Finite Element Representation of Muscles ... Node 179 Node 204 Node 205 Node 206 Node 227 Node 228 Node

Finite Element Representation of Muscles ... Node 179 Node 204 Node 205 Node 206 Node 227 Node 228 Node

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  • Finite Element Representation of Muscles Peter James Nugent, Supervisor: Dr. Andrew Phillips

    Department of Civil and Environmental Engineering, Imperial College London

    S16

    Figure 1: Conversion from tetrahedral to truss elements Figure 2: Mesh of the muscle

    Final Muscle Model • Utilised a hyper elastic material that accurately captured the passive response of the muscle (Figure 4)

    • The model could be subject to both compressive and tensile forces (Figures 3 & 4)

    • Eight connector elements around the exterior of the muscle induced the compressive force

    • The wires that followed the geometry were similar to those found in the literature (Böl and Reese, 2008)

    ϵ [-] ×10-3 -4 -3 -2 -1 0 1 2 3 4

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    Node 1 Node 4 Node 12 Node 19 Node 20 Node 27 Node 28 Node 35 Node 64 Node 65 Node 66 Node 89 Node 90 Node 91 Node 140 Node 141 Node 142 Node 177 Node 178 Node 179 Node 204 Node 205 Node 206 Node 227 Node 228 Node 229 Node 264 Node 265 Node 266 Node 277 Node 278 Node 279

    Figure 3: Force-strain graph in the X direction ϵ [-]

    -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

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    1 Node 13 Node 14 Node 17 Node 18 Node 32 Node 34 Node 41 Node 43 Node 101

    Figure 4: Force strain graph in the Y direction

    Figure 5: Anatomical model of the elbow system

    Biceps brachii

    Brachialis

    Brachioradialis

    Humerus

    Radius Ulna

    Figure 6: Elbow system in Abaqus

    CPRESS

    +0.000e+00 +6.415e−01 +1.283e+00 +1.924e+00 +2.566e+00 +3.207e+00 +3.849e+00 +4.490e+00 +5.132e+00 +5.773e+00 +6.415e+00 +7.056e+00 +7.698e+00

    X

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    CPRESS

    +0.000e+00 +6.415e−01 +1.283e+00 +1.924e+00 +2.566e+00 +3.207e+00 +3.849e+00 +4.490e+00 +5.132e+00 +5.773e+00 +6.415e+00 +7.056e+00 +7.698e+00

    X

    Y

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    CPRESS

    +0.000e+00 +6.415e−01 +1.283e+00 +1.924e+00 +2.566e+00 +3.207e+00 +3.849e+00 +4.490e+00 +5.132e+00 +5.773e+00 +6.415e+00 +7.056e+00 +7.698e+00

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    +0.000e+00 +6.415e−01 +1.283e+00 +1.924e+00 +2.566e+00 +3.207e+00 +3.849e+00 +4.490e+00 +5.132e+00 +5.773e+00 +6.415e+00 +7.056e+00 +7.698e+00

    X

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    Figure 7: Contact pressure on the humerus

    Aims • Create a generalised muscle model capable of being subject to compressive and tensile loads

    • Implement the muscle model in to an elbow system and capture the interaction between the deformed muscle and the bone

    Current Models • Existing muscle models use complex material sub routines that are computationally expensive

    • Some focus on the microscopic and mesoscopic scale of muscles such as the binding between actin and myosin proteins (Gielen et al., 2000)

    • Some also utilise MRI and CT scans that render the models subject specific

    Mesh & Geometry • A mesh was created using tetrahedral elements, which were then converted to truss elements (Figure 1)

    • This reduced the computational cost because truss elements have a single degree of freedom and hence can only deform axially, this is synonymous with the behaviour of a muscle

    3D Elbow Mechanism • The biceps brachii was chosen as the muscle to model in three

    dimensions because it makes contact with the humerus in the system that was adapted from the literature (Siemienski, 1992; Rasmussen et al., 2001)

    • The brachialis and brachioradialas were modelled as wires

    • The ulna and radius were combined to model the forearm (Figures 5 & 6)

    • The contact between the biceps brachii and the humerus was modelled using a node to surface contact

    Conclusions • The muscle model correctly captured the passive behaviour of the muscle and leaves scope for further

    work to manipulate the active response of the muscle

    • The elbow mechanism accurately modelled the contact pressure between the humerus and biceps brachii (Figure 7)

    • A musculoskeletal model can be used to obtain muscle forces, implemented in to the elbow mechanism model and the resulting contact pressures can be applied to finite element models of bones

    References Böl, M. and Reese, S. (2008). Micromechanical modelling of skeletal muscles based on the finite element method. Computer methods in biomechanics and biomedical engineering, 11(5):489–504. Gielen, A. W. J., Oomens, C. W. J., Oomens, C. W. J., Arts, T., and Janssen, J. D. (2000). A finite element approach for skeletal muscle using a distributed moment model of contraction. Computer methods in biomechanics and biomedical engineering, 3(3):231– 244. Rasmussen, J., Damsgaard, M., and Voigt, M. (2001). Muscle recruitment by the min/max criteriona comparative numerical study. Journal of Biomechanics, 34(3):409–415. Siemienski, A. (1992). Soft saturationan idea for load sharing between muscles. application to the study of human locomotion. In Cappozzo, A., Marchetti, M., and Virgilio, T., editors, Biolocomotion: A Century of Research Using Moving Pictures, pages 293–303.

    Acknowledgements I would like to thank Dr Phillips and his research team for their support and guidance throughout this project