Learning Compact q -Space Representations for Multi-Shell Diffusion-Weighted MRI

DIMOND: DIffusion Model OptimizatioN with Deep Learning

Diffusion magnetic resonance imaging is an important tool for mapping tissue microstructure and structural connectivity non-invasively in the in vivo human brain. Numerous diffusion signal models are proposed to quantify microstructural properties. Nonetheless, accurate estimation of model parameters is computationally expensive and impeded by image noise. Supervised deep learning-based estimation approaches exhibit efficiency and superior performance but require additional training data and may be not generalizable. A new DIffusion Model OptimizatioN framework using physics-informed and self-supervised Deep learning entitled "DIMOND" is proposed to address this problem. DIMOND employs a neural network to map input image data to model parameters and optimizes the network by minimizing the difference between the input acquired data and synthetic data generated via the diffusion model parametrized by network outputs. DIMOND produces accurate diffusion tensor imaging results and is generalizable across subjects and datasets. Moreover, DIMOND outperforms conventional methods for fitting sophisticated microstructural models including the kurtosis and NODDI model. Importantly, DIMOND reduces NODDI model fitting time from hours to minutes, or seconds by leveraging transfer learning. In summary, the self-supervised manner, high efficacy, and efficiency of DIMOND increase the practical feasibility and adoption of microstructure and connectivity mapping in clinical and neuroscientific applications.

Outliers in diffusion-weighted MRI: Exploring detection models and mitigation strategies

Diffusion-weighted MRI (dMRI) is a medical imaging method that can be used to investigate the brain microstructure and structural connections between different brain regions. The method, however, requires relatively complex data processing frameworks and analysis pipelines. Many of these approaches are vulnerable to signal dropout artefacts that can originate from subjects moving their head during the scan. To combat these artefacts and eliminate such outliers, researchers have proposed two approaches: to replace outliers or to downweight outliers during modelling and analysis. With the rising interest in dMRI for clinical research, these types of corrections are increasingly important. Therefore, we set out to investigate the differences between outlier replacement and weighting approaches to help the dMRI community to select the best tool for their data processing pipelines. We evaluated dMRI motion correction registration and single tensor model fit pipelines using Gaussian Process and Spherical Harmonic based replacement approaches and outlier downweighting using highly realistic whole-brain simulations. As a proof of concept, we applied these approaches to dMRI infant data sets that contained varying numbers of dropout artefacts. Based on our results, we concluded that the Gaussian Process based outlier replacement provided similar tensor fit results to Gaussian Process based outlier detection and downweighting. Therefore, if only the least-squares estimate of the single tensor model is of interest, our recommendation is to use outlier replacement. However, outlier downweighting can potentially provide a more accurate estimate of the model precision which could be relevant for applications such as probabilistic tractoraphy.

The Developing Human Connectome Project Neonatal Data Release

The Developing Human Connectome Project has created a large open science resource which provides researchers with data for investigating typical and atypical brain development across the perinatal period. It has collected 1228 multimodal magnetic resonance imaging (MRI) brain datasets from 1173 fetal and/or neonatal participants, together with collateral demographic, clinical, family, neurocognitive and genomic data from 1173 participants, together with collateral demographic, clinical, family, neurocognitive and genomic data. All subjects were studied in utero and/or soon after birth on a single MRI scanner using specially developed scanning sequences which included novel motion-tolerant imaging methods. Imaging data are complemented by rich demographic, clinical, neurodevelopmental, and genomic information. The project is now releasing a large set of neonatal data; fetal data will be described and released separately. This release includes scans from 783 infants of whom: 583 were healthy infants born at term; as well as preterm infants; and infants at high risk of atypical neurocognitive development. Many infants were imaged more than once to provide longitudinal data, and the total number of datasets being released is 887. We now describe the dHCP image acquisition and processing protocols, summarize the available imaging and collateral data, and provide information on how the data can be accessed.

Predicting age and clinical risk from the neonatal connectome

The development of perinatal brain connectivity underpins motor, cognitive and behavioural abilities in later life. Diffusion MRI allows the characterisation of subtle inter-individual differences in structural brain connectivity. Individual brain connectivity maps (connectomes) are by nature high in dimensionality and complex to interpret. Machine learning methods are a powerful tool to uncover properties of the connectome which are not readily visible and can give us clues as to how and why individual developmental trajectories differ. In this manuscript we used Deep Neural Networks and Random Forests to predict demographic and neurodevelopmental characteristics from neonatal structural connectomes in a large sample of babies (n = 524) from the developing Human Connectome Project. We achieved an accurate prediction of post menstrual age (PMA) at scan in term-born infants (mean absolute error (MAE) = 0.72 weeks, r = 0.83 and p<0.001). We also achieved good accuracy when predicting gestational age at birth in a cohort of term and preterm babies scanned at term equivalent age (MAE = 2.21 weeks, r = 0.82, p<0.001). We subsequently used sensitivity analysis to obtain feature relevance from our prediction models, with the most important connections for prediction of PMA and GA found to predominantly involve frontal and temporal regions, thalami, and basal ganglia. From our models of PMA at scan for infants born at term, we computed a brain maturation index (predicted age minus actual age) of individual preterm neonates and found a significant correlation between this index and motor outcome at 18 months corrected age. Our results demonstrate the applicability of machine learning techniques in analyses of the neonatal connectome and suggest that a neural substrate of brain maturation with implications for future neurodevelopment is detectable at term equivalent age from the neonatal connectome.

Practical computation of the diffusion MRI signal based on Laplace eigenfunctions: permeable interfaces

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal, called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the tissue geometry and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. In a previous publication, we presented a simulation framework that we implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for biological cells subject to impermeable membrane boundary conditions. In this work, we extend our simulation framework to include geometries that contain permeable cell membranes. We describe the new computational techniques that allowed this generalization and we analyze the effects of the magnitude of the permeability coefficient on the eigendecomposition of the diffusion and Bloch-Torrey operators. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.

dStripe: Slice artefact correction in diffusion MRI via constrained neural network

MRI scanner and sequence imperfections and advances in reconstruction and imaging techniques to increase motion robustness can lead to inter-slice intensity variations in Echo Planar Imaging. Leveraging deep convolutional neural networks as universal image filters, we present a data-driven method for the correction of acquisition artefacts that manifest as inter-slice inconsistencies, regardless of their origin. This technique can be applied to motion- and dropout-artefacted data by embedding it in a reconstruction pipeline. The network is trained in the absence of ground-truth data on, and finally applied to, the reconstructed multi-shell high angular resolution diffusion imaging signal to produce a corrective slice intensity modulation field. This correction can be performed in either motion-corrected or scattered source-space. We focus on gaining control over the learned filter and the image data consistency via built-in spatial frequency and intensity constraints. The end product is a corrected image reconstructed from the original raw data, modulated by a multiplicative field that can be inspected and verified to match the expected features of the artefact. In-plane, the correction approximately preserves the contrast of the diffusion signal and throughout the image series, it reduces inter-slice inconsistencies within and across subjects without biasing the data. We apply our pipeline to enhance the super-resolution reconstruction of neonatal multi-shell high angular resolution data as acquired in the developing Human Connectome Project.

Multi-band- and in-plane-accelerated diffusion MRI enabled by model-based deep learning in q-space and its extension to learning in the spherical harmonic domain

PURPOSE

To propose a new method for the recovery of combined in-plane- and multi-band (MB)-accelerated diffusion MRI data.

METHODS

Combining MB acceleration with in-plane acceleration is crucial to improve the time efficiency of high (angular and spatial) resolution diffusion scans. However, as the MB factor and in-plane acceleration increase, the reconstruction becomes challenging due to the heavy aliasing. The new reconstruction utilizes an additional q-space prior to constrain the recovery, which is derived from the previously proposed qModeL framework. Specifically, the qModeL prior provides a pre-learned representation of the diffusion signal space to which the measured data belongs. We show that the pre-learned q-space prior along with a model-based iterative reconstruction that accommodate multi-band unaliasing, can efficiently reconstruct the in-plane- and MB-accelerated data. The power of joint reconstruction is maximally utilized by using an incoherent under-sampling pattern in the k-q domain. We tested the proposed method on single- and multi-shell data, with high/low angular resolution, high/low spatial resolution, healthy/abnormal tissues, and 3T/7T field strengths. Furthermore, the learning is extended to the spherical harmonic basis, to provide a rotational invariant learning framework.

RESULTS

The qModeL joint reconstruction is shown to simultaneously unalias and jointly recover DWIs with reasonable accuracy in all the cases studied. The reconstruction error from 18-fold accelerated multi-shell datasets was <3%. The microstructural maps derived from the accelerated acquisitions also exhibit reasonable accuracy for both healthy and abnormal tissues. The deep learning (DL)-enabled reconstructions are comparable to those derived using traditional methods.

CONCLUSION

qModeL enables the joint recovery of combined in-plane- and MB-accelerated dMRI utilizing DL.

Cross-scanner reproducibility and harmonization of a diffusion MRI structural brain network: A traveling subject study of multi-b acquisition

Characterization of brain networks by diffusion MRI (dMRI) has rapidly evolved, and there are ongoing movements toward data sharing and multi-center studies. To extract meaningful information from multi-center data, methods to correct for the bias caused by scanner differences, that is, harmonization, are urgently needed. In this work, we report the cross-scanner differences in structural network analyses using data from nine traveling subjects (four males and five females, 21-49 years-old) who underwent scanning using four 3T scanners (public database available from the Brain/MINDS Beyond Human Brain MRI project (http://mriportal.umin.jp/)). The reliability and reproducibility were compared to those of data from another set of four subjects (all males, 29-42 years-old) who underwent scan-rescan (interval, 105-147 days) with the same scanner as well as scan-rescan data from the Human Connectome Project database. The results demonstrated that the reliability of the edge weights and graph theory metrics was lower for data including different scanners, compared to the scan-rescan with the same scanner. Besides, systematic differences between scanners were observed, indicating the risk of bias in comparing networks obtained from different scanners directly. We further demonstrate that it is feasible to reduce inter-scanner variabilities while preserving the inter-subject differences among healthy individuals by modeling the scanner effects at the level of network matrices, when traveling-subject data are available for calibration between scanners. The present data and results are expected to serve as a basis for developing and evaluating novel harmonization methods.

Scattered slice SHARD reconstruction for motion correction in multi-shell diffusion MRI

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Subject motion in dMRI leads to a set of scattered slices with unique contrast.

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We introduce a slice-to-volume reconstruction framework for multi-shell HARDI data

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Based on a data-driven representation as spherical harmonics and radial decomposition (SHARD).

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The method is evaluated in test-retest scans and in the neonatal dHCP cohort.

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Results show robust reconstruction in severely motion-corrupted scans.

Diffusion MRI offers a unique probe into neural microstructure and connectivity in the developing brain. However, analysis of neonatal brain imaging data is complicated by inevitable subject motion, leading to a series of scattered slices that need to be aligned within and across diffusion-weighted contrasts. Here, we develop a reconstruction method for scattered slice multi-shell high angular resolution diffusion imaging (HARDI) data, jointly estimating an uncorrupted data representation and motion parameters at the slice or multiband excitation level. The reconstruction relies on data-driven representation of multi-shell HARDI data using a bespoke spherical harmonics and radial decomposition (SHARD), which avoids imposing model assumptions, thus facilitating to compare various microstructure imaging methods in the reconstructed output. Furthermore, the proposed framework integrates slice-level outlier rejection, distortion correction, and slice profile correction. We evaluate the method in the neonatal cohort of the developing Human Connectome Project (650 scans). Validation experiments demonstrate accurate slice-level motion correction across the age range and across the range of motion in the population. Results in the neonatal data show successful reconstruction even in severely motion-corrupted subjects. In addition, we illustrate how local tissue modelling can extract advanced microstructure features such as orientation distribution functions from the motion-corrected reconstructions.

Practical computation of the diffusion MRI signal of realistic neurons based on Laplace eigenfunctions

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the biological cell and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. Up to now, this representation, though mathematically elegant, has not been often used as a practical model of the diffusion MRI signal, due to the difficulties of calculating the Laplace eigendecomposition in complicated geometries. In this paper, we present a simulation framework that we have implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for realistic neurons using the finite element method. We show that the matrix formalism representation requires a few hundred eigenmodes to match the reference signal computed by solving the Bloch-Torrey equation when the cell geometry originates from realistic neurons. As expected, the number of eigenmodes required to match the reference signal increases with smaller diffusion time and higher b-values. We also convert the eigenvalues to a length scale and illustrate the link between the length scale and the oscillation frequency of the eigenmode in the cell geometry. We give the transformation that links the Laplace eigenfunctions to the eigenfunctions of the Bloch-Torrey operator and compute the Bloch-Torrey eigenfunctions and eigenvalues. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.

A data-driven approach to optimising the encoding for multi-shell diffusion MRI with application to neonatal imaging

Diffusion MRI has the potential to provide important information about the connectivity and microstructure of the human brain during normal and abnormal development, noninvasively and in vivo. Recent developments in MRI hardware and reconstruction methods now permit the acquisition of large amounts of data within relatively short scan times. This makes it possible to acquire more informative multi-shell data, with diffusion sensitisation applied along many directions over multiple b-value shells. Such schemes are characterised by the number of shells acquired, and the specific b-value and number of directions sampled for each shell. However, there is currently no clear consensus as to how to optimise these parameters. In this work, we propose a means of optimising multi-shell acquisition schemes by estimating the information content of the diffusion MRI signal, and optimising the acquisition parameters for sensitivity to the observed effects, in a manner agnostic to any particular diffusion analysis method that might subsequently be applied to the data. This method was used to design the acquisition scheme for the neonatal diffusion MRI sequence used in the developing Human Connectome Project (dHCP), which aims to acquire high quality data and make it freely available to the research community. The final protocol selected by the algorithm, and currently in use within the dHCP, consists of 20 b=0 images and diffusion-weighted images at b = 400, 1000 and 2600 s/mm2 with 64, 88 and 128 directions per shell, respectively.

Abnormal Microstructural Development of the Cerebral Cortex in Neonates With Congenital Heart Disease Is Associated With Impaired Cerebral Oxygen Delivery

Background Abnormal macrostructural development of the cerebral cortex has been associated with hypoxia in infants with congenital heart disease ( CHD ). Animal studies have suggested that hypoxia results in cortical dysmaturation at the cellular level. New magnetic resonance imaging techniques offer the potential to investigate the relationship between cerebral oxygen delivery and cortical microstructural development in newborn infants with CHD . Methods and Results We measured cortical macrostructural and microstructural properties in 48 newborn infants with serious or critical CHD and 48 age-matched healthy controls. Cortical volume and gyrification index were calculated from high-resolution structural magnetic resonance imaging. Neurite density and orientation dispersion indices were modeled using high-angular-resolution diffusion magnetic resonance imaging. Cerebral oxygen delivery was estimated in infants with CHD using phase contrast magnetic resonance imaging and preductal pulse oximetry. We used gray matter-based spatial statistics to examine voxel-wise group differences in cortical microstructure. Microstructural development of the cortex was abnormal in 48 infants with CHD , with regions of increased fractional anisotropy and reduced orientation dispersion index compared with 48 healthy controls, correcting for gestational age at birth and scan (family-wise error corrected for multiple comparisons at P<0.05). Regions of reduced cortical orientation dispersion index in infants with CHD were related to impaired cerebral oxygen delivery ( R²=0.637; n=39). Cortical orientation dispersion index was associated with the gyrification index ( R²=0.589; P<0.001; n=48). Conclusions This study suggests that the primary component of cerebral cortex dysmaturation in CHD is impaired dendritic arborization, which may underlie abnormal macrostructural findings reported in this population, and that the degree of impairment is related to reduced cerebral oxygen delivery.

Development of Microstructural and Morphological Cortical Profiles in the Neonatal Brain

Interruptions to neurodevelopment during the perinatal period may have long-lasting consequences. However, to be able to investigate deviations in the foundation of proper connectivity and functional circuits, we need a measure of how this architecture evolves in the typically developing brain. To this end, in a cohort of 241 term-born infants, we used magnetic resonance imaging to estimate cortical profiles based on morphometry and microstructure over the perinatal period (37–44 weeks postmenstrual age, PMA). Using the covariance of these profiles as a measure of inter-areal network similarity (morphometric similarity networks; MSN), we clustered these networks into distinct modules. The resulting modules were consistent and symmetric, and corresponded to known functional distinctions, including sensory–motor, limbic, and association regions, and were spatially mapped onto known cytoarchitectonic tissue classes. Posterior regions became more morphometrically similar with increasing age, while peri-cingulate and medial temporal regions became more dissimilar. Network strength was associated with age: Within-network similarity increased over age suggesting emerging network distinction. These changes in cortical network architecture over an 8-week period are consistent with, and likely underpin, the highly dynamic processes occurring during this critical period. The resulting cortical profiles might provide normative reference to investigate atypical early brain development.

On the need for bundle-specific microstructure kernels in diffusion MRI

Probing microstructure with diffusion magnetic resonance imaging (dMRI) on a scale orders of magnitude below the imaging resolution relies on biophysical modelling of the signal response in the tissue. The vast majority of these biophysical models of diffusion in white matter assume that the measured dMRI signal is the sum of the signals emanating from each of the constituent compartments, each of which exhibits a distinct behaviour in the b-value and/or orientation domain. Many of these models further assume that the dMRI behaviour of the oriented compartments (e.g. the intra-axonal space) is identical between distinct fibre populations, at least at the level of a single voxel. This implicitly assumes that any potential biological differences between fibre populations are negligible, at least as far as is measurable using dMRI. Here, we validate this assumption by means of a voxel-wise, model-free signal decomposition that, under the assumption above and in the absence of noise, is shown to be rank-1. We evaluate the effect size of signal components beyond this rank-1 representation and use permutation testing to assess their significance. We conclude that in the healthy adult brain, the dMRI signal is adequately represented by a rank-1 model, implying that biologically more realistic, but mathematically more complex fascicle-specific microstructure models do not capture statistically significant or anatomically meaningful structure, even in extended high-b diffusion MRI scans.

Enabling Multi-Shell b-Value Generalizability of Data-Driven Diffusion Models with Deep SHORE

Intra-voxel models of the diffusion signal are essential for interpreting organization of the tissue environment at micrometer level with data at millimeter resolution. Recent advances in data driven methods have enabled direct comparison and optimization of methods for in-vivo data with externally validated histological sections with both 2-D and 3-D histology. Yet, all existing methods make limiting assumptions of either (1) model-based linkages between b-values or (2) limited associations with single shell data. We generalize prior deep learning models that used single shell spherical harmonic transforms to integrate the recently developed simple harmonic oscillator reconstruction (SHORE) basis. To enable learning on the SHORE manifold, we present an alternative formulation of the fiber orientation distribution (FOD) object using the SHORE basis while representing the observed diffusion weighted data in the SHORE basis. To ensure consistency of hyper-parameter optimization for SHORE, we present our Deep SHORE approach to learn on a data-optimized manifold. Deep SHORE is evaluated with eight-fold cross-validation of a preclinical MRI-histology data with four b-values. Generalizability of in-vivo human data is evaluated on two separate 3T MRI scanners. Specificity in terms of angular correlation (ACC) with the preclinical data improved on single shell: 0.78 relative to 0.73 and 0.73, multi-shell: 0.80 relative to 0.74 (p < 0.001). In the in-vivo human data, Deep SHORE was more consistent across scanners with 0.63 relative to other multi-shell methods 0.39, 0.52 and 0.57 in terms of ACC. In conclusion, Deep SHORE is a promising method to enable data driven learning with DW-MRI under conditions with varying b-values, number of diffusion shells, and gradient directions per shell.

SHORE-based detection and imputation of dropout in diffusion MRI

PURPOSE

In diffusion MRI, dropout refers to a strong attenuation of the measured signal that is caused by bulk motion during the diffusion encoding. When left uncorrected, dropout will be erroneously interpreted as high diffusivity in the affected direction. We present a method to automatically detect dropout, and to replace the affected measurements with imputed values.

METHODS

Signal dropout is detected by deriving an outlier score from a simple harmonic oscillator-based reconstruction and estimation (SHORE) fit of all measurements. The outlier score is defined to detect measurements that are substantially lower than predicted by SHORE in a relative sense, while being less sensitive to measurement noise in cases of weak baseline signal. A second SHORE fit is based on detected inliers only, and its predictions are used to replace outliers.

RESULTS

Our method is shown to reliably detect and accurately impute dropout in simulated data, and to achieve plausible results in corrupted in vivo dMRI measurements. Computational effort is much lower than with previously proposed alternatives.

CONCLUSIONS

Deriving a suitable outlier score from SHORE results in a fast and accurate method for detection and imputation of dropout in diffusion MRI. It requires measurements with multiple b values (such as multi-shell or DSI), but is independent from the models used for analysis (such as DKI, NODDI, deconvolution, etc.).