This is how mathematics helps us understand mental illness

How is it possible that our sophisticated brain is capable of deceiving us by perceiving voices that do not exist with the same clarity with which we hear those of those who speak to us? How can it make us feel so miserable for no reason that we want to stop living? Or prevent us from pushing aside ideas that we recognize as completely useless?

These are three very frequent questions in patients with psychiatric problems, whose cerebral foundations we do not know. It is surprising because, as long as we accept that human mental activity is based in the brain, the logical thing would be to find an alteration in brain function at the base of those problems. So why is it so hard for us to find it?

There are several reasons that can help us understand our failure to identify these disturbances.

The main one is that we do not understand the basis of normal mental activity. In the rest of medicine, we define diseases as disturbances in the known functions of organs or systems. The heart pumps blood, and the components that allow it to do so can be altered. For example, we can find pump failures (myocardial diseases, in turn of various causes), valves (which narrow or do not close well) or blood vessels (such as high blood pressure).

In the case of the brain, however, no one knows for sure how the material activity of neurons (their bioelectric changes, mediated by the passage of ions from one side of their membrane to the other) give rise to that immaterial property to which we call mind.

Mathematics to the rescue

What we do know is that mental contents depend on the synchronous activity of neuronal groups distributed throughout much or all of the brain. This rapidly changing activity manifests itself in very faint electric and magnetic fields. These fields can be collected and analyzed with techniques such as electroencephalography and magnetoencephalography.

Analyzing with sophisticated mathematical procedures the changes in these fields during the performance of a task, we can get to assess the brain correlates of mental activity. Which is already a step.

In addition, some techniques allow us to assess the changes in these fields in each sensor in which we collect them. For example, those that allow the analysis of the regularity or entropy of the signal and its changes with mental activity.

Other techniques help to understand the characteristics of the organization of the brain network as a whole , such as techniques derived from graph theory. Using measurements based on the synchronization of the signals collected in different sensors, these techniques make it possible to assess the global integration of the network and its specialization by areas, as well as the balance between both parameters. As the brain functions in an integrated way in terms of mental function, we hope that mathematics will help us better understand what changes it shows in mental disorders.

Our group, among others, has applied these analyzes to the study of schizophrenia . So far we have found in these patients a hyperactive brain and unable to modulate adequately, even to adapt to simple tasks.

In addition, the activity of this brain may have less organized overall characteristics than those of other people. For example, patients with this disease show less functional communication between different areas that should be synchronized. In other words, your brain seems to function in a less integrated way, making it difficult for your mental activity.

Not all the mentally ill are the same

Today, we make diagnoses of mental illnesses based on combinations of symptoms reported by patients or signs that we observe in them. These diagnostic modes are essentially agreements between experts, which change as knowledge progresses. But the net result is that, for many disorders, the possible diagnoses allow a huge variety of patients to receive them.

This implies that the group of people who receive one of these diagnoses, such as schizophrenia, is very heterogeneous. This is one of the possible sources of error when trying to define the brain basis of a problem like this. We may actually be trying to identify what people who have different conditions underlying their different symptoms have in common in the brain.

If so, the first thing we should do is identify groupings (“clusters”) within a heterogeneous group, applying the statistics. The idea is to use the common alterations of certain brain parameters to find out which groups can be defined within a psychiatric syndrome. These cluster analyzes (or groups within a given diagnosis) have been and are used to find what diseases are within those diagnoses.

Our team has identified, for example, that within what we now call schizophrenia there is a population with marked alterations in the connections between brain areas. That is, a group with a lower efficiency of the fibers that connect relevant areas to each other. In this group, this connective alteration manifests itself in cognitive alterations . For example, memory, attention, speed and ability to solve problems.

These alterations in brain connections and cognitive ability did not occur in other patients who, however, had received the same diagnosis of schizophrenia. One possible conclusion is that they are, in fact, different diseases, the common study of which obscures the results regarding their possible brain bases.

Perhaps when it comes to mental health, mathematics can make the invisible visible.