A novel extended Granger Causal Model approach demonstrates brain hemispheric differences during face recognition learning

Abstract

Two main approaches in exploring causal relationships in biological systems using time-series data are the application of Dynamic Causal model (DCM) and Granger Causal model (GCM). These have been extensively applied to brain imaging data and are also readily applicable to a wide range of temporal changes involving genes, proteins or metabolic pathways. However, these two approaches have always been considered to be radically different from each other and therefore used independently. Here we present a novel approach which is an extension of Granger Causal model and also shares the features of the bilinear approximation of Dynamic Causal model. We have first tested the efficacy of the extended GCM by applying it extensively in toy models in both time and frequency domains and then applied it to local field potential recording data collected from in vivo multi-electrode array experiments. We demonstrate face discrimination learning-induced changes in inter- and intra-hemispheric connectivity and in the hemispheric predominance of theta and gamma frequency oscillations in sheep inferotemporal cortex. The results provide the first evidence for connectivity changes between and within left and right inferotemporal cortexes as a result of face recognition learning.

Figure 1. Results on Toy Model 1.

A. Traces of the time series. B. The causal relationships considered in Toy Model 1 between the three state variables. C. The estimated parameters , , and for the simulated data in Toy Model 1. The initial values of the three parameters are all set to 0. The covariance matrix is first set to decay slowly to achieve faster convergence and then set to decay faster after two hundred time points to ensure a better accuracy. D. Frequency decomposition of all kinds of relationships between the state variables. Significant causal influences are marked by red.

Figure 2. Results on Toy Model 2.

Network structures with and without stimulus. A. Confidence intervals of all links between units. The data is generated with Eq. (15), but we use (without input) in our algorithms and a traditional VAR(10) model to detect the causal influence. B. The network structure of the state variables corresponding to A. Two additional causal relationships are marked by the dashed line. C. Confidence intervals of all links between units. The data is generated with Eq. (16) where and , are generated with normal distribution (with input). D. The network structure of the state variables corresponding to C.

Figure 3. An example of the application of EGCM.

The network detected by EGCM (top-panel) and the corresponding frequency decomposition (bottom-panel) for six randomly selected electrodes. In the frequency decomposition, significant causal influences are marked by red.

Figure 4. Asymmetry between left and right hemisphere in the time domain.

A. A summary of the results in B, but locations in inferotemporal cortex are not precise, only for illustrative purposes. B. The mean connections from left hemisphere to right hemisphere, right hemisphere to left hemisphere and within both regions with the three bars corresponding to the results before learning (blue bar), after learning (green bar), and one month after learning (purple bar) in Sheep B. Significant changes after t-test are marked by arrows (right to left, all pairs are not significant, as indicated by “none”; within the right hemisphere, all pairs are significant, marked by “all”) . For Sheep C, an additional bar (one week after learning) is added (the third bar). Only significant changes from left to right and within the right hemisphere are indicated by arrows. C. Statistic summaries of results in B.

Figure 5. Asymmetry in the frequency domain interactions.

A. Mean and maximum ratio using all the three sheep before and after learning. B. Upper panel: Mean and maximum ratio of sheep B (see Experiment subsection in Methods section) before learning, after learning and one month after learning (see Fig. 4). Bottom panel: Mean and maximum ratio of sheep C before learning (the first bar), immediately after learning (the second bar), one week after learning and one month after learning (the third and the fourth bar). C. Summaries of results in B.