Mixture theory-based poroelasticity as a model of interstitial tissue growth

Chemically Responsive Hydrogel Deformation Mechanics: A Review

A hydrogel is a polymeric three-dimensional network structure. The applications of this material type are diversified over a broad range of fields. Their soft nature and similarity to natural tissue allows for their use in tissue engineering, medical devices, agriculture, and industrial health products. However, as the demand for such materials increases, the need to understand the material mechanics is paramount across all fields. As a result, many attempts to numerically model the swelling and drying of chemically responsive hydrogels have been published. Material characterization of the mechanical properties of a gel bead under osmotic loading is difficult. As a result, much of the literature has implemented variants of swelling theories. Therefore, this article focuses on reviewing the current literature and outlining the numerical models of swelling hydrogels as a result of exposure to chemical stimuli. Furthermore, the experimental techniques attempting to quantify bulk gel mechanics are summarized. Finally, an overview on the mechanisms governing the formation of geometric surface instabilities during transient swelling of soft materials is provided.

Mechanobiological Stability of Biological Soft Tissues

Like all other materials, biological soft tissues are subject to general laws of physics, including those governing mechanical equilibrium and stability. In addition, however, these tissues are able to respond actively to changes in their mechanical and chemical environment. There is, therefore, a pressing need to understand such processes theoretically. In this paper, we present a new rate-based constrained mixture formulation suitable for studying mechanobiological equilibrium and stability of soft tissues exposed to transient or sustained changes in material composition or applied loading. These concepts are illustrated for canonical problems in arterial mechanics, which distinguish possible stable versus unstable mechanobiological responses. Such analyses promise to yield insight into biological processes that govern both health and disease progression.

Coupling tumor growth and bio distribution models

We couple a tumor growth model embedded in a microenvironment, with a bio distribution model able to simulate a whole organ. The growth model yields the evolution of tumor cell population, of the differential pressure between cell populations, of porosity of ECM, of consumption of nutrients due to tumor growth, of angiogenesis, and related growth factors as function of the locally available nutrient. The bio distribution model on the other hand operates on a frozen geometry but yields a much refined distribution of nutrient and other molecules. The combination of both models will enable simulating the growth of a tumor in a whole organ, including a realistic distribution of therapeutic agents and allow hence to evaluate the efficacy of these agents.

Numerical modeling of bone as a multiscale poroelastic material by the homogenization technique

Bone is a complex material showing a hierarchical and porous structure but also a natural ability to remodel thanks to cells sensitive to fluid flows. Based on these characteristics, a multiscale numerical model has been developed in order to represent the bone response under mechanical solicitation. It relies on the homogenization technique, simulating bone as a homogeneous structure having a porous microstructure saturated with bone fluid. The numerical modeling of the loading of a finite volume of bone enables the determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid boundary conditions, the study of the corresponding structural response provides an overview of the fluid contribution to the poroelastic behavior, impacting the stiffness of the considered material. This parameter is either reduced (when the fluid can flow out of the structure) or increased (when the fluid is kept inside the structure) and quantified through this model. The presented poroelastic numerical model is here developed in the perspective of providing a bio-reliable model of bones, to determine the critical parameters that might impact bone remodeling.

Differential Activity-Driven Instabilities in Biphasic Active Matter

Active stresses can cause instabilities in contractile gels and living tissues. Here we provide a generic hydrodynamic theory that treats these systems as a mixture of two phases of varying activity and different mechanical properties. We find that differential activity between the phases causes a uniform mixture to undergo a demixing instability. We follow the nonlinear evolution of the instability and characterize a phase diagram of the resulting patterns. Our study complements other instability mechanisms in mixtures driven by differential adhesion, differential diffusion, differential growth, and differential motion.

Governing Equations of Tissue Modelling and Remodelling: A Unified Generalised Description of Surface and Bulk Balance

Several biological tissues undergo changes in their geometry and in their bulk material properties by modelling and remodelling processes. Modelling synthesises tissue in some regions and removes tissue in others. Remodelling overwrites old tissue material properties with newly formed, immature tissue properties. As a result, tissues are made up of different “patches”, i.e., adjacent tissue regions of different ages and different material properties, within evolving boundaries. In this paper, generalised equations governing the spatio-temporal evolution of such tissues are developed within the continuum model. These equations take into account nonconservative, discontinuous surface mass balance due to creation and destruction of material at moving interfaces, and bulk balance due to tissue maturation. These equations make it possible to model patchy tissue states and their evolution without explicitly maintaining a record of when/where resorption and formation processes occurred. The time evolution of spatially averaged tissue properties is derived systematically by integration. These spatially-averaged equations cannot be written in closed form as they retain traces that tissue destruction is localised at tissue boundaries. The formalism developed in this paper is applied to bone tissues, which exhibit strong material heterogeneities due to their slow mineralisation and remodelling processes. Evolution equations are proposed in particular for osteocyte density and bone mineral density. Effective average equations for bone mineral density (BMD) and tissue mineral density (TMD) are derived using a mean-field approximation. The error made by this approximation when remodelling patchy tissue is investigated. The specific signatures of the time evolution of BMD or TMD during remodelling events are exhibited. These signatures may provide a way to detect remodelling events at lower, unseen spatial resolutions from microCT scans.

Interstitial growth and remodeling of biological tissues: tissue composition as state variables

Growth and remodeling of biological tissues involves mass exchanges between soluble building blocks in the tissue's interstitial fluid and the various constituents of cells and the extracellular matrix. As the content of these various constituents evolves with growth, associated material properties, such as the elastic modulus of the extracellular matrix, may similarly evolve. Therefore, growth theories may be formulated by accounting for the evolution of tissue composition over time in response to various biological and mechanical triggers. This approach has been the foundation of classical bone remodeling theories that successfully describe Wolff's law by establishing a dependence between Young's modulus and bone apparent density and by formulating a constitutive relation between bone mass supply and the state of strain. The goal of this study is to demonstrate that adding tissue composition as state variables in the constitutive relations governing the stress-strain response and the mass supply represents a very general and straightforward method to model interstitial growth and remodeling in a wide variety of biological tissues. The foundation for this approach is rooted in the framework of mixture theory, which models the tissue as a mixture of multiple solid and fluid constituents. A further generalization is to allow each solid constituent in a constrained solid mixture to have its own reference (stress-free) configuration. Several illustrations are provided, ranging from bone remodeling to cartilage tissue engineering and cervical remodeling during pregnancy.