Single and bi-compartment poro-elastic model of perfused biological soft tissues: FEniCSx implementation and tutorial

Thomas Lavigne; Stéphane Urcun; Pierre-Yves Rohan; Giuseppe Sciumè; Davide Baroli; Stéphane P A Bordas

doi:10.1016/j.jmbbm.2023.105902

Single and bi-compartment poro-elastic model of perfused biological soft tissues: FEniCSx implementation and tutorial

J Mech Behav Biomed Mater. 2023 Jul:143:105902. doi: 10.1016/j.jmbbm.2023.105902. Epub 2023 May 11.

Authors

Thomas Lavigne¹, Stéphane Urcun², Pierre-Yves Rohan³, Giuseppe Sciumè⁴, Davide Baroli⁵, Stéphane P A Bordas⁶

Affiliations

¹ Institute of Computational Engineering, Department of Engineering, University of Luxembourg, 6, avenue de la Fonte, Esch-sur-Alzette, L-4364, Luxembourg; Arts et Metiers Institute of Technology, IBHGC, 151 bd de l'hopital, Paris, 75013, France; Arts et Metiers Institute of Technology, Univ. of Bordeaux, CNRS, Bordeaux INP, INRAE, I2M Bordeaux, Avenue d'Aquitaine, Pessac, 33607, France.
² Institute of Computational Engineering, Department of Engineering, University of Luxembourg, 6, avenue de la Fonte, Esch-sur-Alzette, L-4364, Luxembourg.
³ Arts et Metiers Institute of Technology, IBHGC, 151 bd de l'hopital, Paris, 75013, France.
⁴ Arts et Metiers Institute of Technology, Univ. of Bordeaux, CNRS, Bordeaux INP, INRAE, I2M Bordeaux, Avenue d'Aquitaine, Pessac, 33607, France.
⁵ Università della Svizzera Italiana, Euler Institute, Lugano, Switzerland. Electronic address: davide.baroli@usi.ch.
⁶ 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.

PMID: 37209595
DOI: 10.1016/j.jmbbm.2023.105902

Abstract

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.

Keywords: Bi-compartment; FEniCSx; Mixed space; Poro-elasticity.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Biomechanical Phenomena
Elasticity
Finite Element Analysis
Models, Biological*
Stress, Mechanical
Viscosity