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Computational Phase Constrast Magnetic Resonance Imaging based on Legendre Polynomials

One of the most exciting modern developments in Magnetic Reso- nance Imaging (MRI) is the non invasive and non radiation measurements of tissue metabo lism in patients. However, different tissue have different hemody- namic respon ses, 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 de- fine the orbital angular momentum quantum number as the ratio of the spin lat- tice relaxation time and the spin-spin relation time. This enables the computa- tion of hemodynamic responses from different tissue quantum mechanically by designating angular momentum states to each biological tissue.