Diffusion-time dependence of diffusional kurtosis in the mouse brain

Abstract

Purpose: To investigate diffusion-time dependency of diffusional kurtosis in the mouse brain using pulsed-gradient spin-echo (PGSE) and oscillating-gradient spin-echo (OGSE) sequences.

Methods: 3D PGSE and OGSE kurtosis tensor data were acquired from ex vivo brains of adult, cuprizone-treated, and age-matched control mice with diffusion-time (t_D ) ~ 20 ms and frequency (f) = 70 Hz, respectively. Further, 2D acquisitions were performed at multiple times/frequencies ranging from f = 140 Hz to t_D = 30 ms with b-values up to 4000 s/mm² . Monte Carlo simulations were used to investigate the coupled effects of varying restriction size and permeability on time/frequency-dependence of kurtosis with both diffusion-encoding schemes. Simulations and experiments were further performed to investigate the effect of varying number of cycles in OGSE waveforms.

Results: Kurtosis and diffusivity maps exhibited significant region-specific changes with diffusion time/frequency across both gray and white matter areas. PGSE- and OGSE-based kurtosis maps showed reversed contrast between gray matter regions in the cerebellar and cerebral cortex. Localized time/frequency-dependent changes in kurtosis tensor metrics were found in the splenium of the corpus callosum in cuprizone-treated mouse brains, corresponding to regional demyelination seen with histological assessment. Monte Carlo simulations showed that kurtosis estimates with pulsed- and oscillating-gradient waveforms differ in their sensitivity to exchange. Both simulations and experiments showed dependence of kurtosis on number of cycles in OGSE waveforms for non-zero permeability.

Conclusion: The results show significant time/frequency-dependency of diffusional kurtosis in the mouse brain, which can provide sensitivity to probe intrinsic cellular heterogeneity and pathological alterations in gray and white matter.

Keywords: brain; diffusion time; kurtosis; non-Gaussian diffusion; oscillating gradient; permeability; pulsed gradient.

Fig. 1:

Comparison of PGSE- and OGSE-based mean diffusivity (MD) and mean kurtosis (MK) maps of an adult mouse brain. a, b) A horizontal slice from 3D PGSE and OGSE tensor datasets acquired with Δ = 22 ms and f = 70 Hz, respectively, is shown. Maps representing the difference between PGSE- and OGSE-based MD and MK (ΔMD and ΔMK, respectively) reveal selective enhancement of distinct gray and white matter regions in the brain, as seen by comparison with the Nissl-stained section (c). Arrowheads indicate the dramatic reduction in MK observed in the granule cell layer of the cerebellum (Cbgr) in OGSE-based maps. The Nissl-stained section is from [62]. Abbreviations are: Cx: cortex, cc: corpus callosum, DG: dentate gyrus, Cbgr: cerebellar granule cell layer.

Fig. 2:

Plots showing signal attenuation as a function of b-value for PGSE and OGSE in gray matter regions of the mouse brain. a) Sagittal MK sections show sharply reduced kurtosis in the Cbgr compared to the cortex (Cx) in OGSE maps. b, c) Signal attenuation (ln S/S₀) along one representative direction plotted as a function of b-value. The ln(S/S₀) plot for OGSE in the Cbgr is approximately linear, indicating that kurtosis approaches zero at f = 70 Hz. Plots for the cortex exhibit a distinct curvature for both PGSE and OGSE data. Data points in (b, c) denote mean (± standard deviation) measurements over the regions of interest. Solid curves represent fits of the experimental data to Eq. [2].

Fig. 3:

Time-dependence of kurtosis and diffusivity in gray matter regions of the mouse brain. Kurtosis (a, b) and diffusivity (c, d) values fitted from OGSE and PGSE data over 9 b-values at each diffusion time/frequency are plotted. For visualization, OGSE data (squares) are plotted against 1/4f and PGSE data (circles) are plotted against t_D (= Δ-δ/3). Data points represent the mean (± standard deviation) values over regions of interest in the Cbgr and cortex. Asterisks in (a) and (b) indicate the peak kurtosis positions for each ROI. Diffusivity values for the PVP phantom are plotted in (c) for reference. Corresponding maps of diffusivity and kurtosis for the mouse brain at all sampled diffusion times/frequencies can be found in Supporting Information Fig. S1.

Fig. 4:

Group-averaged maps of control and cuprizone-treated mouse brains (n=5 each) showing changes in PGSE (Δ = 22 ms) and OGSE (f = 70 Hz) based diffusion kurtosis contrasts in the corpus callosum. a) Sagittal sections from ΔMK (MK_PGSE-MK_OGSE) maps reveal a selective loss of contrast in the splenium (scc) of cuprizone-treated mice (red arrowheads) as compared to the genu (gcc). b) Group-averaged PGSE- and OGSE-based MK, RK, and AK maps of control and cuprizone-treated mouse brains at the level of the scc. The anatomical location of the coronal slices is indicated by the dashed white line in (a).

Fig. 5:

Time-dependence of kurtosis and diffusivity in the corpus callosum of control and cuprizone-treated mouse brains. Kurtosis (a, b) and diffusivity (c, d) values from OGSE and PGSE data acquired along tetrahedral directions distributed at ~54.7° relative to the long-axis of the corpus callosum in the midsagittal plane are shown. For visualization, OGSE data (squares) are plotted against 1/4f while PGSE data (circles) are plotted against t_D (= Δ-δ/3). Data points represent the mean (± standard deviation) values over regions of interest in the genu (gcc) and splenium (scc) of the corpus callosum.

Fig. 6:

Black Gold II-stained sections of the corpus callosum from control and cuprizone-treated mouse brains. Coronal sections at the level of the genu (gcc) and splenium (scc) of the corpus callosum from a control mouse (left) and two mice after 4-weeks of cuprizone-treatment (right) are shown. Extensive demyelination is seen in the scc of the cuprizone-treated mice, with relative sparing of the gcc. Scale bar = 200 μm.

Fig. 7:

MC simulation results for the same diffusion-encoding gradient waveforms and parameters as those used in the mouse brain experiments, showing the coupled effects of varying restriction size and permeability on the time-dependent kurtosis curves. Fits from simulated signals for OGSE and PGSE waveforms are plotted against 1/4f and t_D, respectively. Shaded area demarcates the approximate effective diffusion-time range (≤ 5 ms) probed with OGSE sequences. Plots of kurtosis (K) and diffusivity (D) for different cylinder radii (R) and membrane permeabilities (p) are shown in the top and bottom rows, respectively. Plots for randomly-packed cylinders are included in Supporting Information Figure S2.

Fig. 8:

Surface plots showing comparison of fitted kurtosis (a, b) and diffusivity (c, d) from MC simulations for pulsed and oscillating encoding waveforms over an extended time/frequency range. The x- and y- axes are normalized to t_D/t_R and t_R/τ_ex, respectively, with t_R= R²/2D₀ and τ_ex=αR/2κ, where α is the extracellular volume fraction and κ is the permeability corresponding to p [63]. Kurtosis for both PGSE and OGSE waveforms showed a biphasic response with diffusion time/frequency, and a monotonic decay with permeability. OGSE-based measurements of kurtosis showed a more rapid rate of decrease with increasing permeability than PGSE-based measurements for similar values of t_D and 1/4f.

Fig. 9:

Effect of varying number of cycles (N) in OGSE waveforms on diffusivity and kurtosis estimates. a) Results from MC simulations for f = 105 Hz and N = 1 and 2, showing plots of fitted diffusivity (D) and kurtosis (K) as a function of permeability. b) Experimental OGSE data from an adult mouse brain with f = 105 Hz and N = 1 and 2, showing diffusivity and kurtosis measurements (mean ± standard deviation) for two regions corresponding to the cortex (Cx) and deep cerebellar nuclei (CbN). Examples of ln(S) versus b-value curves for N = 1 and 2 in both regions are shown in the plot on the right. Solid lines represent fits of the experimental data to Eq [2].