Fundamental Quantum Mechanical Dynamics in Computational Magnetic Resonance Imaging from Low Field to High Field

In recent years, it has been discovered that heterogeneous diseases such as cardiovascular diseases, diabetes, hepatitis and cancer may be attacked effectively by developing specific treatment plans that are generally referred to as personalized treatments. This new approach in medicine involves using novel methodology as a bridge between diagnostic and therapeutic applications to form a single agent, allowing for diagnosis, drug delivery and treatment response monitoring. This method is time- and cost-effective because it is a one in all procedure which combines diagnosis and therapy. This novel methodology involving atomic nuclei could be studied with NMR since their unique resonant frequencies lead to the production of distinct spectra for diagnostic imaging. Atomic nuclei are quantum objects and most of their properties can be accurately explained only by resorting to quantum mechanical formulation. In this study, we have solved the Bloch NMR flow equation quantum mechanically to describe the evolution of magnetic resonance imaging from low magnetic field to high magnetic field. We must note that, the expression \({\upgamma }\left( {{\text{B}}_{{\text{o}}} + g} \right) \ll \frac{\hbar }{{\beta m_{o} \alpha^{2} }}\) gives the order of magnitude of the low static magnetic field Bo and \({\upgamma }\left( {{\text{B}}_{{\text{o}}} + g} \right) \gg \frac{\hbar }{{\beta m_{o} \alpha^{2} }}\) for high static magnetic field Bo where mo is the mass of the particle and β is a dimensionless constant. Spatial magnetic field gradients (g) are usually required to alter the polarising magnetic field such that the field seen by each nucleus within an object are location-dependent. In accordance with the uncertainty relation, a particle confined in a volume with radius of the order \(\alpha\) would have the momentum of the order \(\frac{\hbar }{\alpha }\) . This expression equals the minimum depth of a spherical potential well of radius \(\alpha\) at which a bound state of a particle with discrete energy level appears.