PHY 212 Net Research Project for 4/26/2004

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!)

What makes MRI possible is the phenomenon of nuclear magnetic resonance (NMR). Each nucleon (proton or neutron) in the nucleus of an atom has an intrinsic spin. This intrinsic spin is responsible for the nucleon's magnetic dipole moment. The cause of the magnetic moment for a proton is easy to visualize in the classical model, in which the proton is a spinning sphere of positive charge. The spinning charge constitutes a current loop which creates the magnetic dipole moment.

However, this model has some serious faults. First, all reasonable predictions for the magnitude of the magnetic moment of the proton do not match experimental fact. (And the neutral neutron should have no magnetic 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. It is primarily the net magnetic moment of the protons of the hydrogen atoms in water molecules that is involved with MRI. But the the net magnetic moment of other nucleii make contributions as well. We will simply refer to the nucleus in the discussion below.

The Classical Picture

First, we consider the classical picture of how MRI works. 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 nucleus has intrinsic angular momentum along the same axis as the magnetic moment. The external torque is perpendicular to the magnetic moment and hence to the angular momentum as well. So what happens? The torque will cause the nucleus to precess, in the same way that a spinning top precesses in a gravitational field. 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 (Region Of Interest) 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 nucleii increase along this direction as well. Nucleii with the same x-coordinate will have the same precessional frequency. These nucleii lie along a planar slice in the y-z plane. The resonant response to bursts of RF (Radio Frequency) electromagnetic waves at the precessional frequencies of the nucleii, 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 nucleii along the corresponding slice and hence, is related to the nuclear density of the tissue along that slice. Bone, fluids, muscle tissue, nerve tissue, etc. will all respond with a different magnitude. A map of this density (primarily water density) can be created. Presently, very large magnetic fields are required for MRI and the equipment needed to produce such fields is large and expensive. But work on MRI with ultralow magnetic fields is in progress by several research groups.

The Quantum Picture

There is an alternative way to look at what is happening. As we will see in the next few days, quantum mechanics dictates that the electrons in an atom occupy discrete energy states. Similarly, the magnetic moment of a nucleus may have only certain discrete orientations relative to the external field. The nucleii involved in MRI have intrinsic spin one-half, and there are only two allowed 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 the two discrete orientations correspond to two discrete energy levels.

The RF radiation can also be view in the quantum mechanical picture. In this picture, the radiation consists of "photons", each with an energy proportional to the RF frequency. ( Recall that E_g = hf. ) An RF photon with energy equal to the difference in the energy of the two spin orientations can be absorbed by the nucleus as it is "flipped" into the orientation of higher energy. Just as the precessional frequency in the classical picture is proportional to the magnitude of the applied magnetic field, so is the energy difference between the two spin states. Hence, each slice will absorb a specific frequency of photons. In keeping with the Correspondence Principle that provides a bridge between the classical and quantum pictures, the photon frequency (quantum physics) is exactly the same as that of the precessional frequency (classical physics).

To obtain a 2-D picture, like the one of Daves's spine, many overlaping slices from different directions are required. The response information is stored and the image is reconstructed with computer software. Even 3-D pictures can be constructed by combining the information of many slices, creating a matrix of information of small volume elements, called voxels. (The details of just how this is done are quite complex and beyond the scope of this discussion.)

The MRI Tutorial by Joseph P. Hornak is an excellent site that will provide you with many more explanations and details of the physics. Historical information can be found on the Introduction page.

(You can also get MRI physics and technology information from the University of Florida MRI site.