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

Coupled flow and biomass-nutrient growth at pore-scale with permeable biofilm, adaptive singularity and multiple species

In this paper we describe a coupled model for flow and microbial growth as well as nutrient utilization. These processes occur within and outside the biofilm phase formed by the microbes. The primary challenge is to address the volume constraint of maximum cell density but also to allow some microbial presence outside the contiguous biofilm phase. Our model derives from the continuum analogues of the mechanism of cell shoving introduced in discrete biomass models, and in particular from the models exploiting singular diffusivity as well as from models of variational inequality type which impose explicit constraints. We blend these approaches and propose a new idea to adapt the magnitude of the diffusivity automatically so as to ensure the volume constraint without affecting the reactions; this construction can be implemented in many variants without deteriorating the overall efficiency. The second challenge is to account for the flow and transport in the bulk fluid phase adjacent to the biofilm phase. We use the Brinkman flow model with a spatially variable permeability depending on biomass amount. The fluid flow allows some advection of the nutrient within the biofilm phase as well as for the flow even when the pores are close to being plugged up. Our entire model is monolithic and computationally robust even in complex pore-scale geometries, and extends to multiple species. We provide illustrations of our model and of related approaches. The results of the model can be easily post-processed to provide Darcy scale properties of the porous medium, e.g., one can predict how the permeability changes depending on the biomass growth in many realistic scenarios.

[Review of studies on the biomechanical modelling of the coupling effect between stent degradation and blood vessel remodeling]

The dynamic coupling of stent degradation and vessel remodeling can influence not only the structural morphology and material property of stent and vessel, but also the development of in-stent restenosis. The research achievements of biomechanical modelling and analysis of stent degradation and vessel remodeling were reviewed; several noteworthy research perspectives were addressed, a stent-vessel coupling model was developed based on stent damage function and vessel growth function, and then concepts of matching ratio and risk factor were established so as to evaluate the treatment effect of stent intervention, which may lay the scientific foundation for the structure design, mechanical analysis and clinical application of biodegradable stent.

Incorporating Cellular Stochasticity in Solid-Fluid Mixture Biofilm Models

The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses, which determine the overall evolution. Incorporating stochastic cellular behavior in macroscopic models of biological media is a challenging task. Herein, we propose hybrid models for bacterial biofilm growth, which couple a two phase solid/fluid mixture description of mechanical and chemical fields with a dynamic energy budget-based cellular automata treatment of bacterial activity. Thin film and plate approximations for the relevant interfaces allow us to obtain numerical solutions exhibiting behaviors observed in experiments, such as accelerated spread due to water intake from the environment, wrinkle formation, undulated contour development, and the appearance of inhomogeneous distributions of differentiated bacteria performing varied tasks.

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

The present work addresses transvascular and interstitial fluid transport inside a solid tumor surrounded by normal tissue (close to an in vivo mimicking setup). In general, biological tissues behave like a soft porous material and show mechanical behavior towards the fluid motion through the interstitial space. In general, forces like viscous drag that are associated with the fluid flow may compress the tissue material. On the macroscopic level, we try to model the motion of fluids and macromolecules through the interstitial space of solid tumor and the normal tissue layer. The transvascular fluid transport is assumed to be governed by modified Starling's law. The poroelastohydrodynamics (interstitial hydrodynamics and the deformation of tissue material) inside the tumor and normal tissue regions is modeled using linearized biphasic mixture theory. Correspondingly, the velocity distribution of fluid is coupled to the displacement field of the solid phase (mainly cellular phase and extracellular matrix) in both the normal and tumor tissue regions. The corresponding velocity field is used within the transport reaction equation for fluids and macromolecules through interstitial space to get the overall solute (e.g., nutrients, drug, and other macromolecules) distribution. This study justifies that the presence of the normal tissue layer plays a significant role in delaying/assisting necrosis inside the tumor tissue. It is observed that the exchange process of fluids and macromolecules across the interface of the tumor and normal tissue affects the effectiveness factor corresponding to the tumor tissue.