A Poroelastic Mixture Model of Mechanobiological Processes in Tissue Engineering. Part II: Numerical Simulations

TL;DR

This paper presents a numerical simulation of a poroelastic mixture model for tissue engineering, demonstrating how force isotropy and nutrient availability influence tissue growth in a simplified 1D setting.

Contribution

It introduces a novel 1D numerical implementation of a mechanobiological tissue growth model, highlighting the effects of mechanical and nutritional factors on cell populations.

Findings

Cellular growth aligns with stress-dependent predictions.

Isotropy indicator is sensitive to growth rate and boundary conditions.

Simulations confirm the model's ability to capture key mechanobiological processes.

Abstract

In Part I of this article we have developed a novel mechanobiological model of a Tissue Engineering process that accounts for the mechanisms through which an isotropic or anisotropic adherence condition regulates the active functions of the cells in the construct. The model expresses mass balance and force equilibrium balance for a multi-phase mixture in a 3D computational domain and in time dependent conditions. In the present Part II, we study the mechanobiological model in a simplified 1D geometrical setting with the purpose of highlighting the ability of the formulation to represent the influence of force isotropy and nutrient availability on the growth of the tissue construct. In particular, an example of isotropy estimator is proposed and coded within a fixed-point solution map that is used at each discrete time level for system linearization and subsequent finite element approximation of the linearized equations. Extensively conducted simulations show that: 1) the spatial and temporal evolution of the cellular populations are in good agrement with the local growth/production conditions predicted by the mechanobiological stress-dependent model; and 2) the isotropy indicator and all model variables are strongly influenced by both maximum cell specific growth rate and mechanical boundary conditions enforced at the interface between the biomass construct and the interstitial fluid.