Knowing the Beast

Chaos theory was a novel idea in the late 1980s. That was when Leon Iasemidis first began his work on a method to predict epileptic seizures. The ASU biomedical engineering professor was a doctoral student at the University of Michigan at the time. Scientists and engineers were just beginning to apply chaos theory to a variety of problems.

“There were no ‘real world’ biological applications of chaos theory at that time,” says University of Florida neurologist J. Chris Sackellares, a former advisor and longtime collaborator with Iasemidis.

The human brain includes more than 100 billion neurons firing back and forth at different rates at different times. The brain represents perhaps the ultimate chaotic system. In the case of research on epileptic seizures, scientists say that chaos does not refer to a “random” event. A seizure may appear to be a random event, but it is not.

Chaos in this case is more like the behavior of the ball whirling around a roulette wheel. When the ball drops onto the wheel, players know that it will obey the law of gravity. What they don’t know is exactly where the ball will land. If they did, casinos around the country would go broke.

Scientists say that the goal of chaos theory is to interpret and predict such randomly appearing complex behavior. At the root of chaos theory are a predictable group of mathematical equations that generate an unpredictable behavior over time. Iasemidis’ idea was to apply chaos theory to epilepsy. He thought that it might provide a means to predict seizures.

He and his colleagues studied thousands of electroencephalograms (EEG). “We were able to see the brain get into an ordered state and then, within seconds to a couple of minutes, come right back out of it,” says Iasemidis. “That’s what was really fascinating to me.”

Once an epileptic seizure is complete, patients usually return to a relative state of calm. Iasemidis thought the role of epileptic seizures might be to reset the brain, much like rebooting a network of computers. He and his group have used mathematics to prove that idea.

Seizures are innate for each epilepsy patient. As a result, Iasemidis didn’t have to worry about the influence of external factors clouding the interpretation of his results.

“We had an ideal setting for study. We could look at real patients under real conditions,” he explains “The hallmarks of epilepsy are seizures and the existence of epileptic spikes in the EEG. The coming and going of seizures appears to work randomly, so, in that sense, epilepsy is a dynamic disorder.”

Since the 1960s, doctors have used continuous videotape recording and simultaneous EEGs to help diagnose epilepsy. They study the EEG activity from electrodes that monitor different portions of the brain.

“We’ve known for decades that there is a synchronization of different brain areas during the seizure itself,” Iasemidis says. Unlike the patterns seen on a heart monitor, the wave patterns seen on an EEG are irregular.

“The traditional view is that seizures occur randomly. We have proven that seizures are not random events,” he continues. “We are able to define mathematically the existence of a long-term pre-seizure period.”

Iasemidis and his colleagues took a very close look at the pre-seizure period. That is where what he calls a “dynamical entrainment” of critical brain areas occurs. When drawn on paper, an EEG signal is viewed as a one-dimensional line of valleys and peaks. The ASU researchers analyze each signal. They use mathematics to convert the one-dimensional signal into an image that covers seven dimensions. The result is what mathematicians call a fractal.

Fractals are characterized by rough geometric shapes. Fractals are abundant in nature. They can be seen in the natural shapes of mountains and clouds, even lightning.

“We can see the ‘fractal creature’ during an epileptic seizure. We can mathematically prove it to be a fractal,” Iasemidis says. “Whenever there is order in the system, our fractal beast appears on the scene, much like Beowulf’s nemesis, Grendel.”

Iasemidis and his team examined lots of EEGs. They saw the pattern emerge within the data. Every time a seizure occurred, the fractal beast progressively appeared. When there was no seizure, the beast disappeared and the brain’s neurons fired away in chaotic bliss. When the next seizure began, the fractal appeared again.

Iasemidis and his colleagues now view epileptic seizures as a recurring cycle of chaos, order, chaos, order, and so on. They have seen the beast. They know when it is about to arrive.

Iasemidis says this knowledge will be valuable to physicians and patients. Physicians can intervene in many ways if they have an early warning of an impending seizure. They can use a variety of treatments to lessen the severity of a seizure or even help to fend it off entirely. Patients who suffer from epileptic seizures may get a tool that can help restore some semblance of order to their lives.—Joe Caspermeyer