A poroelastic mixture model of mechanobiological processes in biomass growth: theory and application to tissue engineering

Abstract

In this article we propose a novel mathematical description of biomass growth that combines poroelastic theory of mixtures and cellular population models. The formulation, potentially applicable to general mechanobiological processes, is here used to study the engineered cultivation in bioreactors of articular chondrocytes, a process of Regenerative Medicine characterized by a complex interaction among spatial scales (from nanometers to centimeters), temporal scales (from seconds to weeks) and biophysical phenomena (fluid-controlled nutrient transport, delivery and consumption; mechanical deformation of a multiphase porous medium). The principal contribution of this research is the inclusion of the concept of cellular ''force isotropy'' as one of the main factors influencing cellular activity. In this description, the induced cytoskeletal tensional states trigger signalling transduction cascades regulating functional cell behavior. This mechanims is modeled by a parameter which estimates the influence of local force isotropy by the norm of the deviatoric part of the total stress tensor. According to the value of the estimator, isotropic mechanical conditions are assumed to be the promoting factor of extracellular matrix production whereas anisotropic conditions are assumed to promote cell proliferation. The resulting mathematical formulation is a coupled system of nonlinear partial differential equations comprising: conservation laws for mass and linear momentum of the growing biomass; advection-diffusion-reaction laws for nutrient (oxygen) transport, delivery and consumption; and kinetic laws for cellular population dynamics. To develop a reliable computational tool for the simulation of the engineered tissue growth process the nonlinear differential problem is numerically solved by: (1) temporal semidiscretization; (2) linearization via a fixed-point map; and (3) finite element spatial approximation. The biophysical accuracy of the mechanobiological model is assessed in the analysis of a simplified 1D geometrical setting. Simulation results show that: (1) isotropic/anisotropic conditions are strongly influenced by both maximum cell specific growth rate and mechanical boundary 123Meccanica (2017) 52: 3273-3297 DOI 10.1007/s11012-017-0638-9 conditions enforced at the interface between the biomass construct and the interstitial fluid; (2) experimentally measured features of cultivated articular chondrocytes, such as the early proliferation phase and the delayed extracellular matrix production, are well described by the computed spatial and temporal evolutions of cellular populations.

A Continuum Mechanics Model of Enzyme-Based Tissue Degradation in Cancer Therapies

“…Many mathematical models of passive transport into a poroelastic medium do not take into account exchanges between phases (Basser 1992;Støverud et al 2011;Chapelle and Moireau 2014). In (Fusi et al 2006;Lemon et al 2006;Sacco et al 2017), models including exchanges between phases are presented on closed poroelastic mixtures (no external sources or sinks). However, the changes are not mediated by external species.…”

Incorporating Cellular Stochasticity in Solid–Fluid Mixture Biofilm Models

“…If we need to track the variations of the nutrient concentration, we may use effective continuity equations for chemical concentration in tissues [30,31]. For the limiting concentration c n :…”

“…We update the cellular fields solving (30) with the stationary concentration values for (31). The time derivatives in (31) are small, so that time evolution is driven by the source terms reflecting cell activity and changes in the biofilm boundaries.…”

Special issue on ‘active behavior in soft matter and mechanobiology’

“…The topic of fluid flow in biological tissues is analyzed in the papers [1][2][3][4]. The paper by Sacco, Causin, Lelli, and Raimondi applies concepts from mixture theory to the processes of biomass growth for applications in tissue engineering [1].…”

“…The paper by Sacco, Causin, Lelli, and Raimondi applies concepts from mixture theory to the processes of biomass growth for applications in tissue engineering [1]. Grillo, Carfagna, and Federico examine non-Darcian effects in solvent transport in fiber-reinforced biological tissues [2].…”