The Numerical Solution for a Maxwell Integral Equation: MRI Brain Scan

This paper uses Maxwell’s 4th integral equation model to approximate the magnetic field of an MRI machine given the electric field. MRI scans are a popular method for brain mapping and vital to monitor degenerative diseases of the brain such as Dementia and Alzheimer's. The integral is not analytically solvable, so a numerical approximation is obtained using the Gaussian quadrature method and Romberg’s integral method. The approximations are compared in order to obtain good convergence results. The model considers an electrical current and a time dependent electric field. Additionally, understanding the electrical permittivity and conductivity of the brain is critical to tuning the radio frequency of the scan. The assumption is that the MRI scan is of the patient’s head.