Lower Limb Stiffness Estimation during Running: The Effect of Using Kinematic Constraints in Muscle Force Optimization Algorithms

Transcription

1 Lwer Limb Stiffness Estimatin during Running: The Effect f Using Kinematic Cnstraints in Muscle Frce Optimizatin Algrithms Rbert Brtlett 1, Enric Pagell 1, and Davide Pivesan 2 1 Intelligent Autnmus Systems Labratry (IAS-Lab), Department f Infrmatin Engineering, University f Padua, Italy 2 Bimedical Prgram, Mechanical Engineering Department, Gannn University, Erie, Pennsylvania, USA INTELLIGENT AUTONOMOUS SYSTEMS LAB

2 Backgrund IAS-LAB Muscle-driven dynamic simulatins Mathematical mdels f muscle activatin and cntractin dynamics Estimatin f physilgical parameters that cannt be easily measured in viv Hill-type mdel Hill-type muscle frce mdel Optimizatin algrithms Cst functin depends n physical parameters (energy, muscle stress, muscle activatin,...) T mdulate the generated muscle frces and the crrespnding limb stiffness Existing studies: Hip, knee, and ankle jint stiffness *The incidence f the adpted muscle-mdel n the jint stiffness estimatin * Brtlett, R., Pagell, E., Pivesan, D. (Wrkshp n Neur-Rbtics fr Patient-Specific Rehabilitatin, July 2014, Padua) Hw different human muscle mdels affect the estimatin f lwer limb jint stiffness during running

3 Objective IAS-LAB Tw main research tpics: The use f frward dynamic neur-musculskeletal mdeling and simulatin Muscle frces, jint mments, jint kinematics,... The use f muscle shrt-range stiffness Lwer limb jint stiffness T evaluate hw the adptin f different muscle frce ptimizatin algrithms affects the lwer limb stiffness during running

4 Methds Dataset IAS-LAB «Muscle functin f vergrund running acrss a range f speeds»* Hw the leg muscle crdinate mtin f the bdy segments during running Electrmygraphic (EMG) Mtin Capture (MC) Grund Reactin Frces (GRFs) Unimpaired male subject (age, 19 years; masss, 75.9 Kg; height, 1.82 m; leg length, 1.00 m) Running speeds: 3.5 ms -1, 5.2 ms -1, 7.0 ms -1, 9.0 ms -1 * Drn, T. W., Schache, A. G. and Pandy, M. G. (J Exp Bil 215, , 2012) Muscular strategy shift in human running: dependence f running speed n hip and ankle muscle perfrmance

5 Methds Musculskeletal Mdel IAS-LAB Subject-specific 3D Human Musculskeletal Mdel 7 bdy segments fr each leg 5 bdy segments fr each arm 92 muscle-tendn actuatrs Yamaguchi, G.T., Zajac, F.E. (J. Bimech. 22, 1 10, 1989) A planar mdel f the knee jint t characterize the knee extensr mechanism Delp, S.L., Lan, J.P., Hy, M.G., Zajac, F.E., Tpp, E.L., Rsen, J.M. (IEEE Trans. Bimed. Eng. 37(8), ) An Interactive Graphics-Based Mdel f the Lwer Extremity t Study Orthpaedic Surgical Prcedures Andersn, F.C., Pandy, M.G. (Cmput. Methds Bimech. Bimed. Engin. 2(3), , 1999) A Dynamic Optimizatin Slutin fr Vertical Jumping in Three Dimensins Ward, S.R., Eng, C.M., Smallwd, L.H., Lieber, R.L. (Clin. Orthp. Relat. Res. 467, , 2009) Are current measurements f lwer extremity muscle architecture accurate?

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9 Methds Trque-based Muscle Frce Optimizatin IAS-LAB u = min τ j = M i=1 M i=1 F m,i 0 F m,i 2 r ij F m,i a m,i Muscle Activatin Level 0 < a m,i 1 i = 1,2,, M; j = 1,2,, N Muscle Mment Arm f the i-th muscle abut the j-th jint 0 0 F m,i F m,i Muscle Maximum Ismetric Frce

10 Methds Trque/Kinematic-based Muscle Frce Optimizatin IAS-LAB u = min τ j = M i=1 M i=1 F m,i 0 F m,i 2 a m,i F 0 m,i r ij a m,i Muscle Activatin Level 0 < a m,i 1 i = 1,2,, M; j = 1,2,, N Muscle Mment Arm f the i-th muscle abut the j-th jint 0 0 F m,i F m,i Muscle Maximum Ismetric Frce C j = q j q j Equality cnstraints The desired acceleratins are cmputed using the fllwing PD cntrl law q t + T = q exp t + T + k v q exp t q t + k p [q exp t q(t)]

11 K m = γf m l 0 m Stiffness f the muscle fibers Optimal Muscle Fiber Length Methds Mdel-based Stiffness Estimatin IAS-LAB Picture taken frm Thelen2003 Muscle mdel details page: K t = F t l t l s t Stiffness f the tendn Tendn Slack Length K mt = K m K t K m + K t Shrt-range stiffness f the muscle-tendn unit J Jacbian matrix relating changes in muscle jint angles t changes in muscle length K j = J T K mt J + JT θ F m Jint Stiffness K mt F m J T θ F m Diagnal matrix with the stiffness fr each muscle in the mdel Vectr f muscle frces Hw angle dependent changes in muscle mment arms influence jint stiffness

12 Maximum values f the crss-crrelatin functins cmputed between muscle frces and the prcessed EMG signal

13 Prcessed EMG signal prfiles cmpared t estimated muscle frces

14 Right Lwer Limb Jint Stiffness estimated values Right Lwer Limb Intra-Jint Stiffness estimated values

15 Cnclusins IAS-LAB Tw different whle-muscle frce ptimizatin algrithms Hw different algrithms may affect the estimatin f jint stiffness Decmpsing the jint stiffness cmputatin: A muscle-tendn mdel is required nly in the cmputatin f the gemetrical parameters Future research will fcus n: Muscle mdels Muscle-tendn frce ptimizatin algrithms Stiffness estimatin prcedures

16 IAS-LAB Thank yu fr yur attentin! Acknwledgements This research has been supprted by Cnsrzi Ethics thrugh a grant fr research activity n the prject Rehabilitatin Rbtics, and by the Faculty research grant at Gannn University.