Scientists have developed a novel, general framework for comparing various oscillations, providing important insights into neurological and cardiac science. By transforming the problem of comparing oscillators into a linear algebra problem, the team can now compare and understand oscillators previously thought to have different properties, with applications that could range from understanding heart and brain oscillations to analyzing the sway of skyscrapers.
An international team of researchers has proposed a universal structure to explain "oscillations."
Life's random rhythms surround us -- from the hypnotic synchronized blinks of fireflies... to the back-and-forth sway of a child on a swing... to the subtle changes in the otherwise steady "pop-pop" of the human heart.
However, scientists still have no idea how to truly understand these patterns, known as stochastic or stochastic oscillations. Despite some progress in analyzing brain waves and heart rhythms, researchers and clinicians are still unable to compare or catalog the countless changes and sources.
"If we can gain a deeper understanding of the underlying causes of oscillations, we can make advances in neuroscience, cardiac science, and many different fields," said Peter Thomas, professor of applied mathematics at Case Western Reserve University.
Thomas is part of an international team of researchers who say they have developed a novel, general framework for comparing and contrasting oscillations - regardless of their underlying mechanisms - that could one day be a key step towards fully understanding oscillations.
Their findings were recently published in the Proceedings of the National Academy of Sciences.
"We turned the problem of comparing oscillators into a linear algebra problem," Thomas said. What we did was much more precise than previous studies. This is a big conceptual advance. "
Others can now compare, better understand and even manipulate oscillators previously thought to have completely different properties, the researchers say.
For example, if your heart cells get out of sync, you can die from atrial fibrillation. But if your brain cells are too synchronized, you can develop Parkinson's disease or epilepsy, depending on where the synchronization occurs in the brain. By using our new framework, heart or brain scientists may be able to better understand what oscillations might mean and how the heart or brain works or changes over time.
Thomas said researchers, including collaborators from universities in France, Germany and Spain, have discovered a new way to use complex numbers to describe the timing of oscillators and their "noise," or imprecise timing. Most oscillations are irregular to some extent. For example, heart rhythm is not 100% regular. A natural variation of 5%-10% in heartbeat is considered healthy. The problem of comparing oscillators can be illustrated by two distinct examples: brain rhythms and swaying skyscrapers.
"In San Francisco, modern skyscrapers sway in the wind, buffeted by randomly changing air currents - they are pushed slightly out of vertical, but the mechanical properties of the structure pull them back," he said. "This combination of flexibility and elasticity helps tall buildings withstand shaking during earthquakes. You wouldn't think this process could be compared to brain waves, but our new framework allows you to do so."
It may still be unclear how their discovery will help the two disciplines of mechanical engineering and neuroscience. He likened this conceptual advance to Galileo's discovery of Jupiter's orbiting moons.
He said: "What Galileo realized was a new perspective. Although our discovery is not as far-reaching as Galileo's, it is still a change in perspective. What we report in the paper is a completely new perspective on stochastic oscillators."