Lyapunov stability of competitive cells dynamics in tumor mechanobiology

Abstract

Poromechanics plays a key role in modelling hard and soft tissue behaviours, by providing a thermodynamic framework in which chemo-mechanical mutual interactions among fluid and solid constituents can be consistently rooted, at different scale levels. In this context, how different biological species (including cells, extra-cellular components and chemical metabolites) interplay within complex environments is studied for characterizing the mechanobiology of tumor growth, governed by intratumoral residual stresses that initiate mechanotransductive processes deregulating normal tissue homeostasis and leading to tissue remodelling. Despite the coupling between tumor poroelasticity and interspecific competitive dynamics has recently highlighted how microscopic cells and environment interactions influence growth-associated stresses and tumor pathophysiology, the nonlinear interlacing among biochemical factors and mechanics somehow hindered the possibility of gaining qualitative insights into cells dynamics. Motivated by this, in the present work we recover the linear poroelasticity in order to benefit of a reduced complexity, so first deriving the well-known Lyapunov stability criterion from the thermodynamic dissipation principle and then analysing the stability of the mechanical competition among cells fighting for common space and resources during cancer growth and invasion. At the end, the linear poroelastic model enriched by interspecific dynamics is also exploited to show how growth anisotropy can alter the stress field in spherical tumor masses, by thus indirectly affecting cell mechano-sensing. GraphicAbstract

Ultrasound waves in tumors via needle irradiation for precise medicine

“…These ratios inevitably produce an alteration of the tissues’ acoustic impedance, as also evincible from elastographic analyses 54 – 56 , and could be associated to a local densification of the tissue induced by tumor hyperproliferation. Such differences were also found experimentally from simple compression tests on breast tumor masses grown at different stages 32 , and the material remodeling was well traced back by predictive interspecific models of nonlinearly growing tumors 43 , 44 . The obtained stiffness data are directly correlated to the evolution of the solid tumor Young modulus through the formula (considering nonadhesive contact of an elastic sphere with radius , stiffness and Poisson ratio between two rigid plates 57 , as also reported in Fig.…”

“…More precisely, tumor stage-dependent elastic properties are assigned by starting from theoretical and experimental outcomes obtained by some of the present authors in a previous work 41 . Therein, by implementing nonlinear mechanical models coupled with interspecific dynamics 41 , 43 , 44 , the evolution of solid tumor spheroids growing in vivo within a heterogeneous environment were investigated, so predicting the development of tumor masses and related intratumoral stresses. As above mentioned, growth (as inelastic pre-stretch) and residual stresses induce the progressive remodeling of the tumor material properties, consequently changing also its acoustic response.…”

Competition between epithelial tissue elasticity and surface tension in cancer morphogenesis

“…Concerning the connection with tumor morphogenesis, as reviewed in [30], the available models address multiple mechanical factors as responsible for the disruption of normal tissue architecture besides the abnormal acto-myosin concentration gradient from basal to apical region [31], which is the mechanical effect that we address in the present paper; in particular, other factors include cancer cells proliferation [11,12,13], lateral cell adhesion [23], elasticity of the basement membrane [27].…”

A lesson from earthquake engineering for selectively damaging cancer cell structures

“…1 and in detail described in what follows, were thus used to verify if selective discrimination between tumor and healthy cells can be established at the cells' aggregate level as well, in this way overcoming the limitations related to the analyses of singlecell systems. In combination with the biomechanical analysis of solid tumor growth (Guiot et al, 2006;Carotenuto et al, 2018;Fraldi and Carotenuto, 2018;Carotenuto et al, 2021) and residual stress-induced remodeling (Carotenuto et al, 2019), it is felt that the theoretical predictions of critical frequencies that put into vibration selectively cancer cells in aggregates at different stages of tumor progression could highly impact on possible therapeutic applications of LITUS in cancer treatments.…”