The basis of MRI is the directional magnetic field, or moment, associated with charged particles in motion. Nuclei containing an odd number of protons and/or neutrons have a characteristic motion or precession. Because nuclei are charged particles, this precession produces a small magnetic moment.
When a human body is placed in a large magnetic field, many of the free hydrogen nuclei align themselves with the direction of the magnetic field. The nuclei precess about the magnetic field direction like gyroscopes. This behavior is termed Larmor precession.
The frequency of Larmor precession is proportional to the applied magnetic field strength as defined by the Larmor frequency, :
where is the gyromagnetic ratio and is the strength of the applied magnetic field. The gyromagnetic ratio is a nuclei specific constant. For hydrogen, .
To obtain an MR image of an object, the object is placed in a uniform magnetic field, , of between 0.5 to 1.5 Tesla. As a result, the object's hydrogen nuclei align with the magnetic field and create a net magnetic moment, , parallel to . This behavior is illustrated in Figure 2.1.
Figure 2.1: In the absence of a strong magnetic field, hydrogen nuclei are randomly aligned as in (a). When the strong magnetic field, , is applied, the hydrogen nuclei precess about the direction of the field as in (b).
Next, a radio-frequency (RF) pulse, , is applied perpendicular to . This pulse, with a frequency equal to the Larmor frequency, causes to tilt away from as in Figure 2.2a.
Figure 2.2: (a) The RF pulse, , causes the net magnetic moment of the nuclei, , to tilt away from . (b) When the RF pulse stops, the nuclei return to equilibrium such that is again parallel to . During realignment, the nuclei lose energy and a measurable RF signal
Once the RF signal is removed, the nuclei realign themselves such that their net magnetic moment, , is again parallel with . This return to equilibrium is referred to as relaxation. During relaxation, the nuclei lose energy by emitting their own RF signal (see Figure 2.2b). This signal is referred to as the free-induction decay (FID) response signal. The FID response signal is measured by a conductive field coil placed around the object being imaged. This measurement is processed or reconstructed to obtain 3D grey-scale MR images.
To produce a 3D image, the FID resonance signal must be encoded for each dimension. The encoding in the axial direction, the direction of , is accomplished by adding a gradient magnetic field to . This gradient causes the Larmor frequency to change linearly in the axial direction. Thus, an axial slice can be selected by choosing the frequency of to correspond to the Larmor frequency of that slice. The 2D spatial reconstruction in each axial slice is accomplished using frequency and phase encoding. A ``preparation'' gradient, , is applied causing the resonant frequencies of the nuclei to vary according to their position in the -direction. is then removed and another gradient, , is applied perpendicular to . As a result, the resonant frequencies of the nuclei vary in the -direction due to and have a phase variation in the -direction due to the previously applied . Thus, -direction samples are encoded by frequency and -direction samples are encoded by phase. A 2D Fourier Transform is then used to transform the encoded image to the spatial domain.
The voxel intensity of a given tissue type (i.e. white matter vs grey matter) depends on the proton density of the tissue; the higher the proton density, the stronger the FID response signal. MR image contrast also depends on two other tissue-specific parameters:
measures the time required for the magnetic moment of the displaced nuclei to return to equilibrium (ie. realign itself with ). indicates the time required for the FID response signal from a given tissue type to decay.
When MR images are acquired, the RF pulse, , is repeated at a predetermined rate. The period of the RF pulse sequence is the repetition time, . The FID response signals can be measured at various times within the interval. The time between which the RF pulse is applied and the response signal is measured is the echo delay time, . By adjusting and the acquired MR image can be made to contrast different tissue types.
The MR images used in this thesis were all acquired using a Multiple Echo Spin Echo pulse sequence in which two images are acquired simultaneously. and are adjusted such that tissues with a high proton density appear bright in the first image and tissues with a long appear bright in the second image. The two images are said to be proton density-weighted (PD-weighted) and T2-weighted respectively. Figure 2.3 shows 2D slices from the weighted MRI volumes.
Figure 2.3: (a) A proton density (PD) weighted MR image slice. (b) The same T2-weighted slice.