Details
| Original language | English |
|---|---|
| Article number | 22 |
| Number of pages | 26 |
| Journal | Advanced Modeling and Simulation in Engineering Sciences |
| Volume | 11 |
| Issue number | 1 |
| Publication status | Published - 11 Dec 2024 |
Abstract
In this paper, we present a computationally efficient reduced order model for obtaining blood perfusion profiles within parametric functional units of the liver called ‘lobules’. We consider Darcy’s equation in two-dimensional hexagonal lobule domains with six flow inlets and one outlet, whose positions are parameterized to represent varying lobule geometries. To avoid the meshing effort for every new lobule domain, we map the parametric domain onto a single reference domain. By making use of the contra-variant Piola mapping, we represent solutions of the parametric domains in the reference domain. We then construct a reduced order model via proper orthogonal decomposition (POD). Additionally, we employ the discrete empirical interpolation method (DEIM) to treat the non-affine parameter dependence that appears due to the geometric mapping. For sampling random shapes and sizes of lobules, we generate Voronoi diagrams (VD) from Delaunay triangulations and use an energy minimization problem to control the packing of the lobule structures. To reduce the dimension of the parameterized problem, we exploit the mesh symmetry of the full lobule domain to split the full domain into six rotationally symmetric subdomains. We then use the same set of reduced order basis (ROB) functions within each subdomain for the construction of the reduced order model. We close our study by a thorough investigation of the accuracy and computational efficiency of the resulting reduced order model.
Keywords
- Blood perfusion, Dimension reduction, Discrete empirical interpolation, Liver mechanics, Model order reduction, Proper orthogonal decomposition
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Engineering (miscellaneous)
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Applied Mathematics
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In: Advanced Modeling and Simulation in Engineering Sciences, Vol. 11, No. 1, 22, 11.12.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Reduced order modeling of blood perfusion in parametric multipatch liver lobules
AU - Siddiqui, Ahsan Ali
AU - Jessen, Etienne
AU - Stoter, Stein K.F.
AU - Néron, David
AU - Schillinger, Dominik
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/12/11
Y1 - 2024/12/11
N2 - In this paper, we present a computationally efficient reduced order model for obtaining blood perfusion profiles within parametric functional units of the liver called ‘lobules’. We consider Darcy’s equation in two-dimensional hexagonal lobule domains with six flow inlets and one outlet, whose positions are parameterized to represent varying lobule geometries. To avoid the meshing effort for every new lobule domain, we map the parametric domain onto a single reference domain. By making use of the contra-variant Piola mapping, we represent solutions of the parametric domains in the reference domain. We then construct a reduced order model via proper orthogonal decomposition (POD). Additionally, we employ the discrete empirical interpolation method (DEIM) to treat the non-affine parameter dependence that appears due to the geometric mapping. For sampling random shapes and sizes of lobules, we generate Voronoi diagrams (VD) from Delaunay triangulations and use an energy minimization problem to control the packing of the lobule structures. To reduce the dimension of the parameterized problem, we exploit the mesh symmetry of the full lobule domain to split the full domain into six rotationally symmetric subdomains. We then use the same set of reduced order basis (ROB) functions within each subdomain for the construction of the reduced order model. We close our study by a thorough investigation of the accuracy and computational efficiency of the resulting reduced order model.
AB - In this paper, we present a computationally efficient reduced order model for obtaining blood perfusion profiles within parametric functional units of the liver called ‘lobules’. We consider Darcy’s equation in two-dimensional hexagonal lobule domains with six flow inlets and one outlet, whose positions are parameterized to represent varying lobule geometries. To avoid the meshing effort for every new lobule domain, we map the parametric domain onto a single reference domain. By making use of the contra-variant Piola mapping, we represent solutions of the parametric domains in the reference domain. We then construct a reduced order model via proper orthogonal decomposition (POD). Additionally, we employ the discrete empirical interpolation method (DEIM) to treat the non-affine parameter dependence that appears due to the geometric mapping. For sampling random shapes and sizes of lobules, we generate Voronoi diagrams (VD) from Delaunay triangulations and use an energy minimization problem to control the packing of the lobule structures. To reduce the dimension of the parameterized problem, we exploit the mesh symmetry of the full lobule domain to split the full domain into six rotationally symmetric subdomains. We then use the same set of reduced order basis (ROB) functions within each subdomain for the construction of the reduced order model. We close our study by a thorough investigation of the accuracy and computational efficiency of the resulting reduced order model.
KW - Blood perfusion
KW - Dimension reduction
KW - Discrete empirical interpolation
KW - Liver mechanics
KW - Model order reduction
KW - Proper orthogonal decomposition
UR - http://www.scopus.com/inward/record.url?scp=85212085240&partnerID=8YFLogxK
U2 - 10.1186/s40323-024-00274-2
DO - 10.1186/s40323-024-00274-2
M3 - Article
AN - SCOPUS:85212085240
VL - 11
JO - Advanced Modeling and Simulation in Engineering Sciences
JF - Advanced Modeling and Simulation in Engineering Sciences
IS - 1
M1 - 22
ER -