A cut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing

Autor: Jack Hale, Sofia Farina, Alexander Skupin, Susanne Claus, Stéphane Bordas
Přispěvatelé: Fonds National de la Recherche - FnR [sponsor]
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Discretization
Computer science
unfitted methods
Energy metabolism
CutFEM
Reaction diffusion system
010103 numerical & computational mathematics
Cell morphology
01 natural sciences
lcsh:TA168
reaction diffusion system
energy metabolism
medicine
0101 mathematics
Engineering (miscellaneous)
Computer science [C05] [Engineering
computing & technology]
Unfitted methods
FEM
Partial differential equation
Applied Mathematics
Numerical analysis
Function (mathematics)
Complex cell
Sciences informatiques [C05] [Ingénierie
informatique & technologie]
level sets
Finite element method
Computer Science Applications
010101 applied mathematics
medicine.anatomical_structure
lcsh:Systems engineering
Modeling and Simulation
Level sets
Biological system
lcsh:Mechanics of engineering. Applied mechanics
lcsh:TA349-359
Zdroj: Advanced Modeling and Simulation in Engineering Sciences, Vol 8, Iss 1, Pp 1-32 (2021)
ISSN: 2213-7467
Popis: A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In addition, astrocytes provide scaffolding and homeostatic functions to neighboring neurons and contribute to the blood–brain barrier. Recent investigations indicate that the complex morphology of astrocytes impacts upon their function and in particular the efficiency with which these cells metabolize nutrients and provide neurons with energy, but a systematic understanding is still elusive. Modelling and simulation represent an effective framework to address this challenge and to deepen our understanding of brain energy metabolism. This requires solving a set of metabolic partial differential equations on complex domains and remains a challenge. In this paper, we propose, test and verify a simple numerical method to solve a simplified model of metabolic pathways in astrocytes. The method can deal with arbitrarily complex cell morphologies and enables the rapid and simple modification of the model equations by users also without a deep knowledge in the numerical methods involved. The results obtained with the new method (CutFEM) are as accurate as the finite element method (FEM) whilst CutFEM disentangles the cell morphology from its discretisation, enabling us to deal with arbitrarily complex morphologies in two and three dimensions.
Databáze: OpenAIRE
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