Weighing roughly one-and-a-half kilos, with a volume more or less half that of a medium-sized coconut, the human brain with its about 100 billion neurons, each with some 10,000 interconnections, is probably the most complex structure that we know. Yet, that structural complexity hardly begins to hint at the incredible variety and the enormity of its functions. Surely, this is a case of a whole that is vastly greater than the sum of its parts.
The brain is the seat of our consciousness and of our emotions, the repository of our memories. It synthesizes and analyzes our sensory inputs, decides what behavioral responses are appropriate or necessary to promote our continued survival. And when parts of it fail to perform properly, we are saddled with depression, or schizophrenia, or Alzheimer’s disease, or other such debilitating disorders. The ancient Greek physician Hippocrates put it well: “Men ought to know that from nothing else but the brain come joys, delights, laughter and sports, and sorrows, griefs, despondency, and lamentations.â€
No wonder the brain has been the subject of intense scientific scrutiny for a very long time. A currently active area of study concerns the “connectivities†of the brain. Physiologists distinguish “structural†or “anatomical†connectivity from “functional†connectivity and both from “effective†connectivity. The first merely means the physical connections between groups of neurons. The second refers to correlated behaviors of different brain regions. The last involves the transfer of information from one region to another, possibly affecting the behavior of the latter — a causal connection.
Anatomical connectivity has traditionally been studied invasively. That is, by dissecting and staining dead brains. This technique is not very effective for looking at the other two types. There are a number of noninvasive techniques used to study these. Here, I discuss one that my colleagues and students in the United States and at Mindanao State University-Iligan Institute of Technology (MSU-IIT) have been using to analyze brain electrical activity namely, time series analysis of electroencephalographic (EEG) data.
EEGs record the summed electrical activity of a few tens of thousands of neurons. This activity consists of oscillations of electrical potential (voltage) with amplitudes of the order of one ten-thousandths of a volt at frequencies ranging from about a half to approximately 100 cycles per second. To obtain the EEG, electrodes are placed on the scalp. Sometimes they are placed on or in the cortex (the outermost layer of the brain) through a hole in the skull. Variations in the electrical potential of one location relative to another are measured, amplified, and recorded to yield either traces on graph paper or, more commonly nowadays, digital files in a computer. Depending on the nature of the study, the data may be recorded from a few to well over a hundred sites.
Physicians often use visual observation of EEG traces to diagnose some neurological disorders, but seeking functional or effective connectivities between different brain regions requires analysis of the records using more sophisticated computational tools. Traditional statistical tools are used to measure linear correlations between data. That is, if data from one site are plotted against those from another, do they fall more or less on a straight line? Measures of linear correlation tell us how closely they do — the closer the plotted points are to a straight line, the more correlated. If the resulting graph shows a pattern that is more complicated than a straight line, there may exist nonlinear correlations between the data which linear measures cannot capture. One quantity that measures nonlinear correlations is “mutual information,†which tells us how much of one data set we can predict by measuring the other.
Correlations, whether linear or nonlinear, only indicate how similar two data sets are. They do not tell us if one data stream is transferring information to the other, or is influencing the time evolution of the other. They do not give us information about causal relationships. One quantity that does this is “transfer entropy†which measures the influence of one data set on the time evolution of the other.
In the past few years, my colleagues and students at MSU-IIT have undertaken a number of studies exploring the feasibility of using the measures described above to study how patterns of connectivity in the human brain change when the visual system is engaged. Their data consisted of 10-channel EEG recordings from 13 healthy human subjects taken when the subjects had their eyes open, and again when they had their eyes closed. The subjects were otherwise not engaged in any specific cognitive activities. The MSU-IIT studies have shown that:
• The usual statistical measures of linear correlation are all equally effective in distinguishing between the eyes open and eyes closed conditions.
• The different scalp sites are more linearly correlated when the eyes are closed indicating that when the visual system is not engaged, different brain regions are generating similar signals. This, however, changes once the eyes are opened. Mutual information tells pretty much the same story.
• Transfer entropy tells a much more dramatic story — average information transfer between sites doubles when the eyes are opened. The largest information transfers are to and from the occipital lobe, at the back of the head, which is greatly involved in vision. There are also considerable transfers of information to and from the frontal lobes, at the front of the head, which are associated with attention, short-term memory tasks, planning, and motivation.
These results are preliminary. There are other, more challenging and more interesting questions that need to be asked such as, are different cognitive activities characterized by distinctive patterns of connectivity? Do the connectivities change with neurological disease or with brain injury? Can knowledge of these changes eventually be used by physicians for diagnosis or to assist with the evaluation of therapy? More work clearly awaits.
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Alfonso M. Albano is Marion Reilly professor of Physics Emeritus at Bryn Mawr College in Bryn Mawr, Pennsylvania, USA. He is a corresponding member of the NAST. He can be reached at aalbano2010@gmail.com.