Simultaneous Acquisition of Diffusion Tensor and Dynamic Diffusion MRI

Abstract

Background:

Dynamic diffusion MRI (ddMRI) metrics can assess transient microstructural alterations in tissue diffusivity but requires additional scan time hindering its clinical application.

Purpose:

To determine whether a diffusion gradient table can simultaneously acquire data to estimate dynamic and diffusion tensor imaging (DTI) metrics.

Study Type:

Prospective

Subjects:

7 healthy subjects, 39 epilepsy patients (15 female, 31 male, age ±15)

Field Strength/Sequence:

2D diffusion MRI (b=1000 s/mm²) at a field strength of 3T. Sessions in healthy subjects - standard ddMRI (30 directions), standard DTI (15 and 30 directions) and nested cubes scans (15 and 30 directions). Sessions in epilepsy patients - two 30 direction (standard ddMRI, 10 nested cubes) or two 15 direction scans (standard DTI, 5 nested cubes).

Assessment:

15 direction DTI was repeated twice for within session test-retest measurements in healthy subjects. Bland-Altman analysis computed bias and limits of agreement for DTI metrics using test-retest scans and standard 15 direction versus 5 nested cubes scans. Intraclass correlation (ICC) analysis compared tensor metrics between 15 direction DTI scans (standard versus 5 nested cubes) and the coefficients of variation (CoV) of trace and apparent diffusion coefficient (ADC) between 30 direction ddMRI scans (standard versus 10 nested cubes).

Statistical Tests:

Bland-Altman and ICC analysis using a p-value of 0.05 for statistical significance.

Results:

Correlations of mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were strong and significant in gray (ICC>0.95) and white matter (ICC>0.95) between standard versus nested cubes DTI acquisitions. Correlation of white matter fractional anisotropy was also strong (ICC>0.95) and significant. Intraclass correlations of the CoV of dynamic ADC measured using repeated cubes and nested cubes acquisitions were modest (ICC>0.60), but significant in gray matter.

Conclusion:

A nested cubes diffusion gradient table produces tensor-based and dynamic diffusion measurements in a single acquisition.

INTRODUCTION

Diffusion MRI (dMRI) is a widely used clinical imaging modality used to assess alterations in tissue microstructure (1). In neurological insults such as stroke, changes in apparent diffusion coefficient (ADC) are measured using dMRI and are used to evaluate the region of affected brain tissue over the course of hours to days (2, 3). Unlike stroke, neurological insults such as the cortical spreading depolarizations underlying migraine aura are transient in nature (4) and under these conditions, abnormal electrical activity results in recoverable cellular swelling (5) that evolves on the order of minutes. Measurements of ADC or other diffusion properties with sufficient temporal resolution would provide a three dimensional, noninvasive method to monitor these dynamic changes in gray matter, and allow for the detection and localization of the source of abnormal electrical activity (6, 7).

Studies of dynamic changes in diffusion properties in vitro have shown that, in contrast to spontaneous neuronal activity, an applied stimulus can induce cell swelling that restricts water diffusion to a degree that is detectable using dynamic diffusion imaging (8). In animal models, mechanical insult, application of potassium chloride, and focal ischemia have all demonstrated transient reductions in the ADC between 15–30% that last on a temporal scale of minutes (9–11). Moreover, dynamic diffusion imaging in healthy volunteers performing a visual stimulation task has shown that activation of the visual cortex is detectable as a recoverable decrease in ADC that corresponds with a temporary decrease in the ability of water to diffuse in the extracellular space (12).

Although these dynamic diffusion imaging studies have been successful in paradigms where data is collected almost immediately following the applied stimulus, studies in clinical populations have been limited and have yet to reproduce these results (13). One reason for this is the challenge of collecting data during a transient event in a clinical setting with limited scan time. Previous dynamic dMRI methods obtained time series measurements of ADC by acquiring diffusion weighted images (DWIs) across a repeated triplet of mutually orthogonal directions over the course of a relatively long scanning session (approximately twenty minutes duration) following insult such as cardiac arrest, or ischemic stroke (9–11). In a clinical setting where imaging time is limited, particularly within minutes of the injury, acquisition of dynamic ADC maps may not provide clinically diagnostic information to justify the time needed for a lengthy dynamic diffusion scan. Therefore, an alternative approach that collects diffusion data to calculate additional descriptive metrics of diffusion beyond dynamic and mean ADC would improve scan time efficiency.

Diffusion tensor imaging (DTI) is an extension of dMRI that has become increasingly prevalent because of its ability to not only measure ADC, but also estimate diffusion anisotropy and white matter fiber orientation (14). A typical DTI acquisition requires collection of diffusion volumes across at least six directions, depending on the application, and more commonly fifteen or more directions (15). Consequently, DTI requires several minutes of scan time compared to the time required to collect three DWIs to measure ADC. This inherently reduces the temporal resolution of tensor-based ADC when considering using a standard DTI sequence to collect dynamic diffusion measurements. However, the requirement of increased scan time allotted for DTI creates an opportunity to simultaneously collect necessary data for dynamic diffusion and tensor-based measurements of diffusivity and anisotropy. Use of a DTI gradient table comprised of diffusion weighted vectors that can be used to obtain measurements of dynamic diffusion provides flexibility and can be implemented across a range of scanners without alterations to scanner hardware or pulse sequence development.

The aim of this work is to evaluate whether data for dynamic diffusion and DTI can be acquired simultaneously and produce tensor-based and dynamic diffusion measurements comparable with standard acquisition methods.

MATERIALS AND METHODS

Participants

All subjects provided written informed consent under an Institutional Review Board approved protocol at the National Institutes of Health prior to each scanning session. Seven healthy volunteers (three female, four male) were recruited with the following inclusion criteria: (1) age 18 years or older. 39 patients with epilepsy (12 female, 27 male) were recruited with the following inclusion criteria: (1) age 8 years or older (2) known or suspected diagnosis of epilepsy. Participants were excluded from recruitment with the following criteria: (1) patients with unstable medical conditions that makes participation unsafe. Epilepsy patients were not in the peri-ictal or ictal phases of seizure during the time of scanning.

Derivation of Diffusion Gradient Tables

The proposed diffusion acquisition gradient tables were derived by determining a set of vectors uniformly distributed across a spherical shell, with the constraint that the vector set is comprised of sequential triplets of mutually orthogonal directions. Each triplet can be geometrically represented as the vertex of a cube with unique orientation nested within an icosahedron. When diffusion weighting is applied along directions corresponding to the vertex of each nested cube, each sequential set of three DWIs can be used to calculate the ADC. Additionally, the complete volume of DWIs is acquired at angular resolution sufficient to reconstruct the diffusion tensor. We have referred to such a modified gradient table as a “nested cubes” DTI table, beginning with a 15- direction configuration followed by the more commonly applied 30 direction solution. The latter approach, however, is generalizable to any number of directions.

A 15-direction gradient table set was derived using a geometric analytic solution. Briefly, a regular dodecahedron with vertices equidistant from the origin was inscribed within a unit sphere. Eight of the vertices of the dodecahedron are shared with a cube also inscribed within the sphere (16). The set of edges of this cube represented a triplet of mutually orthogonal directions that formed the vertices of a cube (Figure 1). This cube can be nested in five unique orientations within the dodecahedron. Completion of the compound of five cubes resulted in a set of 15 total vertices uniformly sampling a sphere (17). A 15-direction gradient table was implemented using the five triplets of vertices that comprise these five nested cubes (Figure 1).

Figure 1. Derivation and arrangement of nested cubes diffusion tensor imaging vector sets.

Five distinct triplets of mutually orthogonal vectors were computed using a geometric approach to nest five cubes in a regular dodecahedron (top row). The 15 distinct directions corresponding to the corners of each cube provide uniform coverage over a spherical shell. A numerical solution was used to distribute thirty directions across a spherical shell. This solution was constrained by the condition that the vector set should consist only of triplets of mutually orthogonal vectors. For each vector configuration, diffusion weighting was applied sequentially across each triplet of mutually orthogonal directions. This allows for simultaneous acquisition of data useful for tensor estimation for diffusion tensor imaging (DTI) and a time series of measurements of apparent diffusion coefficient (ADC).

We next sought to derive a nested cubes style gradient table with greater angular resolution. However, a regular dodecahedron constructed using regular pentagonal faces is the Platonic solid with the greatest number of vertices and it cannot be used to derive a nested cubes table with more than 15 directions. We therefore used a numerical solution to derive a modified gradient table. Numerical solutions have previously been used to compute gradient tables for DTI where a set of noncollinear directions is computed to uniformly cover a spherical shell by iteratively minimizing a distance-based interaction term between the directional vectors (18). In our approach, an additional constraint of orthogonal triplets within the gradient table is required within the optimization algorithm. This was implemented using a customized Mathematica (Wolfram Research, Illinois, USA) script.

An overview of this numerical approach follows. Rotation of an initial vector v = (v_x,v_y,v_z) about unit vector u = (u_x,u_y,u_z) clockwise by θ can be described using Rodrigues’ formula(19):

$${\mathit{v}}_{rot}=\mathit{Rv}$$

$$\mathit{R}={\mathit{e}}^{\mathit{\theta U}}$$

Where U is the cross product matrix for u

$$\mathit{U}=\left[\begin{array}{ccc}0& -{\mathit{u}}_{\mathit{z}}& {\mathit{u}}_{\mathit{y}}\\ {\mathit{u}}_z& 0& -{\mathit{u}}_{\mathit{x}}\\ -{\mathit{u}}_{\mathit{y}}& {\mathit{u}}_{\mathit{z}}& 0\end{array}\right]$$

This rotation matrix was applied to an initial triplet of mutually orthogonal vectors v1 = (1,0,0), v2 = (0,1,0), and v3 = (0,0,1). The electrostatic energy between the x, y, and z components of these rotated vectors was used as a measure of interaction between each rotated set of orthogonal triplets (20). The angular rotation between triplets was maximized in order to provide uniform coverage of the spherical shell and to minimize the interaction between triplets. The configuration of ten triplets with minimum electrostatic energy cost function was selected as the final output. Using this approach, one can compute a set of any arbitrary number of noncollinear vectors that is a multiple of three. In this work, we focused only on 30 gradient directions, comprised of ten unique cubes nested within a sphere (Figure 1).

MRI Protocol and Data Processing

MR datasets were acquired on a Philips 3T Achieva scanner (Eindhoven, The Nederlands) using an 8 channel Sense head coil. Participants were placed head-first and supine inside the scanner. Three dimensional T1 weighted (TR/TE = 7.19/3.29 ms, 0.75 mm in-plane spatial resolution, 0.8 mm slice thickness) and two dimensional T2 weighted (TR/TE = 8000.0/90.0 ms, 0.50 mm in-plane spatial resolution, 2.0 mm slice thickness) fat suppressed volumes were collected for each subject to perform motion and distortion correction. Diffusion data was acquired using a 2D echo-planar sequence with 2.0 mm in-plane spatial resolution with the following parameters: TR/TE = 8800.0/75.0 ms, FOV = 224×224 mm, data matrix = 112×112, 70 slices, slice thickness = 2.0 mm, SENSE factor = 2, 6/8 partial Fourier sampling). No multisense (multiband) acceleration was employed. With these parameters, the acquisition times for the 15 direction and 30 direction diffusion weighted scans were 2.5 minutes and 5 minutes respectively.

Supplemental Figure 1 shows the diffusion data MRI protocols acquired in the two cohorts of subjects (healthy volunteer and patients under evaluation for epilepsy). All experiments were performed with diffusion weighting (b = 1000 s/mm²). In healthy volunteers (n = 7), the following diffusion gradient tables were used: standard 15 direction DTI repeated twice for test-retest intrasession reproducibility measurements, standard 30 direction DTI, nested cubes DTI (5 and 10 nested cubes), and a repeated triplet of orthogonal vectors along the x y and z axes (10 repeated cubes). Total acquisition time was limited to no more than two hours. Acquisition times for diffusion scans across fifteen and thirty directions were 2.5 minutes and five minutes, respectively. Patients were divided into two groups. In a first subset of epilepsy patients (n = 22), diffusion data was acquired using standard 15 direction DTI and 5 nested cubes DTI gradient tables. In the second subset of epilepsy patients (n = 17), diffusion data was acquired using 10 repeated cubes and 10 nested cubes gradient tables. In scans performed in healthy volunteers and epilepsy patients, one non-diffusion weighted (b = 0 s/mm²) volume was collected along with the DWIs as part of each diffusion gradient table. Acquisition time was limited to one hour. No contrast agents were administered during this study.

Diffusion data were coregistered and processed to correct for motion and eddy current distortion in TORTOISE (21, 22). Briefly, the T2 weighted and non-diffusion weighted volumes were both resampled to have isotropic 1mm resolution. The T2 weighted volume was then rigidly registered to the up-sampled b0 volume. The registered T2 weighted volume was used as the structural target for motion and distortion correction in TORTOISE.

Computation of Diffusion Metrics

We sought to compare tensor-based and dynamic diffusion metrics computed using the nested cubes gradient tables with those produced using standard dynamic and DTI acquisition methods. A nonlinear least square method was used for tensor estimation and subsequent calculation of DTI metrics, including fractional anisotropy (FA), directional encoded color (DEC) maps, mean diffusivity (MD), axial diffusivity (AD), radial diffusivity (RD) and the principal eigenvector, were performed using TORTOISE for the corrected standard and nested cubes diffusion datasets. A segmentation based approach, as described below was used to generate voxel based gray and white matter masks. The intracranial T1 weighted volume was obtained using the ROBEX (version 1.2, https://www.nitrc.org/projects/robex) skull stripping algorithm (23). FreeSurfer (version 7.2.0; http://surfer.nmr.mgh.harvard.edu) was used to segment the skull stripped brain into gray and white matter regions (24). The T1 was rigidly registered from FreeSurfer native space to the skull-stripped T2 in diffusion space from TORTOISE processing. The transformation matrix used to register the T1 to the T2 was applied to the FreeSurfer based gray and white matter segmentation volumes to obtain gray and white matter masks in diffusion space. In voxels classified as gray and white matter, root mean square errors (RMSE) normalized and expressed as a percentage of the range of the observed diffusion metrics were used to determine the magnitude of differences in tensor-based metrics between DTI acquisitions: standard 15 direction DTI test-retest, standard 15 direction DTI versus five nested cubes DTI. The angular agreement for fiber tract orientation was calculated in degrees as the arccosine of the dot product between the principal eigenvectors (ε₁, ε₂) on a voxel wise basis, where the magnitude of each principal eigenvector was used to restrict the domain of the angular agreement between 0 and 90 degrees.

$${\theta }_{\epsilon 1,\epsilon 2}=arcos\left(\frac{{\epsilon }_1\cdot {\epsilon }_2}{\left|{\epsilon }_1\right|\left|{\epsilon }_2\right|}\right)$$

Time series trace-weighted maps were calculated for the diffusion datasets consisting of 30 directions (10 repeated cubes, 10 nested cubes, 30 direction DTI) using the geometric mean of each triplet of sequentially acquired DWIs, (DWI_v, DWI_v+1, DWI_v+2).

$$trac{e}_{DWI}= \sqrt[3]{DW{I}_v*DW{I}_{v+2}*DW{I}_{v+3}}$$

Corresponding temporal ADC maps were computed as

$$ADC= \frac{1}{b}ln\left(\frac{trac{e}_{DWI}}{S_{b0}}\right)$$

Where S_b0 is the non-diffusion weighted volume and b is the diffusion weighted b-value (b = 1000 s/mm²). The temporal resolution of the time series maps was computed by multiplying the TR by number of diffusion weighted volumes in each triplet of DWIs (8800 ms x 3 DWIs = 26.4 seconds). Temporal signal-to-noise ratio (tSNR) was calculated by dividing the temporal mean intensity of each metric by its standard deviation. The temporal coefficient of variation (CoV) of each time series was computed as the inverse of the tSNR and multiplied by 100.

Statistical Analysis

All statistical analyses were performed in R (version 3.6.1; The R Foundation for Statistical Computing, Vienna, Austria; http://www.r-project.org). Bland-Altman scatter plots were generated for seven healthy volunteers to determine the reproducibility of tensor-based diffusivity metrics (MD, AD, and RD) from a test-retest 15 direction DTI acquisition. The percent difference was plotted against the mean between acquisitions for voxels included in the skull stripped intracranial brain mask. Because the residuals of the tensor-based metrics were not normally distributed, the median percent change was used to measure bias, and the limits of agreement were computed using the lower and upper 2.5^th percentiles of the percent change between acquisitions (25). Similarly, voxel-wise Bland-Altman scatter plots were generated for the same seven healthy volunteers to assess differences in tensor-based metrics measured using the standard 15 direction DTI and 5 nested cubes acquisitions. Due to the high density of datapoints when plotting intracranial voxels (approximately 0.996 × 10⁶) from all the healthy volunteers, every 2500^th datapoint was plotted on the scatterplots.

When computing the normalized RMSE for tensor-based metrics in the seven healthy volunteers, the median normalized RMSE was computed for each subject in voxels classified as gray matter or white matter and then averaged across all seven subjects to obtain summary statistics of the normalized RMSE with lower and upper 95% confidence intervals for each tensor-based metric. The medians of tensor-based metrics and the CoV of dynamic diffusion measurements in gray matter and white matter voxels were used as the summary statistic for each subject in order to compute the intraclass correlation coefficient (ICC) and compare metrics measured using standard diffusion and nested cubes acquisitions. Datasets that were not normally distributed (Shapiro-Wilk test) were transformed (using inverse, logarithmic, or inverse-logarithmic transformations) in order to use a parametric ICC analysis. Transformations applied to each dataset are shown in Supplemental Table 1. The ICC R and 95% confidence intervals were computed across subjects using a single-measurement, absolute agreement, two-way mixed effects model for the comparisons of tensor based metrics between a standard 15 direction DTI and 5 nested cubes DTI acquisition and the CoV of dynamic diffusion measurements between a 10 repeated cubes and 10 nested cubes acquisition. Evaluation of DTI measurements was performed using four tensor-based metrics (MD, AD, RD and FA) in two voxel classes (gray matter, white matter). Evaluation of the CoV of dynamic measurements (temporal trace, temporal ADC) was performed as a separate analysis for two diffusivity metrics in two voxel classes (gray matter, white matter). A p-value of 0.05 was used in statistical tests to determine significance and adjusted using Bonferroni’s correction for multiple comparisons.

RESULTS

Standard 15 direction DTI Test-retest Reproducibility

Table 1 shows the bias with limits of agreement obtained from the Bland-Altman scatterplots for MD, AD or RD metrics in each of the seven healthy volunteers. The mean biases across healthy subjects with lower and upper 95% confidence levels specified in brackets were 1.28% [0.03, 2.53], 1.13% [0.19, 2.07] and 1.57% [−0.05, 3.18] percent difference for MD, AD and RD respectively. Supplemental Figure 2 shows the Bland-Altman scatter plots of tensor-based metrics from a representative participant. For each metric of diffusivity, the outliers in percent difference that are beyond the limits of agreement correspond to means below 1.5 × 10⁻³ mm²/s, while the middle 95% of the differences are tightly clustered about the median. There are limited outliers corresponding to means between acquisitions above 1.5 × 10⁻³ mm²/s for MD, AD and RD. Figure 2 shows the Bland-Altman plots of the percent differences versus the means in tensor-based diffusivity metrics showing every 2500^th pair, and the bias with limits of agreement computed across masked intracranial voxels from the seven subjects. When computed across all masked intracranial voxels, the biases with lower and upper limits of agreement were 1.32% [−23.17, 32.16], 1.15% [−24.13, 33.23] and 1.66% [−29.93, 44.17] for MD, AD and RD respectively.

Table 1. Differences in tensor-based metrics between nested cubes and standard DTI acquisitions and between repeated standard DTI acquisitions.

Percent differences in mean diffusivity (ΔMD), axial diffusivity (ΔAD), and radial diffusivity (ΔRD) were computed for seven healthy volunteers on a voxel wise basis for a within session repeated standard diffusion tensor imaging (DTI) acquisition and a standard and five nested cubes DTI acquisition. All diffusion acquisitions consisted of 15 diffusion weighted directions. The bias and limits of agreement, computed using the median and upper and lower 2.5^th percentiles of differences (lower bound (lb), upper bound(ub)) for each tensor-based metric, were consistent when comparing the test-retest standard DTI with the standard and nested cubes DTI Bland-Altman plots.

n = 7	DTI Scan 1 vs DTI Scan 2			DTI vs Nested Cubes
	ΔMD (%) (lb,ub)	ΔAD (%) (lb,ub)	ΔRD (%) (lb,ub)	ΔMD (%) (lb,ub)	ΔAD (%) (lb,ub)	ΔRD (%) (lb,ub)
Subject 1	−0.58 (−27.13, 58.20)	−0.05 (−26.14, 36.68)	−1.00 (−33.85, 48.02)	0.54 (−25.65, 46.10)	1.13 (−26.02, 44.67)	0.34 (−31.77, 60.09)
Subject 2	2.82 (−18.84, 31.37)	2.32 (20.84, 31.90)	3.43 (−24.67, 43.31)	3.04 (−22.11, 48.63)	1.15 (−23.70, 40.40)	4.79 (26.94, 64.27)
Subject 3	1.37 (−17.78, 21.36)	1.13 (−20.98, 25.41)	1.72 (−23.93, 30.57)	2.36 (−19.14, 33.61)	0.76 (−21.66, 30.07)	3.85 (−23.24, 44.63)
Subject 4	1.28 (−31.80, 45.34)	1.23 (−30.43, 43.81)	1.58 (−30.02, 58.83)	2.45 (−22.30, 48.29)	0.51 (−25.40, 40.15)	4.61 (−26.64, 64.51)
Subject 5	1.80 (−22.41, 31.72)	1.65 (−23.86, 32.95)	2.14 (−29.79, 44.47)	2.88 (−16.65, 29.76)	1.33 (−19.91, 27.41)	4.41 (−21.86 42.46)
Subject 6	2.69 (−27.20, 27.81)	2.01 (−20.97, 29.60)	3.52 (−23.34, 39.75)	3.27 (−16.28, 28.81)	2.25 (−20.44, 27.79)	4.43 (−22.49, 36.78)
Subject 7	−0.41 (−21.54, 26.64)	−0.39 (−22.20, 29.83)	−0.43 (−27.70, 37.18)	0.04 (−22.60, 28.12)	−0.31 (−23.06, 28.52)	0.24 (−28.20, 39.05)

Figure 2. Bland-Altman subsampled plots of diffusivity metrics between two acquisitions within a single scan session.

Bland-Altman scatterplots of voxel-wise differences versus the means of mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) between two scans were computed for intracranial voxels within the skull stripped brain masks across seven subjects. Each datapoint corresponds to a voxel compared between two acquisitions. Due to the density of the voxels (>0.9 × 10⁶ voxels being compared), every 2500^th) pair was plotted as a datapoint. The bias (gray line) with limits of agreement (grey dashed lines), were defined as the median with lower and upper 2.5^th percentiles respectively of the percent change in each diffusivity metric, and were computed using all masked intracranial voxels.

Standard 15 Direction DTI versus 5 Nested Cubes DTI

Bland-Altman plots of differences versus the means of MD, AD, and FA from the diffusion data acquired using five nested cubes versus standard 15 direction gradient tables in a representative subject show that the bias, indicated by the median of the differences, is at or near to zero (Supplemental Figure 2). Importantly, these comparisons with the test-retest acquisitions obtained in the same representative subject show bias and limits of agreement of MD, AD or RD that are comparable. The bias and limits of agreement of tensor-based metrics measured using the standard and nested cubes DTI acquisitions, shown in Table 1, indicate that the middle 95 percent of the differences are densely clustered about the bias line for all seven of the subjects. The average biases across healthy subjects with lower and upper 95% confidence levels specified in brackets were 2.08% [0.91, 3.26], 0.97% [0.25, 1.70], and 3.24% [1.36, 5.12] between acquisitions for MD, AD and RD respectively. The Bland-Altman plots of the percent differences versus the means in tensor-based diffusivity metrics between the standard DTI and five nested cubes acquisitions are shown in Figure 2, plotting every 2500^th pair, and the bias with limits of agreement computed across all intracranial voxels from the seven subjects. When computed across all voxels from these seven subjects, the biases with lower and upper limits of agreement were 2.16% [−21.11, 37.83], 1.07% [−23.14, 34.50] and 3.35% [−26.40, 51.34] for MD, AD and RD respectively.

The overall scatter point plots of the five nested cubes versus standard DTI and corresponding plots of the test-retest scan showed similar spreads and distributions. Bland-Altman analysis showed that using a nested cubes acquisition produces biases and limits of agreement within the same range as a test-retest standard 15 direction DTI.

Figure 3 shows comparisons of the RMSE of tensor-based metrics acquired using within session test-retest scans with the same standard 15 direction DTI gradient table from an exemplar subject. As expected, the diffusivity maps from the scans using the same gradient tables appear nearly identical in both gray and white matter voxels, while the FA and DEC maps show no visually apparent differences in white matter voxels. Quantitatively, the normalized RMSE in gray matter between the test-retest 15 direction DTI acquisitions averaged across the seven subjects with lower and upper 95% confidence levels specified in brackets were 0.94% [0.02, 1.87], 0.87% [0.006, 1.80], and 0.99% [0.04, 1.95] for MD, AD, and RD respectively. In white matter, the normalized RMSE between the test-retest 15 direction DTI acquisitions averaged across the seven subjects were 0.69% [0.06, 1.13], 0.88% [0.008, 1.76], 0.79% [0.08, 1.50] and 5.25 [4.7, 5.8] for MD, AD, RD and FA respectively. The angular error of white matter fiber orientation between acquisitions averaged across subjects was 14.6 [13.2,16.1] degrees.

Figure 3. Comparison of root mean square error of tensor-based diffusivity metrics using standard and five nested cubes diffusion tensor imaging gradient tables.

Tensor metrics were compared between two repeated standard 15 direction DTI acquisitions (column four) and standard 15 direction and five nested cubes DTI acquisitions (right column). Both comparison show that the majority of voxels have low root mean squared error (RMSE), with the exception bein regions contaminated by cerebrospinal fluid (CSF). The majority of white matter voxels show low RMSE of fractional anisotropy (FA) and low angular error (θ) of fiber orientation measured between acquisitions (ε₁, ε₂).

Figure 3 also shows comparisons of tensor-based metrics measured using a standard 15 direction DTI and a five nested cubes acquisition within the same scan session. The diffusivity maps have low RMSE error in gray and white matter voxels. In white matter, the RMSE of FA between acquisitions and the angular errors of measured fiber orientation DEC maps are increased in the corpus callosum near the ventricles and in thalamic white matter regions. These errors persist when increasing the number of diffusion sampling directions. Supplemental Figure 3 shows tensor-based metrics from the same exemplar subject and scan session shown in Figure 3 measured using a standard 30 direction DTI and a 10 nested cubes acquisition, which both use 30 diffusion weighted directions. The diffusivity maps for MD, AD and RD have low RMSE in gray and white matter, with higher errors in regions with cerebrospinal fluid (CSF) contamination. The RMSE in white matter FA and angular error of fiber orientation are increased in the corpus callosum near the ventricles and thalamic white matter regions.

In gray matter, the median normalized RMSE of tensor-based metrics between the standard 15 direction and five nested cubes DTI acquisitions had a mean of 1.02% [0.08,1.96], 0.83% [0.2,1.63] and 1.09% [0.09, 2.09] for MD, AD and RD respectively. In white matter, the median normalized RMSE between the standard 15 direction and five nested cubes DTI acquisitions had a mean of 0.68% [0.07,1.28], 0.09% [0.004,1.73], 0.79% [0.09,1.49] and 5.10% [4.72, 5.48] for MD, AD, RD and FA respectively. The median angular error of white matter fiber orientation between the two acquisitions averaged across subjects was 13.6 [12.0, 15.1] degrees.

For ICC analysis, there was no effect of cohort (healthy volunteer vs patients under evaluation for epilepsy) and we therefore collapsed datasets across cohorts. The median of each tensor-based metric across voxels are plotted in Supplemental Figure 4 for each subject. Table 2 shows with the ICC and lower and upper 95% confidence intervals specified in brackets performed across the 29 subjects (22 epilepsy patients and 7 healthy volunteers) in gray matter and white matter. In gray matter, there was strong and significant correlation of MD (0.99 [0.98, 0.99]), AD (0.99 [0.98, 0.99]) and RD (0.99 [0.98,0.99]) measured using standard 15 direction DTI and 5 nested cubes DTI gradient tables. Similarly in white matter, there was strong and significant correlation of MD (0.99 [0.77, 0.98]), AD (0.98 [0.78, 0.99]) and RD (0.98 [0.82, 0.99]). When measuring FA, there was strong and significant correlation between acquisition methods in white matter (0.99 [0.98, 0.99]), while in gray matter, there was strong correlation that did not remain significant (p = 0.012) after correction for multiple comparisons (0.91 [0.03, 0.98]). The white matter fiber direction measured between the standard 15 direction DTI and 5 nested cubes DTI acquisitions had mean angular error and lower and upper confidence intervals of 15.5 [14.8,16.2] degrees. Taken together, these data show that a nested cubes DTI acquisition can produce tensor-based diffusivity metrics that are consistent with measurements produced using a standard DTI acquisition.

Table 2. Intraclass correlation Analysis of Standard and nested cubes DTI of tensor-based metrics measured in gray and white matter.

Tensor based metrics were computed using both a standard and a five nested cubes DTI acquisition. The median of each metric across voxels classified as gray or white matter was computed for 29 subjects, consisting of seven healthy volunteers and 22 patients under evaluation for epilepsy. Datasets consisting of these medians (Supplemental Figure 4) where the residuals were not normally distributed were transformed (Supplemental Table 1) for statistical analysis. Intraclass correlation coefficients (ICC), and their 95% confidence limits between the two acquisitions were computed across subjects in gray and white matter for each tensor-based metric using a single-rating, absolute agreement, two-way mixed effects model. Acronyms: F – F statistic, ll – lower 95% confidence limit, ul – upper 95% confidence limit, df – degrees of freedom.

n = 29	Mean diffusivity		Axial diffusivity		Radial diffusivity		Fractional Anisotropy
	Gray matter	White matter	Gray matter	White matter	Gray matter	White matter	Gray matter	White matter
ICC [ll,ul]	0.99 [0.98,0.99]	0.98 [0.77, 0.98]	0.99 [0.98, 0.99]	0.98 [0.78, 0.99]	0.99 [0.98, 0.99]	0.98 (.82, 0.99]	0.91 [03, 0.98]	0.99 [0.98, 0.99]
F (df,error)	573.6 (13, 28)	259 (3, 28)	734 (26,28)	185 (3,28)	519 (7,28)	284 (3,28)	91 (2,28)	236 (18,28)
p value	1.1×10−16	4.6×10−16	<1×10−20	2.9×10−4	1.1×10−9	2.4×10−4	0.020	<1×10−20

Repeated cubes versus 10 nested cubes

We next studied the temporal variations of diffusion measurements acquired using a 30 direction dynamic diffusion acquisition. Figure 4 shows the CoVs of the dynamic trace-weighted and ADC maps used to compare the temporal stability of data collected using 10 repeated cubes, 10 nested cubes, and 10 consecutive triplets from the standard DTI acquisition (referred to as unordered triplets). The CoV maps showed minimal differences in the majority of cortical gray matter and white matter, when using gradient tables consisting of triplets of mutually orthogonal diffusion weighted directions. The dynamic trace of the repeated cubes and nested cubes datasets both had CoV less than five percent in the majority of gray matter and white matter voxels. Similarly, the CoV of dynamic ADC in the majority of voxels remained below five percent, with the highest CoV in deep gray matter and the CSF for the nested cubes acquisition. In comparison, the CoV maps of both dynamic trace and ADC from the unordered triplet acquisition have high CoV in white matter and subcortical gray matter. In cortical gray matter, the CoV of dynamic trace and ADC measured using 10 unordered triplets is comparable with the CoVs of the dynamic measurements from the two acquisitions using 10 mutually orthogonal triplets. We next compared the CoVs of dynamic trace and ADC between a 10 repeated cubes and 10 nested cubes acquisition across 24 subjects. Supplemental Figure 5 shows the median CoV in gray and white matter for each subject included in correlation analysis, while Table 3 shows the ICC results. In gray matter, there was a modest, but significant correlation of the CoV of temporal trace (0.61 [0.29, 0.81]) and temporal ADC (0.62 [0.29, 0.81]), between the two acquisition methods. In white matter, there was a weak, but significant correlation of temporal ADC (0.47 [0.09, 0.73]) while the correlation of temporal trace was weak (0.43 [0.04, 0.71]) and did not remain significant (p = 0.016) after correction for multiple comparisons.

Figure 4. Coefficient of variation of dynamic trace and apparent diffusion coefficient.

Coefficients of variation (CoV) of the dynamic trace (top row) and apparent diffusion coefficient (ADC) (bottom row) were computed on a voxel-wise basis from acquisitions using ten repeated cubes (left column), ten nested cubes (middle column) and a standard 30 direction diffusion tensor imaging (DTI) gradient table consisting of non-orthogonal triplets of diffusion weighted directions (right column).

Table 3. Intraclass correlation analysis of ten repeated cubes and ten nested cubes measurements of dynamic trace and apparent diffusion coefficient.

Diffusion weighted data was compared between ten repeated cube and ten nested cubes acquisitions in 24 subjects(7 healthy volunteers and 17 patients under evaluation for epilepsy). The median coefficient of variation (CoV) of dynamic trace-weighted intensities and ADC was computed in voxels classified as gray matter and white matter for each subject (Supplemental Figure 5). These values, where the residuals were not normally distributed, were transformed for statistical analysis (Supplemental Table 1). The intraclass correlation coefficient (ICC) of the CoVs and the 95% confidence intervals were computed across for dynamic trace and ADC in gray and white matter using a single-rating, absolute agreements, two-way mixed effects model. Acronyms: F – F statistic, ll – lower 95% confidence interval, ul – upper 95% confidence interval.

n = 24	Temporal Trace (CoV %)		Temporal ADC (CoV %)
	Gray matter	White matter	Gray matter	White matter
ICC (ll,ul)	0.61 [0.29, 0.81]	0.43 [0.04, 0.71]	0.62 [0.29, 0.81]	0.47 [0.09, 0.73]
F (df,error)	4 (8,23)	3 (6,23)	4 (7,23)	3 (5,23)
p value	5.59×10−4	0.016	5.07×10−4	8.9 × 10−3

The probability distributions of the tSNR in gray and white matter for dynamic trace and ADC are shown in Figure 5 for the 10 repeated and 10 nested cubes acquisitions across all 24 subjects in this analysis. The dynamic trace and ADC measured had highly overlapping probability distributions across gray matter voxels, while the probability distributions in white matter voxels overlapped but to a lesser extent.

Figure 5. Probability distributions of temporal signal-to-noise ratio of trace and apparent diffusion coefficient in gray matter and white matter measured using ten repeated cubes and ten nested cubes gradient tables.

Temporal signal-to-noise ratio (tSNR) was computed on a voxel wise basis in white matter (top row) and gray matter (bottom row) across 24 subjects (seven healthy volunteers, 17 patients under evaluation for epilepsy) using data acquired with ten repeated cubes and ten nested cubes gradient tables. The tSNR of temporal trace (left column) and ADC (right column) have highly overlapping probability distribution functions (pdf). tSNR, computed by dividing the temporal mean by the temporal standard deviation and is therefore proportionate to the inverse of the coefficient of variation. To remain consistent with the transformations applied to the CoV data used for statistical analysis, the tSNR is shown on a natural log scale with arbitrary units. The medians of each pdf are shown with dashed lines, along with the numerical values for each acquisition method (blue – 10 repeated cubes, red – 10 nested cubes).

DISCUSSION

Collection of diffusion data using a nested cubes style gradient table allows for the estimation of DTI metrics and time series measurements of isotropic diffusion within a single acquisition. Low RMSE of diffusivity measurements in both gray and white matter between the nested cubes and standard DTI acquisition methods indicates that the reordering of gradient directions required by the nested cubes had negligible effect on the estimated diffusion tensor and associated metrics, further supported by voxel-based Bland Altman analysis. Moreover, in a complementary intraclass correlation analysis approach, comparisons of tensor estimated metrics across subjects showed strong and significant correlations in a larger cohort of participants. The CoVs of temporal trace and ADC showed modest, but significant correlation between methods in gray matter when comparing repeated cubes and nested cubes acquisitions. Correlations of the CoVs in white matter were weak for temporal trace and ADC. The tSNR, computed by dividing the temporal mean by the standard deviation for dynamic measurements, is proportionate to the inverse of the CoV. Plots of the tSNR probability distributions in gray and white matter corroborated the ICC analysis results comparing CoVs from the same subjects. In both gray and white matter regions, the median tSNR for temporal trace and ADC was higher when using a repeated acquisition, most apparent in white matter voxels. Taken together, these data indicate that a nested cubes gradient acquisition produces metrics comparable with standard DTI and dynamic diffusion acquisitions in gray matter voxels.

We observed several interesting outcomes in our comparisons. A 15 direction solution to the nested cubes DTI problem produced fiber orientation consistent with measurements produced using a standard 15 direction DTI acquisition in the majority of white matter voxels. The exception to this was in regions located near deep gray matter nuclei and the outer regions of the corpus callosum. Voxels in these white matter regions that typically have low FA values and may contain crossing fiber populations have been reported to have high uncertainty in tensor estimated fiber orientation even within a test-retest DTI acquisition with high angular sampling (26). This represents an inherent limitation of using tensor-based methods to provide estimates of fiber orientation in regions that deviate from the assumption that diffusion within a voxel follows a Gaussian profile. These estimates can lead to subsequent inconsistencies in DTI tractography, particularly when using deterministic methods that do not account for the uncertainty in fiber orientation measurements (27).

Dynamic diffusion measurements showed high variability, measured by increased CoV, in subcortical gray matter and portions of white matter adjacent to ventricles. This may be due to brain pulsatile motion, which has been shown to be particularly high in these deep gray nuclei and white matter regions (28). Dynamic diffusion measurements acquired using a nested cubes style gradient table were more sensitive to this artifact compared to a repeated cubes acquisition, likely due to the compounded effects of pulsatile motion and unresolved eddy current distortions caused by switching diffusion gradients (29). Another observation was that the CoV of dynamic diffusion measurements in white matter was increased when using a non-orthogonal triplets of diffusion weighted directions compared to using mutually orthogonal triplets. As expected, this indicates that using the geometric mean of diffusion weighted signal measured across an arbitrary triplet of directions does not provide robust measurements of isotropic diffusion, particularly in regions where white matter with a strong directional component can influence the diffusion profile along one of the three measured vectors (30). The CoVs of dynamic diffusion measurements were relatively low (less than ten percent) in cortical gray matter when using non-orthogonal triplets, and were more consistent with CoVs in cortical gray matter measured using gradient tables consisting of orthogonal triplets of diffusion weighted directions.

Limitations

A nested cubes diffusion gradient table was used to measure dynamic diffusion in regions exhibiting pulsation motion. One method to correct for pulsatile motion is to use a cardiac gating approach, where diffusion data is acquired only during the diastolic period of the cardiac cycle when pulsatile movements are minimal (31). However, implementation of a cardiac gated acquisition would increase the acquisition time nearly two-fold to collect data across thirty diffusion weighted directions (32) and would reduce the temporal resolution of dynamic diffusion measurements.

Cortical gray matter areas, including sulci and regions with close proximity to CSF, can suffer from partial volume effects (30). Measurements of isotropic diffusion and mean ADC at high temporal resolution using our nested cubes approach had relatively high CoV values in regions suffering from partial volume averaging. However, we also found this to be the case when using a repeated cubes acquisition. Moreover, DWIs acquired using our nested cubes approach may suffer from eddy current related fluctuations caused by rapid switching of diffusion weighted gradients. Derivation of the nested cubes gradient tables, which was performed by maximizing the electrostatic interaction between each vector set, maximized the angular rotation between diffusion weighted triplets to provide uniform sampling of spherical q-space. The acquisitions employed diffusion weighted directions across the entire spherical q-space to provide DWIs with opposite diffusion gradient polarity. Acquisition of diffusion weighted data (33), in addition to a single non-diffusion weighted volume as we have implemented along the reversed phase encoding direction or increasing the spatial resolution would improve eddy current and EPI distortion correction and potentially reduce signal contamination at the cost of decreased temporal resolution of diffusion measurements.

Bland-Altman analysis was used to compare the reproducibility of diffusivity metrics when comparing a nested cubes versus within-session test-retest standard DTI acquisitions. Due to the limited sample size of the test-retest acquisitions, a voxel-based approach was employed, which may introduce a limitation due to spatial correlations of voxels within a single subject. We addressed this confounding factor by using percent change as our metric of difference, as well as using the median with lower and upper 2.5^th percentiles of the difference to measure bias with limits of agreement, which is a non-parametric approach to Bland-Altman analysis. Finally, while the voxel-based method has the advantage of providing an unbiased number of samples (e.g. relative to a region of interest based approach), this approach can introduce higher variability when comparing metrics estimated between acquisitions. In the current work, this variability was most apparent when studying the limits of agreement of tensor-based metrics measured between acquisitions within the same scan session. Importantly, the test-retest acquisitions and the standard DTI versus nested cubes acquisitions both had limits of agreement that were on the order of 30%. This is likely due to the inclusion of intracranial voxels where there are regions contaminated by CSF rather than an underlying localized transient alteration in diffusion. In the current work, this resulted in the majority of outliers having mean values exceeding 1.5×10⁻³ mm²/s. These outliers could also be attributed our use of a T1 based segmented mask approach, which included regions that were susceptible to distortion in the diffusion weighted images. An alternative to this segmentation approach would be to use pre-defined cutoff thresholds using a metric such as the DTI based trace, which has been measured to range between 1.9×10⁻³ mm²/s and 2.5×10⁻³ mm²/s (30).

DTI gradient tables consisting of a minimum of twelve directions are typically optimized to provide uniform coverage of a spherical shell in order to accurately reconstruct the diffusion tensor (20), where the temporal order of diffusion weighted directions is not of consequence. In order to acquire data useful for tensor-based and high temporal resolution diffusion measurements, we sought to consider the temporal ordering of these diffusion weighted directions along with the constraint of orthogonality. This approach provided a temporal resolution that was three times the repetition time of the acquisition. The temporal resolution achieved would sufficient to measure a slowly propagating wave of altered diffusion that has been measured in animals imaging studies following triggered spreading depolarization. An alternative approach would be to derive a gradient table consisting of non-collinear directions where the diffusion tensor could be estimated across six DWIs using a sliding window. This method could increase temporal resolution by obtaining multiple measurements of ADC within a single TR, and also provide dynamic estimates DTI metrics that cannot be computed using the three scan trace approach used in the current work. Diffusion tables designed for use in populations with a high likelihood of movement, such as infants (35), capable of estimating the tensor even with a subset of the total gradient directions that provide sparse but sufficient coverage of the spherical shell could be derived in an approach analogous to methods used in MR angiography such as the Vastly Undersampled Isotropic Projection (VIPR) (36).

Conclusions

We have demonstrated the feasibility of simultaneously acquiring sufficient data to reconstruct the diffusion tensor and to obtain time series measurements of isotropic diffusion. This method allows for time efficient MRI studies of dynamic diffusion to study conditions such as spreading depolarization underlying migraine aura, and during the ictal and per-ictal phases of epileptic seizure where pathophysiological alterations are transient and evolve over the course of minutes, particularly when DTI is also of interest. The nested cubes style gradient table therefore provides an approach to measuring such alterations concurrently with performing DTI.