Using probability and rules of interaction to simulate the spin relaxation in a MRI

Abstract

A computer code is written that simulates the relaxation back to thermal equilibrium of an ensemble of particles after a pi/2 pulse. Beginning with Bloch's equations the exponential relaxation behavior is discussed and the transition into a step by step process (from the continuous process) is made such that it is possible for the computer code to simulate the action. An analysis of Boltzmann's factor is offered and serves as the link between the temperature of the ensemble and the parameter that is used to determine if a spin is in the up state or the down state. The specifics of the code are discussed and the spins are shown to follow the rules of interaction governed by the physical collisions that can take place. Lastly, graphs of the simulation are provided and a discussion of its usefulness is given.