An introduction to NMR imaging: From the Bloch equation to the imaging equation

The emerging technology of NMR imaging is introduced here as a problem in system identification. We show how selected families of signals may be input into the system ("system," in this case, is almost synonymous with "patient") in order that the system\´s responses to these inputs may be directly interpreted in terms of the system parameters. Once identified, a raster display of the system parameters provides an internal image of the patient. Inputs to the system age four-component functions of time. One component describes the strength of an RF signal, and the other three components govern the strength of three spatially varying, independently controlled magnetic fields (the gradient fields) in which the patient is immersed. In response to these inputs some of the protons in the patient, acting in concordance with the Bloch equation, give rise to local fluctuations in the magnetization which are detected with a tuned antenna and a sensitive receiver. The relationship between this output signal and the system parameters is summarized in the imaging equation.