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 -