Signal processing methods for brain connectivity

Although the human brain has been studied for centuries, and the advent of non-invasive brain imaging modalities in the last century in particular has led to significant advances, there is much left to discover. Current neuroscientific theory likens the brain to a highly interconnected network whose behavior can be better understood by determining its network connections. Correlation, coherence, Granger causality, and blind source separation (BSS) are frequently used to infer this connectivity. Here I propose novel methods to improve their inference from neuroimaging data. Correlation and coherence suffer from being unable to differentiate between direct and indirect connectivity. While partial correlation and partial coherence can mitigate this problem, standard methods for calculating these measures result in significantly reduced statistical inference power and require greater numbers of samples. To address these drawbacks I propose novel methods based on a graph pruning algorithm that leverage the connectivity sparsity of the brain to improve the inference of partial correlation and partial coherence. These methods are demonstrated in applications. In particular, partial correlation is explored in both cortical thickness data from structural MR images and resting state data from functional MR images, and partial coherence is explored in invasive electrophysiological measurements in non-human primates. Granger causality is able to differentiate between direct and indirect connectivity by default and like partial coherence is readily applicable to time series. However unlike partial coherence, it uses the temporal ordering implied by the time series to infer a type of causality on the connectivity. Despite its differences, the inference of Granger causality can also be improved using a similar graph pruning algorithm, and I describe such an extension here. The method is also applied to explore electrophysiological interactions in non-human primate data. BSS methods seek to decompose a dataset into a linear mixture of sources such that the sources best match some target property, such as independence. The second order blind identification (SOBI) BSS method has a number of properties particularly well-suited for data on the cerebral cortex and relies on the calculation of lagged covariance matrices. However while these lagged covariance matrices are readily available in one-dimensional data, they are not straightforward to calculate on the two-dimensional cortical manifold on which certain types of neuroimaging data lie. To address this, I propose a method for calculating the covariance matrices on the cortical manifold and demonstrate its application to cortical gray matter thickness and curvature data on the cerebral cortex.