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

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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.

Section: Incorporation Of the Embedded 1d Fluid Network Into The Vascmentioning

confidence: 99%

“…We model the solid phase, ie, the ECM as the skeleton of the porous medium, where Terzaghi's principle of effective stress

{bold-italicσ}_{eff}^{s} = {bold-italicσ}_{tot}^{s} + p^{s} bold-italicI

can be applied. Herein, the solid pressure

p^{s} = \frac{ε}{ε + ε^{v}} \sum_{α = t, h, l} S^{α} p^{α} + \frac{ε^{v}}{ε + ε^{v}} p^{v}

Section: Incorporation Of the Embedded 1d Fluid Network Into The Vascmentioning

confidence: 99%

Section: Incorporation Of the Embedded 1d Fluid Network Into The Vascmentioning

confidence: 99%

“…Hence, we do not want to account for every single blood vessel but treat it in a homogenized or averaged sense. We assume that the volume fraction of the NV ε v follows an evolution equation

{(|, \frac{\partial ε^{v}}{\partial t})}_{bold-italicX} + ε^{v} bold-italic\nabla \cdot {bold-italicv}^{s} - bold-italic\nabla \cdot ((), D^{v} bold-italic\nabla ε^{v}) + bold-italic\nabla \cdot ((), ε^{v} ε S^{l} χ ((), ω^{T A F \overset{l}{true}}) bold-italic\nabla ω^{T A F \overset{l}{true}}) = 0 in Ω_{t} \times ([], t_{0}, t_{E}),

which we have introduced in Kremheller et al . This equation is an adaption of a very prominent formulation of angiogenesis originally proposed by Anderson and Chaplain .…”

Section: Incorporation Of the Embedded 1d Fluid Network Into The Vascmentioning

confidence: 99%

Section: Numerical Discretization and Computational Frameworkmentioning

confidence: 99%

See 3 more Smart Citations

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

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Validation and parameter optimization of a hybrid embedded/homogenized solid tumor perfusion model

Kremheller

Brandstaeter

Schrefler

et al. 2021

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The goal of this paper is to investigate the validity of a hybrid embedded/homogenized in‐silico approach for modeling perfusion through solid tumors. The rationale behind this novel idea is that only the larger blood vessels have to be explicitly resolved while the smaller scales of the vasculature are homogenized. As opposed to typical discrete or fully resolved 1D–3D models, the required data can be obtained with in‐vivo imaging techniques since the morphology of the smaller vessels is not necessary. By contrast, the larger vessels, whose topology and structure is attainable noninvasively, are resolved and embedded as one‐dimensional inclusions into the three‐dimensional tissue domain which is modeled as a porous medium. A sound mortar‐type formulation is employed to couple the two representations of the vasculature. We validate the hybrid model and optimize its parameters by comparing its results to a corresponding fully resolved model based on several well‐defined metrics. These tests are performed on a complex data set of three different tumor types with heterogeneous vascular architectures. The correspondence of the hybrid model in terms of mean representative elementary volume blood and interstitial fluid pressures is excellent with relative errors of less than 4%. Larger, but less important and explicable errors are present in terms of blood flow in the smaller, homogenized vessels. We finally discuss and demonstrate how the hybrid model can be further improved to apply it for studies on tumor perfusion and the efficacy of drug delivery.

Global sensitivity analysis based on Gaussian‐process metamodelling for complex biomechanical problems

Wirthl

Brandstaeter

Nitzler

et al. 2023

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Biomechanical models often need to describe very complex systems, organs or diseases, and hence also include a large number of parameters. One of the attractive features of physics-based models is that in those models (most) parameters have a clear physical meaning. Nevertheless, the determination of these parameters is often very elaborate and costly and shows a large scatter within the population. Hence, it is essential to identify the most important