0934

Investigation of the time- and frequency-dependence of diffusion kurtosis in the human brain with pulsed and oscillating gradient experiments

Runpu Hao¹, Eric S. Michael¹, Franciszek Hennel¹, and Klaas P. Pruessmann¹
¹Institute for Biomedical Engineering, ETH Zurich and University of Zurich, Zurich, Switzerland

Synopsis

Keywords: DWI/DTI/DKI, Microstructure, Kurtosis, OGSE, PGSE, Frequency dependence, Time dependence, Human brain

Motivation: Investigation of the time- and frequency-dependence of diffusion kurtosis, a valuable probe of microstructure and exchange, is becoming feasible in humans due to advances of gradient hardware.

Goal(s): To provide more data regarding time- and frequency-dependent diffusion kurtosis in the human brain.

Approach: Diffusion MRI with pulsed and oscillating gradients (PGSE/OGSE) at different but partially overlapping diffusion times using a head gradient insert and spiral readouts.

Results: Biphasic kurtosis behavior (i.e., increase with time in the short-time range and decrease with time in the long-time range covered by OGSE/PGSE, respectively) was observed, with an explainable mismatch between both sequences in the overlapping range.

Impact: Studying the time- and frequency-dependence of diffusion kurtosis using both PGSE and OGSE experiments over a range of diffusion times and length scales can provide valuable information about brain tissue complexity, heterogeneity, and inter-compartmental water exchange.

Introduction

Diffusion kurtosis imaging (DKI) assesses the non-Gaussianity of the diffusive displacements of water molecules, providing valuable microstructural information about biological tissues complementary to conventional DWI.¹ Such experiments typically employ the pulsed gradient spin-echo (PGSE) sequence,² but the oscillating gradient spin-echo (OGSE) sequence,³ in which the diffusion-sensitizing gradient waveforms sinusoidally oscillate, can be used to probe shorter effective diffusion times (Δ_eff) than are achievable in PGSE experiments.

By using both diffusion encoding methods, the frequency dependence or, correspondingly, the Δ_effdependence of diffusion kurtosis, can be studied, aiding our understanding of tissue complexity and processes like inter-compartmental water exchange.^4,5 Such dependency has been extensively studied using preclinical scanners.^4,6,7 However, due to gradient demands, this relationship has only been explored by few studies in the human brain.^5,8,9 In this work, we investigate the frequency and diffusion time dependence of axial, mean, and radial kurtosis (AK, MK, and RK, respectively) in the in vivo human brain using a high-performance gradient insert¹⁰ with OGSE and PGSE sequences over an extended yet overlapping range of frequencies and Δ_eff.

Methods

Scanning was performed using a Philips 3T Achieva system (Philips Healthcare, Best, the Netherlands) equipped with a high-performance gradient insert coil (G_max = 200 mT/m)¹⁰ on two healthy volunteers. Each volunteer was scanned using four OGSE and three PGSE protocols with spiral readouts. Each protocol consisted of a three-shell acquisition with b-values of 500, 1000 and 2000 s/mm² and 15, 15, and 32 diffusion directions, respectively. The centroid frequencies of the OGSE waveforms^11,12 were 11, 20, 34, and 51 Hz (Figure 1). The Δ_eff of the PGSE waveforms were 12.5, 22.7 and 50 ms, calculated using $$$\Delta_{eff}=\Delta-\frac{\delta}{3}$$$; the 22.7 and 12.5 ms PGSE measurements correspond in terms of Δ_eff to OGSE at 11 and 20 Hz,¹³ respectively. Other imaging parameters were: 20 slices, spatial resolution = 2×2×3 mm³, interslice gap = 2 mm, TE/TR = 97/6000 ms, two and four b = 0 acquisitions for each protocol for the two subjects.

The raw reconstructed images were processed using the DESIGNER pipeline,¹⁴ including: denoising,¹⁵ unringing,¹⁶ rigid body registration, and Rician bias correction.¹⁷ AK, MK, and RK were computed from fitted diffusion kurtosis tensors.¹⁸ Global white and gray matter masks were generated using FSL’s FAST.¹⁹ White and gray matter ROIs were segmented using the JHU DTI-based white-matter atlas²⁰ and the Harvard-Oxford cortical and subcortical structural atlas.²¹

Results

Figure 2 shows AK, MK, and RK maps for a representative slice from the seven protocols. Figure 3 displays kurtosis difference maps between the OG51 and OG11 protocols.

Figure 4 plots kurtosis values versus frequency and Δ_eff for global white and gray matter. Figure 5 plots the same variables for two white matter ROIs (posterior limb of internal capsule and corpus callosum) and two gray matter ROIs (hippocampus and thalamus).

Discussion and Conclusion

White matter shows a significantly higher RK than AK across all probed diffusion times (Figures 2 and 4), indicating anisotropic tissue structure. For gray matter, the smaller difference between RK and AK indicates less anisotropic tissue than white matter. For both white and gray matter, kurtosis decreases with increasing OGSE frequency from 11 Hz to 51 Hz, implying fewer interactions of water molecules with restrictions and more Gaussian diffusive displacements. Additionally, AK displays the steepest decrease, whereas RK displays the shallowest decrease. Notably, the contributions to non-zero kurtosis at 51 Hz include the residual interactions at short diffusion times and the existence of multiple compartments within each imaging voxel.

In Figures 4 and 5, discrepancies are present in measured kurtosis values at the same Δ_eff using PGSE and OGSE sequences. One explanation is the inadequacy in the $$$\Delta_{eff}=\frac{1}{4f}$$$ convention.¹³ In the presence of exchange, differences in gradient shapes will also cause differences in kurtosis estimations at a given Δ_eff.^4,22

In Figure 5, the kurtosis values of the posterior limb of the internal capsule and corpus callosum measured using PGSE sequences are only weakly time-dependent, suggesting rather slow inter-compartmental water exchange and a small effect of coarse graining on the tissue structure. However, for the hippocampus and thalamus, which exhibit faster exchange,^23,24 biphasic kurtosis behavior can be clearly observed. Such behavior also exists in global white and gray matter (Figure 4); similar findings were reported only in rat brains.⁴ The initial increase in kurtosis with decreasing Δ_eff demonstrates the homogenizing effect of both exchange and coarse graining of disordered structure at long diffusion times.⁵ As Δ_eff further decreases below the exchange time, structural disorder determines the behavior of kurtosis, which starts to decrease because the interactions of water molecules with restrictions become more scarce.

Acknowledgements

No acknowledgement found.

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Figures

Figure 1: Pulsed gradient (PG) and oscillating gradient (OG) encoding spectra, and gradient waveforms of the four OG diffusion sequences. The encoding spectra are scaled to have the same spectral area. The effect of the refocusing RF pulse is included in the gradient waveforms. The waveforms are scaled to have the same amplitude for visibility. The 11 Hz diffusion encoding was achieved by using a conventional first-order motion-compensated diffusion sequence.²⁵

Figure 2: Maps of axial kurtosis (AK), mean kurtosis (MK), and radial kurtosis (RK) from the seven encoding protocols. All maps have the same color limits. The number following ‘PG’ refers to the effective diffusion time, whereas the number following ‘OG’ refers to the centroid encoding frequency. PG22.7 and OG11 protocols were designed to probe the same Δ_eff of 22.7 ms; PG12.5 and OG20 protocols were designed to probe the same Δ_eff of 12.5 ms.

Figure 3: Axial, mean, and radial kurtosis difference maps, obtained by subtracting OG11 kurtosis maps from OG51 kurtosis maps. The same slice of the same subject as that shown in Figure 2 is shown here. All maps have the same color limits. CSF is masked out using a mean diffusivity threshold. Clear white matter delineation is observed, in particular, in MK and RK difference maps.

Figure 4: Computed kurtosis values of global white and gray matter from PG (dashed lines with circle markers) and OG (solid lines with asterisk markers) acquisitions. The lower x-axis shows frequency and the upper x-axis shows effective diffusion time. Δ_eff = 1/(4f) was used for converting the centroid OG frequency to an effective diffusion time.¹³ Each point represents the average of the median values across masked regions of the two subjects. The error bars represent inter-subject standard deviation. Non-monotonic time-dependence of kurtosis can be observed in both plots.

Figure 5: Computed kurtosis values of four white and gray matter ROIs from PG (dashed lines with circle markers) and OG (solid lines with asterisk markers) acquisitions. (a) Posterior limb of the internal capsule, left and right. (b) Hippocampus, left and right. (c) Genu and splenium of corpus callosum, left and right. (d) Thalamus, left and right. The non-monotonic, biphasic time-dependence of kurtosis is clearly present in the hippocampus and thalamus. For the posterior limb of the internal capsule and corpus callosum, the time-dependence of kurtosis is more monotonic.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

0934

DOI: https://doi.org/10.58530/2024/0934