"The human brain is an intriguing and complex system. Understanding it not only presents profound implications of our existence, it also provides an important endeavor for scientific and medical research," said David Cai, principal investigator of NYU Abu Dhabi's Computational Modeling of Normal and Abnormal Cortical Processing Project and professor of Mathematics and Neural Science at NYU's Courant Institute.
The computational neuroscience research group at NYUAD headed by Cai has been developing theoretical and computational models of neuronal processing in the normal and abnormal brain to further our understanding of how our brain works in such states. To do so, understanding the relationship between functional connectivity and anatomical connectivity of the brain is vital. Functional connectivity, which can be measured by modern imaging tools such as EEG or fMRI, describes the statistical correlation and dependencies of different areas of the brain.
"We want to help answer the question 'what do these statistical correlations mean structurally and dynamically?'" Cai said. The research team aims to study the underlying network structure of the brain observed through imaging techniques and find out if there is a strong causal relationship in addition to the statistical correlation between these connectivities.
The functional connectivity, causal connectivity, and structural connectivity are different manifestations of underlying dynamics between neurons. However, proving causal connectivity is challenging; statistical methods to indicate causation, beyond establishing correlation, are limited. One such method, the Granger causality test, has been used to predict causality in time-sequenced events. However, it has not been adequately assessed as a tool when applied to nonlinear dynamical systems, such as those in the brain. In 2013, the team published a paper to establish theoretical relationships between the various connectivity and neurophysiological signals in Physical Review Letters. "Our research has demonstrated that the Granger causality approach can actually be very effective in understanding certain structural connectivity using neurophysiological data," Cai explained.
The human brain is an intriguing and complex system. Understanding it not only presents profound implications of our existence, it also provides an important endeavor for scientific and medical research.
New technologies such as multi-electrode recordings can provide extensive data by measuring electrophysiological signals in the brain; but with more than 100 electrodes used in this process, reading and analyzing the information embedded in the recording is a challenging and difficult task. To make this a more effective tool in exploring neural processing, the NYUAD research team is trying to devise new mathematical methods, combining insights from nonlinear network dynamics and highdimensional statistics, to help reveal the information hidden in these recordings. "For neuroscience, it is extremely important to be able to read far more than 100 electrodes simultaneously," Cai added.
In addition to improving the tools and methods for neuroscience research, the team has made significant progress in advancing theoretical knowledge on the visual cortex, with their findings published in the Proceedings of National Academy of Sciences in 2013. Using experimental results on the visual cortex as a basis, the team devised a theoretical computational model with greater opportunity for exploration. For example, in contrast to the traditional computational modeling of visual cortex that were usually limited to an anesthetized brain state of animals, Cai mentioned, "in some sense, the new theoretical approaches suggested that the computational modeling is capable of tackling phenomena which can be associated with the awake state of the brain."
"We are able to confirm certain observations and tell trustworthy data based on our mathematical analysis and network modeling of the dynamics of the visual cortex," he added.
The research team will continue to build a large computational model of various areas of the brain to study the diverse phenomena and to extend their current findings.
With Cai's lead, the research project aims to make computational approaches in neuroscience a truly powerful methodology capable of unifying invasive and noninvasive observations in both healthy and abnormal brain states.