Multibody dynamic simulation of knee contact mechanics.

Multibody dynamic musculoskeletal models capable of predicting muscle forces and joint contact pressures simultaneously would be valuable for studying clinical issues related to knee joint degeneration and restoration. Current three-dimensional multibody knee models are either quasi-static with deformable contact or dynamic with rigid contact. This study proposes a computationally efficient methodology for combining multibody dynamic simulation methods with a deformable contact knee model. The methodology requires preparation of the articular surface geometry, development of efficient methods to calculate distances between contact surfaces, implementation of an efficient contact solver that accounts for the unique characteristics of human joints, and specification of an application programming interface for integration with any multibody dynamic simulation environment. The current implementation accommodates natural or artificial tibiofemoral joint models, small or large strain contact models, and linear or nonlinear material models. Applications are presented for static analysis (via dynamic simulation) of a natural knee model created from MRI and CT data and dynamic simulation of an artificial knee model produced from manufacturer's CAD data. Small and large strain natural knee static analyses required 1 min of CPU time and predicted similar contact conditions except for peak pressure, which was higher for the large strain model. Linear and nonlinear artificial knee dynamic simulations required 10 min of CPU time and predicted similar contact force and torque but different contact pressures, which were lower for the nonlinear model due to increased contact area. This methodology provides an important step toward the realization of dynamic musculoskeletal models that can predict in vivo knee joint motion and loading simultaneously.

[1]  A. Seireg,et al.  A Mathematical Programming Method for Design of Elastic Bodies in Contact , 1971 .

[2]  E. Chao,et al.  Prediction of antagonistic muscle forces using inverse dynamic optimization during flexion/extension of the knee. , 1999, Journal of biomechanical engineering.

[3]  Gerald E. Farin,et al.  Curves and surfaces for computer-aided geometric design - a practical guide, 4th Edition , 1997, Computer science and scientific computing.

[4]  N. Nuño,et al.  Sagittal profile of the femoral condyles and its application to femorotibial contact analysis. , 2001, Journal of biomechanical engineering.

[5]  T. Andriacchi Dynamics of knee malalignment. , 1994, The Orthopedic clinics of North America.

[6]  T. Andriacchi,et al.  Dynamic knee loads during gait predict proximal tibial bone distribution. , 1998, Journal of biomechanics.

[7]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[8]  Stefan M. Gabriel,et al.  Three-dimensional determination of femoral-tibial contact positions under in vivo conditions using fluoroscopy. , 1998, Clinical biomechanics.

[9]  Jaco F Schutte,et al.  Determination of patient-specific multi-joint kinematic models through two-level optimization. , 2005, Journal of biomechanics.

[10]  A. J. van den Bogert,et al.  In vivo determination of the anatomical axes of the ankle joint complex: an optimization approach. , 1994, Journal of biomechanics.

[11]  J. G. Andrews,et al.  Non-uniqueness of the bicompartmental contact force solution in a lumped-parameter mathematical model of the knee. , 1990, Journal of biomechanics.

[12]  Gerard A. Ateshian,et al.  Patellofemoral Stresses during Open and Closed Kinetic Chain Exercises , 2001, The American journal of sports medicine.

[13]  H J Sommer,et al.  A technique for kinematic modeling of anatomical joints. , 1980, Journal of biomechanical engineering.

[14]  R. Woledge,et al.  The forces in the distal femur and the knee during walking and other activities measured by telemetry. , 1998, The Journal of arthroplasty.

[15]  G. Ateshian A B-spline least-squares surface-fitting method for articular surfaces of diarthrodial joints. , 1993, Journal of biomechanical engineering.

[16]  M. Hull,et al.  Contact Mechanics of the Medial Tibial Plateau after Implantation of a Medial Meniscal Allograft , 2000, The American journal of sports medicine.

[17]  Yasin Y Dhaher,et al.  The effect of vastus medialis forces on patello-femoral contact: a model-based study. , 2002, Journal of biomechanical engineering.

[18]  Ellis Horowitz,et al.  Fundamentals of data structures in C , 1976 .

[19]  D. Paley,et al.  Malalignment and degenerative arthropathy. , 1994, The Orthopedic clinics of North America.

[20]  S L Delp,et al.  The use of basis functions in modelling joint articular surfaces: application to the knee joint. , 2000, Journal of biomechanics.

[21]  Scott A. Banks,et al.  Weight-bearing knee kinematics in subjects with two types of anterior cruciate ligament reconstructions , 2002, Knee Surgery, Sports Traumatology, Arthroscopy.

[22]  Benjamin J Fregly,et al.  Computational wear prediction of a total knee replacement from in vivo kinematics. , 2005, Journal of biomechanics.

[23]  D. Dennis,et al.  In Vivo Fluoroscopic Analysis of the Normal Human Knee , 2003, Clinical orthopaedics and related research.

[24]  S. Goldstein,et al.  Functional tissue engineering: the role of biomechanics in articular cartilage repair. , 2001, Clinical orthopaedics and related research.

[25]  P. Walker,et al.  Computer model to predict subsurface damage in tibial inserts of total knees , 1998, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[26]  Benjamin J Fregly,et al.  Experimental evaluation of an elastic foundation model to predict contact pressures in knee replacements. , 2003, Journal of biomechanics.

[27]  J. Kalker,et al.  A minimum principle for frictionless elastic contact with application to non-Hertzian half-space contact problems , 1972 .

[28]  D. Bartel,et al.  Stresses in polyethylene components of contemporary total knee replacements. , 1995, Clinical orthopaedics and related research.

[29]  Scott L. Delp,et al.  A computational framework for simulating and analyzing human and animal movement , 2000, Comput. Sci. Eng..

[30]  J. Stiehl,et al.  Mathematical model of the lower extremity joint reaction forces using Kane's method of dynamics. , 1997, Journal of biomechanics.

[31]  S. Delp,et al.  Accuracy of muscle moment arms estimated from MRI-based musculoskeletal models of the lower extremity. , 2000, Computer aided surgery : official journal of the International Society for Computer Aided Surgery.

[32]  W. Herzog,et al.  In vivo knee joint loading and kinematics before and after ACL transection in an animal model. , 1997, Journal of biomechanics.

[33]  S. D. Kwak,et al.  A Mathematical Formulation for 3D Quasi-Static Multibody Models of Diarthrodial Joints , 2000, Computer methods in biomechanics and biomedical engineering.

[34]  G E Loeb,et al.  Advanced modeling environment for developing and testing FES control systems. , 2003, Medical engineering & physics.

[35]  J. Barbera,et al.  Contact mechanics , 1999 .

[36]  S. Delp,et al.  Evaluation of a Deformable Musculoskeletal Model for Estimating Muscle–Tendon Lengths During Crouch Gait , 2001, Annals of Biomedical Engineering.

[37]  Scott Tashman,et al.  In-vivo measurement of dynamic joint motion using high speed biplane radiography and CT: application to canine ACL deficiency. , 2003, Journal of biomechanical engineering.

[38]  P. Walker,et al.  Forces and moments telemetered from two distal femoral replacements during various activities. , 2001, Journal of biomechanics.

[39]  David R Wilson,et al.  Evaluation of a computational model used to predict the patellofemoral contact pressure distribution. , 2004, Journal of biomechanics.

[40]  J Wismans,et al.  A three-dimensional mathematical model of the knee-joint. , 1980, Journal of biomechanics.

[41]  S J Piazza,et al.  Three-dimensional dynamic simulation of total knee replacement motion during a step-up task. , 2001, Journal of biomechanical engineering.

[42]  T. Andriacchi,et al.  Tractive forces during rolling motion of the knee: implications for wear in total knee replacement. , 1997, Journal of biomechanics.

[43]  Gerard A. Ateshian,et al.  Computer Simulations of Patellofemoral Joint Surgery , 2003, The American journal of sports medicine.

[44]  P S Walker,et al.  Influence of muscle activity on the forces in the femur: an in vivo study. , 1997, Journal of biomechanics.

[45]  B. Paul,et al.  Contact Pressures on Closely Conforming Elastic Bodies , 1981 .

[46]  W. Herzog,et al.  The role of muscles in joint adaptation and degeneration , 2003, Langenbeck's Archives of Surgery.

[47]  J. Callaghan Medical engineering & physics. , 2005, Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference.

[48]  S. M. Kurt,et al.  Miniature specimen shear punch test for UHMWPE used in total joint replacements. , 2002, Biomaterials.

[49]  Alan D. George,et al.  DETERMINATION OF PATIENT-SPECIFIC FUNCTIONAL AXES THROUGH TWO-LEVEL OPTIMIZATION , 2003 .

[50]  P. Walker,et al.  The Dominance of Cyclic Sliding in Producing Wear in Total Knee Replacements , 1991, Clinical orthopaedics and related research.

[51]  Thomas R. Kane,et al.  THEORY AND APPLICATIONS , 1984 .

[52]  H. Grootenboer,et al.  Articular contact in a three-dimensional model of the knee. , 1991, Journal of Biomechanics.

[53]  David J. Mooney,et al.  Functional Tissue Engineering , 2001, Springer New York.

[54]  M. Hull,et al.  A finite element model of the human knee joint for the study of tibio-femoral contact. , 2002, Journal of biomechanical engineering.

[55]  E. Abdel-Rahman,et al.  Three-dimensional dynamic behaviour of the human knee joint under impact loading. , 1998, Medical engineering & physics.

[56]  T. Kepple,et al.  Relative contributions of the lower extremity joint moments to forward progression and support during gait , 1997 .

[57]  Peeter Pruuden Opiskelijankatu Master of Science Thesis , 1999 .

[58]  MARCUS G. Pandy,et al.  A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 2: Analysis of Ligament Function. , 1998, Computer methods in biomechanics and biomedical engineering.

[59]  E. Chao,et al.  A comparison of different methods in predicting static pressure distribution in articulating joints. , 1997, Journal of biomechanics.

[60]  S.A. Banks,et al.  Accurate measurement of three-dimensional knee replacement kinematics using single-plane fluoroscopy , 1996, IEEE Transactions on Biomedical Engineering.

[61]  M. Pandy,et al.  A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construction , 1997 .

[62]  Edmund Y S Chao Graphic-based musculoskeletal model for biomechanical analyses and animation. , 2003, Medical engineering & physics.

[63]  M. Pandy,et al.  A Dynamic Optimization Solution for Vertical Jumping in Three Dimensions. , 1999, Computer methods in biomechanics and biomedical engineering.

[64]  Leon M Keer,et al.  Non-Hertzian contact stress analysis for an elastic half space-normal and sliding contact , 1983 .

[65]  V. L. Giddings,et al.  Total Knee Replacement Polyethylene Stresses During Loading in a Knee Simulator , 2001 .

[66]  W. A. Hodge,et al.  Polyethylene Damage and Knee Kinematics After Total Knee Arthroplasty , 2001, Clinical orthopaedics and related research.

[67]  T. Andriacchi,et al.  Interaction between active and passive knee stabilizers during level walking , 1991, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[68]  K. An,et al.  Pressure distribution on articular surfaces: application to joint stability evaluation. , 1990, Journal of biomechanics.

[69]  R. R. NEPTUNE,et al.  A Method for Numerical Simulation of Single Limb Ground Contact Events: Application to Heel-Toe Running , 2000, Computer methods in biomechanics and biomedical engineering.

[70]  W Baumann,et al.  The three-dimensional determination of internal loads in the lower extremity. , 1997, Journal of biomechanics.