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Clinical Microscopic Fractional Anisotropy Imaging in 4 Minutes: an Optimization Approach

Nico J. J. Arezza^1,2, Desmond H. Y. Tse², Aidin Arbabi², and Corey A. Baron^1,2
¹Medical Biophysics, Western University, London, ON, Canada, ²Center for Functional and Metabolic Mapping, Robarts Research Institute, London, ON, Canada

Synopsis

Microscopic diffusion anisotropy ($$$\mu A$$$) and microscopic fractional anisotropy ($$$\mu FA$$$) quantify water diffusion anisotropy in tissue with no influence from neuron fiber orientation. Here, we characterized $$$\mu A^2$$$ signal-to-noise ratio using standard error propagation to determine the b-value and ratio of linear to isotropic encodings needed to maximize image quality. This optimization enabled an MRI protocol that utilizes efficient isotropic diffusion encoding to acquire high-quality full-brain $$$\mu A^2$$$ and $$$\mu FA$$$ maps in 2.4 and 4 minutes, respectively, which are demonstrated in two healthy volunteers at 3T.

Introduction

Water diffusion anisotropy in white matter (WM) is an indirect measure of pathology, and reduced anisotropy is observed in diseases like dementia, ¹ Alzheimer’s disease, ² and multiple sclerosis.³ Fractional anisotropy (FA) is the standard diffusion MRI (dMRI) metric to measure diffusion anisotropy, but it cannot distinguish between changes in microstructure and changes in neuron fiber directional coherence.⁴ In contrast, microscopic diffusion anisotropy ($$$\mu A$$$) and its normalized counterpart, microscopic fractional anisotropy ($$$\mu FA$$$), quantify water diffusion anisotropy independent of fiber orientation.^5,6

To determine the optimal parameters of a $$$\mu A^2$$$ MRI protocol, we characterized the relationship between $$$\mu A^2$$$ signal-to-noise ratio (SNR) and two parameters that can be adjusted: b-value and ratio of isotropic to linear encodings ($$$n_{iso}/n_{lin}$$$). This optimization approach, combined with a minimalistic 6 linear direction scheme, ⁷ enabled high quality 3T clinical $$$\mu A^2$$$ and $$$\mu FA$$$ full-brain imaging in 2.4 and 4 minutes, respectively.

Methods

$$$\mu A^2$$$ is computed via ⁸:$$(1)\qquad\qquad\mu A^2=\frac{ln(S_{lin})-ln(S_{iso})}{b^2}$$where $$$S_{lin}$$$ and $$$S_{iso}$$$ are the powder averages of the linear and isotropic signals, respectively. Standard error propagation theory was used to determine the SNR of $$$\mu A^2$$$:$$(2)\qquad\qquad SNR_{\mu A^2}=\frac{SNR_{lin}ln(\frac{SNR_{lin}}{SNR_{iso}})}{\sqrt{\frac{1}{SNR_{lin}^2n_{lin}}+\frac{1}{SNR_{iso}^2n_{iso}}}}$$where $$$SNR_{lin}$$$ is the SNR of a linear encoded image, $$$SNR_{iso}$$$ is the SNR of an isotropic encoded image, $$$n_{lin}$$$ is the number of linear scans acquired, and $$$n_{iso}$$$ is the number of isotropic scans acquired. Data to aid with optimization was collected from two healthy volunteers on a 3T MRI system (80mT/m strength and 200T/m/s slew rate) using 6 linear and 6 isotropic encodings at b-values from 0s/mm² to 3500s/mm² in increments of 500s/mm². The remaining parameters were TE/TR=125/8700ms, FOV=192x192mm², 2 mm isotropic in-plane resolution, 45 slices (2 mm), rate 2 GRAPPA, 2 averages, 29 min scan time. To encode diffusion isotropically, we developed a method inspired by qmas ⁶ that uses trapezoidal gradients (Fig.1). Signal data used in the optimization was measured in a WM region-of-interest (ROI) and WM T2 was assumed to be 80ms.⁹

To test the optimized protocol, we performed scans on the same two volunteers using 6 averages at b=0s/mm², 6 isotropic averages at b=1200s/mm², and 6 linear directions and 12 isotropic averages at b=2200s/mm² with TE/TR=102/7400ms. The total scan time was 4 min. Post-processing included PCA denoising ¹⁰ and eddy current correction with FSL.¹¹ $$$\mu A^2$$$ was calculated using Eq. 1, and an expression for $$$\mu FA$$$ was determined using the second order cumulant expansion of a diffusion-weighted MRI signal ⁶ and assuming that linear and isotropic encodings performed at the same b-value have the same diffusion coefficient ⁶:$$(3)\qquad\qquad\mu FA=\sqrt{\frac{3}{2}\frac{\mu A^2}{\mu A^2+0.2D^2}}$$where D is the mean diffusivity estimated using the b=0 and b=1200s/mm² scans.

Results

Signal trends in WM ROIs reflects typical behaviour for linear vs. isotropic encoding in those regions ¹² (Fig.2). Using the WM data in Eq. 2 yielded an optimal b-value of 2000s/mm² and optimal $$$n_{iso}/n_{lin}$$$ of 1.7 (Fig.3). The steep drop-off for $$$n_{iso}/n_{lin}<1$$$ occurs because the SNR of the isotropic weighted images is lower than the SNR for linear encoding, on average.

$$$\mu A^2$$$ and $$$\mu FA$$$ images from both volunteers from an optimized protocol at b=2200s/mm² are shown in Fig.4 and Fig.5, respectively. According to Fig.3, this protocol has $$$SNR_{\mu A^2}$$$ equal to 99.3% of the SNR of the optimal design-target protocol with b=2000s/mm² and $$$n_{iso}/n_{lin}$$$=1.7.

Discussion

The 4 minute protocol allows rapid $$$\mu A^2$$$ and $$$\mu FA$$$ mapping and provides enough data to determine diffusion kurtosis for both linear and isotropic cases if the first order cumulant D is assumed to be the same for both isotropic and linear scans. $$$\mu A^2$$$ and $$$\mu FA$$$ images acquired with this protocol have high SNR (Figs. 4 and 5, respectively) and show homogeneity in WM regions, evidence of the technique’s reduced dependence on fiber orientation compared to FA. The short scan time makes the protocol feasible for clinical use at 3T and can be traded off for better SNR by introducing more acquisitions while maintaining the optimal $$$n_{iso}/n_{lin}$$$ ratio.

Isotropic encoding was chosen over double diffusion encoding (DDE) to estimate $$$\mu A^2$$$ because the former method only requires one spin-echo to avoid concomitant gradient errors ¹³; furthermore, $$$SNR_{\mu A^2}$$$ is higher for similar imaging parameters due to increased signal difference between isotropic and linear acquisitions compared to perpendicular DDE and linear acquisitions. Potential limitations arising from anisotropic frequency content of the isotropic waveforms and intracompartmental kurtosis will be the subject of future study.¹⁴ Isotropic-encoding-based methods published to date have utilized a model that assumes a gamma distribution of apparent diffusivities within the voxel, ¹⁵ whereas here a straight-forward derivation of $$$\mu FA$$$ based on a kurtosis model was used (Eq. 1), similar to DDE, ⁸ which may be advantageous for rapid computation in clinical settings. That said, a comparison between the two approaches is warranted.

Eq. 1 is based on the second order cumulant expansion of the dMRI signal and is computed at a single b-value, which can introduce bias if higher order terms are non-negligible.¹⁶ This bias can be corrected for by introducing more b-shells to the scan at the cost of increased scan time. Future work will also investigate optimal scan parameters for grey matter imaging.

Acknowledgements

Natural Sciences and Engineering Research Council of Canada (NSERC)

Canada First Research Excellence Fund to BrainsCAN

Queen Elizabeth II Graduate Scholarship in Science and Technology (QEII-GSST)

References

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Figures

Fig. 1. Schematic representation of the isotropic-encoding pulse sequence, which depicts a spin-echo sequence in which diffusion-encoding gradients in the X, Y, and Z directions have been inserted on both sides of the $$$180^{o}$$$ pulse.

Fig. 2. Linear and isotropic encoded diffusion MRI signals as functions of b-value in white matter. Data was acquired from two healthy volunteers. A sample region-of-interest (ROI) from one of the volunteers is shown on the $$$\mu$$$FA image in the bottom left corner. Error bars depict the standard deviation of $$$ln(S/S_0)$$$ in the ROI. The dotted lines represent the joint $$$3^{rd}$$$ order cumulant fits of the signal data over both volunteers.

Fig. 3. Microscopy anisotropy signal-to-noise ratio ($$$SNR_{\mu A^2}$$$) as a function of b-value and the ratio of isotropic averages to linear directions. $$$SNR_{\mu A^2}$$$ is maximized when b=2000s/mm² and $$$n_{iso}/n_{lin}$$$=1.7. Note the steep drop-off for $$$n_{iso}/n_{lin}<1$$$ and b<1500s/mm².

Fig. 4. $$$\mu A^2$$$ images acquired using an optimized protocol with b=2200s/mm² and $$$n_{iso}/n_{lin}$$$=2. Axial $$$\mu A^2$$$ slices were acquired from two healthy volunteers: the top row is from volunteer 1 while the bottom row is from volunteer 2. Though the total scan time for the acquisition was 4 minutes, $$$\mu A^2$$$ was computed using a subsampled data set that would only require 2.4 minutes (the b=0s/mm² and b=1200s/mm² acquisitions were discarded).

Fig. 5. $$$\mu FA$$$ images acquired using an optimized 4-minute protocol. Axial $$$\mu FA$$$ slices were acquired from volunteer 1 (top row) and volunteer 2 (bottom row), respectively.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)

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