Ashish Raj

Network diffusion accurately models the relationship between structural and functional brain connectivity networks.

The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brains long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways.

Bayesian Parallel Imaging With Edge-Preserving Priors

Existing parallel MRI methods are limited by a fundamental trade‐off in that suppressing noise introduces aliasing artifacts. Bayesian methods with an appropriately chosen image prior offer a promising alternative; however, previous methods with spatial priors assume that intensities vary smoothly over the entire image, resulting in blurred edges. Here we introduce an edge‐preserving prior (EPP) that instead assumes that intensities are piecewise smooth, and propose a new approach to efficiently compute its Bayesian estimate. The estimation task is formulated as an optimization problem that requires a nonconvex objective function to be minimized in a space with thousands of dimensions. As a result, traditional continuous minimization methods cannot be applied. This optimization task is closely related to some problems in the field of computer vision for which discrete optimization methods have been developed in the last few years. We adapt these algorithms, which are based on graph cuts, to address our optimization problem. The results of several parallel imaging experiments on brain and torso regions performed under challenging conditions with high acceleration factors are shown and compared with the results of conventional sensitivity encoding (SENSE) methods. An empirical analysis indicates that the proposed method visually improves overall quality compared to conventional methods. Magn Reson Med 57:8–21, 2007.

A graph cut algorithm for generalized image deconvolution

The goal of deconvolution is to recover an image x from its convolution with a known blurring function. This is equivalent to inverting the linear system y = Hx. In this paper, we consider the generalized problem where the system matrix H is an arbitrary nonnegative matrix. Linear inverse problems can be solved by adding a regularization term to impose spatial smoothness. To avoid oversmoothing, the regularization term must preserve discontinuities; this results in a particularly challenging energy minimization problem. Where H is diagonal, as occurs in image denoising, the energy function can be solved by techniques such as graph cuts, which have proven to be very effective for problems in early vision. When H is nondiagonal, however, the data cost for a pixel to have a intensity depends on the hypothesized intensities of nearby pixels, so existing graph cut methods cannot be applied. This paper shows how to use graph cuts to obtain a discontinuity preserving solution to a linear inverse system with an arbitrary non-negative system matrix. We use a dynamically chosen approximation to the energy which can he minimized by graph cuts; minimizing this approximation also decreases the original energy. Experimental results are shown for MRI reconstruction from Fourier data

Network Diffusion Model of Progression Predicts Longitudinal Patterns of Atrophy and Metabolism in Alzheimer’s Disease

Alzheimers disease pathology (AD) originates in the hippocampus and subsequently spreads to temporal, parietal, and prefrontal association cortices in a relatively stereotyped progression. Current evidence attributes this orderly progression to transneuronal transmission of misfolded proteins along the projection pathways of affected neurons. A network diffusion model was recently proposed to mathematically predict disease topography resulting from transneuronal transmission on the brains connectivity network. Here, we use this model to predict future patterns of regional atrophy and metabolism from baseline regional patterns of 418 subjects. The model accurately predicts end-of-study regional atrophy and metabolism starting from baseline data, with significantly higher correlation strength than given by the baseline statistics directly. The models rate parameter encapsulates overall atrophy progression rate; group analysis revealed this rate to depend on diagnosis as well as baseline cerebrospinal fluid (CSF) biomarker levels. This work helps validate the model as a prognostic tool for Alzheimers disease assessment.

The Wiring Economy Principle: Connectivity Determines Anatomy in the Human Brain

Minimization of the wiring cost of white matter fibers in the human brain appears to be an organizational principle. We investigate this aspect in the human brain using whole brain connectivity networks extracted from high resolution diffusion MRI data of 14 normal volunteers. We specifically address the question of whether brain anatomy determines its connectivity or vice versa. Unlike previous studies we use weighted networks, where connections between cortical nodes are real-valued rather than binary off-on connections. In one set of analyses we found that the connectivity structure of the brain has near optimal wiring cost compared to random networks with the same number of edges, degree distribution and edge weight distribution. A specifically designed minimization routine could not find cheaper wiring without significantly degrading network performance. In another set of analyses we kept the observed brain network topology and connectivity but allowed nodes to freely move on a 3D manifold topologically identical to the brain. An efficient minimization routine was written to find the lowest wiring cost configuration. We found that beginning from any random configuration, the nodes invariably arrange themselves in a configuration with a striking resemblance to the brain. This confirms the widely held but poorly tested claim that wiring economy is a driving principle of the brain. Intriguingly, our results also suggest that the brain mainly optimizes for the most desirable network connectivity, and the observed brain anatomy is merely a result of this optimization.

T2prep three‐dimensional spiral imaging with efficient whole brain coverage for myelin water quantification at 1.5 tesla

Quantitative assessment of myelination is important for characterizing tissue damage and evaluating response to therapy in white matter diseases such as multiple sclerosis. Conventional multicomponent T2 relaxometry based on the two‐dimensional (2D) multiecho spin echo sequence is a promising method to measure myelin water fraction, but its clinical utility is impeded by the prohibitively long data acquisition and limited brain coverage. The objective of this study was to develop a signal‐to‐noise ratio efficient 3D T2prep spiral gradient echo (3D SPIRAL) sequence for full brain T2 relaxometry and to validate this sequence using 3D multiecho spin echo as reference standard in healthy brains at 1.5 T. 3D SPIRAL was found to provide similar myelin water fraction in six selected white and gray matter areas using region‐of‐interest signal averaging analysis (N = 7, P > 0.05). While 3D multiecho spin echo only provided partial brain coverage, 3D SPIRAL enabled whole brain coverage with a fivefold higher acquisition speed per imaging slice and similar signal‐to‐noise ratio efficiency. Both 3D sequences provided superior signal‐to‐noise ratio efficiency when compared to the conventional 2D multiecho spin echo approach. Magn Reson Med, 2012.

Bayesian algorithm using spatial priors for multiexponential T2 relaxometry from multiecho spin echo MRI

Multiexponential T2 relaxometry is a powerful research tool for detecting brain structural changes due to demyelinating diseases such as multiple sclerosis. However, because of unusually high signal‐to‐noise ratio requirement compared with other MR modalities and ill‐posedness of the underlying inverse problem, the T2 distributions obtained with conventional approaches are frequently prone to noise effects. In this article, a novel multivoxel Bayesian algorithm using spatial prior information is proposed. This prior takes into account the expectation that volume fractions and T2 relaxation times of tissue compartments change smoothly within coherent brain regions. Three‐dimensional multiecho spin echo MRI data were collected from five healthy volunteers at 1.5 T and myelin water fraction maps were obtained using the conventional and proposed algorithms. Compared with the conventional method, the proposed method provides myelin water fraction maps with improved depiction of brain structures and significantly lower coefficients of variance in white matter. Magn Reson Med, 2012.

The Network Modification (NeMo) Tool: Elucidating the Effect of White Matter Integrity Changes on Cortical and Subcortical Structural Connectivity

Accurate prediction of brain dysfunction caused by disease or injury requires the quantification of resultant neural connectivity changes compared with the normal state. There are many methods with which to assess anatomical changes in structural or diffusion magnetic resonance imaging, but most overlook the topology of white matter (WM) connections that make up the healthy brain network. Here, a new neuroimaging software pipeline called the Network Modification (NeMo) Tool is presented that associates alterations in WM integrity with expected changes in neural connectivity between gray matter regions. The NeMo Tool uses a large reference set of healthy tractograms to assess implied network changes arising from a particular pattern of WM alteration on a region- and network-wise level. In this way, WM integrity changes can be extrapolated to the cortices and deep brain nuclei, enabling assessment of functional and cognitive alterations. Unlike current techniques that assess network dysfunction, the NeMo tool does not require tractography in pathological brains for which the algorithms may be unreliable or diffusion data are unavailable. The versatility of the NeMo Tool is demonstrated by applying it to data from patients with Alzheimers disease, fronto-temporal dementia, normal pressure hydrocephalus, and mild traumatic brain injury. This tool fills a gap in the quantitative neuroimaging field by enabling an investigation of morphological and functional implications of changes in structural WM integrity.

Widespread white matter degeneration preceding the onset of dementia

Brain atrophy in subjects with mild cognitive impairment (MCI) introduces partial volume effects, limiting the sensitivity of diffusion tensor imaging to white matter microstructural degeneration. Appropriate correction isolates microstructural effects in MCI that might be precursors of Alzheimers disease (AD).

A pilot study of quantitative MRI measurements of ventricular volume and cortical atrophy for the differential diagnosis of normal pressure hydrocephalus.

Current radiologic diagnosis of normal pressure hydrocephalus (NPH) requires a subjective judgment of whether lateral ventricular enlargement is disproportionate to cerebral atrophy based on visual inspection of brain images. We investigated whether quantitative measurements of lateral ventricular volume and total cortical thickness (a correlate of cerebral atrophy) could be used to more objectively distinguish NPH from normal controls (NC), Alzheimers (AD), and Parkinsons disease (PD). Volumetric MRIs were obtained prospectively from patients with NPH (n = 5), PD (n = 5), and NC (5). Additional NC (n = 5) and AD patients (n = 10) from the ADNI cohort were examined. Although mean ventricular volume was significantly greater in the NPH group than all others, the range of values overlapped those of the AD group. Individuals with NPH could be better distinguished when ventricular volume and total cortical thickness were considered in combination. This pilot study suggests that volumetric MRI measurements hold promise for improving NPH differential diagnosis.