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Dr. Frances K. Skinner is using complex mathematical models to better understand what’s happening inside our heads.Thomas Bollmann

For the last 20 years, Dr. Frances K. Skinner, a senior scientist at the Krembil Brain Institute, has been using mathematical modelling to figure out how the brain functions. While Dr. Skinner doesn’t find mathematical modelling to be particularly complicated, those of us who dreaded high school calculus may find the concept a little abstract.

Mathematical modelling is the use of equations as a language to explain how a specific system works. Often used in engineering, physics and economics, mathematical models can also be applied to the human body. Currently, the only medical field that commonly uses mathematical modelling is the targeting of radiation treatment in cancer patients. But, says Dr. Skinner, more and more health researchers are recognizing the potential of mathematical modelling for solving real-world problems.

In Dr. Skinner’s lab, that process starts with well-established math equations that represent the brain’s neurons and their electrical connections. These equations are then further developed and modified so that they are applicable to both the specific part of the brain that is being studied and to the experimental data that the models are being built with. The resulting models can then be analyzed, usually with computers, and used to create assessments of what’s happening inside our heads.

Diving into the details

Many researchers are focused on neuro-related experiments, but Dr. Skinner says that the lab alone can’t treat brain disorders. “The brain is horrendously complicated,” she says, explaining that because the organ is non-linear and performs so many functions, “you need to understand it at multiple levels simultaneously. [Lab] experiments in and of itself themselves can’t do that.”

There are many mathematical models Dr. Skinner can use to better understand the brain, but according to Dr. William Lytton, a neurologist and professor of physiology and pharmacology at New York City’s SUNY Downstate Medical Center who is familiar with Dr. Skinner’s work, their approach involves “looking at the details of the brain.”

Dr. Lytton compares their work to weather modelling – both are built on basic physics equations you likely studied back in high school. Rapid advances in technology have also allowed researchers in both fields to collect copious amounts of data. For example, weather balloons and satellites give us reams of information about weather patterns, while MRIs and CT scans can give doctors thousands of data points about a patient’s brain. However, for that bounty of information to be useful, “You have to model it, because it’s just way too complex to understand in your mind,” says Dr. Lytton.

He adds that once the equations and the models become more accurate, “We’ll be able to say, ‘Hey, try this experiment, because this is going to really show something.’ Researchers won’t be working in the dark as much.”

A new way to diagnose brain diseases?

While mathematical models can be applied to many different physiological systems and diseases, Dr. Skinner’s focus has been on the cellular level of the hippocampus – the part of the brain that regulates emotions, learning and memories. It’s also connected to disorders such as epilepsy, Alzheimer’s disease and schizophrenia.

One of Dr. Skinner’s previous collaborations was with colleagues at McGill University’s Douglas Hospital Research Centre, where the two teams used math models to explore the brain’s oscillations – the rhythmic electrical activity more informally known as brainwaves.

Some experiments revealed that diseased brains generate abnormal oscillation activity, which are brainwaves that are faster or more intense then what is seen in a neuro-typical brain. “If our models can predict how these changes in the oscillations are coming about, then they could potentially be an early diagnostic of what’s happening,” says Dr. Skinner. This is important, since the sooner a diagnosis can be made, the sooner treatment can begin.

Collaboration is key

Math models alone can’t be turned into diagnostic tools, says Dr. Skinner. She’s a huge advocate of getting what she calls “math people and experimental people” to collaborate early in the research cycle.

While math might be crucial to learning more about the brain, it’s this collaborative approach that she believes is essential to making the new discoveries that might one day help us diagnose and treat complex brain disorders. “That’s why Krembil, by having people like myself – mathematical, computational, theoretical people – in the hospital talking and developing ideas and discussion, over time, is so important,” she says.

It’s an approach that’s starting to generate results. Dr. Skinner says that her team is now at the stage where it can start “translating these results to humans.” How? By taking her lab’s more promising mathematical models, tweaking them so that they appropriately represent the human hippocampus’ cellular connections, and then combining them with fresh-from-the-lab experimental data.

Dr. Skinner is optimistic about these new projects, though she’s quick to note that, “It’s not like a clinician is going to take our equations and use them directly.” Instead, any practical applications her lab generates will be in the background, disentangling the mysteries of the brain by using the power of math.

If all goes according to plan, says Dr. Skinner, “We’ll have an informed understanding of what’s going on in the brain so that we’re targeting it in an intentional way instead of by trial and error.” This, she explains, it where the real power of mathematical modelling lies. Both Dr. Skinner and Dr. Lytton believe that while mathematical modelling is currently underappreciated in the field of brain health, their work will eventually form the future basis for how many experiments are structured and analysed.

It’s “very, very early days,” says Dr. Skinner, but a strong partnership between mathematical modelling and lab work could lead to more effective drug treatments and new tools that will be able to help interpret abnormal brainwave activity.

It’ll also likely lead to more questions. Because when it comes to the brain, says Dr. Skinner, “The more you know, the more you realize you don’t know.”

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