Quantitative magnetic resonance image analysis via the EM algorithm with stochastic variation

Abstract

Quantitative Magnetic Resonance Imaging (qMRI) provides researchers insight into pathological and physiological alterations of living tissue, with the help of which, researchers hope to predict (local) therapeutic efficacy early and determine optimal treatment schedule. However, the analysis of qMRI has been limited to ad-hoc heuristic methods. Our research provides a powerful statistical framework for image analysis and sheds light on future localized adaptive treatment regimes tailored to the individual's response. We assume in an imperfect world we only observe a blurred and noisy version of the underlying pathological/physiological changes via qMRI, due to measurement errors or unpredictable influences. We use a hidden Markov Random Field to model the spatial dependence in the data and develop a maximum likelihood approach via the Expectation-Maximization algorithm with stochastic variation. An important improvement over previous work is the assessment of variability in parameter estimation, which is the valid basis for statistical inference. More importantly, we focus on the expected changes rather than image segmentation. Our research has shown that the approach is powerful in both simulation studies and on a real dataset, while quite robust in the presence of some model assumption violations.

Change point estimation in multi-subject fMRI studies

“…As in the two-state change point problem described above, if we phrase the problem as one of missing data, where the missing data is the set of class labels X , we can again employ an EM-algorithm. In our implementation we use an EM-algorithm with stochastic variation (Zhang, Johnson, Little, and Cao, 2008) to estimate clusters. Using this approach the expectation of the conditional log likelihood given the observed data is computed stochastically in the E-step using the Swendsen-Wang algorithm (Swendsen and Wang, 1987); an efficient sampler developed specifically for the Potts model.…”

“…The appropriate number of clusters is determined using the AIC-criterion (Akaike, 1973). For more details about the EM-algorithm we refer interested readers to Zhang et al (Zhang, Johnson, Little, and Cao, 2008). …”

“…As a final step of our analysis, we perform spatial clustering of voxels according to onset and duration values and anatomical location using a hidden Markov random field model. These types of models have been successfully used to segment images based on structural characteristics (Zhang, Brady, and Smith, 2001; Zhang, Johnson, Little, and Cao, 2008). Here we use a multivariate hidden Markov random field (HMRF) model to estimate the grouping of voxels based on their activation characteristics.…”

Evaluation of image registration spatial accuracy using a Bayesian hierarchical model

“…To account for this variation, we propose a Bayesian hierarchical model to borrow strength across readers, DIRs, and patient images. Related Bayesian hierarchical spatial models have been proposed by Xu, Johnson, Nichols and Nee (2009) to analyze inter-subject variability in functional MRI image data, and Zhang, Johnson, Little and Yao (2008) to identify pathological alternations of gliomas using quantitative MRI image data. We also describe an efficient Markov chain Monte Carlo algorithm to fit the proposed model.…”

A Bayesian image analysis of radiation induced changes in tumor vascular permeability

“…We then discuss its implementation in Section 3. In Section 4, we present results from simulation studies and compare the results with the EM algorithm of Zhang et al (2008). We also investigate the performance under violations to model assumptions and present results from the motivating example.…”