The excitation, precession, and return to equilibrium of hydrogen nuclei were modelled and used to reconstruct a 1-dimensional object defined by its spatial π2β 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 π1 and π2 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, π2β. 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 π2β illustration. To demonstrate the use of NMR for object imaging, the signal response of an object with varying spatial π2β 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.