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Benchmarking Granger-causality analysis in a model brain

The definitive version of this post was originally published on October 1 2014 on the PLOS Neuroscience Community website, where I serve as an editor.


What is causation, and how do you proceed to measure it? The question has kept humans thinking for millennia. Now, researchers in Switzerland and Italy have been making inroads in determining causation—albeit in a much restricted sense: that of validating measures of effective brain connectivity from EEG recordings in the context of neural networks. The team, led by Gijs Plomp from the University of Geneva, Switzerland, reported this progress in two recent articles, published in Neuroimage and the European Journal of Neuroscience respectively, that will be briefly discussed here (NB: the articles are not Open Access).

Effective brain connectivity: a measure of causal influence

Studying how the brain is wired (structural connectivity) and how distinct regions work together (functional connectivity) always was an important part of neuroscience research, but the field of brain connectivity has become a particularly hot topic in the last few years. One aspect of this research that has gathered attention–and some controversy–concerns effective connectivity, or the assessment of causal relationships with respect to the activity of brain regions. That is, structural connectivity establishes that areas A and B are physically connected with each other, and functional connectivity that they tend to activate at the same time. But is it possible to determine whether A causes B to activate, or vice versa?

pm_granger_figure1_pubmed

In order to tackle this question, neuroscientists turned towards Granger causality, a method (or rather a family of methods) that had originally been developed to make predictions in economics. Several variants of the original models were designed to adapt them to the characteristics of neural signals, but uncertainty nevertheless persisted regarding the physiological plausibility of the results that they yielded. Scientists were lacking a simple, well-defined biological system with which to test the predictions made by the causal models.

The rat somatosensory system as a large-scale neural network

This is precisely what the authors of the present work have done. Using large-scale high-density EEG recordings in rats, Plomp and colleagues have applied Granger-causal methods to analyze the brain responses to brief deflections of the animals’ whiskers. It turns out that these responses, and the networks of neurons that generate them, are one of the most thoroughly studied systems among mammalian brains. They involve in a well-defined sequence the primary somatosensory cortex of the hemisphere contralateral to tactile stimulation, followed by activation of the motor cortex and transcallosal transfer to the somatosensory and motor cortices ipsilateral to the stimulus.

The setup used to record multi-channel EEG recordings and whisker deflection-evoked responses.

The setup used to record multi-channel EEG recordings and whisker deflection-evoked responses.

This wealth of knowledge allowed the authors to test several variants of Granger-causality measures and compare their predictions to the actual physiology of the whisker sensory network. They found that different variants of Granger-causality analysis sometimes yielded very different predictions regarding the interplay of activity among the areas of the somatosensory-motor network, some of which were clearly at odds with its known physiology. Their findings were published in Neuroimage earlier this year.

Plomp et al. fine-tuned Granger-causality measures to reflect optimally the well-known physiology of whisker-evoked brain responses. (source: http://sites.google.com/site/fbmlab/data)

Plomp et al. fine-tuned Granger-causality measures to reflect optimally the well-known physiology of whisker-evoked brain responses. (source: http://sites.google.com/site/fbmlab/data)

“Against methodological chauvinism”—freely available benchmark dataset

Do the adjustments presented in the present paper represent a panacea that should replace all other algorithms? For Plomp, that is not the case: “There are more flavors of Granger-causality around than we could test.” Accordingly, the authors have made the dataset that they used in the study freely available in order to let other researchers benchmark their particular implementation of effective connectivity measures.

Interhemispheric transfer in the somatosensory system

In a further paper, Plomp, Quairiaux and colleagues have applied their refined algorithms to study transcallosal information transfer between the two primary somatosensory cortices. Using laminar arrays of micro-electrodes that resolved activity in individual cortical layers, they found that inter-hemispheric transfer happened at very early latencies and prominently involved the infragranular layers of the cortex. That research was published online in the European Journal of Neuroscience. The authors are currently busy exploring how Granger-causal modeling can help better understand the propagation of epileptic activity in human patients.

One of the interesting aspects of this work is its focus on large-scale neuronal networks: neurophysiology in animal models has brought us an extremely detailed picture of local cortical function, thanks to the use of ever-denser electrode arrays inserted into small patches of cortex. Studies where the activity of the animal brain is considered as a whole, however, are much rarer. Here, the authors used an array of macro-electrodes that closely resembles traditional electroencephalography as it is performed in humans. The present work shows the necessity of such an approach in order to improve our understanding of the measurements used in human neuroscience.

References

Plomp, G., Quairiaux, C., Michel, C., & Astolfi, L. (2014). The physiological plausibility of time-varying Granger-causal modeling: Normalization and weighting by spectral power NeuroImage, 97, 206-216 DOI: 10.1016/j.neuroimage.2014.04.016

Plomp, G., Quairiaux, C., Kiss, J., Astolfi, L., & Michel, C. (2014). Dynamic connectivity among cortical layers in local and large-scale sensory processing European Journal of Neuroscience DOI: 10.1111/ejn.12687

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