Application of Diffusion Magnetic Resonance Equation in the Detection of Tracheomalacia

Abstract

This research examines the application of Magnetic Resonance Equation in the detection of a disease called Tracheomalacia. The mathematical model applied evolved from the fundamental Bloch equations and was transformed into general flow equations. With appropriate boundary conditions, the method of separation of variables was used to obtain the solutions in two cases: Case 1 – free flow situation and Case 2 – diseased situation. The solution obtained was graphically plotted. From the graphs, the values of magnetization exhibited by the free flow demonstrated free induction decay (FID) with a range of value of 1.26026E-05 to 0.18 while those exhibited by the diseased situation manifest a deformity with a range of value of 1.26026E-05 to 1.5. As shown mathematically from the work, MRI has become an important tool in non-invasive methods of diagnosis and treatment in humans.