tibio-femoral force on the analog knee. A series of stiff nonlinearsprings connected by small spheres and contacts between thespheres and surfaces of the analog knee represented the pulleymechanism of the patello-femoral joint.

Control Profile Generation. In the computational model, lin-ear feedback algorithms were used to control the magnitudes of the axis force vectors in order to obtain desired model motion orloading. For the walking profile demonstrated, hip flexion anglewas maintained through PID control of the force vector represent-ing the KKS quadriceps axis hydraulic cylinder. In addition, de-sired tibia axial compression was maintained through PID controlof a KKS axis applying a vertical load to the hip sled verticalload axis and desired tibial axis internal/external torque wasmaintained through PID control of a KKS axis applying a torqueabout a vertical axis at the ankle vertical torque axis. Model

inputs were the time histories of desired loading at respective

Table 1 Verification Tests

AxisQuadriceps (hip flexion angle) Vertical Ad / Ab Vertical Torque

AnkleFlexion

ControlMode

Position deg Force N Force N Torque N-mm Force N

Squat 23±13 @ 0.1 Hz 200 0 0 0

Laxity 1,2,3 10, 23, 36 44.5 0± 44.5 @ 0.05 Hz 0 0

Laxity 4,5,6 10, 23, 36 44.5 0 0± 6778 @ 0.05 Hz 0

Fig. 1 Photograph of the Kansas Knee Simulator with analogknee „adduction/abduction actuator below picture…

Fig. 2 KKS computational model with analog knee and con-trollable axes

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locations or axes about the knee and model outputs were KKSaxis input profiles needed to reproduce the desired knee loading.

Model Verification. To verify that the model accurately repre-sented the forces generated by the actuators, mass, and inertia of the KKS and the transfer of loading to the analog knee from theseforces, a squat profile and six laxity tests were performed Table1. For all tests, the quadriceps axis was in position control of hipflexion angle and the remaining KKS axes were in load control.Hip flexion angle was defined as 0 deg when the femur was par-allel to a vertical axis and 90 deg when the femur was parallel tothe ground. During the squat profile, the quadriceps axis followed

a sinusoidal profile of 23 deg±13 deg hip flexion angle at 0.1 Hzand the vertical load axis maintained a constant 200-N hip load.The remaining axes followed zero load profiles. For the six laxitytests the quadriceps axis maintained constant hip flexion angles of 10, 23, and 36 deg and the axis loading shown in Table 1.

Control Profile Verification. A walking profile was used toverify the capability of the computational model to develop simu-lator control profiles that reproduced the desired loading and mo-tion at the analog knee. The walking profile included knee flexion/ extension angle, compressive force along the tibial axis, andinternal/external rotational torque about the tibial axis from ISOspecification 14243-1. In addition, an adduction/abduction loadfrom Hersh 10 scaled for a body mass of 86 kg 190 lb wasapplied at the ankle. The walking cycles were for a right knee and

were run at a frequency of 0.05 Hz.

Results

The root-mean-square rms errors between predicted and mea-sured loading for the squat profile were 49, 44, 71, and 28 N,respectively, for the medial axial compression, lateral axial com-pression, medial posterior, and lateral posterior positions. Figure 3displays one cycle of measured and predicted loading for the squatat all four measurement positions. The difference between pre-dicted maximum load and measured maximum for one cycle of

testing was −4, 2, 69, and 59 N, or −0.2%, 0.1%, 13.3%, and11.5% of maximum predicted loading.

In both the KKS and computational model of the KKS, thequadriceps axis was used to maintain desired hip flexion angle.Root-mean-square error between predicted and measured quadri-

ceps axis loading was 151 N. Measured and predicted quadricepsload is shown in Fig. 4 along with vertical load tracking for onecycle. The measured quadriceps load lags the predicted load witha greater force than predicted during the extension phase of thesquat and a lower force than predicted during the flexion phase. Aconstant 200 N was the desired vertical load for the KKS to main-tain during the flexion-extension cycle. The actual force applied tothe hip sled varied from a maximum of 227 N during extension toa low of 168 N during flexion.

The laxity tests were used to confirm the ability of the model topredict knee loading produced by the out-of-plane axes. Figure 5provides a graph of rms errors between predicted and measuredloading for the six laxity verification tests as well as the squat test.Axial compression errors were greater when out-of-plane loadingwas applied compared to the squat profile.

For the walking profile

Fig. 6, rms errors were 154, 107, 35,and 41 N, respectively for the medial axial compression, lateral

axial compression, medial posterior, and lateral posterior posi-tions. The difference in peak loading between measured and pre-dicted axial compression was 241, 80, 37, and 61 N, or 15.8%,7.4%, 12.8%, and 25.3% for the four measurement positions. Theone-cycle rms error between predicted and measured quadricepsload was 119 N. During stance phase, the model consistently over-estimated the quad load required to maintain the desired flexionangle and consequently overestimated the tibia axial knee loading.The predicted vertical load profile required to generate compres-sive loading was underestimated as the quadriceps load providedthe additional compressive load in the model. Input profiles gen-

erated by the model and KKS tracking for one walking cycle areshown in Fig. 7. Except for the initial peak during stance andswing phase in the vertical load axis, the KKS closely follows thereference signals.

Fig. 3 Predicted „– – –… and measured „—… loading for onecycle of the squat profile at the medial axial compression „a …,lateral axial compression „b …, medial posterior „c …, and lateralposterior sensor positions „d …

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Fig. 6 Predicted „– – –… and measured „—… loading for onecycle of walking at the medial axial compression „a …, lateralaxial compression „b …, medial posterior „c …, and lateral poste-rior sensor positions „d …

Fig. 7 Control axis reference „– – –… and measured feedback „—… for one cycle of walking at the quadriceps axis „a …, verticalload axis „b …, vertical torque axis „c …, and adduction/abductionaxis „d …

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Acknowledgments

Funding for this project was provided by The University of Kansas New Faculty General Research Fund, Award No.2301811-RPSGNF.

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