The subject of today’s Fractal Friday is no less than the human heart, the small fist of muscle tissue in the chest that keeps each cell in the body well supplied with sugar, oxygen, and whatever else it could desire. Thinking about the slow, regular thudding that most of us associate with the heart, you might be inclined to think that no organ could be more dependable. What could be less likely to be the home of fractal shenanigans than the heart?
Well, actually, as it turns out, pretty much everything. Measuring heart rate against time for several different patients (some with heart disease, some healthy), a team of doctors found that, contrary to expectations, the unhealthy hearts produced the neatest patterns. Analysing the signal further showed that the healthier hearts were in fact displaying ‘non-zero fractal dimension over a range of exponents’ – i.e., fractal behaviour was showing up on a number of different size scales, causing the pattern to look the same no matter how far you zoomed in. In other words, the healthy hearts’ signals produced the kind of self-similarity responsible for the beauty of fractal patterns like the Mandelbrot set.
Graphs of heart rate against time, each one showing a different patient. Contrary to expectations, graph B shows the healthy person.
(Image here, credit Ary L. Goldberger et al. Copyright National Academy of Sciences, 2002)
Conversely, the diseased hearts, and those of older patients, were found to give notably less complex patterns, suggesting the fractal quality of the heartbeat is increasingly lost with age or sickness. Pausing for a moment, this is a weird idea – casting your mind back to old biology classes, you might remember being taught about homeostasis, or the idea that the body seeks to maintain an equilibrium at all times. When it can’t, things start to go wrong – lack of sugar equilibrium leads to diabetes, lack of temperature equilibrium leads to enzymes ceasing to function and so illness, lack of water equilibrium leads to dehydration. Looking at the heart from this point of view, we might expect that the healthy hearts should settle down to a smooth equilibrium when left to their own devices. But once again, nature surprises us.
Awareness of these differences could prove useful in medicine – in cases where a patient’s mean heart rate looks normal, doctors might be able to compare a plot of their heart rate against time to healthy and unhealthy examples and decide whether or not there might be underlying problems that conventional tests aren’t as effective at picking up on. It’s also been suggested that treatments could be developed to re-introduce chaotic behaviour into the heart, hopefully giving a boost to patients recovering from coronary disease.
As to why fractal heartbeats seem to be so beneficial, it’s thought that the loss of complexity in the system leads to a reduction in the information it contains, leaving it less adaptable and more vulnerable to changes in its environment. So, if you’ve been lucky enough to avoid heart attacks so far, consider thanking a fractal today.
- Cipra, B.A., 2003. A Healthy Heart Is a Fractal Heart. SIAM News. (https://www.siam.org/pdf/news/353.pdf)
- Goldberger, A.L., 1999. Nonlinear Dynamics, Fractals, and Chaos Theory for Clinicians. PhysioNet. (https://www.physionet.org/tutorials/ndc/)
Header image from here, credit not known.