Multi-compartment poroelastic models of perfused biological soft tissues: implementation in FEniCSx

Autor: Lavigne, Thomas, Urcun, Stéphane, Rohan, Pierre-Yves, Sciumè, Giuseppe, Baroli, Davide, Bordas, Stéphane P. A.
Rok vydání: 2023
Předmět:
Druh dokumentu: Working Paper
DOI: 10.1016/j.jmbbm.2023.105902
Popis: Soft biological tissues demonstrate strong time-dependent and strain-rate mechanical behavior, arising from their intrinsic visco-elasticity and fluid-solid interactions (especially at sufficiently large time scales). The time-dependent mechanical properties of soft tissues influence their physiological functions and are linked 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 multi-phasic 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.
Comment: https://github.com/Th0masLavigne/Dolfinx_Porous_Media.git
Databáze: arXiv
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