We have obtained from the Bloch nuclear magnetic resonance (NMR) equations the correct dependence of the single component My and Mz at resonance (NMR/magnetic resonance imaging (MRI)) on relaxation times, rf B1 field (pulsed or continuous), blood(nuclear spin) flow velocity, etc., in the rotating frame of reference. We find that the new formulation for the first time uniquely describes the true relationship between individual single component My or Mz of magnetization of flowing nuclear spin with the above quantities (excluding diffusion and gradient fields) during NMR/MRI excitation. The equations are applicable for both continuous wave (CW) and pulsed NMR experiments with or without flow of spins. Our approaches can be extended easily to include gradient fields and diffusion of spins, if needed in NMR/MRI experiments. We also discuss the application of our equations to a specific case of magnetic resonance (MR) excitation scheme: Free induction decay. The new equations and further equations that can be derived with the methodologies used here can advance the techniques of noninvasive blood flow estimation by MR and also accurate extraction of parameters of clinical importance by enabling accurate simulation of the MR images (of blood flow and tissue) and comparison with experimental MR images. The detailed simulations from the equations will be published in the next paper.

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