Preliminary evaluation of accelerated microscopic diffusional kurtosis imaging (μDKI) in a rodent model of epilepsy

Abstract

Purpose:

Our study aimed to develop accelerated microscopic diffusional kurtosis imaging (μDKI) and preliminarily evaluated it in a rodent model of chronic epilepsy.

Methods:

We investigated two μDKI acceleration schemes of reduced sampling density and angular range in a phantom and wild-type rats, and further tested μDKI method in pilocarpine-induced epilepsy rats using a 4.7 Tesla MRI. Single slice average μD_app and μK_app maps were derived, and Nissl staining was obtained.

Results:

The kurtosis maps from two accelerated μDKI sampling schemes (sampling density and range) are very similar to that using fully sampled data (SSIM>0.95). For the epileptic models, μDKI showed noticeably different contrast from those obtained with conventional DKI. Specifically, the average μK_app was significantly less than that of the average of K_app (0.15±0.01 vs. 0.47±0.02) in the ventricle.

Conclusions:

Our study demonstrated the feasibility of accelerated in vivo μDKI. Our work revealed that μDKI provides complementary information to conventional DKI method, suggesting that advanced DKI sequences are promising to elucidate tissue microstructure in neurological diseases.

Introduction

Diffusional kurtosis imaging (DKI) measures the degree of non-Gaussian diffusion and has been increasingly used for neuroimaging [1, 2]. DKI reveals sub-voxel tissue heterogeneity and complexity in central nervous system disorders including epilepsy, Alzheimer’s disease (AD) and stroke [3–7]. For example, DKI refines the heterogeneous diffusion-weighted imaging (DWI) lesion that is associated with graded metabolic derangement, which can be used for enhanced characterization of ischemic tissue injury [8–10]. It’s helpful to point that routine DKI is based on single diffusion encoding (SDE), a pair of pulsed gradients that encode the diffusional displacement. Recently, double diffusion encoding (DDE) MRI has shown promise to extract important information that could not be easily inferred from the SDE experiments [10–17]. For instance, angular DDE can quantify microscopic properties affecting the spin’s diffusion, including estimation of cell size [18, 19], pore diameter [20], and microscopic anisotropy [16, 21–23].

The routine kurtosis measurement can arise from both restricted diffusion and diffusional heterogeneity [1, 24]. Recently, microscopic diffusional kurtosis imaging (μDKI) based on symmetrized DDE (s-DDE) echo planar imaging (EPI) has been demonstrated by Ji et al. [25]. In vivo μDKI displayed some unique image features that complement conventional DKI. However, the initial μDKI scan required diffusion sampling along a large number of directions, resulting in a prolonged acquisition time. Efficient μDKI acquisition and processing schemes are necessary in order to expedite its translation to the routine in vivo applications. The current work aimed to shorten the scan time of μDKI by reducing the sampling density and range of the modulation angle. Of note, cerebral atrophy is associated with epilepsy, resulting in noticeable diffusional heterogeneity [26–28]. As a result, we preliminarily tested μDKI in a rodent model of chronic epilepsy and evaluated its potential diagnostic value.

Material and methods

2.1. Phantom

The μDKI was tested using a three-compartment phantom. The left centrifugal tube comprised 40% sucrose mixed with 1% agarose and 1% agarose alone, representing two superimposed Gaussian diffusion pools. The right centrifugal tube comprised 20 μm monosphere acrylic beads (MX-2000, Esprix Technologies, Sarasota, FL) mixed with 1% agarose. The third compartment (the space between two centrifugal tubes) was filled with 1% agarose gel.

2.2. Animal model of temporal lobe epilepsy

In vivo experiments have been approved by the local Institutional Animal Care and Use Committee. Adult male Sprague-Dawley (Harlan/Envigo, Indianapolis, IN) were divided into a control group (n=5) and a lithium-pilocarpine-induced chronic epilepsy group (n=5) [29, 30]. Briefly, rats were injected intraperitoneally with 3 mmol/kg lithium chloride, followed by 1 mg/kg methylscopolamine subcutaneously after thirteen hours. The subcutaneous injection was repeated with 30 mg/kg pilocarpine thirty minutes later to trigger status epilepticus within 10–30 minutes. Status epilepticus was defined as continuous behavioral seizure activity scored as stage 4 or 5 according to the Racine score and lasting at least 90 minutes [31]. Diazepam (10 mg/kg, i.p.) was administered after 1 hour of status epilepticus to terminate seizures. Repeated diazepam (5 mg/kg) was injected unless status epilepticus was terminated. Two weeks after status epilepticus, rats were video recorded (8 hours/day, 5days per week) for monitoring chronic spontaneous recurrent seizures. The chronic epilepsy model was considered successful when three or more spontaneous recurrent seizures were observed. For the control group, lithium preconditioning was followed by saline administration instead of pilocarpine. Rats were anesthetized with 1.5–2.0% isoflurane air during the MRI experiment. Respiratory rate and body temperature were monitored online (SA Instruments, Stony Brook, NY), and the temperature was maintained by a circulating warm water jacket positioned around the torso (Stryker Temperature Therapy Pad, Kalamazoo, MI).

2.3. MRI

MRI scans were performed using a 4.7 T small-bore Biospec MRI (Bruker, Billerica, MA) with a dual radiofrequency (RF) coil setup. For the phantom scan, μDKI was acquired with 4 b-values (0, 1000, 1500 and 2500 s/mm²), 26 angles evenly spanning from 0 to 360° in the x-y plane (NAE = 4 and scan time = 11 min), field of view (FOV) of 50×50 mm² and 8 mm slice thickness (Matrix size= 64×64, repetition time (TR)/echo time (TE) = 3000/76 ms). For in vivo scans, we performed DKI using both tensor-based DKI and μDKI methods (FOV= 20×20 mm², Matrix = 64×64, slice thickness =2 mm). For the standard DKI protocol, diffusion images (1000 and 2500 s/mm²) were acquired along 30 diffusion directions in addition to a single reference image of b=0 (δ/Δ = 4/17.5 ms, TR/TE = 3000/75.8ms, NAE = 4, and scan time = 10 min 50 s) [32]. μDKI was acquired with 3 b-values (1000 and 2500 s/mm²), 26 angles evenly spanning from 0 to 360° through x-y, x-z and y-z planes, respectively, in addition to a single reference image of b=0 (NAE = 8, TR/TE = 3000/75.8 ms, and scan time = 66 min). T₂-weighted EPI images were obtained with two TE of 30 and 100 ms (TR=3250 ms, NAE=16). Moreover, a high-resolution rapid acquisition with relaxation enhancement (RARE) image was performed (FOV= 20×20 mm², Matrix = 128×128, TE=35 ms).

2.4. Data Processing

Images were processed in MATLAB (Mathworks, Natick, MA). Conventional DKI was analyzed using established routines [33, 34]. For μDKI, the diffusion-induced signal can be formulated as,

$$ln\left\{\frac{E\left(q,\varphi \right)}{E_0}\right\}=E_{c,\tilde{0}}+E_{c,\tilde{2}}\cos \left(2\varphi \right)+E_{c,\tilde{4}}\cos \left(4\varphi \right)+\mathrm{ }\cdots +E_{s,\tilde{2}}\sin \left(2\varphi \right)+\cdots$$ (1)

where ${E_{c,\tilde{n}}}_{\mathrm{ }}$ and ${E_{s,\tilde{n}}}_{\mathrm{ }}$ are amplitudes of nth-cycle cosine and sine terms of the natural logarithm of the μDKI signal with respect to ϕ. We investigated three sampling schemes of ϕ: 1) [0°, 360°] with intervals of 13.8°. 2) [0°, 360°] with intervals of 27.7°, and 3) [0, 180°] with intervals of 13.8°. The diffusion and kurtosis terms were calculated according to,

$$D=\frac{E_{c,\tilde{0}}-{3E}_{c,\tilde{4}}}{-b}$$ (2.a)

$$K=\frac{{4!E}_{c,\tilde{4}}}{{\left(E_{c,\tilde{0}}-3E_{c,\tilde{4}}\right)}^2}$$ (2.b)

The in vivo μDKI was repeated along x-y, x-z, and y-z planes, and the diffusion and kurtosis metrics were denoted as average apparent μD (average μD_app) and average apparent μK (average μK_app), respectively. In addition, the diffusional kurtosis tensor W_ijkl was calculated from the tensor-based DKI approach, which was used to calculate apparent diffusion (D_app) and apparent kurtosis (K_app). To compare with μDKI, the average D_app and K_app along x-y, x-z, and y-z planes are calculated and denoted as average apparent diffusion (average D_app) and average apparent kurtosis (average K_app), respectively.

We calculated structural similarity (SSIM) index to assess the accuracy of accelerated μDKI schemes. Diffusion and kurtosis from three representative regions of interests (ROIs) of white matter (WM), gray matter (GM), and ventricle were reported as their mean ± standard deviation (SD). We compared the diffusion and kurtosis indexes from conventional DKI and μDKI using two-tailed paired Student’s t-test in control and epilepsy groups. Indices from the same ROIs were also compared using two-tailed unpaired Student’s t-test between control and epilepsy groups. In addition, the false discovery rate (FDR, n=6) correction was performed for statistical analysis. P values less than 0.05 were considered statistically significant.

2.5. Histology

Animals were euthanized after MRI, followed by transcardial perfusion with PBS and exsanguination. Brains were dissected and frozen in 2-methylbutane on dry ice at −35 C°. Coronal cryosections were collected every 30 μm throughout the entire brain and the standard Nissl staining was performed.

Results

Figure 1A shows the μDKI pulse sequence. Two pairs of diffusion gradients (g₁ and g₂) were applied consecutively with their relative magnitude modulated by trigonometric functions of ϕ. The echo time (TE) in μDKI sequence can be expressed as TE=TE’+TE”+Δ. In vivo μDKI was repeated with gradients along x-y, x-z and y-z plane (Fig. 1B), in which the angle ϕ spans from 0 to 360°, uniformly with intervals of 13.8° in each plane.

Figure 1:

The diagrams of the μDKI pulse sequence. A) Two pairs of diffusion gradients (g₁ and g₂) are orthogonal to one another, with their magnitudes modulated by the trigonometry of angle ϕ. B) The μDKI diffusion sampling scheme used in our study. The arrows indicate the directions of the 78 independent vectors $\stackrel{\rightharpoonup }{q}=\text{γgδ}(\text{g}\cdot \text{cos}\left(\varphi \right)\stackrel{\rightharpoonup }{e_1}+\text{g}\cdot \text{sin}\left(\varphi \right)\stackrel{\rightharpoonup }{e_2})$, which are uniformly distributed in x-y, x-z, and y-z planes.

The accelerated μDKI schemes were first evaluated using a triple compartment phantom (Figure 2A). Figure 2B shows the diffusion and kurtosis maps from different sampling schemes. The original μDKI approach with denoted as (0, 360°)₂₆ with ϕ from 0 to 360° in 26 steps. The second scheme halved the sampling density from 26 to 13 (i.e., (0, 360°)₁₃) and the third scheme reduced ϕ from 0 to 360° to 0 to 180° (i.e., (0, 180°)₁₃). The kurtosis from the left ROI (mixed Gaussian compartment) was nearly zero from all three schemes. The kurtosis from the right ROI (monosphere beads gel compartment) showed little difference among the three approaches (0.42±0.03, 0.42±0.03 and 0.41±0.03), with their SNR being 16.5, 13.7 and 15.2, respectively.

Figure 2:

Phantom validation of the expedited μDKI. A) A schematic illustration of the triple-compartment diffusion phantom. B) Diffusion and kurtosis maps obtained from three sampling schemes of μDKI, 0 to 360° with 26 steps (i.e., (0–360°)₂₆), 0 to 360° with 13 steps (i.e., (0–360°)₁₃) and 0 to 180° with 13 steps (i.e., (0–180°)₁₃).

We then evaluated μDKI in normal rats. Figure 3A shows signals from WM and GM as a function of ϕ for diffusion b value of 1000 and 2500 s/mm² from a representative normal rat. The signal displays a prominent 4ϕ oscillation pattern for both WM and GM. The amplitude of oscillation in WM is larger than that in GM, consistent with the fact that diffusion in WM is more restricted than that of GM [35]. Figure 3B shows the diffusion and kurtosis maps from conventional DKI and three μDKI approaches ((0, 360°)₂₆, (0, 360°)₁₃ and (0, 180°)₁₃). μDKI appears to provide higher contrast between corpus callosum and cortex, consistent with that observed in Ji et al. [25]. To compare the accelerated μDKI images, we calculated SSIM between kurtosis images derived from the two accelerated μDKI schemes with respect to that using the fully sampled μDKI data, being 0.96±0.04 and 0.97±0.05, respectively. This shows that accelerated μDKI schemes provide nearly identical images as the fully sampled μDKI approach.

Figure 3:

Demonstration of μDKI from a representative normal rat. A) The normalized and natural logarithmic μDKI signals as a function of ϕ. B) Average D_app and K_app maps obtained from conventional DKI, average μD_app and μK_app maps obtained from three sampling schemes of μDKI, 0 to 360° with 26 steps (i.e., (0–360°)₂₆), 0 to 360° with 13 steps (i.e., (0–360°)₁₃) and 0 to 180° with 13 steps (i.e., (0–180°)₁₃).

Figure 4A shows μDKI from a representative chronic epilepsy rat brain. The average D_app map from conventional DKI and the average μD_app map from μDKI are in good agreement with each other. In contrast, the average μK_app map displayed a different pattern from that of the average K_app map, particularly in the ventricle. Figure 4B shows T₂-weighted RARE image and Nissl staining from control and epileptic rats. The epileptic brain had noticeable atrophy with enlarged ventricles, consistent with the chronic epilepsy model [28]. Diffusion and kurtosis values in WM, GM, and ventricle from the control and epilepsy groups were listed in Table 1. Of importance, the average μK_app is significantly lower than average K_app in CSF from the epilepsy group (0.15±0.01 vs 0.47±0.02, P<0.05). In addition, the average μK_app of WM is significantly higher in the epilepsy group than that in control group (0.75±0.02 vs 0.69±0.04, P<0.05) while the average K_app did not show a significant difference.

Figure 4:

Demonstration of μDKI from a representative chronic epilepsy rat. A) Comparison of diffusion and kurtosis images from the conventional DKI (average D_app and K_app) and μDKI (average μD_app and μK_app). B) T₂-weighted RARE image and the Nissl-staining from control and chronic epileptic rats.

Table 1.

Comparison of in vivo conventional DKI and μDKI measurements in white matter (WM), gray matter (GM) and ventricle of wild-type and epilepsy rat brains (Mean ± SD). Paired t-tests were performed in control and epilepsy groups, and unpaired t-tests were performed between control and epilepsy group. A false discovery rate (FDR, n=6) correction was performed. Letters in superscript (e.g., a, b) indicate the statistically significant difference between metrics.

		Control	Epilepsy
Average Dapp	WM	0.81±0.03	0.78±0.04
(μm2/ms)	GM	0.80±0.04	0.82±0.05
	CSF	1.89±0.11ae	2.81±0.22e
Average Kapp	WM	0.73±0.06b	0.76±0.02
	GM	0.55±0.05	0.54±0.03
	CSF	0.63±0.09cf	0.47±0.02df
Average μDapp	WM	0.80±0.03	0.78±0.03
(μm2/ms)	GM	0.82±0.04	0.83±0.03
	CSF	2.08±0.14ag	2.82±0.12g
Average μKapp	WM	0.69±0.04bh	0.75±0.02h
	GM	0.53±0.04	0.55±0.02
	CSF	0.27±0.09ci	0.15±0.01di

^aSignificant difference between average D_app and average μD_app of CSF in the control group (p<0.05).

^bSignificant difference between average K_app and average μK_app of WM in the control group (p<0.05).

^cSignificant difference between average K_app and average μK_app of CSF in the control group (p<0.05).

^dSignificant difference between average K_app and average μK_app of CSF in epilepsy rat group (p<0.05).

^eSignificant difference of average D_app of CSF between control and epilepsy rat group (p<0.05).

^fSignificant difference of average K_app of CSF between control and epilepsy rat group (p<0.05).

^gSignificant difference of average μD_app of CSF between control and epilepsy rat group (p<0.05).

^hSignificant difference of average μK_app of WM between control and epilepsy rat group (p<0.05).

ⁱSignificant difference of average μK_app of CSF between control and epilepsy rat group (p<0.05).

Discussion

μDKI is a relatively new diffusion MRI methodology that isolates compartmental kurtosis from diffusional heterogeneity. Establishment of expedited μDKI acquisition scheme is needed before it can be translated to routine preclinical and clinical applications. Our study evaluated two μDKI sampling schemes to reduce its acquisition time and validated them both in phantom and in vivo. The μDKI approach employs two pairs of gradients modulated as a function of ϕ, which needs to span a range of at least 180° with a 2-cycle modulation, per the Nyquist criterion. Indeed, our results confirmed that the acquisition time can be noticeably shortened while providing satisfactory images (SSIM > 0.95), promising for in vivo applications.

Interestingly, the μDKI shows a noticeable difference from conventional DKI in the animal model of chronic epilepsy. μK_app displays enlarged ventricle, consistent with cerebral atrophy in the model [27]. The average K_app in the ventricle is significantly higher than μK_app. The inflated ventricular average K_app is likely due to partial volume effect and/or diffusional heterogeneity. It’s worth mentioning that μK_app was significantly different between epilepsy and control groups in WM, which is likely attributable to chronic epilepsy-induced structural changes. Indeed, it has shown that patients with temporal lobe epilepsy have diffusion abnormalities in WM [36, 37]. Histopathological examinations documented disruption of myelin sheaths and altered axonal density [38]. Our results suggest that μDKI is promising to complement routine DKI for detection of microstructural changes following epilepsy.

Our study has a few limitations. First, we used a single slice μDKI pulse sequence for in vivo application. Although the μDKI pulse sequence can be extended for multi-slice readout due to the separation of s-DDE preparation and fast EPI readout, the inter-slice relaxation recovery needs to be properly accounted for. This may require correction based on relaxation measurement that is beyond the scope of our current work. Second, the s-DDE preparation was repeated in x-y, x-z, and y-z planes to estimate the average μD_app and μK_app metrics in vivo. Such an approach, strictly speaking, may not be rotationally invariant. Nevertheless, μDKI provides a reasonable estimation of tissue diffusion and kurtosis images that are clearly different from conventional DKI. Further evaluation of its diagnostic value is needed to investigate μDKI in a host of disorders including epilepsy and acute stroke.

Conclusion

Our study investigated accelerated μDKI acquisition and processing approaches and preliminarily demonstrated its utility in a rodent model of chronic epilepsy. The results suggest that advanced DKI complements routine diffusion MRI for improved characterization of tissue microstructure changes in neurological disorders such as epilepsy.