Harmonic Oscillator Model for Computational Analysis of Tissue Elasticity Using Modified Bloch NMR Flow Equation

Abstract

Visualization of MRI system as harmonic oscillator provides a great insight into relationship be oscillating nuclei and tissues elasticity under the influence of effective magnetic field. This study Modified Bloch NMR flow equation by placing appropriate restriction on the system to characterize displacement function for the investigation of wavelength, velocity and tissue elasticity relation. The dimension of harmonic oscillator wave function in tissue was found to be strongly dependent on wavelength and velocity propagated wave, as it indicates the elastic nature of the tissue under investigation. Therefore, spatial dis wave as it passes through different regions in a material can be utilized to map tissue elasticity. The to oscillator signal was expressed to be the product of transverse wave function (Hermite Polynomial) and exponential function to explore the unique property of Hermite polynomial to represent signal both in Fourier domain for fast and robust image processing in spatial and image domain. Further studies are required to develop the theories and mathematical formulations using actual moving phantoms in MR scanners and optimize NMR parameters should be carried out using designed and constructed mechanical actuator.