Analytic solution to boundary integral computation of susceptibility induced magnetic field inhomogeneities

• Published in: Mathematical and computer modelling Vol. 39; no. 4; pp. 437 - 455
• Main Authors: Balac, S, Benoit-Cattin, H, Lamotte, T, Odet, C
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 2004; Elsevier Science; Elsevier
• Subjects: Boundary integrals; Computer Science; Exact sciences and technology; Integral transforms, operational calculus; Magnetostatics; Mathematical analysis; Mathematics; Medical Imaging; Numerical Analysis; Numerical analysis. Scientific computation; Partial differential equations, boundary value problems; Sciences and techniques of general use; Susceptibility artifacts; Susceptibility artifacts; Boundary integrals; Magnetostatics; Triangular finite element; Convergence rate; Resonance; Mathematical model; Magnetic field; Integral representation; Analytical solution; Boundary integral method
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/S0895-7177(04)90516-X

A method to compute the magnetic field induced by susceptibility inhomogeneities in magnetic resonance imaging is presented. It is based on a boundary integral representation formulae. The integral is set over the surfaces between media of different magnetic susceptibilities. The computational procedure consists of approximating these surfaces with triangular mesh elements and using analytical expressions to compute the integral over each triangle. The proposed method supplies high accuracy and is easily paralleled. A detailed analysis for the convergence rate of the method is performed. Numerical results obtained for several samples, including a human head, are presented.