Fiber Orientation Estimation Research Articles

Brain connections derived from diffusion MRI tractography can be highly anatomically accurate-if we know where white matter pathways start, where they end, and where they do not go.

MR Tractography, which is based on MRI measures of water diffusivity, is currently the only method available for noninvasive reconstruction of fiber pathways in the brain. However, it has several fundamental limitations that call into question its accuracy in many applications. Therefore, there has been intense interest in defining and mitigating the intrinsic limitations of the method. Recent studies have reported that tractography is inherently limited in its ability to accurately reconstruct the connections of the brain, when based on voxel-averaged estimates of local fiber orientation alone. Several validation studies have confirmed that tractography techniques are plagued by both false-positive and false-negative connections. However, these validation studies which quantify sensitivity and specificity, particularly in animal models, have not utilized prior anatomical knowledge, as is done in the human literature, for virtual dissection of white matter pathways, instead assessing tractography implemented in a relatively unconstrained manner. Thus, they represent a worse-case scenario for bundle-segmentation techniques and may not be indicative of the anatomical accuracy in the process of bundle segmentation, where streamline filtering using inclusion and exclusion regions-of-interest is common. With this in mind, the aim of the current study is to investigate and quantify the upper bounds of accuracy using current tractography methods. Making use of the same dataset utilized in two seminal validation papers, we show that prior anatomical knowledge in the form of manually placed or template-driven constraints can significantly improve the anatomical accuracy of estimated brain connections. Thus, we show that it is possible to achieve a high sensitivity and high specificity simultaneously, and conclude that current tractography algorithms, in combination with anatomically driven constraints, can result in reconstructions which very accurately reflect the ground truth white matter connections.

On the use of orientation tensors to represent prepreg platelet orientation state and variability

Prepreg platelet molding compounds (PPMCs) have mesoscale (platelet scale) features that are not found in injection molding materials. Beyond the fiber orientation state, the platelet normal orientation state and the expected orientation state variabilities are desirable outputs from flow simulations of PPMC systems. However, theoretical understanding and efficient numerical molding simulation capabilities have primarily been developed for injection molding. Using exact solutions of Jeffery’s equation, two methods are developed: approximation of the second-order normal orientation tensor as a function of the second-order fiber orientation tensor and estimation of the variability in predicted orientation tensors due to scale similarity of the platelets and typical molded geometry thicknesses. These methods are validated using orientation state data obtained from computed tomography for five replicates of a PPMC bracket structure. Finally, the methods are applied as postprocessing of a fiber orientation simulation results, showing good comparison with the experimental data. The developed methods allow existing simulation capabilities to be applied to PPMCs as a reduced order model to enable efficient design iterations for PPMC manufacturing.

Cardiac fiber tracking on super high-resolution CT images: a comparative study.

.Purpose: High-resolution cardiac imaging and fiber analysis methods are required to understand cardiac anatomy. Although refraction-contrast x-ray CT (RCT) has high soft tissue contrast, it cannot be commonly used because it requires a synchrotron system. Microfocus x-ray CT () is another commercially available imaging modality.Approach: We evaluate the usefulness of for analyzing fibers by quantitatively and objectively comparing the results with RCT. To do so, we scanned a rabbit heart by both modalities with our original protocol of prepared materials and compared their image-based analysis results, including fiber orientation estimation and fiber tracking.Results: Fiber orientations estimated by two modalities were closely resembled under the correlation coefficient of 0.63. Tracked fibers from both modalities matched well the anatomical knowledge that fiber orientations are different inside and outside of the left ventricle. However, the volume caused incorrect tracking around the boundaries caused by stitching scanning.Conclusions: Our experimental results demonstrated that scanning can be used for cardiac fiber analysis, although further investigation is required in the differences of fiber analysis results on RCT and .

Progress in brain fiber voxel microstructure estimation algorithms

Diffusion magnetic resonance imaging (dMRI) is the only available technique for the noninvasive and in vivo reconstruction of white matter microarchitecture. A crucial aspect of the image results is the accuracy of the estimation of fiber orientation. Recently, a number of high angular resolution imaging techniques have been used to estimate fiber orientation. In this paper, we review several white fiber reconstruction algorithms, including the widely used spherical deconvolution. We describe advances in the spherical deconvolution optimization algorithm by the development of the optimization algorithm, including $L_2$ regularization, $L_1$ regularization, $L_1$, and $L_2$ regularization. In addition, we conduct experiments to analyze typical reconstruction algorithm. Finally, future research and development of reconstruction algorithm are discussed.

Measuring Fiber Orientation of Elliptical Fibers from Optical Microscopy

The orientation of fibers with elliptical cross-sections cannot be estimated using standard optical microscopy analysis methods in which the ratio of the minor-axis to the major-axis and orientation of the major-axis are directly used to determine the fiber spherical coordinates, θ and ϕ . A new method for estimating the orientation of fibers with elliptical cross-sections is presented and validated using both simulations and experiments. Fibers with elliptical cross-sections rather than circular possess a roll degree of freedom, which significantly affects the dimensions of projected cross-sections in viewing planes. The equations of the projected ellipse of an elliptic cylinder onto a viewing plane are determined in terms of typical spherical coordinate system angles, θ and ϕ , the roll angle, α , and the fiber semi-major and semi-minor diameters. Fiber angles are determined by numerical fitting of the developed equations to measured ellipses. An ambiguity in the determined angles is identified, and, in the special case of fiber bundles, a scheme is presented by which the ambiguity can be resolved. Validation experiments showed that the method is quite effective at estimating fiber orientation from micrographs when fiber cross-section dimensions are measured beforehand, and the additional ambiguity is resolved easily in the case of fiber bundles.

Automatic Muscle Fiber Orientation Tracking in Ultrasound Images Using a New Adaptive Fading Bayesian Kalman Smoother.

This paper proposes a new algorithm for automatic estimation of muscle fiber orientation (MFO) in musculoskeletal ultrasound images, which is commonly used for both diagnosis and rehabilitation assessment of patients. The algorithm is based on a novel adaptive fading Bayesian Kalman filter (AF-BKF) and an automatic region of interest (ROI) extraction method. The ROI is first enhanced by the Gabor filter (GF) and extracted automatically using the revoting constrained Radon transform (RCRT) approach. The dominant MFO in the ROI is then detected by the RT and tracked by the proposed AF-BKF, which employs simplified Gaussian mixtures to approximate the non-Gaussian state densities and a new adaptive fading method to update the mixture parameters. An AF-BK smoother (AF-BKS) is also proposed by extending the AF-BKF using the concept of Rauch-Tung-Striebel smoother for further smoothing the fascicle orientations. The experimental results and comparisons show that: 1) the maximum segmentation error of the proposed RCRT is below nine pixels, which is sufficiently small for MFO tracking; 2) the accuracy of MFO gauged by RT in the ROI enhanced by the GF is comparable to that of using multiscale vessel enhancement filter-based method and better than those of local RT and revoting Hough transform approaches; and 3) the proposed AF-BKS algorithm outperforms the other tested approaches and achieves a performance close to those obtained by experienced operators (the overall covariance obtained by the AF-BKS is 3.19, which is rather close to that of the operators, 2.86). It, thus, serves as a valuable tool for automatic estimation of fascicle orientations and possibly for other applications in musculoskeletal ultrasound images.

Generalized diffusion spectrum magnetic resonance imaging (GDSI) for model-free reconstruction of the ensemble average propagator

Diffusion spectrum MRI (DSI) provides model-free estimation of the diffusion ensemble average propagator (EAP) and orientation distribution function (ODF) but requires the diffusion data to be acquired on a Cartesian q-space grid. Multi-shell diffusion acquisitions are more flexible and more commonly acquired but have, thus far, only been compatible with model-based analysis methods. Here, we propose a generalized DSI (GDSI) framework to recover the EAP from multi-shell diffusion MRI data. The proposed GDSI approach corrects for q-space sampling density non-uniformity using a fast geometrical approach. The EAP is directly calculated in a preferable coordinate system by multiplying the sampling density corrected q-space signals by a discrete Fourier transform matrix, without any need for gridding. The EAP is demonstrated as a way to map diffusion patterns in brain regions such as the thalamus, cortex and brainstem where the tissue microstructure is not as well characterized as in white matter. Scalar metrics such as the zero displacement probability and displacement distances at different fractions of the zero displacement probability were computed from the recovered EAP to characterize the diffusion pattern within each voxel. The probability averaged across directions at a specific displacement distance provides a diffusion property based image contrast that clearly differentiates tissue types. The displacement distance at the first zero crossing of the EAP averaged across directions orthogonal to the primary fiber orientation in the corpus callosum is found to be larger in the body (5.65 ± 0.09 μm) than in the genu (5.55 ± 0.15 μm) and splenium (5.4 ± 0.15 μm) of the corpus callosum, which corresponds well to prior histological studies. The EAP also provides model-free representations of angular structure such as the diffusion ODF, which allows estimation and comparison of fiber orientations from both the model-free and model-based methods on the same multi-shell data. For the model-free methods, detection of crossing fibers is found to be strongly dependent on the maximum b-value and less sensitive compared to the model-based methods. In conclusion, our study provides a generalized DSI approach that allows flexible reconstruction of the diffusion EAP and ODF from multi-shell diffusion data and data acquired with other sampling patterns.

A fiber coherence index for quality control of B-table orientation in diffusion MRI scans

PurposeThe diffusion MRI “b-vector” table describing the diffusion sensitization direction can be flipped and permuted in dimension due to different orientation conventions used in scanners and incorrect or improperly utilized file formats. This can lead to incorrect fiber orientation estimates and subsequent tractography failure. Here, we present an automated quality control procedure to detect when the b-table is flipped and/or permuted incorrectly. MethodsWe define a “fiber coherence index” to describe how well fibers are connected to each other, and use it to automatically detect the correct configuration of b-vectors. We examined the performance on 3981 research subject scans (Baltimore Longitudinal Study of Aging), 1065 normal subject scans of high image quality (Human Connectome Project), and 202 patient scans (Vanderbilt University Medical Center), as well as 9 in-vivo and 9 ex-vivo animal data. ResultsThe coherence index resulted in a 99.9% (3979/3981) and 100% (1065/1065) success rate in normal subject scans, 98% (198/202) in patient scans, and 100% (18/18) in both in-vivo and ex-vivo animal data in detecting the correct gradient table in datasets without severe image artifacts. The four failing cases (4/202) in patient scans, and two failures in healthy subject scans (2/3981), all showed prominent motion or signal dropout artifacts. ConclusionsThe fiber coherence measure can be used as an automatic quality assurance check in any diffusion analysis pipeline. Additionally, the success of this fiber coherence measure suggests potential broader applications, including evaluating data quality, or even providing diagnostic value as a biomarker of white matter integrity.

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

Mapping non-invasively the complex microstructural architecture of the living human brain, diffusion magnetic resonance imaging (dMRI) is one of the core imaging modalities in current population studies. For the application in longitudinal population imaging, the dMRI protocol should deliver reliable data with maximum potential for future analysis. With the recent introduction of novel MRI hardware, advanced dMRI acquisition strategies can be applied within reasonable scan time. In this work we conducted a pilot study based on the requirements for high resolution dMRI in a long-term and high throughput population study. The key question was: can diffusion spectrum imaging accelerated by compressed sensing theory (CS-DSI) be used as an advanced imaging protocol for microstructure dMRI in a long-term population imaging study? As a minimum requirement we expected a high level of agreement of several diffusion metrics derived from both CS-DSI and a 3-shell high angular resolution diffusion imaging (HARDI) acquisition, an established imaging strategy used in other population studies. A wide spectrum of state-of-the-art diffusion processing and analysis techniques was applied to the pilot study data including quantitative diffusion and microstructural parameter mapping, fiber orientation estimation and white matter fiber tracking. When considering diffusion weighted images up to the same maximum diffusion weighting for both protocols, group analysis across 20 subjects indicates that CS-DSI performs comparable to 3-shell HARDI in the estimation of diffusion and microstructural parameters. Further, both protocols provide similar results in the estimation of fiber orientations and for local fiber tracking. CS-DSI provides high radial resolution while maintaining high angular resolution and it is well-suited for analysis strategies that require high b-value acquisitions, such as CHARMED modeling and biomarkers from the diffusion propagator.

Joint spatial-angular sparse coding for dMRI with separable dictionaries.

Diffusion MRI (dMRI) provides the ability to reconstruct neuronal fibers in the brain, in vivo, by measuring water diffusion along angular gradient directions in q-space. High angular resolution diffusion imaging (HARDI) can produce better estimates of fiber orientation than the popularly used diffusion tensor imaging, but the high number of samples needed to estimate diffusivity requires longer patient scan times. To accelerate dMRI, compressed sensing (CS) has been utilized by exploiting a sparse dictionary representation of the data, discovered through sparse coding. The sparser the representation, the fewer samples are needed to reconstruct a high resolution signal with limited information loss, and so an important area of research has focused on finding the sparsest possible representation of dMRI. Current reconstruction methods however, rely on an angular representation per voxel with added spatial regularization, and so, for non-zero signals, one is required to have at least one non-zero coefficient per voxel. This means that the global level of sparsity must be greater than the number of voxels. In contrast, we propose a joint spatial-angular representation of dMRI that will allow us to achieve levels of global sparsity that are below the number of voxels. A major challenge, however, is the computational complexity of solving a global sparse coding problem over large-scale dMRI. In this work, we present novel adaptations of popular sparse coding algorithms that become better suited for solving large-scale problems by exploiting spatial-angular separability. Our experiments show that our method achieves significantly sparser representations of HARDI than is possible by the state of the art.

High-resolution whole-brain diffusion MRI at 7T using radiofrequency parallel transmission.

Investigating the utility of RF parallel transmission (pTx) for Human Connectome Project (HCP)-style whole-brain diffusion MRI (dMRI) data at 7 Tesla (7T). Healthy subjects were scanned in pTx and single-transmit (1Tx) modes. Multiband (MB), single-spoke pTx pulses were designed to image sagittal slices. HCP-style dMRI data (i.e., 1.05-mm resolutions, MB2, b-values = 1000/2000 s/mm2 , 286 images and 40-min scan) and data with higher accelerations (MB3 and MB4) were acquired with pTx. pTx significantly improved flip-angle detected signal uniformity across the brain, yielding ∼19% increase in temporal SNR (tSNR) averaged over the brain relative to 1Tx. This allowed significantly enhanced estimation of multiple fiber orientations (with ∼21% decrease in dispersion) in HCP-style 7T dMRI datasets. Additionally, pTx pulses achieved substantially lower power deposition, permitting higher accelerations, enabling collection of the same data in 2/3 and 1/2 the scan time or of more data in the same scan time. pTx provides a solution to two major limitations for slice-accelerated high-resolution whole-brain dMRI at 7T; it improves flip-angle uniformity, and enables higher slice acceleration relative to current state-of-the-art. As such, pTx provides significant advantages for rapid acquisition of high-quality, high-resolution truly whole-brain dMRI data.

Estimation of fiber orientation and length distribution in cashmere fibrous assemblies

In a general fibrous assembly, single fiber orientation as well as fiber length distributions are important characteristics because they directly influence the properties of textiles. An X-ray micro-tomography experiment with a high resolution of 3 μm was for the first time conducted on a randomly oriented inner Mongolia cashmere fibrous assembly to get a series of two-dimensional projections from different angles and the corresponding cone–beam algorithm proposed by Feldkamp and volume rendering technique were used to realize the three-dimensional (3D) reconstruction. An automated segmentation algorithm described by Rigort and Weber was used to trace and detect single fibers from tomographic 3D data. Local normalized cross-correlation of the tomograms was computed with a cylindrical template that mimics a short microtubule segment to get two new objects, named the correlation and orientation fields. Tracing results of fiber length and orientation distributions were given in this paper statistically.

Estimating fiber orientation distribution from diffusion MRI with spherical needlets.

We present a novel method for estimation of the fiber orientation distribution (FOD) function based on diffusion-weighted magnetic resonance imaging (D-MRI) data. We formulate the problem of FOD estimation as a regression problem through spherical deconvolution and a sparse representation of the FOD by a spherical needlets basis that forms a multi-resolution tight frame for spherical functions. This sparse representation allows us to estimate the FOD by ℓ1-penalized regression under a non-negativity constraint on the estimated FOD. The resulting convex optimization problem is solved by an alternating direction method of multipliers (ADMM) algorithm. The proposed method leads to a reconstruction of the FOD that is accurate, has low variability and preserves sharp features. Through extensive experiments, we demonstrate the effectiveness and favorable performance of the proposed method compared to three existing methods. Specifically, we demonstrate that the proposed method is able to successfully resolve fiber crossings at small angles and automatically identify isotropic diffusion. We also apply the proposed method to real 3T D-MRI data sets of healthy individuals. The results show realistic depictions of crossing fibers that are more accurate, less noisy, and lead to superior tractography results compared to competing methods.

Estimating Full Regional Skeletal Muscle Fibre Orientation from B-Mode Ultrasound Images Using Convolutional, Residual, and Deconvolutional Neural Networks

This paper presents an investigation into the feasibility of using deep learning methods for developing arbitrary full spatial resolution regression analysis of B-mode ultrasound images of human skeletal muscle. In this study, we focus on full spatial analysis of muscle fibre orientation, since there is an existing body of work with which to compare results. Previous attempts to automatically estimate fibre orientation from ultrasound are not adequate, often requiring manual region selection, feature engineering, providing low-resolution estimations (one angle per muscle) and deep muscles are often not attempted. We build upon our previous work in which automatic segmentation was used with plain convolutional neural network (CNN) and deep residual convolutional network (ResNet) architectures, to predict a low-resolution map of fibre orientation in extracted muscle regions. Here, we use deconvolutions and max-unpooling (DCNN) to regularise and improve predicted fibre orientation maps for the entire image, including deep muscles, removing the need for automatic segmentation and we compare our results with the CNN and ResNet, as well as a previously established feature engineering method, on the same task. Dynamic ultrasound images sequences of the calf muscles were acquired (25 Hz) from 8 healthy volunteers (4 male, ages: 25–36, median 30). A combination of expert annotation and interpolation/extrapolation provided labels of regional fibre orientation for each image. Neural networks (CNN, ResNet, DCNN) were then trained both with and without dropout using leave one out cross-validation. Our results demonstrated robust estimation of full spatial fibre orientation within approximately 6° error, which was an improvement on previous methods.

Design and validation of diffusion MRI models of white matter.

Diffusion MRI is arguably the method of choice for characterizing white matter microstructure in vivo. Over the typical duration of diffusion encoding, the displacement of water molecules is conveniently on a length scale similar to that of the underlying cellular structures. Moreover, water molecules in white matter are largely compartmentalized which enables biologically-inspired compartmental diffusion models to characterize and quantify the true biological microstructure. A plethora of white matter models have been proposed. However, overparameterization and mathematical fitting complications encourage the introduction of simplifying assumptions that vary between different approaches. These choices impact the quantitative estimation of model parameters with potential detriments to their biological accuracy and promised specificity. First, we review biophysical white matter models in use and recapitulate their underlying assumptions and realms of applicability. Second, we present up-to-date efforts to validate parameters estimated from biophysical models. Simulations and dedicated phantoms are useful in assessing the performance of models when the ground truth is known. However, the biggest challenge remains the validation of the "biological accuracy" of estimated parameters. Complementary techniques such as microscopy of fixed tissue specimens have facilitated direct comparisons of estimates of white matter fiber orientation and densities. However, validation of compartmental diffusivities remains challenging, and complementary MRI-based techniques such as alternative diffusion encodings, compartment-specific contrast agents and metabolites have been used to validate diffusion models. Finally, white matter injury and disease pose additional challenges to modeling, which are also discussed. This review aims to provide an overview of the current state of models and their validation and to stimulate further research in the field to solve the remaining open questions and converge towards consensus.

Dictionary-based fiber orientation estimation with improved spatial consistency.

Diffusion magnetic resonance imaging (dMRI) has enabled in vivo investigation of white matter tracts. Fiber orientation (FO) estimation is a key step in tract reconstruction and has been a popular research topic in dMRI analysis. In particular, the sparsity assumption has been used in conjunction with a dictionary-based framework to achieve reliable FO estimation with a reduced number of gradient directions. Because image noise can have a deleterious effect on the accuracy of FO estimation, previous works have incorporated spatial consistency of FOs in the dictionary-based framework to improve the estimation. However, because FOs are only indirectly determined from the mixture fractions of dictionary atoms and not modeled as variables in the objective function, these methods do not incorporate FO smoothness directly, and their ability to produce smooth FOs could be limited. In this work, we propose an improvement to Fiber Orientation Reconstruction using Neighborhood Information (FORNI), which we call FORNI+; this method estimates FOs in a dictionary-based framework where FO smoothness is better enforced than in FORNI alone. We describe an objective function that explicitly models the actual FOs and the mixture fractions of dictionary atoms. Specifically, it consists of data fidelity between the observed signals and the signals represented by the dictionary, pairwise FO dissimilarity that encourages FO smoothness, and weighted ℓ1-norm terms that ensure the consistency between the actual FOs and the FO configuration suggested by the dictionary representation. The FOs and mixture fractions are then jointly estimated by minimizing the objective function using an iterative alternating optimization strategy. FORNI+ was evaluated on a simulation phantom, a physical phantom, and real brain dMRI data. In particular, in the real brain dMRI experiment, we have qualitatively and quantitatively evaluated the reproducibility of the proposed method. Results demonstrate that FORNI+ produces FOs with better quality compared with competing methods.

Fast and Accurate Estimation of the HARDI Signal in Diffusion MRI Using a Nearest-Neighbor Interpolation Approach

In the diffusion MRI domain, the HARDI methods were proposed to better characterize the complex biological tissues such as the white matter. In fact, they allow to overcome the problem of crossing fibers detection in the case of the Diffusion Tensor Imaging (DTI). However, the HARDI technique requires a very large number of Diffusion Weighted (DW) magnetic resonance images and thus it takes a long acquisition time, restricting its use in the clinical practice. We propose, in this paper, to develop a novel method for accelerating the reconstruction of the HARDI signal from a few number of DW images of the brain. The approach is a triangulation-based geometrical interpolation of existing signals. It consists on recovering non-acquired data according to their neighborhood from a reduced set of diffusion orientations on the sphere of the q-space. The accuracy of the proposed method was performed on two different phantom datasets for a qualitative and quantitative evaluation against known ground truths. We test also the robustness of the proposed approach under the noise. The obtained results demonstrate that the novel method can approximately halve the scan time and simultaneously obtain a proper fiber orientation estimation. In fact, the estimated FOD (e.g. FOD, Fiber Orientation Distribution) function based on only 34 directions is nearly identical to the one calculated with the full HARDI acquisitions (65 directions). Comparative evaluation on standard phantoms show that the proposed approach outperforms a large selection of methods of state-of-the-art according to the success rate and the angular error criteria.

Estimation of Fibre Orientation in Injection Moulding Plastics Parts

Fibre orientation in short fibre reinforced thermoplastics depends on injection moulding parameters. There are a lot of different parameters that must be established and controlled to achieve proper injection moulding of a plastic part. These parameters fall within four major areas: pressure, temperature, time, and distance. The aim of this article is estimation of fibre orientation in injection moulding plastics parts and comparison of these results with numerical simulated ones. Stereological metallography was used for estimation of experimental orientation of fibres. The orientation of simple fibre may be defined by the two angles θ and Φ. In a Short Fibre Reinforced Thermoplastic (SFRT) component there are frequently millions of fibres, therefore each individual fibre orientation specifying is very impractical. The fibres orientation in space can be described by the probability distribution function (PDF), Ψ(θ, Φ). Numerical modelling of fibre orientation was realised using MOLDEX3D software. Moldex3D is the CAE product for the plastics injection moulding industry. This software allows to view results of fibre orientation as an orientation of the X direction, Y direction, Z direction, the total orientation and orientation at surface. These first three orientations are relevant for the establishment of second-order orientation tensor. They belong to tensor ́s values a11, a22 and a33. Utilization of stereological metallography for short fibre orientation in plastic matrix is very similar to its utilization for estimation of grain boundaries orientation in polycrystalline alloys cased by plastic deformation. In the case of short glass fibres reinforced thermoplastics it’s structure consist of thermoplastic matrix and reinforcing fibres, which has some preferred orientation in most of cases – the structure is anisotropy. The way of scalar measurement of structure anisotropy is determination of degree of orientation. The anisotropic microstructure is decomposed into isotropic, planar or linear oriented components using stereology methods.

A Novel Richardson-Lucy Model with Dictionary Basis and Spatial Regularization for Isolating Isotropic Signals.

Diffusion-weighted magnetic resonance imaging is a non-invasive imaging method that has been increasingly used in neuroscience imaging over the last decade. Partial volume effects (PVEs) exist in sampling signal for many physical and actual reasons, which lead to inaccurate fiber imaging. We overcome the influence of PVEs by separating isotropic signal from diffusion-weighted signal, which can provide more accurate estimation of fiber orientations. In this work, we use a novel response function (RF) and the correspondent fiber orientation distribution function (fODF) to construct different signal models, in which case the fODF is represented using dictionary basis function. We then put forward a new index Piso, which is a part of fODF to quantify white and gray matter. The classic Richardson-Lucy (RL) model is usually used in the field of digital image processing to solve the problem of spherical deconvolution caused by highly ill-posed least-squares algorithm. In this case, we propose an innovative model integrating RL model with spatial regularization to settle the suggested double-models, which improve noise resistance and accuracy of imaging. Experimental results of simulated and real data show that the proposal method, which we call iRL, can robustly reconstruct a more accurate fODF and the quantitative index Piso performs better than fractional anisotropy and general fractional anisotropy.

Fiber Orientation Estimation Guided by a Deep Network.

Diffusion magnetic resonance imaging (dMRI) is currently the only tool for noninvasively imaging the brain's white matter tracts. The fiber orientation (FO) is a key feature computed from dMRI for tract reconstruction. Because the number of FOs in a voxel is usually small, dictionary-based sparse reconstruction has been used to estimate FOs. However, accurate estimation of complex FO configurations in the presence of noise can still be challenging. In this work we explore the use of a deep network for FO estimation in a dictionary-based framework and propose an algorithm named Fiber Orientation Reconstruction guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a smaller dictionary encoding coarse basis FOs to represent diffusion signals. To estimate the mixture fractions of the dictionary atoms, a deep network is designed to solve the sparse reconstruction problem. Second, the coarse FOs inform the final FO estimation, where a larger dictionary encoding a dense basis of FOs is used and a weighted ℓ1-norm regularized least squares problem is solved to encourage FOs that are consistent with the network output. FORDN was evaluated and compared with state-of-the-art algorithms that estimate FOs using sparse reconstruction on simulated and typical clinical dMRI data. The results demonstrate the benefit of using a deep network for FO estimation.