SIAM News Blog

Understanding Epilepsy With Mathematics

By Lina Sorg

According to the Centers for Disease Control, epilepsy is a chronic brain disorder that affects approximately 3 million people in the United States, and 65 million people around the world. The disorder is characterized by recurring, unprovoked seizures, the severity of which depends on the seizure’s initial location in the brain, the way it moves over the brain’s surface, how much of the brain is affected, and the length of the seizure. As a result, some epileptic patients experience other neurological complications as well. Possible treatments include medication, biofeedback, and in some cases temporal lobe resection, a surgery that removes the part of the brain believed to control seizures. Yet because there is limited understanding of the electrical processes in the brain that lead to seizures, one-third of epileptic patients are not able to sufficiently control their seizures.

The reasons behind a seizure’s spontaneous onset is a fundamental question of epileptology, and researchers in mathematical neuroscience are working to better understand brain activity during epileptic seizures. In a presentation titled “Data Analysis and Mathematical Modeling of Multiscale Dynamics in Human Cortex,” part of a minisymposium on the dynamics and structure of neuronal networks at the 2016 SIAM Conference on the Life Sciences, Mark Kramer (Boston University) presented a model that simulates brain activity during a seizure.

Using recordings from human subjects, Kramer, Louis-Emmanuel Martinet (Harvard University, Massachusetts General Hospital), Grant Fiddyment (Boston University), Jessica Nadalin (Boston University), and Sydney Cash (Harvard University, Massachusetts General Hospital) focus on the spatiotemporal patterns that occur during epileptic seizures. They developed a computational modeling framework that simulates the neuronal and ionic processes that control the spatiotemporal dynamics that occur during unprovoked seizures. The model observables match data from standard clinical electrodes (located on the scalp) and microelectrode arrays from affected human patients.  

By studying rhythmic pulses of electricity and voltage data from the electrodes, which pick up electrical pulses from neurons, Kramer et al. look for neuronal patterns or relationships present before, during, and after the seizure. Although they are based on normal neuronal firing patterns, the resulting equations often behave in unanticipated ways, giving rise to novel mathematics that further streamline the field of mathematical neuroscience. The researchers hope that modeling brain rhythms and the dynamics of neuron networks in the cortex will yield a more thorough understanding of how and why seizures move across the brain’s surface. A more comprehensive understanding of this phenomena will improve treatment methods and increase the chance of managing or halting epileptic seizures with medication or surgery. 

  Lina Sorg is the associate editor of SIAM News.  


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