Modelling the compression and reorganization of cell aggregates

Abstract

In this paper, we study the mechanical behaviour of multicellular aggregates using the notion of multiple natural configurations. In particular, we extend the elasto-visco-plastic model proposed in Preziosi et al. (2010, An elasto-visco-plastic model of cell aggregates. J. Theor. Biol., 262, 35-47) taking into account the liquid constituent present in cellular spheroids. Aggregates are treated as porous materials, composed of cells and filled with water. The cellular constituent is responsible for the elastic and the plastic behaviour of the material. The plastic component is due to the rearrangement of adhesion bonds between cells and it is translated into the existence of a yield stress in the macroscopic constitutive equation. On the other hand, the liquid constituent is responsible for the viscous-like response during deformation. The general framework is then applied to describe uniaxial homogeneous compression both when a constant load is applied and when a fixed deformation is imposed and subsequently released. We compare the results of the model with the dynamics observed during the experiments in Forgacs et al. (1998, Viscoelastic properties of living embryonic tissues: a quantitative study. Biophys. J., 74, 2227-2234).

A poroplastic model of structural reorganisation in porous media of biomechanical interest

“…In the case of cellular aggregates [42], this type of remodelling manifests itself through the structural transformation of the actin network in the cells, and the reorganisation of the adhesion bonds among the cells. In soft tissues, such as articular cartilage, the considered remodelling might represent the rearrangement of the cross-links of the fibre network forming the extracellular matrix.…”

“…In soft tissues, such as articular cartilage, the considered remodelling might represent the rearrangement of the cross-links of the fibre network forming the extracellular matrix. These processes can be described in terms of "plastic distortions" [42]. It is important to recall that this kind of remodelling is characterised by timescales (in fact, those induced by the mechanical loads) that allow to decouple it from the structural evolution ascribable to growth.…”

“…e.g. [22,65,69] for the case of finite strain elastoplasticity, and [31,40,42,45,48,49,61,64] for the case of growth and remodelling of biological tissues), and stems from the hypothesis that the strain energy density of the solid phase,Ŵ sκ , can be written as a constitutive function of the elastic part of the overall deformation alone, C e , as done in (9). By relating F p with the production of material inhomogeneities in uniform bodies [31], a rationale for this constitutive hypothesis is obtained by invoking the principle of material uniformity [29][30][31]83].…”

“…Hence, as we would do in the theory of elastoplasticity, we search for an evolution law for the remodelling variable B p in the form of a generalised plastic "flow rule". To this end, following [42], we imitate the theory of associative, rate-independent elastoplasticity [22,93], and articulate in two steps the determination of the flow rule. In the first step, we postulate that a yield surface exists in the space of the deviatoric Kirchhoff stress tensors, which can be defined by the equation…”

A Parametric Study of a Multiphase Porous Media Model for Tumor Spheroids and Environment Interactions

“…Recently, it has become clear that a collective effort from all the physical sciences is required to improve our understanding of this illness and design new strategies for therapeutical treatments [3][4][5][6]. The development of effective computational models to investigate the growth of a tumor mass is certainly a valid contribution to this field.…”