Various biological and physiological properties of living tissue can be studied by means of nuclear magnetic resonance techniques. Unfortunately, the basic physics of extracting the relevant information from the solution of Bloch nuclear magnetic resource (NMR) equations to accurately monitor the clinical state of biological systems is still not yet fully understood. Presently, there are no simple closed solutions known to the Bloch equations for a general RF excitation. Therefore the translational mechanical analysis of the Bloch NMR equations presented in this study, which can be taken as deÿnitions of new functions to be studied in detail may reveal very important information from which various NMR ow parameters can be derived. Fortunately, many of the most important but hidden applications of blood ow parameters can be revealed without too much di culty if appropriate mathematical techniques are used to solve the equations. In this study we are concerned with a mathematical study of the laws of NMR physics from the point of view of translational mechanical theory. The important contribution of this study is that solutions to the Bloch NMR ow equations do always exist and can be found as accurately as desired. We shall restrict our attention to cases where the radio frequency ÿeld can be treated by simple analytical methods. First we shall derive a time dependant second-order non-homogeneous linear di erential equation from the Bloch NMR equation in term of the equilibrium magnetization M0, RF B1(t) ÿeld, T1 and T2 relaxation times. Then, we would develop a general method of solving the di erential equation for the cases when RF B1(t) = 0, and when RF B1(t) = 0. This allows us to obtain the intrinsic or natural behavior of the NMR system as well as the response of the system under investigation to a speciÿc in uence of external force to the system. Speciÿcally, we consider the case where the RF B1 varies harmonically with time.
Here the complete motion of the system consists of two parts. The ÿrst part describes the motion of the transverse magnetization My in the absence of RF B(t) ÿeld. The second part