Biological feedback – quantitative and qualitative models

In a recent paper we speculated on the presence of a geometric phase or phase memory in the bilateral nasal cycle, using a certain analogy between the mechanics of the circulatory system and a gauge field such as the electromagnetic one [34], and taking into account that Maxwell’s equations are a particular case of the fluid equations. It is known that shortly after its discovery, the geometric phase was generalized well beyond the adiabatic or even the cyclic cases, and that today it is studied even in dissipative open systems and in various cases of animal locomotion. The analogy may be relevant despite the fact that the respiratory system obviously operates in a gaseous phase instead of a liquid one, while still being coupled to the blood circulation.

According to V. D. Tsvetkov, the ratio between systolic and diastolic time in humans and other mammals averages the same reciprocal values of the golden mean, and also the ratio of the maximum systolic pressure to the minimum diastolic pressure points to a relative value of 0.618/0.382 on average. Although these values may be arbitrarily approximate, we would have an excellent opportunity here to contrast them mechanically and see if there really is some kind of underlying optimization, since the systolic time already echoes the reflected vascular wave, and the same is true of the diastolic time.

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