A tumor growth model with deformable ECM

Abstract

Existing tumor growth models based on fluid analogy for the cells do not generally include the extracellular matrix (ECM), or if present, take it as rigid. The three-fluid model originally proposed by the authors and comprising tumor cells (TC), host cells (HC), interstitial fluid (IF) and an ECM, considered up to now only a rigid ECM in the applications. This limitation is here relaxed and the deformability of the ECM is investigated in detail. The ECM is modeled as a porous solid matrix with Green-elastic and elasto-visco-plastic material behavior within a large strain approach. Jauman and Truesdell objective stress measures are adopted together with the deformation rate tensor. Numerical results are first compared with those of a reference experiment of a multicellular tumor spheroid (MTS) growing in vitro, then three different tumor cases are studied: growth of an MTS in a decellularized ECM, growth of a spheroid in the presence of host cells and growth of a melanoma. The influence of the stiffness of the ECM is evidenced and comparison with the case of a rigid ECM is made. The processes in a deformable ECM are more rapid than in a rigid ECM and the obtained growth pattern differs. The reasons for this are due to the changes in porosity induced by the tumor growth. These changes are inhibited in a rigid ECM. This enhanced computational model emphasizes the importance of properly characterizing the biomechanical behavior of the malignant mass in all its components to correctly predict its temporal and spatial pattern evolution.

Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results

“…It is not our intention to review these models here, instead we refer the reader to some basic key literature in this field [71,219,220]. Models that pay special attention to mechanical interaction with ECM and surrounding host tissue are generally more recent developments (see e.g., [221][222][223][224][225]). Continuum models generally have less parameters and they offer some advantages with regard to the information that needs to be analyzed.…”

A monolithic multiphase porous medium framework for (a-)vascular tumor growth

“…This allows us to define consistent inter-phase exchange terms between the neovasculature and the IF. In the following formulation of the novel vascular multiphase model we will adopt the notation of [17], where α denotes a generic phase, s the solid phase, i.e., the ECM, l the interstitial fluid, h the healthy cells and t the tumor cells. In addition, the (neo-)vasculature is identified with index v and all equations are formulated on the macroscopic level.…”

“…However, we do not want to repeat all derivations here, the interested reader is referred to [17] for the original model. As opposed to the derivations there, we will employ an ALE formulation.…”

“…Comparing our formulation of the balance of mass with the one of the previous four-phase model [8,17], three additional terms can be identified, namely, the time derivative of the mass fraction of the neovasculature scaled with the saturation, the additional time derivative of the solid pressure scaled with the negative volume fraction of the neovasculature −ε v and the additional divergence of the grid velocity scaled with the negative volume fraction of the neovasculature −ε v . These terms have been introduced since the modified balance of mass of the solid phase (10) incorporates the neovasculature volume fraction.…”

“…Constitutive relations for tumor growth, necrosis and nutrient, i.e., oxygen consumption have been formulated in [14]. Subsequently, the interactions of the fluid phases have been investigated in [15,16] and a deformable ECM has been introduced in [17]. Recently, the model has been enhanced with cell lysis and matrix deposition [18].…”