Central illustration: At the heart of the Mandelbrot set lies the cardioid, a well-defined mathematical representation (left panel). On the cardioid’s boundary exists an assortment of circles, with each of these circles further continuing its own fractal pattern (right panel; zoomed-in view for illustrative purposes).
When you ponder biomimicry, think design, intelligent design, and creation, but please don’t think evolution. And when considering biomimetic applications, let your imagination know no bounds.
Here we touch briefly on cardiac function and fractal behavior via what we have coined mathematical cardiology. Our intent is to glorify God as the universe’s greatest mathematician.
Mathematical cardiology – a unique pattern
While we have argued that the heart itself is complex and uniquely designed, others offer claims suggesting that the heart is seminally prototypical. In part, evidence in either case points to the intrinsic fractal behavior of the heart. Specifically, fractal descriptions mark the quintessential characteristic of non-linear, dynamical systems, and with respect to the heart such behavior is clearly present. The preeminent example deals with the heart’s electrophysiology. The rhythmic impulse that is ultimately carried through the heart’s conduction pathway can, at times, become quite irregular. In these cases, the rhythm (the irregularity) is called an arrhythmia. What is more, two somewhat related arrhythmias, known as atrial fibrillation and atrial flutter, are regarded as irregularly irregular. This pattern of irregular irregularity is understood to be a chaotic temporal disturbance of atrial origin. Furthermore, although dynamical systems are non-linear and chaotic by nature, at the center of any such system is simple, identifiable deterministic activity (despite a behavior seemingly acting in an erratic way) (Bassingthwaighte & van Beek, 2002). What this means for patients with atrial fibrillation or atrial flutter is that algorithms can be developed to mathematically identify these arrhythmias based on the deterministic, fractal character. This identification translates into a more proactive means of rhythm identification and possible correction. In fact, in the case of an urgent, life-threatening arrhythmia, attempts to convert to normal sinus rhythm via implantable defibrillators become possible sooner (or even anticipated), due to resultant mathematical interpretation of the rhythm’s fractal behavior (Captur, Karperien, Hughes, & Moon, 2017).
Bassingthwaighte, J.B., & van Beek, J.H.G.M. (2002). Lightning and the heart: Fractal behavior in cardiac function. Proceedings of the IEEE: Institute of Electrical and Electronics Engineering, 76(6), 693-699. [View in article] [View in PubMed]
Captur, G., Karperien, A.L., Hughes, A.D., Francis, D.P., & Moon, J.C. (2017). The fractal heart – embracing mathematics in the cardiology clinic. Nature Reviews: Cardiology, 14(1), 56-64. [View in article] [View in PubMed]