TY - JOUR
T1 - An approach for vascular tumor growth based on a hybrid embedded/homogenized treatment of the vasculature within a multiphase porous medium model
AU - Kremheller, Johannes
AU - Vuong, Anh Tu
AU - Schrefler, Bernhard A.
AU - Wall, Wolfgang A.
N1 - Publisher Copyright:
© 2019 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd
PY - 2019/11/1
Y1 - 2019/11/1
N2 - 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.
AB - 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.
KW - 1D-3D coupling
KW - angiogenesis
KW - multiscale models
KW - nonconforming coupling
KW - vascular tumor growth
UR - http://www.scopus.com/inward/record.url?scp=85077021186&partnerID=8YFLogxK
U2 - 10.1002/cnm.3253
DO - 10.1002/cnm.3253
M3 - Article
C2 - 31441222
AN - SCOPUS:85077021186
SN - 2040-7939
VL - 35
JO - International Journal for Numerical Methods in Biomedical Engineering
JF - International Journal for Numerical Methods in Biomedical Engineering
IS - 11
M1 - e3253
ER -