9 1-Tibialis anterior TA 2-

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1 ContributionEstimation Method of Muscle Forces of Lower Limb Considering the Role of Antagonistic Muscles and Biarticular Muscles Estimation of Muscle Forces of Lower Limb during Vertical Jumping, by Isamu NISHIDA, Masato MAEDA, Tsuneo KAWANO & Keiichi SHIRASE. Estimation of muscle forces during human motions is important in the fields of sport, ergonomics and bioengineering in order to improve sport techniques, rehabilitation procedures, product designs and work environments, and so on. In general, in the musculoskeletal models that have been developed, the functions of antagonistic muscles and biarticular muscles are not considered to estimate muscle forces. In this study, a musculoskeletal model that considered the functions of the antagonistic muscles and biarticular muscles was investigated. In this model, muscles acting across the hip, knee and ankle joints were treated simultaneously. Furthermore, in this study, vertical jump as dynamic motion was conducted to validate the proposed model to estimate muscle forces. Surface electromyograms (EMGs) of tibialis anterior, gastrocnemius, soleus, rectus femoris, vastus lateralis, semimembranosus, biceps femoris and short head and gluteus maximus were measured to compare with the estimated muscle forces. The experimental results showed that the muscle forces estimated by the proposed method had a good agreement with the EMGs of msucles Graduate School of Engineering, Kobe University Graduate School of Human Development and Environment, Kobe University School of Faculty of Science & Technology, Setsunan University Tibialis anteriorta2-244

2 GastrocnemiusGAS3-SoleusSOL4-Rectus femoris RF5-Vastus lateralisvas6-semimembranosus SM7-Biceps femoris and short headbfsh8- IliopsoasIL9-Gluteus maximusgmax a f1e1f2e2f3e3 f1e11f2e22 f3e31 2 2,3 36 F mf1 F me1 F mf2 F me2 F mf3 F me3 2a 2,3 2b a f1e2e3100 e1f2f f2e2 f4e4f5e5 f2e2 f5 e5 6 62f2 e21 1 Fig. 1 Muscle arrangements at the human lower extremity. c b 2 d F ' mf F ' me F ' mf F ' mf F ' me F ' me a e f 2 Fig. 2 Musculoskeletal model considering the role of antagonistic muscle and biarticular muscle. 245

3 e59 19 Tibialis anteriortae4gastrocnemius GASf5SoleusSOLf4Rectus femorisrfe3vastus lateralisvase2 SemimembranosusSMf3Biceps femoris and short headbfshf2iliopsoasil e1gluteus maximusgmaxf1 f2e2 BFSHf2 VASe2 2 Spector 4 i f imax A i f imax A i σ σ 57 σ50 N/cm 2 8 MRIPCSA PCSA 4 3 Fig. 3 Adaptation of musculoskeletal model considering the role of antagonistic muscle and biarticular muscle to the lower leg. 4 Fig. 4 MRI 8 Estimate values of physical cross-sectional areas. F F r r 5 Fig. 5 The mechanism of muscle levers. f imax F imax 5 Lr FF F F F = F r/ L 1 Hoy 9 f imax F imax 3 6 L F 246

4 f y M hip l thigh θ knee l M knee leg θ ankle f x 6 Fig. 6 Relationship between output force on the distal extremity and net moment. a b f ~ T f T l T l MT ε α l M cosα f T 6xf x y f y θ ankle θ knee l thigh l leg M hip M knee M hip M knee f x f y f x f y M = ( l sinθ + l sin θ ) f hip leg ankle thigh knee x ( l cosθ + l cos θ ) f leg ankle thigh knee y M = ( l sin θ ) f ( l cos θ ) f knee leg ankle x leg ankle y 2 3 f x f y 2a 2b 2-3Hill Hill Hill 7Delp 10 CE PEESEE3 c d f ~ ce f~ pe f~ ce l ~ M v ce v 7 ahill 10 b 11 c 11 d 11 Fig. 7 ahill muscle model, brelationship between normalized force and ratio of tendon length, c Relationship between normalized force and normalized length, drelationship between normalized force and normalized velocity. αl 0M l st Hoy 9 7CEPEE SEEf ce f pe f T

5 f imax T f l ce l pe l T l MT l M l ce l pe l MT α l = l cosα + l 4 T ce pe f = ( f + f )cosα 5 ε T T l ls ε = 6 T l Delp 11 7bdv 0 10l 0M m/sl 0M 12 T a f ε ce M f l pe M f l gv ce ce /v 0 ce ce M ce ce f = fi max f ( l ) g ( v / 0 v ) a 7 pe pe M f = fimax f ( l ) 8 T T f = f f ( ) ε 9 v ce l M v MT M T ce l = s imax M l t M prev f ce 10 l M prevl M t f T 97b6l T 4l M l MT 87c PEEf pe 5 CEf ce 710 7da f pe cm86.6 kg Hz TAGAS SOLRFVASSMBFSHGMAX HzGMAX IL IL Butterworth 13,14 6 Hz Newton-Euler 15, Critically-damped 18 6 Hz Maximum Voluntary Contraction MVCBorland C++ Builder 6 4 VASBFSH 8 9 MVC10 248

6 8 Fig. 8 VASBFSH Comparison of muscle activation level of VAS and BFSH between thigh model and leg model. 9 Fig. 9 Net moments of ankle, knee and hip joints. 1 Tab. 1 Correlations between the proposed method and the EMG. 1 VASBFSHVAS8 VAS BFSH VASBFSH 9 TA GAS SOL GASSOL RFVAS SM BFSH GAS GMAXSM RF 249

7 10 Fig. 10 Comparison of muscle activation level between the proposed method and the EMG MVC No Crowninshield R. D., Brand R. A.A Physiologically Based Criterion of Muscle Force Prediction in Locomotion, Journal of Biomechanics, 14, , ,,,, 6512, ,

8 3,,,, C, 63607, , Spector S. A., Gardiner P. F., Zernicke R. F., Roy R. R. and Edgerton V. R.Muscle architecture and force-velocity characteristics of cat soleus and medial gastrocnemius: implications for neural control, Journal Neuro-physiol, 44, , Wickiewicz T. L., Roy R. R., Powell P. L., Edgerton V. R.Muscle architecture of the human lower limb, Clin. orthop. Rel. Res, 179, , Brad R. A., Pedersen D. R., Frienderich J. A.The sensitivity of muscle force predictions to changes in physiologic cross-sectional area, Journal of Biomechanics, 19, , Chang Y. W., Hughes R. E., Su F. C., Itoi E., An K. N. Prediction of muscle force involved in shoulder internal rotation, Journal of Shoulder and Elbow Surgery, 93, , MRI,, 442, , Hoy M. G., Zajac F. E., Gordon M. E.A Musculoskeletal Model of the Human Lower Extremity: The Effect of Muscle, Tendon, and Moment Arm on the Moment-Angle Relationship of Musculotendon Actuators at the Hip, Knee, and Ankle, Journal of Biomechanics, 232, , Delp S., Loan P., Hoy M., Zajac F. E., Fisher S., Rosen J.An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures, IEEE Trans. on Biomedical Engineering, 378, , Delp S., Loan P.A computational framework for simulation and analysis of human and animal movement, IEEE Computing in Science and Engineering, 25, 46-54, Pandy M. G., Zajac F. E., Sim E., Levine W. S.An optimal control model for maximum-height human jumping, Journal of Biomechanics, 2312, , Winter D. A., Sidwall H. G., Hobson D. A.Measurement and reduction of noise in kinematics of locomotion, Journal of Biomechanics, 7, , Pezzack J. C., Winter D. A., Norman R. W. An assessment of derivative determining techniques for motion analysis, Journal of Biomechanics, 10, , Stepanenko Y., Vukobratovic M.Dynamics of articulated open-chain active mechanisms, Mathematical Biosciences, 28, , Orin D. E., McGhee R. B., Vukobratovic M., Hartoch G.Kinematic and kinetic analysis of open-chain linkage utilizing Newton-Euler method, Mathematical Biosciences, 43, , ,,,, 11, 23-33, Robertson D. G. E., Dowling J. J.Design and responses of Butterworth and critically damped digital filters, Journal of Electromyography and Kinesiology, 13, ,

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