Fast approximate solution of Bloch equation for simulation of RF artifacts in Magnetic Resonance Imaging

10Citations
Citations of this article
64Readers
Mendeley users who have this article in their library.

Abstract

The technique used to spot information in Magnetic Resonance Imaging (MRI) uses electromagnetic fields. Even minor perturbations of these magnetic fields can disturb the imaging process and may render clinical images inaccurate or useless. Modelling and numerical simulation of the effects of static field inhomogeneities are now well established. Less attention has been paid to mathematical modelling of the effects of radio-frequency (RF) field inhomogeneities in the imaging process. When considering RF field inhomogeneities, the major difficulty is that the mathematical expression of the magnetisation vector is not anymore explicitly known in contrast with the unperturbed case. Indeed, the Bloch equation becomes an ordinary differential equation with nonconstant coefficients that cannot be solved analytically. The use of standard numerical schemes for ordinary differential equations to compute the magnetisation vector appears to be costly and not well suited for MRI image simulation. In this paper, we present an original method for solving the Bloch equation based on a truncated series expansion of the solution. The computational cost of the method reduces to the computation of the eigenelements of a block tridiagonal matrix of a very small size. © 2008 Elsevier Ltd. All rights reserved.

Cite

CITATION STYLE

APA

Balac, S., & Chupin, L. (2008). Fast approximate solution of Bloch equation for simulation of RF artifacts in Magnetic Resonance Imaging. Mathematical and Computer Modelling, 48(11–12), 1901–1913. https://doi.org/10.1016/j.mcm.2007.05.021

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free