The Geometries of Neuronal Responses

We are trying to measure the texture and shape of brain activity in humans using the non-invasive medical imaging technique called functional Magnetic Resonance Imaging (fMRI). This is a very powerful way for scientists and clinicians to see the brain in action. However, currently we blur these images to get a general idea of the brain’s response, which makes it difficult to pin down exactly which bit is active. A way to get better quality images would be to blur only parts of the image, but herein lies the problem; how do we identify these regions? This is challenging as it requires an idea of how different regions of the brain talk to each other and many calculations to compute the final image. Advances in processing general images, such as photographs, and Bayesian modelling, which deals gracefully with uncertainty inherent in this problem, can be used to do this. An important application is measuring changes in shape of activity during the early stages of Age-related Macular Degeneration (an acquired disease affecting the eyes). This research is hoped to improve human health by enabling more informed decisions about fMRI data in scientific and medical contexts, which could impact on rehabilitation strategies.

Aims
The aims are to (i) build on existing expertise gained whilst working at the Wellcome Trust Centre for Neuroimaging on an advanced method to analysis human brain imaging data that uses a spatial model of functional responses informed by geometric features, e.g. boundaries between functionally selective regions, (ii) acquire skills necessary to generalize this approach to non-Cartesian images, e.g. where each spatial location contains a matrix instead of a single number, (iii) develop the method in an application-based approach using data that is better explained by such images, (iv) take an inter-disciplinary approach involving neuroscientists and computer scientists, (v) use a hypothesis-driven Bayesian analysis, where a hypothesis is represented by a graphical model comprising nodes (random variables) connected by edges (conditional dependences), (vi) approximate the posterior probability of a hypothesis using variational Bayes (VB), (vii) make inferences about spatially distributed neuronal responses, given this posterior, (viii) apply the method to functional magnetic resonance imaging (fMRI) data collected from patients and high resolution fMRI and magneto-encephalographic (MEG) data from normal subjects, (ix) assess the accuracy of a VB approximation against the full model.


Objectives
To (i) produce freely available software for users and (ii) publish results of each application of our analysis in peer reviewed journals.


Design
The project is divided into theoretical development and applications. All data will be collected by our collaborators from normal subjects and patients during visual experiments. fMRI data will be used during the first two years and MEG in the second and third. The first year of each will involve theoretical development and data analysis in the second. All results will be collated in the final year.


Methodology
We will use a Bayesian paradigm to learn empirical priors of a hierarchical model. These spatial priors will be implemented using spectral methods on graphs, in particular the diffusion kernel of a weighted graph Laplacian. This will be generalized to non-Cartesian images using Lie group theory.

Scientific and medical opportunities
This research promises to increase the spatial precision of statistical images and allow neuroimagers to make inferences about the spatial extent of brain responses, currently not possible with SPM (statistical parametric mapping) software. We expect this to benefit both scientific and medical users by enabling more informed decisions about data. In particular, we hope this research will enable investigators to evaluate whether acquired retinal lesions in humans lead to cortical reorganization, which could impact on rehabilitation programmes.