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Wolfgang A. Wall - One of the best experts on this subject based on the ideXlab platform.
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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.
International Journal for Numerical Methods in Biomedical Engineering, 2019Co-Authors: Johannes Kremheller, Anh-tu Vuong, Bernhard A. Schrefler, Wolfgang A. WallAbstract: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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an approach for vascular tumor growth based on a hybrid embedded homogenized treatment of the vasculature within a multiphase Porous Medium Model
International Journal for Numerical Methods in Biomedical Engineering, 2019Co-Authors: Johannes Kremheller, Anh-tu Vuong, Bernhard A. Schrefler, Wolfgang A. WallAbstract: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.
Bernhard A. Schrefler - One of the best experts on this subject based on the ideXlab platform.
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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.
International Journal for Numerical Methods in Biomedical Engineering, 2019Co-Authors: Johannes Kremheller, Anh-tu Vuong, Bernhard A. Schrefler, Wolfgang A. WallAbstract: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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an approach for vascular tumor growth based on a hybrid embedded homogenized treatment of the vasculature within a multiphase Porous Medium Model
International Journal for Numerical Methods in Biomedical Engineering, 2019Co-Authors: Johannes Kremheller, Anh-tu Vuong, Bernhard A. Schrefler, Wolfgang A. WallAbstract: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.
Johannes Kremheller - One of the best experts on this subject based on the ideXlab platform.
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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.
International Journal for Numerical Methods in Biomedical Engineering, 2019Co-Authors: Johannes Kremheller, Anh-tu Vuong, Bernhard A. Schrefler, Wolfgang A. WallAbstract: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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an approach for vascular tumor growth based on a hybrid embedded homogenized treatment of the vasculature within a multiphase Porous Medium Model
International Journal for Numerical Methods in Biomedical Engineering, 2019Co-Authors: Johannes Kremheller, Anh-tu Vuong, Bernhard A. Schrefler, Wolfgang A. WallAbstract: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.
John Stockie - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic and Numerical Analysis of a Porous Medium Model for Transpiration-Driven Sap Flow in Trees
SIAM Journal on Applied Mathematics, 2018Co-Authors: Bebart Maisar Janbek, John StockieAbstract:We develop a 3D Porous Medium Model for sap flow within a tree stem, which consists of a nonlinear parabolic partial differential equation with a suitable transpiration source term. Using an asymptotic analysis, we derive approximate series solutions for the liquid saturation and sap velocity for a general class of coefficient functions. Several important dimensionless parameters are identified that can be used to characterize various flow regimes. We investigate the relative importance of stem aspect ratio versus anisotropy in the sapwood hydraulic conductivity, and how these two effects impact the radial and vertical components of sap velocity. The analytical results are validated by means of a second-order finite volume discretization of the governing equations, and comparisons are drawn to experimental results on Norway spruce trees.
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Asymptotic and numerical analysis of a Porous Medium Model for transpiration-driven sap flow in trees
arXiv: Fluid Dynamics, 2017Co-Authors: Bebart Maisar Janbek, John StockieAbstract:We develop a 3D Porous Medium Model for sap flow within a tree stem, which consists of a nonlinear parabolic partial differential equation with a suitable transpiration source term. Using an asymptotic analysis, we derive approximate series solutions for the liquid saturation and sap velocity for a general class of coefficient functions. Several important non-dimensional parameters are identified that can be used to characterize various flow regimes. We investigate the relative importance of stem aspect ratio versus anisotropy in the sapwood hydraulic conductivity, and how these two effects impact the radial and vertical components of sap velocity. The analytical results are validated by means of a second-order finite volume discretization of the governing equations, and comparisons are drawn to experimental results on Norway spruce trees.
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Porous Medium Model of Sap Flow in Trees
2009Co-Authors: Kevin Lorimer, John StockieAbstract:In an effort to better understand the dynamics of sap flow, with a particular interest in winter sap flow in maple trees, a PDE Model is created and tested. The Model follows the work done by Chuang et al., and treats the wood as a Porous Medium. Darcy’s Law and conservation laws are used to link sap flux to transpiration. A comparison of results to those of Chuang et al. is made to determine the validity of the Model.
Anh-tu Vuong - One of the best experts on this subject based on the ideXlab platform.
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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.
International Journal for Numerical Methods in Biomedical Engineering, 2019Co-Authors: Johannes Kremheller, Anh-tu Vuong, Bernhard A. Schrefler, Wolfgang A. WallAbstract: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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an approach for vascular tumor growth based on a hybrid embedded homogenized treatment of the vasculature within a multiphase Porous Medium Model
International Journal for Numerical Methods in Biomedical Engineering, 2019Co-Authors: Johannes Kremheller, Anh-tu Vuong, Bernhard A. Schrefler, Wolfgang A. WallAbstract: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.