Compressed Sensing Diffusion Spectrum Imaging for Accelerated Diffusion Microstructure MRI in Long-Term Population Imaging

Diffusion imaging genomics provides novel insight into early mechanisms of cerebral small vessel disease

Cerebral small vessel disease (cSVD) is a leading cause of stroke and dementia. Genetic risk loci for white matter hyperintensities (WMH), the most common MRI-marker of cSVD in older age, were recently shown to be significantly associated with white matter (WM) microstructure on diffusion tensor imaging (signal-based) in young adults. To provide new insights into these early changes in WM microstructure and their relation with cSVD, we sought to explore the genetic underpinnings of cutting-edge tissue-based diffusion imaging markers across the adult lifespan. We conducted a genome-wide association study of neurite orientation dispersion and density imaging (NODDI) markers in young adults (i-Share study: N = 1 758, (mean[range]) 22.1[18-35] years), with follow-up in young middle-aged (Rhineland Study: N = 714, 35.2[30-40] years) and late middle-aged to older individuals (UK Biobank: N = 33 224, 64.3[45-82] years). We identified 21 loci associated with NODDI markers across brain regions in young adults. The most robust association, replicated in both follow-up cohorts, was with Neurite Density Index (NDI) at chr5q14.3, a known WMH locus in VCAN. Two additional loci were replicated in UK Biobank, at chr17q21.2 with NDI, and chr19q13.12 with Orientation Dispersion Index (ODI). Transcriptome-wide association studies showed associations of STAT3 expression in arterial and adipose tissue (chr17q21.2) with NDI, and of several genes at chr19q13.12 with ODI. Genetic susceptibility to larger WMH volume, but not to vascular risk factors, was significantly associated with decreased NDI in young adults, especially in regions known to harbor WMH in older age. Individually, seven of 25 known WMH risk loci were associated with NDI in young adults. In conclusion, we identified multiple novel genetic risk loci associated with NODDI markers, particularly NDI, in early adulthood. These point to possible early-life mechanisms underlying cSVD and to processes involving remyelination, neurodevelopment and neurodegeneration, with a potential for novel approaches to prevention.

Research Progress in Diffusion Spectrum Imaging

Studies have demonstrated that many regions in the human brain include multidirectional fiber tracts, in which the diffusion of water molecules within image voxels does not follow a Gaussian distribution. Therefore, the conventional diffusion tensor imaging (DTI) that hypothesizes a single fiber orientation within a voxel is intrinsically incapable of revealing the complex microstructures of brain tissues. Diffusion spectrum imaging (DSI) employs a pulse sequence with different b-values along multiple gradient directions to sample the diffusion information of water molecules in the entire q-space and then quantitatively estimates the diffusion profile using a probability density function with a high angular resolution. Studies have suggested that DSI can reliably observe the multidirectional fibers within each voxel and allow fiber tracking along different directions, which can improve fiber reconstruction reflecting the true but complicated brain structures that were not observed in the previous DTI studies. Moreover, with increasing angular resolution, DSI is able to reveal new neuroimaging biomarkers used for disease diagnosis and the prediction of disorder progression. However, so far, this method has not been used widely in clinical studies, due to its overly long scanning time and difficult post-processing. Within this context, the current paper aims to conduct a comprehensive review of DSI research, including the fundamental principles, methodology, and application progress of DSI tractography. By summarizing the DSI studies in recent years, we propose potential solutions towards the existing problem in the methodology and applications of DSI technology as follows: (1) using compressed sensing to undersample data and to reconstruct the diffusion signal may be an efficient and promising method for reducing scanning time; (2) the probability density function includes more information than the orientation distribution function, and it should be extended in application studies; and (3) large-sample study is encouraged to confirm the reliability and reproducibility of findings in clinical diseases. These findings may help deepen the understanding of the DSI method and promote its development in clinical applications.

Towards reliable reconstruction of the mouse brain corticothalamic connectivity using diffusion MRI

Diffusion magnetic resonance imaging (dMRI) tractography has yielded intriguing insights into brain circuits and their relationship to behavior in response to gene mutations or neurological diseases across a number of species. Still, existing tractography approaches suffer from limited sensitivity and specificity, leading to uncertain interpretation of the reconstructed connections. Hence, in this study, we aimed to optimize the imaging and computational pipeline to achieve the best possible spatial overlaps between the tractography and tracer-based axonal projection maps within the mouse brain corticothalamic network. We developed a dMRI-based atlas of the mouse forebrain with structural labels imported from the Allen Mouse Brain Atlas (AMBA). Using the atlas and dMRI tractography, we first reconstructed detailed node-to-node mouse brain corticothalamic structural connectivity matrices using different imaging and tractography parameters. We then investigated the effects of each condition for accurate reconstruction of the corticothalamic projections by quantifying the similarities between the tractography and the tracer data from the Allen Mouse Brain Connectivity Atlas (AMBCA). Our results suggest that these parameters significantly affect tractography outcomes and our atlas can be used to investigate macroscopic structural connectivity in the mouse brain. Furthermore, tractography in mouse brain gray matter still face challenges and need improved imaging and tractography methods.

Spatially regularized low-rank tensor approximation for accurate and fast tractography

Tractography based on diffusion Magnetic Resonance Imaging (dMRI) is the prevalent approach to the in vivo delineation of white matter tracts in the human brain. Many tractography methods rely on models of multiple fiber compartments, but the local dMRI information is not always sufficient to reliably estimate the directions of secondary fibers. Therefore, we introduce two novel approaches that use spatial regularization to make multi-fiber tractography more stable. Both represent the fiber Orientation Distribution Function (fODF) as a symmetric fourth-order tensor, and recover multiple fiber orientations via low-rank approximation. Our first approach computes a joint approximation over suitably weighted local neighborhoods with an efficient alternating optimization. The second approach integrates the low-rank approximation into a current state-of-the-art tractography algorithm based on the unscented Kalman filter (UKF). These methods were applied in three different scenarios. First, we demonstrate that they improve tractography even in high-quality data from the Human Connectome Project, and that they maintain useful results with a small fraction of the measurements. Second, on the 2015 ISMRM tractography challenge, they increase overlap, while reducing overreach, compared to low-rank approximation without joint optimization or the traditional UKF, respectively. Finally, our methods permit a more comprehensive reconstruction of tracts surrounding a tumor in a clinical dataset. Overall, both approaches improve reconstruction quality. At the same time, our modified UKF significantly reduces the computational effort compared to its traditional counterpart, and to our joint approximation. However, when used with ROI-based seeding, joint approximation more fully recovers fiber spread.

Establishing the Validity of Compressed Sensing Diffusion Spectrum Imaging

Diffusion Spectrum Imaging (DSI) using dense Cartesian sampling of q-space has been shown to provide important advantages for modeling complex white matter architecture. However, its adoption has been limited by the lengthy acquisition time required. Sparser sampling of q-space combined with compressed sensing (CS) reconstruction techniques has been proposed as a way to reduce the scan time of DSI acquisitions. However prior studies have mainly evaluated CS-DSI in post-mortem or non-human data. At present, the capacity for CS-DSI to provide accurate and reliable measures of white matter anatomy and microstructure in the living human brain remains unclear. We evaluated the accuracy and inter-scan reliability of 6 different CS-DSI schemes that provided up to 80% reductions in scan time compared to a full DSI scheme. We capitalized on a dataset of twenty-six participants who were scanned over eight independent sessions using a full DSI scheme. From this full DSI scheme, we subsampled images to create a range of CS-DSI images. This allowed us to compare the accuracy and inter-scan reliability of derived measures of white matter structure (bundle segmentation, voxel-wise scalar maps) produced by the CS-DSI and the full DSI schemes. We found that CS-DSI estimates of both bundle segmentations and voxel-wise scalars were nearly as accurate and reliable as those generated by the full DSI scheme. Moreover, we found that the accuracy and reliability of CS-DSI was higher in white matter bundles that were more reliably segmented by the full DSI scheme. As a final step, we replicated the accuracy of CS-DSI in a prospectively acquired dataset (n=20, scanned once). Together, these results illustrate the utility of CS-DSI for reliably delineating in vivo white matter architecture in a fraction of the scan time, underscoring its promise for both clinical and research applications.

Optimization of quasi-diffusion magnetic resonance imaging for quantitative accuracy and time-efficient acquisition

PURPOSE

Quasi-diffusion MRI (QDI) is a novel quantitative technique based on the continuous time random walk model of diffusion dynamics. QDI provides estimates of the diffusion coefficient, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mspace/> <mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> in mm²  s^-1 and a fractional exponent, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> , defining the non-Gaussianity of the diffusion signal decay. Here, the b-value selection for rapid clinical acquisition of QDI tensor imaging (QDTI) data is optimized.

METHODS

Clinically appropriate QDTI acquisitions were optimized in healthy volunteers with respect to a multi-b-value reference (MbR) dataset comprising 29 diffusion-sensitized images arrayed between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn></mml:mrow> <mml:annotation>$$ b=0 $$</mml:annotation></mml:semantics> </mml:math> and 5000 s mm^-2 . The effects of varying maximum b-value ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}} $$</mml:annotation></mml:semantics> </mml:math> ), number of b-value shells, and the effects of Rician noise were investigated.

RESULTS

QDTI measures showed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}} $$</mml:annotation></mml:semantics> </mml:math> dependence, most significantly for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> in white matter, which monotonically decreased with higher <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}} $$</mml:annotation></mml:semantics> </mml:math> leading to improved tissue contrast. Optimized 2 b-value shell acquisitions showed small systematic differences in QDTI measures relative to MbR values, with overestimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mspace/> <mml:mspace/> <mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ \kern0.50em {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> and underestimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> in white matter, and overestimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> anisotropies in gray and white matter. Additional shells improved the accuracy, precision, and reliability of QDTI estimates with 3 and 4 shells at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> <mml:mo>=</mml:mo> <mml:mn>5000</mml:mn></mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}}=5000 $$</mml:annotation></mml:semantics> </mml:math>  s mm^-2 , and 4 b-value shells at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> <mml:mo>=</mml:mo> <mml:mn>3960</mml:mn></mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}}=3960 $$</mml:annotation></mml:semantics> </mml:math>  s mm^-2 , providing minimal bias in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> compared to the MbR.

CONCLUSION

A highly detailed optimization of non-Gaussian dMRI for in vivo brain imaging was performed. QDI provided robust parameterization of non-Gaussian diffusion signal decay in clinically feasible imaging times with high reliability, accuracy, and precision of QDTI measures.

Insights from the IronTract challenge: Optimal methods for mapping brain pathways from multi-shell diffusion MRI

Limitations in the accuracy of brain pathways reconstructed by diffusion MRI (dMRI) tractography have received considerable attention. While the technical advances spearheaded by the Human Connectome Project (HCP) led to significant improvements in dMRI data quality, it remains unclear how these data should be analyzed to maximize tractography accuracy. Over a period of two years, we have engaged the dMRI community in the IronTract Challenge, which aims to answer this question by leveraging a unique dataset. Macaque brains that have received both tracer injections and ex vivo dMRI at high spatial and angular resolution allow a comprehensive, quantitative assessment of tractography accuracy on state-of-the-art dMRI acquisition schemes. We find that, when analysis methods are carefully optimized, the HCP scheme can achieve similar accuracy as a more time-consuming, Cartesian-grid scheme. Importantly, we show that simple pre- and post-processing strategies can improve the accuracy and robustness of many tractography methods. Finally, we find that fiber configurations that go beyond crossing (e.g., fanning, branching) are the most challenging for tractography. The IronTract Challenge remains open and we hope that it can serve as a valuable validation tool for both users and developers of dMRI analysis methods.

Safety of Tattoos, Permanent Make-Up, and Medical Implants in Population-Based 3T Magnetic Resonance Brain Imaging: The Rhineland Study

Excluding persons from magnetic resonance imaging (MRI) research studies based on their medical history or because they have tattoos, can create bias and compromise the validity and generalizability of study results. In the population-based Rhineland Study, we limited exclusion criteria for MRI and allowed participants with passive medical implants, tattoos or permanent make-up to undergo MRI. Thereby, we could include 16.6% more people than would have been possible based on common recommendations. We observed no adverse events or artifacts. This supports that most passive medical implants, tattoos and permanent make-up are MRI suitable and can be scanned in research settings.

Retinal layer assessments as potential biomarkers for brain atrophy in the Rhineland Study

Retinal assessments have been discussed as biomarkers for brain atrophy. However, available studies did not investigate all retinal layers due to older technology, reported inconsistent results, or were based on small sample sizes. We included 2872 eligible participants of the Rhineland Study with data on spectral domain-optical coherence tomography (SD-OCT) and brain magnetic resonance imaging (MRI). We used multiple linear regression to examine relationships between retinal measurements and volumetric brain measures as well as fractional anisotropy (FA) as measure of microstructural integrity of white matter (WM) for different brain regions. Mean (SD) age was 53.8 ± 13.2 years (range 30-94) and 57% were women. Volumes of the inner retina were associated with total brain and grey matter (GM) volume, and even stronger with WM volume and FA. In contrast, the outer retina was mainly associated with GM volume, while both, inner and outer retina, were associated with hippocampus volume. While we extend previously reported associations between the inner retina and brain measures, we found additional associations of the outer retina with parts of the brain. This indicates that easily accessible retinal SD-OCT assessments may serve as biomarkers for clinical monitoring of neurodegenerative diseases and merit further research.

High-fidelity approximation of grid- and shell-based sampling schemes from undersampled DSI using compressed sensing: Post mortem validation

While many useful microstructural indices, as well as orientation distribution functions, can be obtained from multi-shell dMRI data, there is growing interest in exploring the richer set of microstructural features that can be extracted from the full ensemble average propagator (EAP). The EAP can be readily computed from diffusion spectrum imaging (DSI) data, at the cost of a very lengthy acquisition. Compressed sensing (CS) has been used to make DSI more practical by reducing its acquisition time. CS applied to DSI (CS-DSI) attempts to reconstruct the EAP from significantly undersampled q-space data. We present a post mortem validation study where we evaluate the ability of CS-DSI to approximate not only fully sampled DSI but also multi-shell acquisitions with high fidelity. Human brain samples are imaged with high-resolution DSI at 9.4T and with polarization-sensitive optical coherence tomography (PSOCT). The latter provides direct measurements of axonal orientations at microscopic resolutions, allowing us to evaluate the mesoscopic orientation estimates obtained from diffusion MRI, in terms of their angular error and the presence of spurious peaks. We test two fast, dictionary-based, L2-regularized algorithms for CS-DSI reconstruction. We find that, for a CS acceleration factor of R=3, i.e., an acquisition with 171 gradient directions, one of these methods is able to achieve both low angular error and low number of spurious peaks. With a scan length similar to that of high angular resolution multi-shell acquisition schemes, this CS-DSI approach is able to approximate both fully sampled DSI and multi-shell data with high accuracy. Thus it is suitable for orientation reconstruction and microstructural modeling techniques that require either grid- or shell-based acquisitions. We find that the signal-to-noise ratio (SNR) of the training data used to construct the dictionary can have an impact on the accuracy of CS-DSI, but that there is substantial robustness to loss of SNR in the test data. Finally, we show that, as the CS acceleration factor increases beyond R=3, the accuracy of these reconstruction methods degrade, either in terms of the angular error, or in terms of the number of spurious peaks. Our results provide useful benchmarks for the future development of even more efficient q-space acceleration techniques.

Diffusion MRI and anatomic tracing in the same brain reveal common failure modes of tractography

Anatomic tracing is recognized as a critical source of knowledge on brain circuitry that can be used to assess the accuracy of diffusion MRI (dMRI) tractography. However, most prior studies that have performed such assessments have used dMRI and tracer data from different brains and/or have been limited in the scope of dMRI analysis methods allowed by the data. In this work, we perform a quantitative, voxel-wise comparison of dMRI tractography and anatomic tracing data in the same macaque brain. An ex vivo dMRI acquisition with high angular resolution and high maximum b-value allows us to compare a range of q-space sampling, orientation reconstruction, and tractography strategies. The availability of tracing in the same brain allows us to localize the sources of tractography errors and to identify axonal configurations that lead to such errors consistently, across dMRI acquisition and analysis strategies. We find that these common failure modes involve geometries such as branching or turning, which cannot be modeled well by crossing fibers. We also find that the default thresholds that are commonly used in tractography correspond to rather conservative, low-sensitivity operating points. While deterministic tractography tends to have higher sensitivity than probabilistic tractography in that very conservative threshold regime, the latter outperforms the former as the threshold is relaxed to avoid missing true anatomical connections. On the other hand, the q-space sampling scheme and maximum b-value have less of an impact on accuracy. Finally, using scans from a set of additional macaque brains, we show that there is enough inter-individual variability to warrant caution when dMRI and tracer data come from different animals, as is often the case in the tractography validation literature. Taken together, our results provide insights on the limitations of current tractography methods and on the critical role that anatomic tracing can play in identifying potential avenues for improvement.

Efficient and accurate EAP imaging from multi-shell dMRI with micro-structure adaptive convolution kernels and dual Fourier Integral Transforms (MiSFIT)

A number of computational techniques have been lately devised to image the Ensemble Average Propagator (EAP) within the white matter of the brain, propelled by the deployment of multi-shell acquisition protocols and databases: approaches like Mean Apparent Propagator Imaging (MAP-MRI) and its Laplacian-regularized version (MAPL) aim at describing the low frequency spectrum of the EAP (limited by the maximum b-value acquired) and afterwards computing scalar indices that embed useful descriptions of the white matter, e. g. the Return-to-Origin, Plane, or Axis Probabilities (RTOP, RTPP, RTAP). These methods resort to a non-parametric, bandwidth limited representation of the EAP that implies fitting a set of 3-D basis functions in a large-scale optimization problem. We propose a semi-parametric approach inspired by signal theory: the EAP is approximated as the spherical convolution of a Micro-Structure adaptive Gaussian kernel with a non-parametric orientation histogram, which aims at representing the low-frequency response of an ensemble of coherent sets of fiber bundles at the white matter. This way, the optimization involves just the 2 to 3 parameters that describe the kernel, making our approach far more efficient than the related state of the art. We devise dual Fourier domains Integral Transforms to analytically compute RTxP-like scalar indices as moments of arbitrary orders over either the whole 3-D space, particular directions, or particular planes. The so-called MiSFIT is both time efficient (a typical multi-shell data set can be processed in roughly one minute) and accurate: it provides estimates of widely validated indices like RTOP, RTPP, and RTAP comparable to MAPL for a wide variety of white matter configurations.

Comparison of q-Space Reconstruction Methods for Undersampled Diffusion Spectrum Imaging Data

PURPOSE

To compare different q-space reconstruction methods for undersampled diffusion spectrum imaging data.

MATERIALS AND METHODS

We compared the quality of three methods: Mean Apparent Propagator (MAP); Compressed Sensing using Identity (CSI) and Compressed Sensing using Dictionary (CSD) with simulated data and in vivo acquisitions. We used retrospective undersampling so that the fully sampled reconstruction could be used as ground truth. We used the normalized mean squared error (NMSE) and the Pearson's correlation coefficient as reconstruction quality indices. Additionally, we evaluated two propagator-based diffusion indices: mean squared displacement and return to zero probability. We also did a visual analysis around the centrum semiovale.

RESULTS

All methods had reconstruction errors below 5% with low undersampling factors and with a wide range of noise levels. However, the CSD method had at least 1-2% lower NMSE than the other reconstruction methods at higher noise levels. MAP was the second-best method when using a sufficiently high number of q-space samples. MAP reconstruction showed better propagator-based diffusion indices for in vivo acquisitions. With undersampling factors greater than 4, MAP and CSI have noticeably more reconstruction error than CSD.

CONCLUSION

Undersampled data were best reconstructed by means of CSD in simulations and in vivo. MAP was more accurate in the extraction of propagator-based indices, particularly for in vivo data.

Insight into the fundamental trade-offs of diffusion MRI from polarization-sensitive optical coherence tomography in ex vivo human brain

In the first study comparing high angular resolution diffusion MRI (dMRI) in the human brain to axonal orientation measurements from polarization-sensitive optical coherence tomography (PSOCT), we compare the accuracy of orientation estimates from various dMRI sampling schemes and reconstruction methods. We find that, if the reconstruction approach is chosen carefully, single-shell dMRI data can yield the same accuracy as multi-shell data, and only moderately lower accuracy than a full Cartesian-grid sampling scheme. Our results suggest that current dMRI reconstruction approaches do not benefit substantially from ultra-high b-values or from very large numbers of diffusion-encoding directions. We also show that accuracy remains stable across dMRI voxel sizes of 1 mm or smaller but degrades at 2 mm, particularly in areas of complex white-matter architecture. We also show that, as the spatial resolution is reduced, axonal configurations in a dMRI voxel can no longer be modeled as a small set of distinct axon populations, violating an assumption that is sometimes made by dMRI reconstruction techniques. Our findings have implications for in vivo studies and illustrate the value of PSOCT as a source of ground-truth measurements of white-matter organization that does not suffer from the distortions typical of histological techniques.

Acceleration of three-dimensional diffusion magnetic resonance imaging using a kernel low-rank compressed sensing method

Diffusion Magnetic Resonance Imaging (dMRI) has shown great potential in probing tissue microstructure and structural connectivity in the brain but is often limited by the lengthy scan time needed to sample the diffusion profile by acquiring multiple diffusion weighted images (DWIs). Although parallel imaging technique has improved the speed of dMRI acquisition, attaining high resolution three dimensional (3D) dMRI on preclinical MRI systems remained still time consuming. In this paper, kernel principal component analysis, a machine learning approach, was employed to estimate the correlation among DWIs. We demonstrated the feasibility of such correlation estimation from low-resolution training DWIs and used the correlation as a constraint to reconstruct high-resolution DWIs from highly under-sampled k-space data, which significantly reduced the scan time. Using full k-space 3D dMRI data of post-mortem mouse brains, we retrospectively compared the performance of the so-called kernel low rank (KLR) method with a conventional compressed sensing (CS) method in terms of image quality and ability to resolve complex fiber orientations and connectivity. The results demonstrated that the KLR-CS method outperformed the conventional CS method for acceleration factors up to 8 and was likely to enhance our ability to investigate brain microstructure and connectivity using high-resolution 3D dMRI.

Comparison of basis functions and q-space sampling schemes for robust compressed sensing reconstruction accelerating diffusion spectrum imaging

Time constraints placed on magnetic resonance imaging often restrict the application of advanced diffusion MRI (dMRI) protocols in clinical practice and in high throughput research studies. Therefore, acquisition strategies for accelerated dMRI have been investigated to allow for the collection of versatile and high quality imaging data, even if stringent scan time limits are imposed. Diffusion spectrum imaging (DSI), an advanced acquisition strategy that allows for a high resolution of intra-voxel microstructure, can be sufficiently accelerated by means of compressed sensing (CS) theory. CS theory describes a framework for the efficient collection of fewer samples of a data set than conventionally required followed by robust reconstruction to recover the full data set from sparse measurements. For an accurate recovery of DSI data, a suitable acquisition scheme for sparse q-space sampling and the sensing and sparsifying bases for CS reconstruction need to be selected. In this work we explore three different types of q-space undersampling schemes and two frameworks for CS reconstruction based on either Fourier or SHORE basis functions. After CS recovery, diffusion and microstructural parameters and orientational information are estimated from the reconstructed data by means of state-of-the-art processing techniques for dMRI analysis. By means of simulation, diffusion phantom and in vivo DSI data, an isotropic distribution of q-space samples was found to be optimal for sparse DSI. The CS reconstruction results indicate superior performance of Fourier-based CS-DSI compared to the SHORE-based approach. Based on these findings we outline an experimental design for accelerated DSI and robust CS reconstruction of the sparse measurements that is suitable for the application within time-limited studies.