Theory, Dynamics and Applications of Magnetic Resonance Imaging-I

Abstract

All Magnetic Resonance Imaging (MRI) techniques are based on the Bloch NMR flow equations. Over the years, researchers have explored the Bloch NMR equations to significantly improve healthcare for accurate diagnosis, prognosis and treatment of deceases. However, MRI scan is still one of the most expensive anywhere. Method to achieve the best image quality with the lowest cost is still a big challenge. In this chapter, the generalized time dependent non-homogenous second order differential equation derived from the Bloch NMR flow equations is modeled into basic and well known equations such as Bessel equation, Diffusion equation, Wave equation, Schrödinger’s equation, Legendre’s equation, Euler’s equation and Boubaker polynomials. Solutions to these equations are abundantly available in standard text books and several research studies on Mathematics, Physics, Chemistry and Engineering. Unexpected NMR/MRI methodological developments may be possible based on the analytical solutions of these equations and may further enhance the power of NMR. There will be spectacular applications in a variety of fields, ranging from cognitive neuroscience, biomedical engineering, imaging-science, molecular imaging to medicine, and providing unprecedented insights into chemical, biological and geophysical processes. This may initiate unforeseen technological and biomedical possibilities based on a much improved understanding of nature.