The excitation, precession, and return to equilibrium of hydrogen nuclei were modelled and used to reconstruct a 1-dimensional object defined by its spatial 𝑇2∗ parameter variation.

Nuclear Magnetic Resonance (NMR) is a physical phenomenon based on the spin property of nuclei. A series of simulations were created to investigate an NMR system. The immersion of magnetic moments in a static magnetic field was modelled, illustrating their precession about the direction of the applied field. Longitudinal and spin-spin (transverse) relaxations were modelled and characterized by the 𝑇1 and 𝑇2 time constants respectively. The effect of magnetic field inhomogeneities across a collection of moments was shown to reduce the spin-spin relaxation due to the de-phasing of their precessions at different Larmor frequencies, resulting in a new effective spin-spin relaxation constant, 𝑇2∗. Simulated 𝜋 and 𝜋/2 radiofrequency pulses were combined into inversion recovery and saturation recovery sequences to demonstrate longitudinal relaxation. Similarly, a spin echo sequence was created to demonstrate spinspin relaxation. The Carr-Purcell and pulse-imperfection-corrected Carr-Purcell-Meiboom-Gill sequences were also simulated for more accurate 𝑇2∗ illustration. To demonstrate the use of NMR for object imaging, the signal response of an object with varying spatial 𝑇2∗ immersed in a known gradient magnetic field after a 𝜋/2 pulse was simulated. A transform to the frequency space of the resulting beating pattern signal was used to reconstruct to original object.