Simulation of angiogenesis in a multiphase tumor growth model

Santagiuliana, Raffaella; Ferrari, Mauro; Schrefler, Bernhard A.

doi:10.1016/j.cma.2016.02.022

Cited by 18 publications

(31 citation statements)

References 30 publications

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“…which results in a standard formulation governing angiogenesis also applied in [30,36]. Herein, the first term on the right hand side represents random motion of EC at sprout tips modeled as molecular diffusion with mass diffusivity D v .…”

Section: Modeling Of Angiogenesismentioning

confidence: 99%

“…They are not transported by the IF flow as nutrients or TAF. Rather, they have to be modeled as a proper phase with their own velocity and volume fraction as already hinted in [36]. This allows us to define consistent inter-phase exchange terms between the neovasculature and the IF.…”

Section: The Vascular Multiphase Tumor Growth Modelmentioning

confidence: 99%

“…Herein, the first term on the right hand side represents random motion of EC at sprout tips modeled as molecular diffusion with mass diffusivity D v . The second term accounts for chemotaxis with a varying chemotactic coefficient χ ( ω T AF l ) as in [30] while in [36] it has been chosen to be constant. The latter one is the response of EC on TAF produced by hypoxic tumor cells, i.e., tumor cells which lack oxygen.…”

Section: Modeling Of Angiogenesismentioning

confidence: 99%

“…In the TCAT tumor growth model the considered species of the IF are oxygen and TAF. As indicated above, angiogenesis has been introduced into the multiphase model before [36], where endothelial cells have been treated as an additional species in the interstitial liquid. However, this is incorrect since endothelial cells do not qualify as a species diffusing within the IF from a biological point of view.…”

Section: The Vascular Multiphase Tumor Growth Modelmentioning

confidence: 99%

“…[34,35]. In the context of the continuum multiphase approach discussed above, endothelial cells have been introduced as an additional species in the IF by [36]. However, this approach is not sufficient and flexible enough to resolve the complex coupling between angiogenesis and tumor growth.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Kremheller

Vuong

Yoshihara

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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We present a dynamic vascular tumor model combining a multiphase porous medium framework for avascular tumor growth in a consistent Arbitrary Lagrangian Eulerian formulation and a novel approach to incorporate angiogenesis. The multiphase model is based on Thermodynamically Constrained Averaging Theory and comprises the extracellular matrix as a porous solid phase and three fluid phases: (living and necrotic) tumor cells, host cells and the interstitial fluid. Angiogenesis is modeled by treating the neovasculature as a proper additional phase with volume fraction or blood vessel density. This allows us to define consistent inter-phase exchange terms between the neovasculature and the interstitial fluid. As a consequence, transcapillary leakage and lymphatic drainage can be modeled. By including these important processes we are able to reproduce the increased interstitial pressure in tumors which is a crucial factor in drug delivery and, thus, therapeutic outcome. Different coupling schemes to solve the resulting five-phase problem are realized and compared with respect to robustness and computational efficiency. We find that a fully monolithic approach is superior to both the standard partitioned and a hybrid monolithic-partitioned scheme for a wide range of parameters. The flexible implementation of the novel model makes further extensions (e.g., inclusion of additional phases and species) straightforward.

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Section: Modeling Of Angiogenesismentioning

confidence: 99%

Section: The Vascular Multiphase Tumor Growth Modelmentioning

confidence: 99%

Section: Modeling Of Angiogenesismentioning

confidence: 99%

Section: The Vascular Multiphase Tumor Growth Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Kremheller

Vuong

Yoshihara

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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

Kremheller

Vuong

Schrefler

et al. 2019

Numer Methods Biomed Eng

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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.

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A simple agent-based model to simulate 3D tumor-induced angiogenesis considering the evolution of the hypoxic conditions of the cells

Benítez

García-Mozos

Santos

et al. 2022

Engineering with Computers

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In tumors, angiogenesis (conformation of a new vasculature from another primal one) is produced with the releasing of tumor angiogenic factors from hypoxic cells. These angiogenic substances are distributed around the tumor micro-environment by diffusion. When they reach the primal blood vessel bed, the sprouting and branching of a new micro-vascular network is produced. These new capillaries will supply oxygen to cells so that their hypoxic state is overcome. In this work, a new and simple 3D agent-based model to simulate tumor-induced angiogenesis is presented. In this approach, the evolution of the hypoxic conditions in cells along the related conformation of the new micro-vessels is considered. The importance that the relative position of the primal vasculature and tumor structure takes in the final distribution of the new micro-vasculature has also been addressed. The diffusion of angiogenic factors and oxygen has been modelled at the targets by numerical convolution superposition of the analytical solution from the sources. Qualitative and quantitative results show the importance of tip endothelial cells in overcoming hypoxic conditions in cells at early stages of angiogenesis. At final stages, anastomosis plays an important role in the reduction of hypoxia in cells.

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Simulation of angiogenesis in a multiphase tumor growth model

Cited by 18 publications

References 30 publications

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

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

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

A simple agent-based model to simulate 3D tumor-induced angiogenesis considering the evolution of the hypoxic conditions of the cells

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