A New Way of Measuring Complexity

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, madalena@mimic.bidmc.harvard.edu , Ary L. Goldberger, 617-667-4267, agoldber@caregroup.harvard.edu and C.-K. Peng, 617-667-7122, peng@physionet.org). 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 (see Update 90).

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.)