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Bayesian Modeling of Complex-valued fMRI Signals

  • Author(s): Yu, Cheng-Han
  • Advisor(s): Prado, Raquel
  • et al.
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Public License
Abstract

Detecting which voxels or brain regions are activated by an external stimulus is a common objective in functional magnetic resonance (fMRI) studies, however, most studies use magnitude-only fMRI data and discard the phase data. We consider a set of statistical models for detecting brain activation at the voxel level that make use of the entire complex-valued fMRI time courses. We develop a regression model on the Cartesian representation of the complex fMRI time courses and use a complex normal spike-and-slab mixture prior on the parameters that determine brain activation at the voxel level. Our model also incorporates autoregressive components to capture temporal structure in the data. We then develop a general complex-valued expectation maximization algorithm (C-EMVS) that allows us to detect brain activation in a computationally efficient manner within this modeling framework.

To further improve detection performance, a computationally efficient Bayesian spatial model is developed to explicitly capture the spatial dependence across voxels through kernel convolution. This model encourages voxels to be activated in clusters and is able to eliminate isolated voxels that are incorrectly labeled as active in models that do not assume a spatial structure. The kernel-based method significantly reduces the computational burden compared to other spatial approaches, as it leads to dimension reduction.

We then generalize the spatial model mentioned above from a single-subject to a multi-subject model, and use the information from multiple subjects to infer brain connectivity. This model is general and practical due to its ability to infer brain activation and connectivity simultaneously in multi-subject studies.

We illustrate the performance of our statistical models and tools in extensive and physically realistic simulation studies and also in the analysis of human complex-valued fMRI data from a task-related study.

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