An approach for vascular tumor growth based on a hybrid embedded/homogenized treatment of the vasculature within a multiphase porous medium model

Abstract

The aim of this work is to develop a novel computational approach to facilitate the modeling of angiogenesis during tumor growth. The preexisting vasculature is modeled as a 1D inclusion and embedded into the 3D tissue through a suitable coupling method, which allows for nonmatching meshes in 1D and 3D domain. The neovasculature, which is formed during angiogenesis, is represented in a homogenized way as a phase in our multiphase porous medium system. This splitting of models is motivated by the highly complex morphology, physiology, and flow patterns in the neovasculature, which are challenging and computationally expensive to resolve with a discrete, 1D angiogenesis and blood flow model. Moreover, it is questionable if a discrete representation generates any useful additional insight. By contrast, our model may be classified as a hybrid vascular multiphase tumor growth model in the sense that a discrete, 1D representation of the preexisting vasculature is coupled with a continuum model describing angiogenesis. It is based on an originally avascular model which has been derived via the thermodynamically constrained averaging theory. The new model enables us to study mass transport from the preexisting vasculature into the neovasculature and tumor tissue. We show by means of several illustrative examples that it is indeed capable of reproducing important aspects of vascular tumor growth phenomenologically.

Extension of a multiphase tumour growth model to study nanoparticle delivery to solid tumours

“…with the lymphatic filtration coefficient L p S V � � ly . This is similar to the mass transfer term for drainage of fluid from the IF as presented in Kremheller et al [13,14]. In the following, we assume p ly � 0.…”

“…Our multiphase tumour growth model is based on Sciumè et al [17] with the extension to a five-phase model including the vasculature as presented in Kremheller et al [13,14]. The model is based on the Thermodynamically Constrained Averaging Theory (TCAT) [27], which has several benefits.…”

“…The model aims to predict the accumulation of nanoparticles in the tumour and allows a deeper insight into nanoparticle transport mechanisms. To this end, the previously developed multiphase tumour model [13,14] is extended by nanoparticle transport. The multiphase tumour growth model in its original form, including the macroscopic balance equations of phases and species, was presented by Sciumè et al [15,16] and enhanced to include a deformable extracellular matrix (ECM) (also by Sciumè et al [17]) as well as ECM deposition and angiogenesis by Santagiuliana et al [18].…”

“…Mascheroni et al experimentally validated the model equations and conducted first studies on in vitro drug delivery and its interaction with mechanical stress [19,20]. Kremheller et al [13] introduced the neovasculature as a proper additional phase and added a hybrid embedded/homogenised treatment of the vasculature [14]. These extensions now allow us to simulate and analyse the transport of nanoparticles as occurring in vivo.…”

Mechanistic modeling of vascular tumor growth: an extension of Biot’s theory to hierarchical bi-compartment porous medium system

“…where ω iα identifies the mass fraction of the species i dispersed with the phase α, ε α r iα is a reaction term that allows to take into account the reactions between the species i and the other chemical species dispersed in the phase α, and u iα is the diffusive velocity of the species i. iα→iκ M are mass exchange terms accounting for mass transport of species i at the κα interface from phase α to phase κ. Applying the product rule and introducing eqn (8), the previous equation can be also written in this alternative form (commonly called distribution form)…”