Off-Resonance Sensitivity

As already discussed in Section 2.3.2 for the spin-echo technique, it is unavoidable in practice that a certain distribution of resonance frequencies exists, i.e. for some of the protons the frequency differs from the value that is expected under ideal conditions.

The origins of the frequency deviations can be divided into three categories. First, it is technically challenging to build magnets with a high homogeneity (especially for high-field systems) and, therefore, the local high-field strength varies within a specified range.

Second, magnetic field variations are induced at susceptibility boundaries of the ob-ject [63], in particular at air-tissue interfaces like the nasal cavities of the head. Third, depending on their (intra- and intermolecular) chemical environment, protons may ex-perience microscopic field variations, which is calledchemical shift effect and best known to occur in fat tissue. All these mechanisms are summarized as off-resonance effects and cause a local phase evolution in the affected regions of the object. To account for the off-resonances, the signal equation (2.18) has to be extended by a spatially- and time-dependent phase term

S(t) = ˆc· Z

e^{i β(x)·t}·ρ(x)·e^2πik(t)·x dx, (4.14)

Figure 4.8: Off-Resonance artifacts obtained for radial sampling with180^◦and360^◦coverage in comparison to (ref) an on-resonant reference case. (Top) Magnified views of the PSF center, and (bottom) magnitude reconstructions of circles with varying deviations of the assumed resonance frequency.

where β(~x) is a function that describes the local deviation of the resonance frequency.

Thus, in the presence of off-resonance effects, the received spatial information is phase modulated, and a proper reconstruction of the object information, i.e. the proton density ρ(x), requires knowledge of the off-resonance map β(x). If this condition is neglected and a conventional FT-based reconstruction is performed, the modulation translates into image artifacts whose appearance and strength depends on the trajectory shape and on the acquisition duration.

In the normal Cartesian scheme, the signal is recorded during a constant velocity move-ment in the readout direction, which is identical for all rows since the sequence rep-etitions differ only in the amplitude of the prephasing gradient. Therefore, also the signal modulation from the off-resonances is identical for all acquired rows, which sim-ply emerges as an overall linear phase modulation along the readout direction. In image space, this corresponds to a translation in the readout direction, where the shift distance depends on the local offset of the resonance frequency. Consequently, object areas with strong off-resonance effects are shifted in the readout direction whereas areas with a match of the frequency remain unchanged, which results in a distortion of the reconstructed object [64]. However, because the readout time is short, the phase drifts encountered in practice are marginal and distortions are hardly noticeable. The

situ-ation changes when several k-space rows are acquired from a single RF excitsitu-ation, as in the echo planar imaging technique [65]. Here, rather strong phase modulations can develop among the acquired rows, which produces significant geometrical distortions and causes a severe loss of spatial accuracy [66]. Nevertheless, for the basic Cartesian scanning techniques the off-resonance problem is not of major relevance.

For radial data acquisitions, the artifacts exhibit in a different and more perceivable way. Because in this sampling geometry the readout direction in k-space varies for all repetitions, the experienced phase evolutions cause a shift of the encoded spatial infor-mation with a different orientation for each spoke. This causes a blurring effect, which can be explained from the impact of the phase modulations on the PSF. As outlined in Section 4.3.1, each spoke creates a backprojection of a profile that is composed of sinc-functions, and the profile maxima overlap in the PSF center. In the presence of off-resonances, the linear phase modulation creates a shift of each backprojection pro-file and, therefore, the maxima of the individual backprojections do not coincide as a central peak anymore, which is demonstrated in Figure 4.8. Here, a difference exists between the radial sampling pattern with a 180^◦ and a 360^◦ coverage (see Section 4.1).

Because for 180^◦ the readout orientation and, thus, also the shift direction is uniformly aligned for all spokes, a U-shaped intensity concentration is obtained in the PSF, which causes unsymmetrical blurrings of the reconstructed object that spread over the entire image. In contrast, for the 360^◦ coverage the opposing orientation of neighboring spokes yields a symmetrical ring-shaped widening of the PSF, which is advantageous because the blurring artifacts become more localized. As a slight drawback, it may lead to increased streaking artifacts, which, however, is secondary to the amelioration of the image blurring.

A correction of the off-resonance artifacts is rather complicated for two reasons. First, an unwinding of the phase modulations requires knowledge of the off-resonance map β(x), which is a priori not given. Information about the local off-resonances can be gained using phase mapping techniques, which employ multiple measurements with different echo times to estimate the phase evolution [67, 68, 69]. However, such mea-surements are often time consuming, and the techniques face additional problems like phase wrappings. Second, because the modulation depends on both, acquisition time and spatial position, the calculation of a corrected image is very computationally in-tensive. To enable a practicable calculation, it is, therefore, necessary to introduce a segmentation of either the time or the frequency deviation [70, 71, 72]. Thus, the de-velopment of a robust compensation technique for routine applications is non-trivial, and a more rational strategy consists in the experimental reduction of off-resonance effects. This is possible with short echo times or RF refocusing techniques, allowing to eliminate most visible artifacts or, at least, to diminish their strength to a degree

that is tolerable. However, for applications that explicitly require long echo times, for example, to obtain a T^?₂ contrast, radial sampling is less suited and certainly a second choice due to the more pronounced off-resonance sensitivity relative to the Cartesian approach.