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The application of muscle wrapping to voxel-based finite element models of skeletal structures

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Abstract

Finite elements analysis (FEA) is now used routinely to interpret skeletal form in terms of function in both medical and biological applications. To produce accurate predictions from FEA models, it is essential that the loading due to muscle action is applied in a physiologically reasonable manner. However, it is common for muscle forces to be represented as simple force vectors applied at a few nodes on the model’s surface. It is certainly rare for any wrapping of the muscles to be considered, and yet wrapping not only alters the directions of muscle forces but also applies an additional compressive load from the muscle belly directly to the underlying bone surface. This paper presents a method of applying muscle wrapping to high-resolution voxel-based finite element (FE) models. Such voxel-based models have a number of advantages over standard (geometry-based) FE models, but the increased resolution with which the load can be distributed over a model’s surface is particularly advantageous, reflecting more closely how muscle fibre attachments are distributed. In this paper, the development, application and validation of a muscle wrapping method is illustrated using a simple cylinder. The algorithm: (1) calculates the shortest path over the surface of a bone given the points of origin and ultimate attachment of the muscle fibres; (2) fits a Non-Uniform Rational B-Spline (NURBS) curve from the shortest path and calculates its tangent, normal vectors and curvatures so that normal and tangential components of the muscle force can be calculated and applied along the fibre; and (3) automatically distributes the loads between adjacent fibres to cover the bone surface with a fully distributed muscle force, as is observed in vivo. Finally, we present a practical application of this approach to the wrapping of the temporalis muscle around the cranium of a macaque skull.

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References

  • Austman RL, Milner JS, Holdsworth DW, Dunning CE (2008) The effect of the density-modulus relationship selected to apply material properties in a finite element model of long bone. J Biomech 41(15): 3171–3176

    Article  Google Scholar 

  • Blemker S, Delp S (2005) Three-dimensional representation of complex muscle architectures and geometries. Ann Biomed Eng 33(5): 661–673

    Article  Google Scholar 

  • Blemker S, Pinksy P, Delp S (2005) A 3D model of muscle reveals the cause of non-uniform strains in the biceps brachii. J Biomech 38: 657–665

    Article  Google Scholar 

  • Camacho DLA, Hopper RH, Lin GM, Myers BS (1997) An improved method for finite element mesh generation of geometrically complex structures with application to the skull base. J Biomech 30: 1067–1070

    Article  Google Scholar 

  • Charras GT, Guldberg RE (2000) Improving the local solution accuracy of large-scale digital image-based finite element analyses. J Biomech 33: 255–259

    Article  Google Scholar 

  • Chen J, Han Y (1990) Shortest paths on a polyhedron. In: SCG ’90: Proceedings of the sixth annual symposium on Computational geometry. ACM, New York, NY, USA, pp 360–369

  • Curtis N, Kupczik K, O’Higgins P, Moazen M, Fagan MJ (2008) Predicting skull loading: applying multibody dynamics analysis to a macaque skull. Anat Rec 291: 491–501

    Article  Google Scholar 

  • Curtis N, Jones M, Evans SE, Shi JF, O’Higgins P, Fagan MJ (2009) Predicting muscle activation patterns from motion and anatomy: modelling the skull of Sphenodon (Diapsida: rhynchocephalia). J Roy Soc Interface. doi:10.1098/rsif.2009.0139

  • Dijkstra E (1959) A note on two problems in connection with graphs. Numer Math 1: 269–271

    Article  MATH  MathSciNet  Google Scholar 

  • Dumont ER, Piccirillo J, Grosse IR (2005) Finite-element analysis of biting behavior and bone stress in the facial skeletons of bats. Anat Rec A 283(2): 319–330

    Google Scholar 

  • Fagan MJ, Dobson CA, Ganney PS, Sisias G, Phillips R, Langton CM (1999) Finite element analysis of cancellous bone resorption. Comput Methods Biomech Biomed Eng 2(4): 257–270

    Article  Google Scholar 

  • Fagan MJ, Curtis N, Dobson CA, Kupczik K, Moazen M, Page L, Phillips R, O’Higgins P (2007) Voxel-based finite element analysis—working directly with microCT scan data. J Morph 268(12): 1071

    Google Scholar 

  • Freeman H (1974) Computer processing of line drawing images. ACM Comput Surv 6(1): 57–94

    Article  MATH  Google Scholar 

  • Gröning F, Liu J, Fagan MJ, O’Higgins P (2009) Validating a voxel-based finite element model of a human mandible using digital speckle pattern interferometry. J Biomech 42(9): 1224–1229

    Article  Google Scholar 

  • Grosse IR, Dumont ER, Coletta C, Tolleson A (2007) Techniques for modelling muscle-induced forces in finite element models of skeletal structures. Anat Rec 290: 1069–1088

    Article  Google Scholar 

  • Guldberg RE, Hollister SJ, Travers GT (1998) The accuracy of digital image-based finite element models. J Biomech Eng 120: 289–295

    Article  Google Scholar 

  • Harrison NM, McDonnell PF, O’Mahoney DC, Kennedy OD, O’Brien FJ, McHugh PE (2008) Heterogeneous linear elastic trabecular bone modelling using micro-CT attenuation data and experimentally measured heterogeneous tissue properties. J Biomech 41(11): 2589–2596

    Article  Google Scholar 

  • Helgason B, Perilli E, Schileo E, Taddei F, Brynjólfsson S, Viceconti M (2008) Mathematical relationships between bone density and mechanical properties: a literature review. Clin Biomech 23(2): 135–146

    Article  Google Scholar 

  • Helgason B, Taddei F, Pálsson H, Schileo E, Cristofolini L, Viceconti M, Brynjólfsson S (2008) A modified method for assigning material properties to FE models of bones. Med Eng Phys 30(4): 444–453

    Article  Google Scholar 

  • Keyak JH, Lee IY, Skinner HB (1994) Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. J Biomed Mater Res 28: 1329–1336

    Article  Google Scholar 

  • Kiryati N, Szekely G (1993) Estimation shortest paths and minimal distances on digitized three-dimensional surfaces. Pattern Recogn 26(11): 1623–1637

    Article  Google Scholar 

  • Kiryati N, Kübler O (1995) Chain code probabilities and optimal length estimators for digitized three-dimensional curves. Pattern Recogn 28(3): 361–372

    Article  Google Scholar 

  • Kupczik K, Dobson CA, Crompton RH, Phillips R, Oxnard CE, Fagan MJ, O’Higgins P (2009) Masticatory loading and bone adaptation in the supraorbital torus of developing macaques. Am J Phys Anthr 139(2): 193–203

    Article  Google Scholar 

  • Kupczik K, Dobson CA, Fagan MJ, Crompton R, Oxnard CE, O’Higgins P (2007) Assessing mechanical function of the zygomatic region in macaques: validation and sensitivity testing of finite element models. J Anat 210: 41–53

    Article  Google Scholar 

  • Langton CM, Ganney PS, Dobson CA, Fagan MJ, Sisias G, Phillips R (2000) Stochastically simulated assessment of anabolic treatment following varying degrees of cancellous bone resorption. Bone 27(1): 111–118

    Article  Google Scholar 

  • Langton CM, Haire TJ, Dobson CA, Fagan MJ (1998) A dynamic stochastic simulation of cancellous bone resorption. Bone 22(4): 375–380

    Article  Google Scholar 

  • Lemos R, Rokne O, Baranoski G, Kawakami Y, Kurihara T (2005) Modeling and simulating the deformation of human skeletal muscle based on anatomy and physiology. Comput Animat Virtual Worlds 16: 319–330

    Article  Google Scholar 

  • Linde F, Hvid I, Madsen F (1992) The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens. J Biomech 25: 359–368

    Article  Google Scholar 

  • McDonnell P, Harrison N, Liebschner MA, Mc Hugh PE (2009) Simulation of vertebral trabecular bone loss using voxel finite element analysis. J Biomech. doi:10.1016/j.jbiomech.2009.07.038 (in press)

  • McHenry CR, Wroe S, Clausen PD, Moreno K, Cunningham E (2007) Super-modeled sabercat, predatory behaviour in Smilodon fatalis revealed by high-resolution 3-D computer simulation. Proc Natl Acad Sci USA 104:16010–16015

    Google Scholar 

  • Mitchell J, Mount D, Papadimitriou C (1987) The discrete geodesic problem. SIAM J Comput 16(4): 647–668

    Article  MATH  MathSciNet  Google Scholar 

  • Moazen M, Curtis N, Evans SE, O’Higgins P, Fagan MJ (2009) Biomechanical assessment of evolutionary changes in the lepidosaurian skull. Proc Natl Acad Sci USA 20: 8273–8277

    Article  Google Scholar 

  • Moazen M, Curtis N, Evans SE, O’Higgins P, Jones MEH, Fagan MJ (2009) Assessment of the role of sutures in a lizard skull—a computer modelling study. Proc Roy Soc B 276: 39–46

    Article  Google Scholar 

  • Moazen M, Curtis N, Evans SE, O’Higgins P, Fagan MJ (2008) Combined finite element and multibody dynamics analysis of biting in a Uromastyx hardwickii lizard skull. J Anat 213: 499–508

    Google Scholar 

  • Moreno K, Wroe S, Clausen P, McHenry C, D’Amore DC, Rayfield EJ, Cunningham E (2008) Cranial performance in the Komodo dragon (Varanus komodoensis) as revealed by high resolution 3-D finite element analysis. J Anat 212: 736–746

    Article  Google Scholar 

  • Piegl L, Tiller W (1997) The NURBS book, 2nd edn. Springer, Berlin

    Book  Google Scholar 

  • Rayfield E (2007) Finite element analysis and understanding the biomechanics and evolution of living and fossil organisms. Annu Rev Earth Planet Sci 35: 541–576

    Article  Google Scholar 

  • Rho JY, Hobatho MC, Ashman RB (1995) Relations of mechanical properties to density and CT numbers in human bone. Med Eng Phys 17: 347–355

    Article  Google Scholar 

  • Richmond BG, Wright BW, Grosse I, Dechow PC, Ross CF, Spencer MA, Strait DS (2005) Finite element analysis in functional morphology. Anat Rec 283(2): 259–274

    Article  Google Scholar 

  • Ross CF (2005) Finite element analysis in vertebrate biomechanics. Anat Rec 283: 253–258

    Article  Google Scholar 

  • Shi JF, Curtis N, Fitton L, O’Higgins P, Fagan MJ (2009) The effect of variations in muscle positions in a complex biomechanical model of a macaque skull. Am J Phys Anth 138: S48

    Google Scholar 

  • Strait DS, Wang Q, Dechow PC, Ross CF, Richmond BG, Spencer MA, Patel BA (2005) Modelling elastic properties in finite element analysis: how much precision is needed to produce an accurate model?. Anat Rec 283: 275–287

    Article  Google Scholar 

  • Strait DS, Weber GW, Neubauer S, Chalk J, Richmond BG, Lucas PW, Spencer MA, Schrein C, Dechow PC, Ross CF, Grosse IR, Wright BW, Constantino P, Wood BA, Lawn B, Hylander WL, Wang Q, Byron C, Slice DE, Smith AL (2009) The feeding biomechanics and dietary ecology of Australopithecus africanus. Proc Natl Acad Sci USA 106(7): 2124–2129

    Article  Google Scholar 

  • Tsubota K, Suzuki Y, Yamada T, Hojo M, Makinouchi A, Adachi T (2009) Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: approach to understanding Wolff’s law. J Biomech 42(8): 1088–1094

    Article  Google Scholar 

  • Ulrich D, van Rietbergen B, Weinans H, Rüegsegger P (1998) Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech 31: 1187–1192

    Article  Google Scholar 

  • Verhulp E, van Rietbergen B, Huiskes R (2006) Comparison of micro-level and continuum-level voxel models of the proximal femur. J Biomech 39(16): 2951–2957

    Article  Google Scholar 

  • Wroe S, Moreno K, Clausen P, McHenry C, Curnoe D (2007) High-resolution three-dimensional computer simulation of hominid cranial mechanics. Anat Rec 290(10): 1248–1255

    Article  Google Scholar 

  • Yeni YN, Christophersin GT, Dong XN, Kim D-G, Fyhrie DP (2005) Effect of microcomputed tomography voxel size on the finite element model accuracy for human cancellous bone. J Biomech Eng 127: 1–8

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Hull, Hull, UK

    Jia Liu & Roger Phillips

  2. Department of Engineering, University of Hull, Cottingham Road, Hull, HU6 7RX, UK

    Junfen Shi & Michael J. Fagan

  3. Hull-York Medical School, The University of York, York, UK

    Laura C. Fitton & Paul O’Higgins

Authors
  1. Jia Liu
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  2. Junfen Shi
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  3. Laura C. Fitton
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  4. Roger Phillips
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  5. Paul O’Higgins
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  6. Michael J. Fagan
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Correspondence to Michael J. Fagan.

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Liu, J., Shi, J., Fitton, L.C. et al. The application of muscle wrapping to voxel-based finite element models of skeletal structures. Biomech Model Mechanobiol 11, 35–47 (2012). https://doi.org/10.1007/s10237-011-0291-5

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  • DOI: https://doi.org/10.1007/s10237-011-0291-5

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