Novel insight into magnetic resonance through a spherical coordinate framework for the bloch equation

Abstract

The behaviour of spins at a classical level in the presence of an external magnetic field is completely described by the Bloch equation. This is the main equation governing the magnetic resonance imaging (MRI) system, and as such the Bloch equation is extensively used for design purposes. Here we have transferred the Bloch equation to the spherical coordinate system that, to the best of our knowledge, has not previously been applied in this field. The mathematical framework and the simulation results show that this fresh view of the Bloch equation provides better insight into the magnetic resonance (MR) phenomenon. In this mathematical framework, without using spinor space, the order of the ..