[en] Soft biological tissues demonstrate strong time-dependent and strain-rate mechanical behavior, arising from their intrinsic visco-elasticity and fluid-solid interactions. The time-dependent mechanical properties of soft tissues influence their physiological functions and are related to several pathological processes. Poro-elastic modeling represents a promising approach because it allows the integration of multiscale/multiphysics data to probe biologically relevant phenomena at a smaller scale and embeds the relevant mechanisms at the larger scale. The implementation of multiphase flow poro-elastic models however is a complex undertaking, requiring extensive knowledge. The open-source software FEniCSx Project provides a novel tool for the automated solution of partial differential equations by the finite element method. This paper aims to provide the required tools to model the mixed formulation of poro-elasticity, from the theory to the implementation, within FEniCSx. Several benchmark cases are studied. A column under confined compression conditions is compared to the Terzaghi analytical solution, using the L2-norm. An implementation of poro-hyper-elasticity is proposed. A bi-compartment column is compared to previously published results (Cast3m implementation). For all cases, accurate results are obtained in terms of a normalized Root Mean Square Error (RMSE). Furthermore, the FEniCSx computation is found three times faster than the legacy FEniCS one. The benefits of parallel computation are also highlighted.
Disciplines :
Mechanical engineering
Author, co-author :
LAVIGNE, Thomas ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
URCUN, Stephane ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Rohan, Pierre-Yves; Arts et Metiers Institute of Technology, IBHGC, 151 bd de l'hopital, Paris, 75013, France
Sciumè, Giuseppe; Arts et Metiers Institute of Technology, Univ. of Bordeaux, CNRS, Bordeaux INP, INRAE, I2M Bordeaux, Avenue d'Aquitaine, Pessac, 33607, France
BAROLI, Davide ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Engineering ; Università della Svizzera Italiana, Euler Institute, Lugano, Switzerland. Electronic address: davide.baroli@usi.ch
Bordas, Stéphane P A; Institute of Computational Engineering, Department of Engineering, University of Luxembourg, 6, avenue de la Fonte, Esch-sur-Alzette, L-4364, Luxembourg, Clyde Visiting Fellow, Department of Mechanical Engineering, The University of Utah, Salt Lake City, UT, United States, Visiting Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
External co-authors :
yes
Language :
English
Title :
Single and bi-compartment poro-elastic model of perfused biological soft tissues: FEniCSx implementation and tutorial.
Publication date :
July 2023
Journal title :
Journal of the Mechanical Behavior of Biomedical Materials
FNR17013182 - CHAMP - Characterisation And Modelling Of Perfusion And Soft Tissue Damage In Pressure Ulcer Prevention, 2022 (01/09/2022-31/08/2025) - Thomas Jeffrey Hugo Marc Lavigne
Funders :
Fonds National de la Recherche Luxembourg
Funding text :
This research was funded in whole, or in part, by the Luxembourg National Research Fund (FNR) , grant reference No. 17013182 . For the purpose of open access, the author has applied a Creative Commons Attribution 4.0 International (CC BY 4.0) license to any Author Accepted Manuscript version arising from this submission. The present project is also supported by the National Research Fund, Luxembourg , under grant No. C20/MS/14782078/QuaC .
Alnæs, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N., The FEniCS project version 1.5. Arch. Numer. Softw., 3, 2015, 10.11588/ANS.2015.100.20553 Starting Point and Frequency:Year: 2013,URL: http://journals.ub.uni-heidelberg.de/index.php/ans/article/view/20553.
Alnæs, M.S., Logg, A., Ølgaard, K.B., Rognes, M.E., Wells, G.N., Unified form language: A domain-specific language for weak formulations of partial differential equations. ACM Trans. Math. Software, 40(2), 2014, 10.1145/2566630.
Argoubi, M., Shirazi-Adl, A., Poroelastic creep response analysis of a lumbar motion segment in compression. J. Biomech. 29:10 (1996), 1331–1339, 10.1016/0021-9290(96)00035-8.
Ateshian, G.A., The role of interstitial fluid pressurization in articular cartilage lubrication. J. Biomech. 42:9 (2009), 1163–1176, 10.1016/j.jbiomech.2009.04.040 URL: https://www.sciencedirect.com/science/article/pii/S0021929009002565.
Biot, M.A., General theory of three-dimensional consolidation. J. Appl. Phys. 12:2 (1941), 155–164.
Budday, S., Ovaert, T.C., Holzapfel, G.A., Steinmann, P., Kuhl, E., Fifty shades of brain: A review on the mechanical testing and modeling of brain tissue. Arch. Comput. Methods Eng. 27:4 (2019), 1187–1230, 10.1007/s11831-019-09352-w.
Bulle, R., A Posteriori Error Estimation for Finite Element Approximations of Fractional Laplacian Problems and Applications to Poro-Elasticity. (Ph.D. thesis), 2022, University of Luxembourg; Université de Bourgogne Franche-Comté URL: https://tel.archives-ouvertes.fr/tel-03652547.
Detournay, E., Cheng, A.H.-D., Fundamentals of Poroelasticity. 1993, Elsevier, 113–171.
Doll, S., Schweizerhof, K., On the development of volumetric strain energy functions. J. Appl. Mech. 67:1 (2000), 17–21.
Fehervary, H., Maes, L., Vastmans, J., Kloosterman, G., Famaey, N., How to implement user-defined fiber-reinforced hyperelastic materials in finite element software. J. Mech. Behav. Biomed. Mater., 110, 2020, 103737, 10.1016/j.jmbbm.2020.103737 URL: https://www.sciencedirect.com/science/article/pii/S1751616120302915.
Franceschini, G., Bigoni, D., Regitnig, P., Holzapfel, G., Brain tissue deforms similarly to filled elastomers and follows consolidation theory. J. Mech. Phys. Solids 54:12 (2006), 2592–2620, 10.1016/j.jmps.2006.05.004.
Gimnich, O.A., Singh, J., Bismuth, J., Shah, D.J., Brunner, G., Magnetic resonance imaging based modeling of microvascular perfusion in patients with peripheral artery disease. J. Biomech. 93 (2019), 147–158, 10.1016/j.jbiomech.2019.06.025.
Gray, W.G., Miller, C.T., Introduction To the Thermodynamically Constrained Averaging Theory for Porous Medium Systems. 2014, Springer International Publishing, 10.1007/978-3-319-04010-3.
Haagenson, R., Rajaram, H., Allen, J., A generalized poroelastic model using FEniCS with insights into the Noordbergum effect. Comput. Methods Appl. Mech. Engrg., 135, 2020, 104399, 10.1016/j.cageo.2019.104399.
Horgan, C.O., Saccomandi, G., Constitutive models for compressible nonlinearly elastic materials with limiting chain extensibility. J. Elasticity 77:2 (2004), 123–138, 10.1007/s10659-005-4408-x.
Hosseini-Farid, M., Ramzanpour, M., McLean, J., Ziejewski, M., Karami, G., A poro-hyper-viscoelastic rate-dependent constitutive modeling for the analysis of brain tissues. J. Mech. Behav. Biomed. Mater., 102, 2020, 103475, 10.1016/j.jmbbm.2019.103475.
Joodat, S., Nakshatrala, K., Ballarini, R., Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions. Comput. Methods Appl. Mech. Engrg. 337 (2018), 632–676, 10.1016/j.cma.2018.04.004 URL: https://www.sciencedirect.com/science/article/pii/S0045782518301749.
Lavigne, T., Sciumè, G., Laporte, S., Pillet, H., Urcun, S., Wheatley, B., Rohan, P.-Y., Société de Biomécanique Young Investigator Award 2021: Numerical investigation of the time-dependent stress–strain mechanical behaviour of skeletal muscle tissue in the context of pressure ulcer prevention. Clin. Biomech., 93, 2022, 105592, 10.1016/j.clinbiomech.2022.105592 URL: https://www.sciencedirect.com/science/article/pii/S0268003322000225.
Marino, M., Constitutive modeling of soft tissues. 2018, 81–110, 10.1016/B978-0-12-801238-3.99926-4.
Mascheroni, P., Stigliano, C., Carfagna, M., Boso, D.P., Preziosi, L., Decuzzi, P., Schrefler, B.A., Predicting the growth of glioblastoma multiforme spheroids using a multiphase porous media model. Biomech. Model. Mechanobiol. 15:5 (2016), 1215–1228, 10.1007/s10237-015-0755-0.
Mazier, A., Hadramy, S.E., Brunet, J.-N., Hale, J.S., Cotin, S., Bordas, S.P.A., SOniCS: Develop intuition on biomechanical systems through interactive error controlled simulations. 2022, 10.48550/ARXIV.2208.11676 URL: https://arxiv.org/abs/2208.11676.
Mazier, A., Ribes, S., Gilles, B., Bordas, S.P., A rigged model of the breast for preoperative surgical planning. J. Biomech., 128, 2021, 110645, 10.1016/j.jbiomech.2021.110645 URL: https://www.sciencedirect.com/science/article/pii/S0021929021004140.
Oftadeh, R., Connizzo, B.K., Nia, H.T., Ortiz, C., Grodzinsky, A.J., Biological connective tissues exhibit viscoelastic and poroelastic behavior at different frequency regimes: Application to tendon and skin biophysics. Acta Biomater. 70 (2018), 249–259, 10.1016/j.actbio.2018.01.041 URL: https://www.sciencedirect.com/science/article/pii/S1742706118300527.
Pence, T.J., Gou, K., On compressible versions of the incompressible neo-Hookean material. Math. Mech. Solids 20:2 (2014), 157–182, 10.1177/1081286514544258.
Peyrounette, M., Davit, Y., Quintard, M., Lorthois, S., Multiscale modelling of blood flow in cerebral microcirculation: Details at capillary scale control accuracy at the level of the cortex. Boltze, J., (eds.) PLOS ONE, 13(1), 2018, e0189474, 10.1371/journal.pone.0189474.
Sciumè, G., Mechanistic modeling of vascular tumor growth: an extension of Biot's theory to hierarchical bi-compartment porous medium systems. Acta Mech. 232:4 (2021), 1445–1478, 10.1007/s00707-020-02908-z.
Sciumè, G., Shelton, S., Gray, W.G., Miller, C.T., Hussain, F., Ferrari, M., Decuzzi, P., Schrefler, B.A., A multiphase model for three-dimensional tumor growth. New J. Phys., 15(1), 2013, 015005, 10.1088/1367-2630/15/1/015005.
Scroggs, M.W., Baratta, I.A., Richardson, C.N., Wells, G.N., Basix: a runtime finite element basis evaluation library. J. Open Source Softw., 7(73), 2022, 3982, 10.21105/joss.03982.
Scroggs, M.W., Dokken, J.S., Richardson, C.N., Wells, G.N., Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes. ACM Trans. Math. Software, 48(2), 2022, 10.1145/3524456.
Selvadurai, A., Suvorov, A., Coupled hydro-mechanical effects in a poro-hyperelastic material. J. Mech. Phys. Solids 91 (2016), 311–333, 10.1016/j.jmps.2016.03.005 URL: https://www.sciencedirect.com/science/article/pii/S0022509615303574.
Siddique, J., Ahmed, A., Aziz, A., Khalique, C., A review of mixture theory for deformable porous media and applications. Appl. Sci., 7(9), 2017, 917, 10.3390/app7090917.
Simms, C.K., Loocke, M.V., Lyons, C.G., Skeletal muscle in compression: Modeling approaches for the passive muscle bulk. Int. J. Multiscale Comput. Eng. 10:2 (2012), 143–154, 10.1615/intjmultcompeng.2011002419.
Simo, J., A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation. Comput. Methods Appl. Mech. Engrg. 66:2 (1988), 199–219, 10.1016/0045-7825(88)90076-X URL: https://www.sciencedirect.com/science/article/pii/004578258890076X.
Treloar, L.G., The Physics of Rubber Elasticity. 1975, OUP Oxford.
Urcun, S., Baroli, D., Rohan, P.-Y., Skalli, W., Lubrano, V., Bordas, S.P., Sciume, G., Non-operable glioblastoma: proposition of patient-specific forecasting by image-informed poromechanical model. Brain Multiph., 2023, 100067.
Urcun, S., Rohan, P.-Y., Sciumè, G., Bordas, S.P., Cortex tissue relaxation and slow to medium load rates dependency can be captured by a two-phase flow poroelastic model. J. Mech. Behav. Biomed. Mater., 126, 2022, 104952, 10.1016/j.jmbbm.2021.104952 URL: https://www.sciencedirect.com/science/article/pii/S175161612100583X.
Urcun, S., Rohan, P.-Y., Skalli, W., Nassoy, P., Bordas, S.P.A., Sciumè, G., Digital twinning of Cellular Capsule Technology: Emerging outcomes from the perspective of porous media mechanics. PLOS ONE 16:7 (2021), 1–30, 10.1371/journal.pone.0254512.
Vaidya, A.J., Wheatley, B.B., An experimental and computational investigation of the effects of volumetric boundary conditions on the compressive mechanics of passive skeletal muscle. J. Mech. Behav. Biomed. Mater., 102, 2020, 103526, 10.1016/j.jmbbm.2019.103526.
Van Loocke, M., Simms, C., Lyons, C., Viscoelastic properties of passive skeletal muscle in compression—Cyclic behaviour. J. Biomech. 42:8 (2009), 1038–1048, 10.1016/j.jbiomech.2009.02.022.
Verruijt, A., Theory and Problems of Poroelasticity, Vol. 71. 2013, Delft University of Technology.
Zulian, P., Kopaničáková, A., Nestola, M.G.C., Fadel, N., Fink, A., VandeVondele, J., Krause, R., Large scale simulation of pressure induced phase-field fracture propagation using Utopia. CCF Trans. High Perform. Comput., 2021, 10.1007/s42514-021-00069-6 arXiv:https://doi.org/10.1007/s42514-021-00069-6.
Zulian, P., Kopaničáková, A., Nestola, M.C.G., Fink, A., Fadel, N., Rigazzi, A., Magri, V., Schneider, T., Botter, E., Mankau, J., Krause, R., Utopia: A performance portable C++ library for parallel linear and nonlinear algebra. Git repository. 2016 URL: https://bitbucket.org/zulianp/utopia.
