PHY 242 Net Research Project for 12/6/99

Magnetic Resonance Imaging

It is likely that you or someone you know has had an "MRI". In this non-invasive method of imaging the interior of the body, the region of interest (ROI) is bathed in an intense, static magnetic field and precisely controlled bursts of radio frequency (RF) electromagnetic waves. The MRI shown is a side view section from the center of Dave Smith's spine taken in October, 1996. The ruptured disc impinging on the spinal nerves is clearly visible. Only a few years ago, exploratory surgery would have been necessary to locate the injury. (Special thanks to Dr. Feuer of the Indianapolis Neurosurgical Group for supplying a copy of the MRI ... and for removing the rupture!)

The MRI Tutorial by Joseph P. Hornak is an excellent site to visit. For historical information, visit the introduction page.

What makes MRI possible is the phenomenum of nuclear magnetic resonance (NMR). Each nucleon (proton or neutron) in an atom has an intrinsic spin (and hence, intrinsic angular momentum) which is responsible for the nucleon's magnetic dipole moment. The cause of the magnetic moment is easy to understand in a classical model of the proton as a spinning sphere of charge. The spinning charge constitutes a current loop which is responsible for the magnetic moment. However, this model has some serious faults. First, all reasonable predictions for the magnitude of the dipole moment for the proton do not match experimental fact. (And the neutral neutron should have no dipole moment ... but it does!) For our purposes, we can simply accept the experimental fact that a nucleon has intrinsic angular momentum and an associated magnetic moment along the same direction; and not concern ourselves with how or why.

Here's the classical picture of what happens. As you learned earlier this semester, an external magnetic field will exert a torque on a magnetic dipole which tends to align the dipole with the external field (t = m x B). However, a simple alignment doesn't happen. The nucleon has intrinsic angular momentum along the same axis as the dipole moment. The external torque is perpendicular to the dipole moment (review Section 28.8 of the text) and hence to the angular momentum as well. So what happens? The torque will cause the nucleon to precess, in the same way that a spinning top precesses in a gravitational field (t = ^dL/_dt). In both cases, increasing the external field strength will increase the torque and hence, increase the precessional frequency. This dependence of the precessional frequency upon the external field is critical to MRI.

The ROI is subjected to a large magnetic field gradient in which the field strength increases along one direction. Call it the x direction, so that we have B = B(x). Consequently, the precessional frequency of the nucleons increase along this direction as well. Nucleons with the same x-coordinate will have the same precessional frequency. These nucleons lie along a planar slice  in the y-z plane. The resonant response to bursts of RF waves at the precessional frequencies of the nucleons ranging from that of the first "slice" to the last are recorded. The magnitude of the resonant response at each frequency is proportional to the number of nucleons along the corresponding slice and hence related to the nuclear density of the tissue along that slice.

There is an alternative way to look at what is happening. As we have just studied, quantum mechanics dictates that the electrons in an atom occupy discrete energy states. Similarly, the magnetic moment of a proton may have only certain discrete orientations relative to the external field. For the proton with intrinsic spin one-half, there are are only two alllowed orientations (called spin up and spin down). There is energy associated with the orientation of the magnetic moment relative to the external field (given by U = -m B cos q). So each discrete orientation corresponds to a discrete energy level. A photon of the correct energy (it turns out that the photon frequency must be exactly that of the classical precessional frequency) can be absorbed by the proton and "flipped" into an orientation with higher energy. This is called a transition and the absorption of photons at this energy is detected.

To obtain a 3-D picture of the ROI, each slice must be further divided into small volume elements (called voxels). This is done with additional, transverse gradient fields. However, the details of just how this is done are quite complex and beyond the scope of this discussion. You can get a much more complete picture of MRI physics and technology from the University of Florida MRI site. It's well worth the time to understand this remarkable new medical technology.