Spatiotemporal Encoding as a Selective Spectral-Spatial Excitation Approach
Although the principles of ultrafast 2D MRS spectroscopy have been described in detail [12, 18, 19], it is convenient to revisit their use for the specific purpose of this study, addressing joint SPSP selectivity. SPEN departs from traditional schemes in that instead of triggering the chemical shift evolution homogenously, it allows various chemical sites to accrue their spin evolution in a spatially heterogeneous fashion. Several alternatives have been proposed for achieving this [20, 21]; for concreteness we consider the application of a chirp pulse lasting a time Te, sweeping a range of offsets ΔO while spins of a given chemical shift Ω—as measured vis-à-vis a carrier offset centered at Ωref—are under the action of a gradient Ge. Assuming that the usual principles of frequency sweeps are fulfilled (ΔOTe>>1, negligible relaxation, small tip angle approximation), different positions will be endowed with a quadratic phase given by [11, 12, 22]:
where is the length of the excited region and zc the slice center for the on-resonance species. The last term in Eq. (1) is a constant hereon disregarded. The final aim of SPEN MRS is to impart an evolution phase that is proportional to both the spins' chemical shift and to their spatial coordinate: ϕevol(z) = CΩ(z − zc), where C is a spatiotemporal constant under the experimentalist's control. Although the quadratic phase in Eq. (1) complicates this goal, this term can be removed by applying a suitable, additional frequency-swept pulse. This second sweep can take many different forms [20, 21]; for concreteness, we center on a 180° pulse, sweeping the same region addressed by the excitation but in half the time; i.e., Tr = Te/2. With this configuration, the first and second frequency-swept pulses can be used as the slice-selective excitation and refocusing pulses of a spin-echo imaging experiment, respectively. When gradients of equal signs and equal senses of sweep are used for excitation and refocusing, i.e., Ge = Gr, a full and simultaneous rephasing of all terms is obtained regardless of chemical shifts; this option has been used for spin-echo imaging with several families of frequency-swept pulses [23-25]. Alternatively, if as shown in Figure 1 the sweeps are kept equally signed but a bipolar gradient with Gr = −Ge is applied, the quadratic term in Eq. (1) vanishes but a site-dependent linear chemical shift term of the kind being sought remains [25-28]. Figure 1b illustrates the spatial characteristics that will then arise for two sites with different chemical shifts. The spatial characteristics of the excited slice will be given by the initial Oi and final Of frequencies, as well as by the profile of the B1+(t) excitation RF pulse. As for the chemical shift effects, this pulse combination will lead to a phase
Figure 1. Mechanism for simultaneous chemical shift and slice selection in an imaging experiment, based on applying a pair of frequency-swept pulses with opposite gradients. Following the spatial excitation, a rephasing gradient of area (black) leads to rephasing of the on-resonance species across the slice; the contribution of off-resonance species to signal is cancelled by a through-slice dephasing. An additional gradient lobe kCS (red) can be used to put an off-resonance species back in phase. The RF amplitude was assumed constant leading to a square-like pattern; amplitude modulation of the first pulse would result in other profiles.
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Given the z-linearity in this equation, a generic Ω will lead to a null overall signal arising from the chosen slice. A suitable post-inversion kcs, however, can bring any particular chemical site into a constructive superposition throughout the slice, leading to a site-specific observable signal. This is the principle used by SPEN for the ultrafast acquisition of indirect-domain spectra ; the important point to highlight in the present context is the fact that an appropriate choice of the pulse duration Te enables this refocusing to visualize one chosen species in the targeted slice, while dephasing the signals of all remaining off-resonance species excited in the region L.
The site-specific response arising from this scheme, assuming for simplicity a uniform spin density ρ across the excited slice L, is given by:
where is a change in slice thickness brought about by the targeted chemical shift offset. For an off-resonance species, the chemical shift will introduce opposite-signed displacements during the excitation and refocusing processes. Only the fraction of the slice that undergoes both pulses contributes to the signal; the remaining spins excited/inverted in the slice will stay longitudinal or be suppressed by crusher gradients. For reasonable gradient and shift values, this loss is expected to be minor. For multi-slice acquisitions, the existence of this slice displacement does not influence the inter-slice spacing that can be achieved; in particular, contiguous slices can be used and the full slice width ( ) can always be achieved for the on-resonance species.
It follows from Eq. (3) that the SPEN-based pulse pair introduces a sinc-like selectivity vis-à-vis offset. For a given pair of sites located a (known) ΔΩ shift separation apart, a zero of this function can be set by choosing a sweep of duration
thus obtaining optimal suppression. p in this equation is an integer whose value can be adjusted to accommodate a maximum RF amplitude that is within hardware limitations for the desired bandwidth. As expected from Fourier principles, Eq. (4) implies that the minimum separation between the selected and suppressed resonances will be inversely proportional to the duration used for the chirp-driven SPEN encoding (for p = 1). By contrast to conventional 2D SPSP pulses, this will also be the time-scale available for achieving selectivity along the spatial dimension. This time is about an order of magnitude longer than what is usually available in the 2D SPSP pulses, boding well in terms of slice selectivity and spatial shaping.