Causal Measures of Structure and Plasticity in Simulated and Living Neural Networks

A major goal of neuroscience is to understand the relationship between neural structures and their function. Recording of neural activity with arrays of electrodes is a primary tool employed toward this goal. However, the relationships among the neural activity recorded by these arrays are often highly complex making it problematic to accurately quantify a network's structural information and then relate that structure to its function. Current statistical methods including cross correlation and coherence have achieved only modest success in characterizing the structural connectivity. Over the last decade an alternative technique known as Granger causality is emerging within neuroscience. This technique, borrowed from the field of economics, provides a strong mathematical foundation based on linear auto-regression to detect and quantify “causal” relationships among different time series. This paper presents a combination of three Granger based analytical methods that can quickly provide a relatively complete representation of the causal structure within a neural network. These are a simple pairwise Granger causality metric, a conditional metric, and a little known computationally inexpensive subtractive conditional method. Each causal metric is first described and evaluated in a series of biologically plausible neural simulations. We then demonstrate how Granger causality can detect and quantify changes in the strength of those relationships during plasticity using 60 channel spike train data from an in vitro cortical network measured on a microelectrode array. We show that these metrics can not only detect the presence of causal relationships, they also provide crucial information about the strength and direction of that relationship, particularly when that relationship maybe changing during plasticity. Although we focus on the analysis of multichannel spike train data the metrics we describe are applicable to any stationary time series in which causal relationships among multiple measures is desired. These techniques can be especially useful when the interactions among those measures are highly complex, difficult to untangle, and maybe changing over time.