Chaos and Coexistence Theory Chaos and Coexistence TheoryBecause most functions in the human body, including the heartbeat, depend on other bodily events, such as hormone and chemical levels, the body is a dynamic system -- very slight changes in startup conditions can result in drastically different outcomes, so that the system is virtually unpredictable. Recognizing this, Chay's research involves applying the insights of a branch of modern mathematical physics known as nonlinear dynamics or, more popularly, chaos theory. This approach involves examining the mathematical description of a physical phenomenon through the full range of its variables, to discern what patterns may exist within the apparent unpredictability. This field of study has come into existence only with the advent of powerful computers, because it requires a tremendous number of iterations of complex differential equations, and Chay's investigations can be accomplished only with supercomputing.
Chay first studied a simple system -- just one cell and how it behaves as it gets sicker. In its healthy state, the cell is perfectly still and ready to receive an impulse from the sinus node. When that occurs, the cell sends the impulse to a neighboring cell and returns to a quiescent state. When the cell is sick, however, it holds too many positive charges, and under these conditions, Chay's calculations show that when an extra impulse arrives at the wrong moment -- known as the vulnerable period -- the cell begins sending its own signals across the heart, which interferes with pulses from the sinus node. As a result, arrhythmia kicks in.
Even for a sick cell, however, when a pulse arrives outside the vulnerable period, nothing happens. Arrived at using an approach from chaos theory called "bifurcation analysis," these results indicate that the beating and quiescent states of a single cell coexist; both possibilities are present, and which of the two occurs depends on the timing and magnitude of the triggering impulse. It is similar to the coexistence of water and ice when temperature is at the melting point. "At a certain level, you have two phases coexisting," Chay says, "so I was able to explain that complex dynamics exist even in a single cardiac cell." Her studies showed this coexistence of states -- dubbed the "coexistence theory" -- for the first time.