biomechanics; finite element analysis; muscle loading algorithm; muscle-induced forces; simulation protocol; Ecology, Evolution, Behavior and Systematics; Ecological Modeling
Abstract :
[en] Finite element analysis (FEA) is a computational method used to predict the behaviour (stresses, strains and deformation) of a structure under predefined loading conditions. It can be applied to different biological structures, such as bone, to study defined muscle-driven scenarios. However, as muscle is an extremely complex structure to model, evolutionary biologists usually model muscle forces indirectly. In 2007, the BONELOAD MATLAB routine was developed to distribute muscle forces on a surface defined by the user. This routine then had to be coupled with a pre-existing FEA software (e.g. Strand7) to perform the analyses and has been widely used ever since. In this manuscript, we present a new method to run muscle-driven finite element simulations on a bone by distributing muscle forces on their insertions area, all within a single environment. We apply this protocol in three different situations: two biting simulations (unilateral and bilateral) and a shoulder flexion simulation. We demonstrate how to prepare the mesh, delineate the muscle origins and insertions, define the constraints, adjust material properties, choose a loading scenario (uniform, tangential or tangential-plus-normal), and extract the results. Our automated script meshes the 3D model, defines the constraints and distributes muscle forces within a single simulation software: ‘Metafor’ (nonlinear solver, owned and distributed by Gesval S.A) or ‘Fossils’ (a new open-source linear static solver developed in the frame of this work). ‘Metafor’ and ‘Fossils’ can perform the entire protocol (from the meshing to the muscle-induced simulations) on high-resolution volumetric meshes (millions of tetrahedra) and rapidly, exceeding the processing time of other widely used software protocols by up to four times. We demonstrate that the results obtained from our protocol are highly congruent with brands such as Strand7. Thus, our protocol opens up the possibility to routinely and rapidly simulate the behaviour of high-precision muscle-driven FE models containing millions of tetrahedra.
Disciplines :
Mechanical engineering Life sciences: Multidisciplinary, general & others
Boman, Romain ; Université de Liège - ULiège > Département d'aérospatiale et mécanique
Fallon Gaudichon, Valentin; Evolution & Diversity Dynamics lab, UR Geology, Université de Liège, Liège, Belgium ; Institut des Sciences de l'Evolution de Montpellier (ISEM), Université de Poitiers-Montpellier, Montpellier, France
MacLaren, Jamie A. ; Evolution & Diversity Dynamics lab, UR Geology, Université de Liège, Liège, Belgium ; Functional Morphology Lab, Department of Biology, Universiteit Antwerpen, Antwerpen, Belgium
Fischer, Valentin ; Université de Liège - ULiège > Département de géologie > Evolution and diversity dynamics lab
Language :
English
Title :
‘Fossils’: A new, fast and open-source protocol to simulate muscle-driven biomechanical loading of bone
F.R.S.-FNRS - Fonds de la Recherche Scientifique FRIA - Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture FWO - Fonds Wetenschappelijk Onderzoek Vlaanderen
Funding text :
Authors would like to thank Prof. Z. Jack Tseng (FAVE Lab, UC Berkeley) for his help, time and dedication in explaining the BONELOAD MATLAB routine and FEA in general. NC is grateful to the whole FAVE Lab for access to the workstation that allowed comparisons with Strand7. NC is supported by a grant of Fonds de la Recherche Scientifique F.R.S.–FNRS (FRIA grant number FRIA FC 36251); additional funding for specimen acquisition was provided by a F.R.S.‐FNRS travel grant (35706165) and FWO Doctoral Fellowship (11Y7615N), both awarded to JAM. Finally, we thank the MEE editorial board, as well as Dr. Stephan Lautenschlager and four anonymous reviewers for their constructive comments on a previous version of the manuscript.
Belytschko, T., Kulak, R. F., Schultz, A. B., & Galante, J. O. (1974). Finite element stress analysis of an intervertebral disc. Journal of Biomechanics, 7(3), 277–285. https://doi.org/10.1016/0021-9290(74)90019-0
Brekelmans, W. A. M., Poort, H. W., & Slooff, T. J. J. H. (1972). A new method to analyse the mechanical behaviour of skeletal parts. Acta Orthopaedica, 43(5), 301–317. https://doi.org/10.3109/17453677208998949
Buser, T. J., Boyd, O. F., Cortes, A., Donatelli, C. M., Kolmann, M. A., Luparell, J. L., Pfeiffenberger, J. A., Sidlauskas, B. L., & Summers, A. P. (2020). The natural Historian's guide to the CT galaxy: Step-by-step instructions for preparing and analyzing computed tomographic (CT) data using cross-platform, open access software. Integrative Organismal Biology, 2(1), obaa009. https://doi.org/10.1093/IOB/OBAA009
Chatar, N., Boman, R., Gaudichon, V., MacLaren, J., & Fischer, V. (2022). A new, fast protocol to simulate biomechanical loading of bone (1.0). Zenodo. https://doi.org/10.5281/zenodo.6719190
Chatar, N., Fischer, V., & Tseng, Z. J. (2022). Many-to-one function of cat-like mandibles highlights a continuum of sabre-tooth adaptations. Proceedings of the Royal Society B: Biological Sciences, 289(1988), 20221627. https://doi.org/10.1098/rspb.2022.1627
Coburn, B. (1980). Electrical stimulation of the spinal cord: Two-dimensional finite element analysis with particular reference to epidural electrodes. Medical & Biological Engineering & Computing, 18(5), 573–584. https://doi.org/10.1007/BF02443129
Currey, J. D. (1987). The evolution of the mechanical properties of amniote bone. Journal of Biomechanics, 20(11–12), 1035–1044. https://doi.org/10.1016/0021-9290(87)90021-2
Currey, J. D., & Brear, K. (1990). Hardness, Young's modulus and yield stress in mammalian mineralized tissues. Journal of Materials Science: Materials in Medicine, 1(1), 14–20. https://doi.org/10.1007/BF00705348
D'Otreppe, V., Boman, R., & Ponthot, J.-P. (2012). Generating smooth surface meshes from multi-region medical images. International Journal for Numerical Methods in Biomedical Engineering, 28, 642–660. https://doi.org/10.1002/cnm.1471
Erickson, G. M., Catanese, J., & Keaveny, T. M. (2002). Evolution of the biomechanical material properties of the femur. Anatomical Record, 268(2), 115–124. https://doi.org/10.1002/ar.10145
Falkingham, P. L., Bates, K. T., Margetts, L., & Manning, P. L. (2011). Simulating sauropod Manus-only trackway formation using finite-element analysis. Biology Letters, 7(1), 142–145. https://doi.org/10.1098/RSBL.2010.0403
Fallon Gaudichon, V., Boman, R., Chatar, N., Maclaren, J., & Fischer, V. (2021, September). Uncovering the biomechanical disparity of cretaceous marine reptile feeding via finite element analysis. 69th symposium on vertebrate palaeontology and comparative anatomy.
Foffa, D., Cuff, A. R., Sassoon, J., Rayfield, E. J., Mavrogordato, M. N., & Benton, M. J. (2014). Functional anatomy and feeding biomechanics of a giant Upper Jurassic pliosaur (Reptilia: Sauropterygia) from Weymouth Bay, Dorset. UK. Journal of Anatomy, 225(2), 209–219. https://doi.org/10.1111/joa.12200
Gröning, F., Fagan, M., & O'Higgins, P. (2012). Modeling the human mandible under masticatory loads: Which input variables are important? The Anatomical Record, 295, 853–863. https://doi.org/10.1002/ar.22455
Grosse, I. R., Dumont, E. R., Coletta, C., & Tolleson, A. (2007). Techniques for modeling muscle-induced forces in finite element models of skeletal structures. Anatomical Record, 290(9), 1069–1088. https://doi.org/10.1002/ar.20568
Grubich, J. R., Huskey, S., Crofts, S., Orti, G., & Porto, J. (2012). Mega-Bites: Extreme jaw forces of living and extinct piranhas (Serrasalmidae). Scientific Reports, 2(1). https://doi.org/10.1038/srep01009
Huiskes, R., & Hollister, S. J. (1993). From structure to process, from organ to cell: Recent developments of FE-analysis in orthopaedic biomechanics. Journal of Biomechanical Engineering, 115, 520–527.
Joshi, J., Manral, A. R., Maurya, S., & Vishnoi, M. (2021). Biomechanical analysis of human tibia bone based on FEA. Materials Today: Proceedings, 44, 1711–1717. https://doi.org/10.1016/J.MATPR.2020.11.877
Krings, W., Marcé-Nogué, J., Karabacak, H., Glaubrecht, M., & Gorb, S. N. (2020). Finite element analysis of individual taenioglossan radular teeth (Mollusca). Acta Biomaterialia, 115, 317–332. https://doi.org/10.1016/J.ACTBIO.2020.08.034
Laurent, C. P., Böhme, B., Mengoni, M., D'Otreppe, V., Balligand, M., & Ponthot, J. P. (2016). Prediction of the mechanical response of canine humerus to three-point bending using subject-specific finite element modelling. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 230(7), 639–649. https://doi.org/10.1177/0954411916644269
Laurent, C. P., Böhme, B., Verwaerde, J., Papeleux, L., Ponthot, J.-P., & Balligand, M. (2020). Effect of orthopedic implants on canine long bone compression stiffness: A combined experimental and computational approach. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 234(3), 255–264. https://doi.org/10.1177/0954411919882603
MacLaren, J. A., & Nauwelaerts, S. (2016). A three-dimensional morphometric analysis of upper forelimb morphology in the enigmatic tapir (Perissodactyla:Tapirus) hints at subtle variations in locomotor ecology. Journal of Morphology, 277(11), 1469–1485. https://doi.org/10.1002/jmor.20588.
Matthews, F. L., & West, J. B. (1972). Finite element displacement analysis of a lung. Journal of Biomechanics, 5(6), 591–600. https://doi.org/10.1016/0021-9290(72)90031-0
Mengoni, M., Ponthot, J. P., & Boman, R. (2016). Mesh management methods in finite element simulations of orthodontic tooth movement. Medical Engineering and Physics, 38(2), 140–147. https://doi.org/10.1016/j.medengphy.2015.11.005
Morales-García, N. M., Burgess, T. D., Hill, J. J., Gill, P. G., & Rayfield, E. J. (2019). The use of extruded finite-element models as a novel alternative to tomography-based models: A case study using early mammal jaws. Journal of the Royal Society Interface, 16(161), 20190674. https://doi.org/10.1098/rsif.2019.0674
Porro, L. B., Holliday, C. M., Anapol, F., Ontiveros, L. C., Ontiveros, L. T., & Ross, C. F. (2011). Free body analysis, beam mechanics, and finite element modeling of the mandible of Alligator mississippiensis. Journal of Morphology, 272(8), 910–937. https://doi.org/10.1002/jmor.10957
Porro, L. B., Metzger, K. A., Iriarte-Diaz, J., & Ross, C. F. (2013). In vivobone strain and finite element modeling of the mandible of Alligator mississippiensis. Journal of Anatomy, 223(3), 195–227. https://doi.org/10.1111/joa.12080
Püschel, T. A., Marcé-Nogué, J., Gladman, J. T., Bobe, R. R., & Sellers, W. I. (2018). Inferring locomotor behaviours in Miocene New World monkeys using finite element analysis, geometric morphometrics and machine-learning classification techniques applied to talar morphology. Journal of the Royal Society Interface, 15(146), 20180520. https://doi.org/10.1098/rsif.2018.0520
Rayfield, E. J., Norman, D. B., Horner, C. C., Horner, J. R., Smith, P. M., Thomason, J. J., & Upchurch, P. (2001). Cranial design and function in a large theropod dinosaur. Nature, 409(6823), 1033–1037. https://doi.org/10.1038/35059070
Rybicki, E. F., Simonen, F. A., & Weis, E. B. (1972). On the mathematical analysis of stress in the human femur. Journal of Biomechanics, 5(2), 203–215. https://doi.org/10.1016/0021-9290(72)90056-5
Smith, J. M., & Cohen, R. J. (1984). Simple finite-element model accounts for wide range of cardiac dysrhythmias. Proceedings of the National Academy of Sciences of the United States of America, 81(1 I), 233–237. https://doi.org/10.1073/pnas.81.1.233
Tseng, Z. J. (2009). Cranial function in a late Miocene Dinocrocuta gigantea (Mammalia: Carnivora) revealed by comparative finite element analysis. Biological Journal of the Linnean Society, 96(1), 51–67. https://doi.org/10.1111/j.1095-8312.2008.01095.x
Wroe, S., Huber, D. R., Lowry, M., McHenry, C., Moreno, K., Clausen, P., Ferrara, T. L., Cunningham, E., Dean, M. N., & Summers, A. P. (2008). Three-dimensional computer analysis of white shark jaw mechanics: How hard can a great white bite? Journal of Zoology, 276(4), 336–342. https://doi.org/10.1111/j.1469-7998.2008.00494.x
Zapata, U., Metzger, K., Wang, Q., Elsey, R. M., Ross, C. F., & Dechow, P. C. (2010). Material properties of mandibular cortical bone in the American alligator. Alligator mississippiensis. Bone, 46(3), 860–867. https://doi.org/10.1016/j.bone.2009.11.010
Zhou, Z., Winkler, D. E., Fortuny, J., Kaiser, T. M., & Marcé-Nogué, J. (2019). Why ruminating ungulates chew sloppily: Biomechanics discern a phylogenetic pattern. PLoS ONE, 14(4), e0214510. https://doi.org/10.1371/JOURNAL.PONE.0214510
Zienkiewicz, O. C., & Morice, P. B. (1971). The finite element method in engineering science (2nd ed.). McGraw-Hill.
Zienkiewicz, O. C., Taylor, R. L., & Zhu, J. Z. (2005). Finite element method for solid and structural mechanics (6th ed.). Elsevier Butterworth-Heinemann.
