Fiber-based modeling and simulation of skeletal muscles

This paper presents a novel fiber-based muscle model for the forward dynamics of the musculoskeletal system. While bones are represented by rigid bodies, the muscles are taken into account by means of one-dimensional cables that obey the laws of continuum mechanics. In contrast to standard force elements such as the Hill-type muscle model, this approach is close to the real physiology and also avoids the issue of wobbling masses. On the other hand, the computational cost is rather low in comparison with full 3D continuum mechanics simulations. The cable model includes sliding contact between individual fibers as well as between fibers and bones. For the discretization, cubic finite elements are employed in combination with implicit time stepping. Several validation studies and the simulation of a motion scenario for the upper limb demonstrate the potential of the fiber-based approach.

[1]  L. Petzold,et al.  A model of macroscale deformation and microvibration in skeletal muscle tissue , 2009 .

[2]  F.E. Zajac,et al.  An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures , 1990, IEEE Transactions on Biomedical Engineering.

[3]  S Schmitt,et al.  A forward dynamics simulation of human lumbar spine flexion predicting the load sharing of intervertebral discs, ligaments, and muscles , 2015, Biomechanics and modeling in mechanobiology.

[4]  Archibald Vivian Hill,et al.  The series elastic componet of muscle , 1950, Proceedings of the Royal Society of London. Series B - Biological Sciences.

[5]  S. Delp,et al.  Three-Dimensional Representation of Complex Muscle Architectures and Geometries , 2005, Annals of Biomedical Engineering.

[6]  Alexander Aurand,et al.  A biologically-assisted curved muscle model of the lumbar spine: Model structure. , 2016, Clinical biomechanics.

[7]  Roger A. Sauer,et al.  An unbiased computational contact formulation for 3D friction , 2015 .

[8]  P. Wriggers.  Nonlinear Finite Element Methods , 2008 .

[9]  K. Schneider,et al.  A comparative study of impact dynamics: wobbling mass model versus rigid body models. , 1998, Journal of biomechanics.

[10]  Oliver Röhrle,et al.  A multi-scale continuum model of skeletal muscle mechanics predicting force enhancement based on actin–titin interaction , 2016, Biomechanics and modeling in mechanobiology.

[11]  Reinhard Blickhan,et al.  Nonlinearities make a difference: comparison of two common Hill-type models with real muscle , 2008, Biological Cybernetics.

[12]  Jon G. Rokne,et al.  Modeling and simulating the deformation of human skeletal muscle based on anatomy and physiology , 2005, Comput. Animat. Virtual Worlds.

[13]  Jeffrey W Holmes,et al.  Strains at the myotendinous junction predicted by a micromechanical model. , 2011, Journal of biomechanics.

[14]  John B. Davidson,et al.  A mathematical model of fatigue in skeletal muscle force contraction , 2007, Journal of Muscle Research and Cell Motility.

[15]  F. Zajac.  Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. , 1989, Critical reviews in biomedical engineering.

[16]  Scott L. Delp,et al.  Accuracy of Muscle Moment Arms Estimated from MRI-Based Musculoskeletal Models of the Lower Extremity , 2000 .

[17]  Maarten F. Bobbert,et al.  The contribution of muscle properties in the control of explosive movements , 1993, Biological Cybernetics.

[18]  John B. Davidson,et al.  Bridging Scales: A Three-Dimensional Electromechanical Finite Element Model of Skeletal Muscle , 2008, SIAM J. Sci. Comput..

[19]  Gerhard A. Holzapfel,et al.  Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science , 2000 .

[20]  Michael Günther,et al.  Electro-mechanical delay in Hill-type muscle models , 2012 .

[21]  Matthew Millard,et al.  Flexing computational muscle: modeling and simulation of musculotendon dynamics. , 2013, Journal of biomechanical engineering.

[22]  S Schmitt,et al.  Hill-type muscle model with serial damping and eccentric force-velocity relation. , 2014, Journal of biomechanics.

[23]  Roger A. Sauer,et al.  A computational contact formulation based on surface potentials , 2013 .

[24]  J. Winters.  Hill-Based Muscle Models: A Systems Engineering Perspective , 1990 .

[25]  Sigrid Leyendecker,et al.  Biomechanical optimal control of human arm motion , 2013 .

[26]  B. Simeon,et al.  Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue , 2019, ArXiv.

[27]  H. Lang,et al.  Multi-body dynamics simulation of geometrically exact Cosserat rods , 2011 .

[28]  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.

[29]  Ian Stavness,et al.  A fast multi-obstacle muscle wrapping method using natural geodesic variations , 2016 .

[30]  Silvia S Blemker,et al.  A micromechanical model of skeletal muscle to explore the effects of fiber and fascicle geometry. , 2010, Journal of biomechanics.

[31]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[32]  Bernd Simeon.  Computational Flexible Multibody Dynamics , 2013 .

[33]  O Röhrle,et al.  A two-muscle, continuum-mechanical forward simulation of the upper limb , 2017, Biomechanics and modeling in mechanobiology.

[34]  M. Pandy,et al.  The Obstacle-Set Method for Representing Muscle Paths in Musculoskeletal Models , 2000, Computer methods in biomechanics and biomedical engineering.