Magnetic Resonance Signal Formation

The proton nuclei of the hydrogen atom possess a small magnetic moment. When placed within a magnetic field, a torque will be exerted upon them, resulting in a slight energetic advantage of one orientation (parallel to the field) over another (the anti-parallel orientation). Over time, random atomic collisions and other perturbations allow the complete system to reach a magnetic and thermal equilibrium with an excess of protons aligned with the magnetic field. The combined alignment of all of these protons results in a net magnetic moment; a subject placed within a magnetic field thus becomes "magnetized." In biological tissues, this magnetization is exceedingly small, and generally not observable.

In addition to their magnetic moment, atomic nuclei possess angular momentum - a quantum property known as "spin." Because of this angular momentum, rather than aligning simply with magnetic fields, the individual nuclei precess about it, much as a spinning top or gyroscope might, when placed in the earth’s gravitational field (figure 1, left). The precessional rate, or frequency, is characteristic of the atomic nucleus (e.g. protons) and is proportional to the strength of the magnetic field (figure 1, right), a property crucial to the process of image formation. With the magnetic field strengths in use for today’s typical MR imagers, the precessional frequency is between 10 MHz and 100 MHz - just below FM radio range.

Figure 2 shows that the proton magnetization can be decomposed into the sum of a stationary (longitudinal) and a rotating (transverse) component. Each proton nucleus within a magnetic field thus yields a tiny field that rotates about that applied field. The rotating field from individual nuclei is in generally aligned at random with respect to other protons in the subject or sample. In macroscopic systems, the average rotating field will effectively be zero, since that arising from any individual nucleus is canceled by another, oppositely oriented, neighbor.

In nuclear magnetic resonance (NMR), a second magnetic field is applied, which is orthogonal to the static field, and which rotates about the static field at the precessional frequency of the atomic nuclei. When the rotating field is present, the nuclei will precess about it, forcing the magnetization away from equilibrium , and causing the ensemble of protons to precess together, or "in-phase." The combined rotating magnetic moment thus produced by the ensemble of protons is observable as a time varying electromagnetic (radio) signal. The second, rotating magnetic field is applied at radio frequencies and is therefore known as an "RF" pulse. These fundamental principles were elucidated more than forty years ago; among the seminal contributions were those of Felix Bloch [4,5] and Erwin Hahn [6].

Signal Characteristics

Two fundamental temporal parameters are used to describe the MR signal. The longitudinal relaxation rate, "T1", is the rate at which nuclei, once placed in a magnetic field, exponentially approach thermal equilibrium, so that the magnetization (M) is described by the formula:

where M0 is the equilibrium magnetization. In biological tissues, the proton T1 is quite long: from tens of milliseconds to seconds. Differences in the T1’s of tissues are one of the primary bases of contrast in clinical MRI.

A second parameter time constant describes the rate at which the MR signal decays. Once an MR signal is formed, i.e. after an RF pulse, it fades quickly; small variations in the local magnetic field, for example those caused by neighboring magnetic nuclei, cause the protons to precess at slightly different rates and therefore to become out of phase with one another. Interactions among the magnetized protons, and motion in inhomogeneous fields, due for example to diffusion, also results in signal dephasing. The observed signal decay rate, (T2*) generally ranges from a few milliseconds to tens of milliseconds and, to a reasonable approximation, also follows first order kinetics. The MR signal, S(t), signal decays according to the formula:

where S0 is the signal strength immediately following the RF excitation pulse. The observed T2* decay is the net effect of all the dephasing terms:

where T2m represents the dephasing due to magnetic field inhomogeneities and T2D is the diffusion-related signal loss.

Like T1, the T2 signal decay rates differ among body tissues. For most current ƒMRI, T2 is the dominant contrast mechanism. As discussed below (box 2), blood oxygen content strongly effects the observed signal decay rate. By waiting for a short period, "TE", following the RF excitation pulse, differences in the signal decay rate will become evident as differences in the MR signal intensity: tissues with longer T2’s will have stronger signals than those with short T2’s, whose signals decay more rapidly (figure 3). Modifications to the pattern of RF excitation (the "pulse sequence") can modulate the contributions of the various relaxation processes to the resulting MR signal. In particular a "spin echo" pulse sequence can be used to nearly eliminate the T2m contribution, increasing the relative contributions of other terms, such as proton diffusion, to the image contrast.