Growing avascular tumours as elasto-plastic bodies by the theory of evolving natural configurations

Giverso, Chiara; Scianna, Marco; Grillo, Alfio

doi:10.1016/j.mechrescom.2015.04.004

Cited by 33 publications

(32 citation statements)

References 36 publications

(69 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Understanding how growth and remodeling are related to each other is a necessary step towards the comprehension of the evolution of biological tissues. In this respect, we remark that the coupling of growth and remodeling has been investigated in several papers, [ , and references therein] without considering strain‐gradient constitutive laws, while second‐order theories have been proposed, for example, by Ciarletta et al to investigate the transport of mass in the presence of morphogenesis (see also Epstein and Maugin for a discussion on this issue).…”

Section: Introductionmentioning

confidence: 99%

A study of growth and remodeling in isotropic tissues, based on the Anand‐Aslan‐Chester theory of strain‐gradient plasticity

et al. 2019

Self Cite

View full text Add to dashboard Cite

Motivated by the increasing interest of the biomechanical community towards the employment of strain‐gradient theories for solving biological problems, we study the growth and remodeling of a biological tissue on the basis of a strain‐gradient formulation of remodeling. Our scope is to evaluate the impact of such an approach on the principal physical quantities that determine the growth of the tissue. For our purposes, we assume that remodeling is characterized by a coarse and a fine length scale and, taking inspiration from a work by Anand, Aslan, and Chester, we introduce a kinematic variable that resolves the fine scale inhomogeneities induced by remodeling. With respect to this variable, a strain‐gradient framework of remodeling is developed. We adopt this formulation in order to investigate how a tumor tissue grows and how it remodels in response to growth. In particular, we focus on a type of remodeling that manifests itself in two different, but complementary, ways: on the one hand, it finds its expression in a stress‐induced reorganization of the adhesion bonds among the tumor cells, and, on the other hand, it leads to a change of shape of the cells and of the tissue, which is generally not recovered when external loads are removed. To address this situation, we resort to a generalized Bilby‐Kröner‐Lee decomposition of the deformation gradient tensor. We test our model on a benchmark problem taken from the literature, which we rephrase in two ways: microscale remodeling is disregarded in the first case, and accounted for in the second one. Finally, we compare and discuss the obtained numerical results.

show abstract

Section: Introductionmentioning

confidence: 99%

A study of growth and remodeling in isotropic tissues, based on the Anand‐Aslan‐Chester theory of strain‐gradient plasticity

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…This is part of our current investigations. We remark that the order with which the tensors F g and F d appear in (68) is not unique, but it becomes irrelevant if F g and F d are assumed to be purely volumetric [43]. Equations (44a) and (44b) are rather standard and constitute the starting point for both poroelastic and poroplastic models of solid-fluid mixtures.…”

Section: Discussionmentioning

confidence: 99%

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

Grillo

Prohl

Wittum

2015

Continuum Mech. Thermodyn.

Self Cite

View full text Add to dashboard Cite

We present a poroplastic model of structural reorganisation in a binary mixture comprising a solid and a fluid phase. The solid phase is the macroscopic representation of a deformable porous medium, which exemplifies the matrix of a biological system (consisting e.g. of cells, extracellular matrix, collagen fibres). The fluid occupies the interstices of the porous medium and is allowed to move throughout it. The system reorganises its internal structure in response to mechanical stimuli. Such structural reorganisation, referred to as remodelling, is described in terms of "plastic" distortions, whose evolution is assumed to obey a phenomenological flow rule driven by stress. We study the influence of remodelling on the mechanical and hydraulic behaviour of the system, showing how the plastic distortions modulate the flow pattern of the fluid, and the distributions of pressure and stress inside it. To accomplish this task, we solve a highly nonlinear set of model equations by elaborating a previously developed numerical procedure, which is implemented in a non-commercial finite element solver.

show abstract

“…To construct the constitutive relations for velocities and fluxes that are consistent with the second law of thermodynamics, we begin with a generalized Helmholtz free energy equation of component interactions, with the added taxis potential term posed by Cristini et al (2009). One way to model the elasticity is by evolving natural configurations and introducing the time derivative of the stress (Giverso and Preziosi, 2012; Giverso et al, 2015; Preziosi et al, 2010). Here, we opted to add the effects of elasticity to the free energy equation via an elastic energy term.…”

Section: Mathematical Modelmentioning

confidence: 99%

Model of vascular desmoplastic multispecies tumor growth

Frieboes

2017

Journal of Theoretical Biology

View full text Add to dashboard Cite

We present a three-dimensional nonlinear tumor growth model composed of heterogeneous cell types in a multicomponent-multispecies system, including viable, dead, healthy host, and extracellular matrix (ECM) tissue species. The model includes the capability for abnormal ECM dynamics noted in tumor development, as exemplified by pancreatic ductal adenocarcinoma, including dense desmoplasia typically characterized by a significant increase of interstitial connective tissue. An elastic energy is implemented to provide elasticity to the connective tissue. Cancer-associated fibroblasts (myofibroblasts) are modeled as key contributors to this ECM remodeling. The tumor growth is driven by growth factors released by these stromal cells as well as by oxygen and glucose provided by blood vasculature which along with lymphatics are stimulated to proliferate in and around the tumor based on pro-angiogenic factors released by hypoxic tissue regions. Cellular metabolic processes are simulated, including respiration and glycolysis with lactate fermentation. The bicarbonate buffering system is included for cellular pH regulation. This model system may be of use to simulate the complex interactions between tumor and stromal cells as well as the associated ECM and vascular remodeling that typically characterize malignant cancers notorious for poor therapeutic response.

show abstract

Growing avascular tumours as elasto-plastic bodies by the theory of evolving natural configurations

Cited by 33 publications

References 36 publications

A study of growth and remodeling in isotropic tissues, based on the Anand‐Aslan‐Chester theory of strain‐gradient plasticity

A study of growth and remodeling in isotropic tissues, based on the Anand‐Aslan‐Chester theory of strain‐gradient plasticity

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

Model of vascular desmoplastic multispecies tumor growth

Contact Info

Product

Resources

About