Improved gradient waveforms for oscillating gradient spin‐echo (OGSE) diffusion tensor imaging

Abstract

The dependence of the diffusion tensor on frequency is of great interest in studies of tissue microstructure because it reveals restrictions to the Brownian motion of water molecules caused by cell membranes. Oscillating gradient spin‐echo (OGSE) sequences can sample this dependence with gradient shapes for which the power spectrum of the zeroth moment is focused at a target frequency. In order to maintain the total spectral power (ie the b‐value), oscillating gradient amplitudes must grow with the frequency squared. For this reason, OGSE applications on clinical MRI scanners are limited to low frequencies, for which it is difficult to obtain a narrow frequency bandwidth of the gradient moment in a useful echo time. In particular, the commonly used pair of single‐period trapezoidal‐cosine pulses separated by a half‐period produces significant side lobes away from the target frequency. To mitigate this effect, improved OGSE waveforms are proposed, which reduce the gap between the two gradient pulses to the minimum duration required for the refocusing RF pulse. Additionally, a slight deviation from the periodicity of the waveforms is proposed in order to permit using the maximum slew rate of the gradient system for all lobes of trapezoidal waveforms while maintaining advantageous spectral properties, which is not the case for the currently used OGSE sequences. Numerical calculations validate these changes, showing that both modifications significantly narrow the gradient moment power spectrum and increase the contribution of its main lobe to the b‐value, thus improving the specificity of the measurement. The utility of the new shapes is demonstrated by diffusion tensor measurements of human white matter in vivo over the range of 30‐75 Hz with a b‐value of nearly 1000 s/mm2, using a high‐performance gradient insert. However, the improvement should increase the sampling precision of OGSE experiments for all gradient systems.

Evaluating diffusion dispersion across an extended range of b‐values and frequencies: Exploiting gap‐filled OGSE shapes, strong gradients, and spiral readouts

“…In comparison to previous in vivo human brain OGSE studies, the data presented here correspond to comparable dispersion rates and are consistent with the relative steps in MD, namely, a larger step from 0 Hz to the first OGSE frequency than between OGSE frequencies 5–7,9,13 . Moreover, the data indicate a clear advantage of favoring higher b‐values instead of a broader spectral range in measuring diffusion dispersion among the regime explored here (i.e., maximum frequency ≤ 125 Hz, b ≤ 1000 s/mm 2 ), which encompasses the parameter ranges used in all human OGSE studies to date.…”

“…The aforementioned Tan et al study utilized such a gradient, 11 achieving b = 450 s/mm 2 for frequencies up to 100 Hz. Using a specialized gradient with similar specifications 12 for human brain OGSE imaging, we reached a b‐value of nearly 1000 s/mm 2 in a similar echo time but at a lower maximum frequency (75 Hz), 13 albeit a frequency that has still not been reached with a standard gradient system. These examples represent the upper limits of frequency and b‐value that have been achieved in published OGSE human brain experiments to date and highlight that there is an implicit tradeoff between these two parameters for a given TE: the highest oscillation frequency within a series of spectral measurements limits the b‐value.…”

Tuned bipolar oscillating gradients for mapping frequency dispersion of diffusion kurtosis in the human brain

“…This equation can also be further generalized to include additional periods, which we note then resembles the method presented by Hennel et al [36] with the added condition of encoding only non-zero spectral components. However, the finite truncation of the gradient waveform -more prominent for our abbreviated FTB rendition, imposes a frequency limit based on the minimum permitted separation time τ RF .…”

“…Conventional OGSE is typically performed with trapezoidal cosine modulated waveforms (Figure 1B) to maximize the achievable b-value [35]. However, recently proposed by Hennel et al [36], the conventional cosine sequence can be modified by optimizing ramp times and reducing the spacing between the two diffusion gradients to the minimum allowable, thereby effectively consolidating the two diffusion gradients into a single waveform. These changes were shown to produce more selective power spectra and increased diffusion weighting capabilities [36].…”

“…However, recently proposed by Hennel et al [36], the conventional cosine sequence can be modified by optimizing ramp times and reducing the spacing between the two diffusion gradients to the minimum allowable, thereby effectively consolidating the two diffusion gradients into a single waveform. These changes were shown to produce more selective power spectra and increased diffusion weighting capabilities [36]. The framework presented by Hennel et al enables the implementation of a non-integer number of periods introducing the N = n + 1/2 convention where N constitutes the total number of periods and n is an integer greater than 1.…”