from The Economist, September 18th, 1999.  http://www.economist.com

             The theory of non-linear dynamics could help scientists to understand, and even
             treat, some medical conditions
 

             THE study of non-linear dynamics, more popularly known as chaos theory, has been
             hailed as the key to understanding everything from weather systems and earthquakes
             to traffic jams and stockmarkets. But it is one thing to show that a particular
             phenomenon displays chaotic behaviour. It is quite another to exploit that knowledge
             for any useful purpose.

             The latest field to embrace the idea of chaos is medicine. Specialists in non-linear
             dynamics are doing their best to understand the workings of the brain, heart and
             immune system using chaos theory. In the most recent example, published in the
             current issue of the journal Chaos, a physicist, Raima Larter, and a neurosurgeon,
             Robert Worth, both at Purdue University in Indianapolis, have used chaos theory to
             simulate what happens in the brain before some kinds of epileptic seizures. Based
             on their work, new treatments of epilepsy that do not require surgery might become
             possible.

             Perhaps surprisingly, chaos in the brain is a sign of health, not disease. During an
             epileptic seizure, the disorderly jumble of brain activity suddenly becomes
             abnormally regular. Dr Larter and Dr Worth were interested in what causes this
             transition in a class of epileptic fits called partial seizures. In these seizures, only
             part of the brain starts off behaving abnormally; but as neighbouring regions are
             co-opted, the seizure spreads to the rest of the brain. Patients who suffer from partial
             seizures are the least responsive to medical treatments and often have to resort to
             surgery, in which the abnormal brain tissue is removed. Surgery is, however,
             ineffective for about 10% of patients, and it is also dangerous: removing too much
             brain tissue can lead to memory loss and to speech and vision impairment.

             Most research into partial seizures has concentrated on trying to find out what was
             wrong with the abnormal part of the brain. Dr Larter and Dr Worth looked at the
             trickier problem of how bad tissue manages to coerce healthy tissue into
             misbehaving, by using a computer to model the behaviour of thousands of the brain’s
             nerve cells, called neurons. Starting with standard non-linear equations that describe
             the behaviour of individual neurons, they linked about a thousand neurons together to
             represent the abnormally behaving part of the brain. They then linked up
             neighbouring groups of healthy neurons.

             While tweaking the equations used in the model, one of Dr Larter’s students, Brent
             Speelman, found that the rate at which the abnormal part of the brain communicated
             with the healthy parts was a crucial factor in determining whether those parts
             continued to behave well. When there was more frequent communication between
             healthy and abnormal parts, the seizure spread. At slower speeds, however, the
             healthy neurons continued their chaotic firing. What makes this finding more than a
             cute mathematical exercise is recent experimental evidence which suggests that the
             brain might possess a mechanism to regulate the rate at which neurons communicate
             with one another.

             Clusters of neurons are usually thought to communicate via the diffusion of
             potassium ions. But the rate at which potassium ions diffuse is constant, so this
             mechanism does not permit variations in the rate of communication between neurons.
             There is, however, another process involving calcium ions that might. Calcium ions
             are present in glial cells, until recently thought to be an inactive glue that held
             neurons together. When these ions are released, they travel through the brain as a
             “chemical wave” at different speeds. Although nobody knows what causes the wave,
             the researchers think an imbalance in the brain makes the wave move faster,
             increasing the speed of communication between neurons—and causing a seizure. So
             it is possible that carefully designed drugs, or suitably administered electrical
             impulses, might slow the waves down and prevent the seizure entirely.

             Disorderly brains, orderly hearts

             The heart is another part of the body where chaos is being brought to bear. It would
             be poetic if physiologists found that the normal state of the heart, like that of the
             brain, was chaotic turmoil; but it is not. Normally, orderly waves of electric activity
             pass through the cardiac tissue, causing the heart muscle to contract. Sometimes,
             however, these waves become horribly distorted and make the heart beat erratically,
             a condition called cardiac fibrillation. At present, the most common treatment is to
             administer a massive (and painful) electric shock.

             Many physicists and physiologists suspect that fibrillation is chaotic, and are trying
             to model it in order to find ways of stabilising the dangerous convulsions. But
             according to Daniel Gauthier, a physicist at Duke University in North Carolina, if
             cardiac fibrillation is chaotic, it is not the usual kind of chaos. Most chaotic signals
             involve unpredictable behaviour over periods of time. But what happens in the heart
             is known as spatio-temporal chaos, since the chaos extends over different locations
             in the heart. The way to stabilise a chaotic heart would be to wait until it comes
             closer to a more periodic state and then give it a small electric shock to nudge it into
             that state. But this would be much harder if different parts of the heart had to be
             nudged in different ways.

             Recent experiments by Dr Gauthier’s group and others have, however, been
             encouraging. One prediction from models of a chaotically beating heart is the
             break-up of regular electrical impulses into spirals, causing uneven contractions.
             Recently, researchers have observed these spirals in both human and animal hearts
             during cardiac fibrillation. Dr Gauthier’s group is now experimenting on sheep to try
             to administer small electric shocks and bring the chaos under control. Another
             group, led by William Ditto at the Georgia Institute of Technology and Francis
             Witkowski at the University of Alberta, is using a dye that lights up in response to
             voltage changes to map the heart’s response. Both groups have had some success in
             controlling chaos in small portions of the heart. The eventual goal is to be able to
             stabilise a fibrillating heart using several tiny shocks, rather than one massive one.

             Meanwhile, another group led by Mark Yeager at Dartmouth College in New
             Hampshire is trying to identify patterns of chaos in the immune system. Dr Yeager
             has done some preliminary experiments that suggest that the erratic activity of white
             blood cells is a form of chaotic behaviour.

             If that is true, then certain drugs designed to affect the immune system might be more
             effective if delivered as small doses at different times, rather than as a single,
             continuous dose. This would be useful in cases of severe injury where the immune
             system turns against the body and causes organs to shut down one by one. Instead of
             using anti-inflammatory drugs simply to suppress the immune system, it might be
             possible to tweak it back to its normal behaviour. Dr Yeager plans to start testing
             this idea later this year. Perhaps he, and other medical researchers, will find delight
             in disorder.

Raima Larter, Robert Worth and Brent Speelman’s article can be ordered from Chaos. Information on William Ditto’s research is available at the Applied Chaos Lab. James Collins has made abstracts of some of his research available at his homepage.