Computational MRI Analysis of Liver Cancer Based on Bloch NMR Flow Equations and Bessel Functions

Abstract

Gastrointestinal neoplasms, including those in the pancreas, always involve the liver before metastasizing to other organs. In addition, breast, lung, renal, and ovarian and other common malignancies spread hematogenously, lymphatically or transperitoneally to the liver. Magnetic resonance imaging (MRI) has proved to be very important in the detection and imaging of liver lesions. However, a standardized MRI imaging method which accommodates most of the observed processes at cellular and sub-cellular level has been very rare. The purpose of this study is to present analytical solutions to the time-independent Bloch NMR flow equation in terms of readily available Bessel algorithm and their properties. The order of the Bessel functions is found in terms of the relaxation times and the duration of the gradient pulse. The NMR signal obtained in terms of these functions are very easy to control and they act like systems that can be switched on and off with changes in the relaxation times. We may therefore be able to detect and image processes in liver cancer even with rapidly changing tissue properties and at sub-millimetre formations.