Computational Phase Contrast Magnetic Resonance Imaging based on Legendre Polynomials

Abstract

One of the most exciting modern developments in Magnetic Resonance Imaging (MRI) is the non invasive and non radiation measurements of tissue metabolism in patients. However, different tissue have different hemodynamic responses, which may not be accurately reflected by the general linear model often used in MRI phase contrast measurements or Magnetic Resonance Spectroscopy (MRS). In this study, we have derived analytical expressions for the NMR transverse magnetizations in terms of Legendre Polynomials. We define the orbital angular momentum quantum number as the ratio of the spin lattice relaxation time and the spin-spin relation time. This enables the computation of hemodynamic responses from different tissue quantum mechanically by designating angular momentum states to each biological tissue.