NMR/MRI blood flow magnetization equation in the rotating frame of reference- Part I

This paper describes thoroughly the need and the method of deriving the first of its kind the NMR/MRI blood flow magnetization (y component) equation in the rotating frame when rf B$_{1}$ field is applied along laboratory X direction. The equation is expected to serve as the mother equation for accurate non invasive blood flow quantification through all NMR/MRI experiments. It is shown how Awojyogbe's equation of blood flow magnetization can be obtained from above equation under assumption of constant $B_{1}$ field and $v_{y}$ = 0. The method of deriving the equation can be applied to modify Bloch Torey Diffusion MRI equation to include relaxation times and flow and also to derive the NMR/MRI spin flow magnetization equation in the laboratory frame of reference. The derivation of the corresponding flow equation for longitudinal component of magnetization will be discussed in a separate paper.