Diffusion-based spatial priors for imaging.

We describe a Bayesian scheme to analyze images, which uses spatial priors encoded by a diffusion kernel, based on a weighted graph Laplacian. This provides a general framework to formulate a spatial model, whose parameters can be optimised. The standard practice using the software statistical parametric mapping (SPM) is to smooth imaging data using a fixed Gaussian kernel as a pre-processing step before applying a mass-univariate statistical model (e.g., a general linear model) to provide images of parameter estimates (Friston et al., 2006). This entails the strong assumption that data are generated smoothly throughout the brain. An alternative is to include smoothness in a multivariate statistical model (Penny et al., 2005). The advantage of the latter is that each parameter field is smoothed automatically, according to a measure of uncertainty, given the data. Explicit spatial priors enable formal model comparison of different prior assumptions, e.g. that data are generated from a stationary (i.e. fixed throughout the brain) or non-stationary spatial process. We describe the motivation, background material and theory used to formulate diffusion-based spatial priors for fMRI data and apply it to three different datasets, which include standard and high-resolution data. We compare mass-univariate ordinary least squares estimates of smoothed data and three Bayesian models spatially independent, stationary and non-stationary spatial models of non-smoothed data. The latter of which can be used to preserve boundaries between functionally selective regional responses of the brain, thereby increasing the spatial detail of inferences about cortical responses to experimental input

Semiparametric Bayesian models for human brain mapping

Functional magnetic resonance imaging (fMRI) has led to enormous progress in human brain mapping. Adequate analysis of the massive spatiotemporal data sets generated by this imaging technique, combining parametric and non-parametric components, imposes challenging problems in statistical modelling. Complex hierarchical Bayesian models in combination with computer-intensive Markov chain Monte Carlo inference are promising tools.The purpose of this paper is twofold. First, it provides a review of general semiparametric Bayesian models for the analysis of fMRI data. Most approaches focus on important but separate temporal or spatial aspects of the overall problem, or they proceed by stepwise procedures. Therefore, as a second aim, we suggest a complete spatiotemporal model for analysing fMRI data within a unified semiparametric Bayesian framework. An application to data from a visual stimulation experiment illustrates our approach and demonstrates its computational feasibility

Fast Fiber Orientation Estimation in Diffusion MRI from kq-Space Sampling and Anatomical Priors

High spatio-angular resolution diffusion MRI (dMRI) has been shown to provide accurate identification of complex fiber configurations, albeit at the cost of long acquisition times. We propose a method to recover intra-voxel fiber configurations at high spatio-angular resolution relying on a kq-space under-sampling scheme to enable accelerated acquisitions. The inverse problem for reconstruction of the fiber orientation distribution (FOD) is regularized by a structured sparsity prior promoting simultaneously voxelwise sparsity and spatial smoothness of fiber orientation. Prior knowledge of the spatial distribution of white matter, gray matter and cerebrospinal fluid is also assumed. A minimization problem is formulated and solved via a forward-backward convex optimization algorithmic structure. Simulations and real data analysis suggest that accurate FOD mapping can be achieved from severe kq-space under-sampling regimes, potentially enabling high spatio-angular dMRI in the clinical setting.Comment: 10 pages, 5 figures, Supplementary Material

Image-Guided Diffuse Optical Fluorescence Tomography Implemented with Laplacian-Type Regularization

A promising method to incorporate tissue structural information into the reconstruction of diffusion-based fluorescence imaging is introduced. The method regularizes the inversion problem with a Laplacian-type matrix, which inherently smoothes pre-defined tissue, but allows discontinuities between adjacent regions. The technique is most appropriately used when fluorescence tomography is combined with structural imaging systems. Phantom and simulation studies were used to illustrate significant improvements in quantitative imaging and linearity of response with the new algorithm. Images of an inclusion containing the fluorophore Lutetium Texaphyrin (Lutex) embedded in a cylindrical phantom are more accurate than in situations where no structural information is available, and edge artifacts which are normally prevalent were almost entirely suppressed. Most importantly, spatial priors provided a higher degree of sensitivity and accuracy to fluorophore concentration, though both techniques suffer from image bias caused by excitation signal leakage. The use of spatial priors becomes essential for accurate recovery of fluorophore distributions in complex tissue volumes. Simulation studies revealed an inability of the “no-priors” imaging algorithm to recover Lutex fluorescence yield in domains derived from T1 weighted images of a human breast. The same domains were reconstructed accurately to within 75% of the true values using prior knowledge of the internal tissue structure. This algorithmic approach will be implemented in an MR-coupled fluorescence spectroscopic tomography system, using the MR images for the structural template and the fluorescence data for region quantification

Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments

Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study focuses on techniques for analyzing Single Particle Tracking (SPT) data experiencing abrupt state changes. We demonstrate the approach on GFP tagged chromatids experiencing metaphase in yeast cells and probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes are induced by factors such as microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, etc. Simulations are used to demonstrate the relevance of the approach in more general SPT data analyses. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One publication available freely as an open-access article at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763

A Bayesian spatial random effects model characterisation of tumour heterogeneity implemented using Markov chain Monte Carlo (MCMC) simulation

The focus of this study is the development of a statistical modelling procedure for characterising intra-tumour heterogeneity, motivated by recent clinical literature indicating that a variety of tumours exhibit a considerable degree of genetic spatial variability. A formal spatial statistical model has been developed and used to characterise the structural heterogeneity of a number of supratentorial primitive neuroecto-dermal tumours (PNETs), based on diffusionweighted magnetic resonance imaging. Particular attention is paid to the spatial dependence of diffusion close to the tumour boundary, in order to determine whether the data provide statistical evidence to support the proposition that water diffusivity in the boundary region of some tumours exhibits a deterministic dependence on distance from the boundary, in excess of an underlying random 2D spatial heterogeneity in diffusion. Tumour spatial heterogeneity measures were derived from the diffusion parameter estimates obtained using a Bayesian spatial random effects model. The analyses were implemented using Markov chain Monte Carlo (MCMC) simulation. Posterior predictive simulation was used to assess the adequacy of the statistical model. The main observations are that the previously reported relationship between diffusion and boundary proximity remains observable and achieves statistical significance after adjusting for an underlying random 2D spatial heterogeneity in the diffusion model parameters. A comparison of the magnitude of the boundary-distance effect with the underlying random 2D boundary heterogeneity suggests that both are important sources of variation in the vicinity of the boundary. No consistent pattern emerges from a comparison of the boundary and core spatial heterogeneity, with no indication of a consistently greater level of heterogeneity in one region compared with the other. The results raise the possibility that DWI might provide a surrogate marker of intra-tumour genetic regional heterogeneity, which would provide a powerful tool with applications in both patient management and in cancer research