Work

Electrical properties reconstruction from MRI data: theoretical and numerical aspects

Year: 2025

Type: article

Abstract: The paper presents an inverse problem for the reconstruction of the electrical properties of the human brain from Magnetic Resonance Imaging $ B_1^+ $-data. We establish a rigorous mathematical framework for the formulation of the inverse problem and provide an identifiability result. To achieve a robust numerical solution, the contrast source inversion method is successfully applied with synthetic data from both a 2D phantom and a 2D brain slice. The finite element method is used to discretize the boundary value problems, allowing complex geometries and realistic boundary conditions to be handled accurately.

Source: Inverse Problems and Imaging

DOI: 10.3934/ipi.2025057

Authors: Stephanie Lohrengel, Charlotte Milano, Stéphanie Salmon

Institutions: Centre National de la Recherche Scientifique, Laboratoire de Mathématiques de Reims, Université de Reims Champagne-Ardenne

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Agence Nationale de la Recherche

Award: ELECTRrical property imaging by MRI: Application to the MR-compatibility of medical devices