A new way of measuring complexity for biological systems has been
proposed by researchers at Harvard Medical School and University of
Lisbon (contact Madalena Costa, 617-667-2428, email@example.com
, Ary L. Goldberger, 617-667-4267, firstname.lastname@example.org and
C.-K. Peng, 617-667-7122, email@example.com). Their method suggests
that disease and aging can be quantified in terms of information loss.
In the researchers' view, a biological organism's complexity is intimately
related to its adaptability (e.g., can it survive hostile environments
on its own?) and its functionality (e.g., can it do higher math?).
In this view, disease and aging reduce an organism's complexity, thereby
making it less adaptive and more vulnerable to catastrophic events.
But traditional yardsticks sometimes contradict this "complexity-loss"
theory of disease and aging. Such conventional metrics, originally developed
for information science, quantify complexity by determining how much
new information a system can generate.
By these traditional measures, a diseased heart with a highly erratic
rhythm like atrial fibrillation is more complex than a healthy one.
That's because a diseased heart can generate completely random variations
("white noise") in its heart rate. These random variations
continually produce "new" information, i.e., information
that cannot be predicted from the heart's past history. On the other
hand, a healthy heart displays a less-random pattern known as 1/f noise
The problem, according to the researchers, is that conventional measures
of complexity ignore multiple time scales. To address the inherent multi-scale
nature of biological organisms, the researchers developed a new "multi-scale
entropy" (MSE) tool for calculating biological complexity.
Their technique works like this: Take a heart rate time series of about
30,000 beats. Then split it into coarse-grained chunks of 20 heartbeats
each and compute the average heart rate in each chunk. Then measure
the heart rate's unpredictability (its variations from chunk to chunk).
More unpredictability means more new information, and greater complexity.
Repeat this complexity calculation numerous times for different-sized
chunks, from 1-19 heartbeats. Such a technique can reveal the complex
arrangement of information over different time scales.
Applied to heartbeat intervals in healthy young and elderly subjects,
patients with severe congestive heart failure, and patients with atrial
fibrillation, the MSE algorithm consistently gives the fluctuations
of healthy hearts a higher complexity rating than the fluctuations of
diseased or aging hearts. (Costa
et al., Physical Review Letters, 5 August 2002.)