This article deals with an advanced approach to organ malfunction and what
could be a potential cause of disease. The use of 'phase space' to represent
complex dimensional fields in a simplified manner also has correlations to the
study of over/unity devices, where a self-sustaining wave can be intentionally
triggered and maintained. We invite your comments on the subject.
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Science Digest - September 1995 (page 20)
Chaotic Body Rhythms
A biologist uses topology to link unrelated phenomena
Purdue biologist Arthur Winfree believes an underlying mathematical model that
describes two seemingly unrelated phenomena - the internal biological clock,
which determines sleep-wake cycles, and an obscure chemical process called the
Belousov-Zhabotinshky reaction - also describes a third: fibrillation, the
uncontrolled, erratic fluttering of the heart that is a major cause of sudden
If he is right, fibrillation can result from such relatively mild, usually
harmless stimuli as the premature firing of a few nerves. Should it happen at
JUST THE WRONG MOMENT of the heartbeat cycle, it TRIGGERS a rotating, three
dimensional wave of electric potential that moves through coronary tissue.
This self-sustaining wave irrevocably overrides the heart's normal, rhythmic
beating; even someone with a healthy heart is susceptible. In fact, this
could explain sudden heart failure in disease-free people.
Winfree is careful to emphasize that his ideas are unproven; yet they earned
him a grant from the MacArthur Foundation last November. He is currently on
leave from Purdue, working at the University of California, San Diego, and at
the La Jolla Veterans Administration Hospital. "I'm trying," he explains, "to
learn some cardiology."
The theory Winfree is pursuing rests on a branch of mathematics known as
TOPOLOGY, the study of the PROPERTIES OF GEOMETRIC SHAPES - and, by analogy,
of systems that can be represented by geometric shapes. "My original work on
the problem had to do with biological clocks," he says.
Biologists had long believed that over the long term an organism would
alternate sleeping and waking at regular intervals. A disturbing stimulus,
such as a change in the pattern of light and darkness, might ADVANCE or RETARD
THE CYCLE without CHANGING its FUNDAMENTAL RHYTHM. In fact, this is just what
happened in experiments.
"I thought that might not be the whole story, though," recalls Winfree. "The
cycle is governed by the INTERACTION of many chemical compounds at many
locations in the body. With topology, you can treat all those concentrations
as a space of many dimensions, called a PHASE SPACE. You needn't define its
structure in DETAIL to examine its PROPERTIES."
Winfree treated the sleep-wake cycle as a one-dimensional slice of this many-
dimensional phase space. He then described a two-dimensional slice, analogous
in structure to a soap film stretched on a circular metal wire. He defined
the wire as the ordinary rhythm - movement around the circle represents
passage through the cycle over time. The soap film is a set of POSSIBLE
In the case of a disruption, represented by a point on the film, the normal
rhythm resumes from some PREDICTABLE SPOT along the metal rim, just as a point
on a soap film rushes to a PARTICULAR spot on the rim when the film breaks.
"Nearly every spot on the film can be assigned a corresponding point on the
rim," says Winfree. "But according to the topological theorem of
NONRETRACTION, this can be true only if there is at least one point on the
surface that does NOT have such a correspondence. A soap bubble cannot
retract onto the rim unless you break it at some point." By analogy, Winfree
predicted, there should be a point in the sleep-wake cycle where an applied
stimulus would not RESTART the cycle but would result in an ARRHYTHMIC
"Eric Patterson, a graduate student in biology, tried it on mosquitoes," he
says, "and found we could PRODUCE a state in which the insects slept, then
woke and buzzed around for a while, then dropped off again, in no DISCERNIBLE
Winfree wondered whether it might be possible to treat other rhythmic
biochemical systems the same way. "Since the mathematical model is abstract,"
explains Winfree, "there seemed to be no reason it couldn't apply to such
things as rhythmic chemical reactions, the cycle of cell reproduction, the
menstrual cycle or even fibrillation."
The jury is still out on menstruation; the analogy just doesn't work when it
comes to cell reproduction. In the Belousov-Zhabotinsky reaction, though, a
TRIGGERING BEAM of ultraviolet light interrupts the orderly interaction of a
mixture of chemicals, sending a ROTATING WAVE FRONT of activity through them.
"We can't say for sure, but the evidence is very good that the same sort of
thing goes on in the heart," Winfree concludes. "The contraction of millions
of heart cells, based on combinations of electrical and chemical stimuli, make
up the phase space. And a mild stimulus occurring AT THE PROPER TIME should
disrupt the pattern ENTIRELY."
Does the mathematical model have a basis in reality? Two pieces of evidence
suggest it does. The first is that electrodes placed on the surface of
laboratory animals' hearts have detected what APPEAR to be the ROTATING SPIRAL
WAVES of electricity that Winfree predicts.
The second comes from the work of George Ralph Mines, a physiologist who did
heart research at the University of Montreal in the early years of this
century. Mines suspected that fibrillation could be caused by mild stimuli to
the heart, though he had no theory to explain it. He may have been proved
right. One day, in 1917, he was found alone in his lab, dying of heart
failure. Attached to his chest were the wires of a machine he had been using
to deliver weak shocks to lab animals.
Michael D. Lemonick