Finite Element Implementation of Mechanochemical Phenomena in Neutral Deformable Porous Media Under Finite Deformation

Abstract

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechano-chemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechano-chemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software).

Computational modelling suggests good, bad and ugly roles of glycosaminoglycans in arterial wall mechanics and mechanobiology

“…Note that the finite-element model accounts further for the effect of the GAGs via a swelling induced contribution to the tangent stiffness matrix (cf. [11,27]). Figure 3 shows data (mean + s.d.)…”

“…Ateshian et al [27] developed a mixture-based finite-element approach to describe nonlinear responses of GAG-endowed continua; this formulation was implemented in the open source software FEBio (www.sci.utah.edu/software/40-mrl/39-febio). They demonstrated the utility of this approach, for example, by studying residual stresses in rodent aortic tissue having layer-specific differences in fixed charge density (FCD; i.e.…”

Combined inverse-forward artificial neural networks for fast and accurate estimation of the diffusion coefficients of cartilage based on multi-physics models

“…Analytical and computational solutions have been developed to interpret experimental data while capturing the real multi-physics phenomena to the maximum possible extent (Arbabi et al, 2015bAteshian et al, 2011;Ateshian et al, 2012).…”

“…Occasionally mathematical fits have been used when analytical solutions were not available, however, since mathematical formulae involving diffusion coefficients are fitted to the experimental data, the physical importance of certain phenomena might be neglected (Kokkonen et al, 2011a). Computational models have been used to obtain the diffusion coefficient of neutral and charged solutes in complex geometries (Arbabi et al, 2015b;Ateshian et al, 2011). Nevertheless, computational models are often associated with optimization algorithms which require advanced computational expertise while being cumbersome and lacking the capacity to recognize pattern of the experimental data.…”

“…Molecular transport (diffusion) plays a key role in monitoring OA progression, delivery of therapeutics and nutrients as well as in the exchange of signaling molecules between cartilage and its surrounding tissues of subchondral bone and synovial fluid (Jackson and Gu, 2009;Pan et al, 2012;Pan et al, 2009). Previous studies used analytical solutions, mathematical fits, and computational models to derive the diffusion coefficients of solutes in cartilage (Arbabi et al, 2015b;Ateshian et al, 2011;Ateshian et al, 2012;Huttunen et al, 2014;Kokkonen et al, 2011a;Kokkonen et al, 2011b). The available analytical solutions can only be applied to problems where either simple geometries are used or simplified assumptions are made (Crank, 1979).…”