Outsmart Alzheimer’s disease with mathematics

Photo: Pedro Ruiz The Duty
Habib Benali teaches in the Department of engineering of Concordia University.

The day when science will allow us to prevent and treat neurodegenerative diseases such as Alzheimer’s or Parkinson’s is not yet arrived, but we could approach it through the power of mathematics.


“Is that a mathematician has its word to say in the context of a process of degeneration of the Alzheimer type, for example ? My deep conviction is that yes, ” says professor Habib Benali, who teaches in the Department of engineering of Concordia University.


At present, imaging techniques allow us to delve into the human brain and detect the presence of a neurodegenerative disease at a given time. But when the diagnosis is made, it is often too late, the available treatments are only able to limit the development or the symptoms of the disease.


Among the many researchers who are trying to provide solutions to some 564 000 Canadians with Alzheimer’s disease or a related dementia, professor Benali borrows an unexpected way. It uses the mathematical modeling and neuro-imaging to predict the onset of diseases many years before they appear.


“Instead of detecting a disease, which is the domain of diagnosis, the paradigm changes a bit,” explains the scientific director interim of PERFORM, an interdisciplinary research center of Concordia devoted to different aspects of human health.


Follow the path


In the case of Alzheimer’s disease, the work of Habib Benali interested in particular to the tau protein. The presence of this protein in certain areas of the brain may be associated with normal ageing or the development of the disease.


By collecting information on the physiology and history of the patient studied, the professor tries to establish what he called a ” trajectory “. To do this, it takes a “picture” of the brain at a given time, and builds a mathematical model taking into account the characteristics of the subject to predict the brain activity in the future. Two years later, he takes a photo and checks if it corresponds to the predictions of the mathematical model.


“If it holds up, so much the better. Otherwise, we adapt the parameters to find the good, ” he said. The challenge is to establish the trajectory of physiological development of the disease, and at the same time, to design intervention tools that will stop it. “


Personalized treatment


The approach of professor Benali opens the door to treatments that are more personalized. “We’re no longer in a prediction model, general,” says he, taking the example of the weather.


Meteorologists can predict that it will snow today in Montreal tomorrow thanks to a mathematical model that takes into account a set of parameters. But in reality, it may be that there’s precipitation in the north of the island, and that the south is spared.


In the same way, a human brain can evolve differently from another, hence the importance of taking account of the specific characteristics of each patient.


Then, can we hope to find soon a cure for Alzheimer disease, and Parkinson’s ? “This is an issue that must be treated with modesty,” responds cautiously Habib Benali.


“I think we are at a turning point, where the cross-disciplinarity is a discipline in itself. We can no longer remain in his field. If one wants to address this question, it is necessary to mix all the expertise and all of the areas, ” he adds. I am hopeful that we will get to find tools that will help prevent the disease, but this hope must be tempered, because the way is long and rough. “

Interview with professor Habib Benali