Parametric spherical deconvolution: inferring anatomical connectivity using diffusion MR imaging

The human brain forms a complex neural network with a connectional architecture that is still far from being known in full detail, even at the macroscopic level. The advent of diffusion MR imaging has enabled the exploration of the structural properties of white matter in vivo. In this article we propose a new forward model that maps the microscopic geometry of nervous tissue onto the water diffusion process and further onto the measured MR signals. Our spherical deconvolution approach completely parameterizes the fiber orientation density by a finite mixture of Bingham distributions. In addition, we define the term anatomical connectivity, taking the underlying image modality into account. This neurophysiological metric may represent the proportion of the nerve fibers originating in the source area which intersect a given target region. The specified inverse problem is solved by Bayesian statistics. Posterior probability maps denote the probability that the connectivity value exceeds a chosen threshold, conditional upon the noisy observations. These maps allow us to draw inferences about the structural organization of the cerebral cortex. Moreover, we will demonstrate the proposed approach with diffusion-weighted data sets featuring high angular resolution.     

Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT)

This article describes an accurate and fast method for fiber orientation mapping using multidirectional diffusion-weighted magnetic resonance (MR) data. This novel approach utilizes the Fourier transform relationship between the water displacement probabilities and diffusion-attenuated MR signal expressed in spherical coordinates. The radial part of the Fourier integral is evaluated analytically under the assumption that MR signal attenuates exponentially. The values of the resulting functions are evaluated at a fixed distance away from the origin. The spherical harmonic transform of these functions yields the Laplace series coefficients of the probabilities on a sphere of fixed radius. Alternatively, probability values can be computed nonparametrically using Legendre polynomials. Orientation maps calculated from excised rat nervous tissue data demonstrate this technique's ability to accurately resolve crossing fibers in anatomical regions such as the optic chiasm. This proposed methodology has a trivial extension to multiexponential diffusion-weighted signal decay. The developed methods will improve the reliability of tractography schemes and may make it possible to correctly identify the neural connections between functionally connected regions of the nervous system.     

Spatially-constrained probability distribution model of incoherent motion (SPIM) for abdominal diffusion-weighted MRI

Quantitative diffusion-weighted MR imaging (DW-MRI) of the body enables characterization of the tissue microenvironment by measuring variations in the mobility of water molecules. The diffusion signal decay model parameters are increasingly used to evaluate various diseases of abdominal organs such as the liver and spleen. However, previous signal decay models (i.e., mono-exponential, bi-exponential intra-voxel incoherent motion (IVIM) and stretched exponential models) only provide insight into the average of the distribution of the signal decay rather than explicitly describe the entire range of diffusion scales. In this work, we propose a probability distribution model of incoherent motion that uses a mixture of Gamma distributions to fully characterize the multi-scale nature of diffusion within a voxel. Further, we improve the robustness of the distribution parameter estimates by integrating spatial homogeneity prior into the probability distribution model of incoherent motion (SPIM) and by using the fusion bootstrap solver (FBM) to estimate the model parameters. We evaluated the improvement in quantitative DW-MRI analysis achieved with the SPIM model in terms of accuracy, precision and reproducibility of parameter estimation in both simulated data and in 68 abdominal in-vivo DW-MRIs. Our results show that the SPIM model not only substantially reduced parameter estimation errors by up to 26%; it also significantly improved the robustness of the parameter estimates (paired Student's t-test, p < 0.0001) by reducing the coefficient of variation (CV) of estimated parameters compared to those produced by previous models. In addition, the SPIM model improves the parameter estimates reproducibility for both intra- (up to 47%) and inter-session (up to 30%) estimates compared to those generated by previous models. Thus, the SPIM model has the potential to improve accuracy, precision and robustness of quantitative abdominal DW-MRI analysis for clinical applications.     

Refinement of optical imaging spectroscopy algorithms using concurrent BOLD and CBV fMRI

We describe the use of the three dimensional characteristics of the functional magnetic resonance imaging (fMRI) blood oxygenation level dependent (BOLD) and cerebral blood volume (CBV) MRI signal changes to refine a two dimensional optical imaging spectroscopy (OIS) algorithm. The cortical depth profiles of the BOLD and CBV changes following neural activation were used to parameterise a 5-layer heterogeneous tissue model used in the Monte Carlo simulations (MCS) of light transport through tissue in the OIS analysis algorithm. To transform the fMRI BOLD and CBV measurements into deoxy-haemoglobin (Hbr) profiles we inverted an MCS of extra-vascular MR signal attenuation under the assumption that the extra-/intravascular ratio is 2:1 at a magnetic field strength of 3 T. The significant improvement in the quantitative accuracy of haemodynamic measurements using the new heterogeneous tissue model over the original homogeneous tissue model OIS algorithm was demonstrated on new concurrent OIS and fMRI data covering a range of stimulus durations.     

Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution

Diffusion-weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers. The diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel. However, this model has been shown to fail in regions containing several fiber populations with distinct orientations. A number of alternative models have been suggested, such as multiple tensor fitting, q-space, and Q-ball imaging. However, each of these has inherent limitations. In this study, we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion-weighted MR data without the need for prior assumptions regarding the number of fiber populations present. We assume that all white matter fiber bundles in the brain share identical diffusion characteristics, thus implicitly assigning any differences in diffusion anisotropy to partial volume effects. The diffusion-weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function (the diffusion-weighted attenuation profile for a typical fiber bundle) with the fiber orientation density function (ODF). The fiber ODF (the distribution of fiber orientations within the voxel) can therefore be obtained using spherical deconvolution. The properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1.5-T clinical scanner. The technique can recover the fiber ODF in regions of multiple fiber crossing and holds promise for applications such as tractography.     

Nonparametric Bayesian inference of the fiber orientation distribution from diffusion-weighted MR images

Diffusion MR imaging provides a unique tool to probe the microgeometry of nervous tissue and to explore the wiring diagram of the neural connections noninvasively. Generally, a forward model is established to map the intra-voxel fiber architecture onto the observable diffusion signals, which is reformulated in this article by adopting a measure-theoretic approach. However, the inverse problem, i.e., the spherical deconvolution of the fiber orientation density from noisy MR measurements, is ill-posed. We propose a nonparametric representation of the tangential distribution of the nerve fibers in terms of a Dirichlet process mixture. Given a second-order approximation of the impulse response of a fiber segment, the specified problem is solved by Bayesian statistics under a Rician noise model, using an adaptive reversible jump Markov chain Monte Carlo sampler. The density estimation framework is demonstrated by various experiments with a diffusion MR dataset featuring high angular resolution, uncovering the fiber orientation field in the cerebral white matter of the living human brain.     

Modeling dendrite density from magnetic resonance diffusion measurements

Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal in this model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (D(L)) and perpendicular (D(T)) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.e., in extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides an estimate of dendrite density from noninvasive MR diffusion measurements, a parameter likely to be of value for understanding normal as well as abnormal brain development and function.     

Magic DIAMOND: Multi-fascicle diffusion compartment imaging with tensor distribution modeling and tensor-valued diffusion encoding

Diffusion tensor imaging provides increased sensitivity to microstructural tissue changes compared to conventional anatomical imaging but also presents limited specificity. To tackle this problem, the DIAMOND model subdivides the voxel content into diffusion compartments and draws from diffusion-weighted data to estimate compartmental non-central matrix-variate Gamma distributions of diffusion tensors. It models each sub-voxel fascicle separately, resolving crossing white-matter pathways and allowing for a fascicle-element (fixel) based analysis of microstructural features. Alternatively, specific features of the intra-voxel diffusion tensor distribution can be selectively measured using tensor-valued diffusion-weighted acquisition schemes. However, the impact of such schemes on estimating brain microstructural features has only been studied in a handful of parametric single-fascicle models. In this work, we derive a general Laplace transform for the non-central matrix-variate Gamma distribution, which enables the extension of DIAMOND to tensor-valued encoded data. We then evaluate this “Magic DIAMOND” model in silico and in vivo on various combinations of tensor-valued encoded data. Assessing uncertainty on parameter estimation via stratified bootstrap, we investigate both voxel-based and fixel-based metrics by carrying out multi-peak tractography. We demonstrate using in silico evaluations that tensor-valued diffusion encoding significantly improves Magic DIAMOND’s accuracy. Most importantly, we show in vivo that our estimated metrics can be robustly mapped along tracks across regions of fiber crossing, which opens new perspectives for tractometry and microstructure mapping along specific white-matter tracts.     

Basic concepts of MR imaging, diffusion MR imaging, and diffusion tensor imaging

MR image contrast is based on intrinsic tissue properties and specific pulse sequences and parameter adjustments. A growing number of MRI imaging applications are based on diffusion properties of water. To better understand MRI diffusion-weighted imaging, a brief overview of MR physics is presented in this article followed by physics of the evolving techniques of diffusion MR imaging and diffusion tensor imaging.     

Progress of intravoxel incoherent motion diffusion-weighted imaging in liver diseases

Traditional magnetic resonance (MR) diffusion-weighted imaging (DWI) uses a single exponential model to obtain the apparent diffusion coefficient to quantitatively reflect the diffusion motion of water molecules in living tissues, but it is affected by blood perfusion. Intravoxel incoherent motion (IVIM)-DWI utilizes a double-exponential model to obtain information on pure water molecule diffusion and microcirculatory perfusion-related diffusion, which compensates for the insufficiency of traditional DWI. In recent years, research on the application of IVIM-DWI in the diagnosis and treatment of hepatic diseases has gradually increased and has achieved considerable progress. This study mainly reviews the basic principles of IVIM-DWI and related research progress in the diagnosis and treatment of hepatic diseases.     

A Dirichlet process mixture model for brain MRI tissue classification

Accurate classification of magnetic resonance images according to tissue type or region of interest has become a critical requirement in diagnosis, treatment planning, and cognitive neuroscience. Several authors have shown that finite mixture models give excellent results in the automated segmentation of MR images of the human normal brain. However, performance and robustness of finite mixture models deteriorate when the models have to deal with a variety of anatomical structures. In this paper, we propose a nonparametric Bayesian model for tissue classification of MR images of the brain. The model, known as Dirichlet process mixture model, uses Dirichlet process priors to overcome the limitations of current parametric finite mixture models. To validate the accuracy and robustness of our method we present the results of experiments carried out on simulated MR brain scans, as well as on real MR image data. The results are compared with similar results from other well-known MRI segmentation methods.     

基于水分子弥散MRI研究进展

目的水分子弥散广泛存在于体内各组织器官中,MRI通过测量和表征水分子在组织内的弥散和灌注等信息,可筛查、诊断多种疾病及评估其预后。采用不同b值及弥散梯度方向衍生出多种MR水分子弥散成像技术。本文对基于水分子弥散的MRI研究及其临床应用进展进行综述。     

An investigation of functional and anatomical connectivity using magnetic resonance imaging

This article examines functional and anatomical connectivity in healthy human subjects measured with magnetic resonance imaging methods. Anatomical connectivity in white matter is obtained from measurements of the diffusion tensor. A Monte-Carlo simulation determines the probability that a particle diffuses between two points, with the probability of a jump in a particular direction from a given voxel being based on the local value of the diffusion tensor components. Functional connectivity between grey matter pixels is assessed without recourse to a specific activation paradigm, by calculating the correlation coefficient between random fluctuations in the blood oxygenation level-dependent signal time course in different pixels. The methods are used to examine the anatomical and functional connectivities between crowns of adjacent gyri. A high functional connectivity was found between grey matter pixels, with white matter displaying only very low correlation. A comparison of the measurements of anatomical and functional connectivity found that there is no simple correlation between these measures, except that low values of functional connectivity were not found together with high values of anatomical connectivity. Furthermore pairs of regions situated around the central sulcus indicated a dependence of the two connectivity measures on each other. These results are in accordance with an interpretation that regions which are clearly directly linked by white matter fiber tracts should show high functional connectivity, but that the inverse need not be true as functional connectivity may also be indirectly mediated via more distant grey matter regions.     

Estimate of attenuation coefficient for ultrasonic tissue characterization using time-varying state-space model

The images generated from ultrasound pulse-echo signals have long been used to aid clinical diagnosis. Recently, there has been a growing interest in quantitatively determining the acoustic parameters of the tissue as a means of classification and diagnosis. For example, the frequency-dependent attenuation is known to be correlated with different diseases in the liver. In this paper we introduce a new technique for estimating the attenuation coefficient. The effect of attenuation on an interrogating signal with a gaussian-shaped spectrum can be obtained by studying the Wigner distribution of reflected rf data based on a one-dimensional signal model. We show that under the condition that the attenuation varies linearly with frequency, the spectral mean of the reflected signal decreases linearly with time. The estimation algorithm models the pulse-echo signal as the output of a second-order time-varying state-space innovations model driven by white noise. The state coupling matrix A and the output coupling vector C vary with time in a known fashion; moreover, they are also functions of an unknown constant parameter theta. The attenuation coefficient, which is one of the elements of theta, can be estimated directly using a recursive system identification algorithm. The algorithm was verified using both computer-generated synthetic data and in-vivo liver data of known diagnosis. The results show correlation between the estimated parameter and the pathological state of the tissue.     

磁共振q-空间扩散成像的初步研究

目的探讨q-空间成像在1.5T 临床用设备上的可行性.方法对12名成年健康志愿者分别用不同的q值进行头部扩散张量成像,通过傅立叶变换得到水分子的位移分布.结果通过对所有被试的平均,能够获得水分子的扩散位移轮廓分布.结论使用q-空间成像可以提供活体内的水分子扩散的定量信息,具有潜在的应用价值.     

T(2)(*) dependence of low frequency functional connectivity

Resting state low frequency (<0.08 Hz) fluctuations in MR timecourses that are temporally correlated between functionally related areas have been observed in recent studies. These fluctuations have been assumed to arise from spontaneous blood oxygenation level-dependent (BOLD) oscillations. This work examines the T(2)(*) characteristics of the low frequency fluctuations (functional connectivity) and compares them to those of task activation induced signal changes. Multi-echo spiral data were fit using a mono-exponential decay model to generate T(2)(*) and intensity (I(0)) parameter timecourses. Resultant correlation maps show that both functional connectivity and BOLD activation modulate T(2)(*), not I(0). Regression analysis also finds that both have a linear dependence on echo time. Thus, functional connectivity and task activation MR signal changes appear to arise from the same BOLD-related origins.     

Evaluation of ultrasonic attenuation in diffuse diseases of spleen and liver

Ultrasonic attenuation has been measured using frequency domain signal processing in clinical trials of patients with liver and spleen diseases. By comparing the variance encountered in local measurements and in measurements at a number of adjoining sites, the need for averaging over large volumes of tissue to avoid the effects of large fluctuations is established. In spleens of patients with myelofibrosis, no correlation between fibrosis and attenuation was found. However it was found that variations in splenic volume were accompanied by inverse changes in attenuation, most likely due to blood pooling. A correlation was found between splenic blood flow per unit organ volume and attenuation. In cirrhotic livers, attenuation was significantly increased with fatty infiltration, but only slightly increased in livers containing minimal fat. These findings tend to reduce the probability of finding successful clinical applications for attenuation slope measurements.     

Perfusion imaging in the pediatric patient

The prevalence of cerebrovascular disease in children is much higher than most clinicians and neuroradiologists suspect, when all primary and secondary causes are considered. Most signal alterations found on MR imaging in childhood central nervous system pathologic conditions result from causes other than a decrease in tissue perfusion. In addition to conventional MR imaging, the ability to assess changes in tissue water by diffusion imaging and tissue perfusion by perfusion-weighted imaging can prove useful to asses cerebral hemodynamics in various pathologic disorders. Exogenous contrast bolus dynamic perfusion-weighted imaging is especially useful in children to differentiate between ischemic injury and other conditions that may alter T2 relaxation, such as demyelination and edema. Perfusion imaging has proved to be a robust and valuable tool to assess the hemodynamic component in childhood CNS disease related to neoplasms and complications from their therapy, cerebrovascular occlusive disease, childhood CNS arteriopathies and trauma.     

体素内不相干运动扩散加权成像在肺部的应用进展

扩散加权成像(diffusion weighted imaging,DWI)技术无需对比剂即可获得组织的水分子扩散情况.然而单指数DWI无法区分组织内单纯水分子扩散和微循环灌注信息,体素内不相干运动扩散加权成像(intravoxel incoherent motion-diffusion weighted imagin...