Fully Bayesian Inference for Structural MRI: Application to Segmentation and Statistical Analysis of T2-Hypointensities.

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: [Formula: see text]; range, [Formula: see text]). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data

Trace plots of the voxel-wise regression model.

<p>Precision parameters (left) and main effect of age for two selected voxels (right). Corresponding MNI coordinates are (top) and (bottom).</p

Segmentation of simulated T2-hypointensities.

<p>Manually delineated T2-hypointensities were added as an extra class to BrainWebs discrete anatomical model. This way, T1-weighted, T2-weighted and FLAIR images were simulated. Hypointensities were then segmented from the simulated images.</p

Segmentation and normalization of T2-hypointensity.

<p>T2-weighted and FLAIR images are first coregistered to the T1-weighted images and then prepared for the segmentation of T2-hypointensities, which includes correction of T2-weighted and FLAIR images for magnetic field inhomogeneity by VBM8 and segmentation of T1-weighted images into the tissue classes of GM, WM, and CSF. These images are then used to segment hypointensities. The resulting T2-hypointensity images are normalized in two steps: First, T1-weighted images are affine normalized and respective parameters applied to FLAIR and T2-hypointensity images. Second, affine normalized T1-weighted and FLAIR images of all subjects are used to produce individual flow fields by DARTEL; these flow fiields are then applied to T2-hypointensity images.</p

Estimated regression coefficients of the simulated data.

<p>Posterior mean image for unsmoothed data of the approach proposed in this paper is shown in the upper left corner. Results of SPM's frequentist and Bayesian implementation are shown in the second and third column for unsmoothed (upper row) and smoothed (lower row) data, respectively. The true parameter image is shown in the lower left corner. The approach proposed in this paper performs best as demonstrated by the MSE and by visual inspection.</p

Trace plots for the Gibbs sampler of the mixture model for T2-hypointensity segmentation of one randomly chosen subject.

<p>Components of (left) and of (right). See text for details.</p

Effect of age on T2-hypointensity.

<p>Increasing T2-hypointensity with increasing age is projected onto the mean normalized FLAIR image. Axial slices are indicated in the upper row. Significance is color-coded according to the -value (Panels A and B) and posterior probability (Panel C) as indicated by the bars on the right. A–B) Results derived from the frequentist approach as implemented in SPM8 are shown after application of different statistical thresholds (Panel A, false-discovery rate 0.05; Panel B, uncorrected -value 0.05) and different smoothing kernels (upper rows, 4 mm; lower rows, 8 mm. C) Fully Bayesian inference could not only identify the globus pallidus, substantia nigra, and red nucleus but also the dentate nucleus. This result was largely independent of smoothing although more voxels were identified after smoothing with 4 mm.</p