Improved Muscle Wrapping Algorithms Using Explicit Path-Error Jacobians
Muscle wrapping computations are an important feature in musculoskeletal simulations. In this paper we present a novel Jacobian-based method for line-based muscle-path computations over multiple general smooth surfaces allowing for second-order Newton-Raphson iterations. The method is based on the analytical determination of infinitesimal displacements along geodesics using Jacobi fields. It does not share the disadvantages of discretized methods in terms of non-smoothness when using surface discretizations, and high computational costs when using discretized spring-mass approaches. The paper focusses on the technical details of the proposed method, while specific biomechanical applications are left for future contributions. An example with three surfaces involving a surface with a general distribution of curvature shows the general applicability of the method.
KeywordsMuscle wrapping Jacobi fields geodesics
Adrian Butscher, Leonidas Guibas, Justin Solomon, and Matthew Millard. This work was supported by the German National Academic Foundation, the Natural Sciences and Engineering Research Council of Canada, and NIH grants U54 GM072970 (Simbios) and R24 HD065690 (NCSRR).
- 1.Desailly, E., Sardain, P., Khouri, N., Yepremian, D., Lacouture, P.: The convex wrapping algorithm: A method for identifying muscle paths using the underlying bone mesh. J. Biomech. 43, 2601–2607Google Scholar
- 2.Gao, F., Damsgaard, M., Rasmussen, J., Christensen, S.T.: Computational method for muscle-path representation in musculoskeletal models. Biol. Cybern. 87, 199–210 (2002)Google Scholar
- 3.Charlton, I.W., Johnson, G.R.: Application of spherical and cylindrical wrapping algorithms in a musculoskeletal model of the upper limb. J. Biomech. 34, 1209–1216 (2001)Google Scholar
- 4.Marsden, S.P., Swailes, D.C., Johnson, G.R.: Algorithms for exact multi-object muscle wrapping and application to the deltoid muscle wrapping around the humerus. In: Proceedings of the Institution of Mechanical Engineers. Part H, Journal of Engineering in Medicine, vol. 222(7), 1081–1095 (2008)Google Scholar
- 5.Garner, B.A., Pandy, M.G.: The obstacle-set method for representing muscle paths in musculoskeletal simulations. Comput. Methods Biomech. Biomed. Eng. 3, 1–30 (1998)Google Scholar
- 6.Stavness, I., Sherman, M., Delp, S.L.: A general approach to muscle wrapping over multiple surfaces, In: Proceedings of the American Society of Biomechanics (2012)Google Scholar
- 7.Do Carmo, M.P.: Differential Geometry of Curves and Surfaces. 1st edn. Prentice Hall, ohio. Feb 1976Google Scholar
- 8.Struik, D.J.: Lectures on Classical Differential Geometry, 2nd edn. Dover Publications, New York, April 1988Google Scholar
- 9.Thielhelm, H., Vais, A., Brandes, D., Wolter, F.-E.: Connecting geodesics on smooth surfaces. Vis. Comput. 28, 529–539 (2012)Google Scholar