## 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.

On the other hand there is the Pulse Wave Velocity, which is a measure of arterial elasticity: both are derived from the second law of mechanics through the Moens-Korteweg equation. This wave velocity varies with pressure, as well as with the elasticity of the vessels, increasing with their stiffness. The return distance of the reflex wave and the time it takes increases with height, and a lower diastolic pressure, which indicates less resistance of the whole vascular system, reduces the magnitude of the reflected wave. Treatment of hypertension should focus, it is said, on decreasing the amplitude of the reflected wave, slowing it down, and increasing the distance between the aorta and the return points of this wave.

Now, we can try to apply here Noskov’s retarded potentials with longitudinal waves, as he emphasized their universality and their place in the most elementary feedback; in fact, there is perhaps no better way of illustrating these waves and their correlation with certain proportions in a complete mechanical system than the circulatory system itself.

Since, to a large extent, it seems that we can consider the elasticity of the reflected wave as a retarded Weber-Noskov potential dependent on distance, force and phase velocity, and check whether this results in coupling or resonance conditions that incidentally tend to the values of the golden section. The myocardium is a self-exciting muscle, but the return of the reflex wave also contributes to this, so we have a fair example of a circuit with tension-pressure-deformation transformations that are fed back and that do not differ in essence from the gauge transformations of modern physics, in which there is also an implicit feedback mechanism.

This would be a perfect instance to explore these correlations in a sort of “closed loop” process, even if the system remains open through the breath, which is not contrary to our approach because for us every natural system is open by definition. It allows both numerical simulation and approximation by real physical models created with elastic tubes and coupled “pumps”, so that it can be approached in the most tangible and direct way [35].

However, the idea that the heart is really a pump, being as it is a spiral muscular band, or that the motion of the blood, which generates vortices in the vessels and the heart, is due to pressure, when it is the pressure that is an effect of the former, should be thoroughly revised. In fact this is an excellent example of how we can give a strictly mechanical description while radically questioning not only the form but the very content of causality —the cause-effect relationship. The essential factor of the pressure created is not the heart, but the open component, in this case, the breath and the atmosphere. And although it is clear that these are very different cases, this is in line with our idea of gauge fields and natural processes in general.

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The dynamics and biomechanics of the blood pulse can be derived from the applied force, but if we look within modern science for a suitable equivalent to Newton’s three principles of mechanics in open systems such as biological organisms, we do not find it. To find something similar we have to look back to principles that are more “archaic” to us, and then look for a quantitative and mathematical translation.

Actually, the triguna of the Indian Samkya system —samkya means proportion- and its application to the human body as the tridosha in Ayurveda is the better match. The triguna, as it were, is a kind of system of coordinates for modalities of the material world in qualitative terms. The three basic qualities, Tamas, Rajas and Satwa, and their reactive forms in the body, Kapha, Pitta and Vata correspond very well to the mass or amount of inertia, the force or energy, and the dynamic equilibrium through motion (let us say: passivity, activity and balance). But it is evident that in this case we are talking about qualities and the systems are considered open from the start without need for further definition.

So, here is the law of conservation of momentum, not the third law of mechanics, what really should hold here, as a system like this implicitly admits a variable degree of interaction with the environment. In harmony with this, the Ayurveda considers that Vata is the guiding principle of the three since it has autonomy to move by itself in addition to moving the other two. Vata defines the sensitivity of the system in relation to the environment, its degree of permeability or lack thereof. In other words, the state of Vata indicates by itself to which extent the system is effectively open.

In the human body the most explicit and continuous form of interaction with the environment is the breath, and therefore it is just in the order of things that Vata governs this function most directly. Although the doshas are modes or qualities, in the pulse they find a faithful translation in terms of dynamic values and the continuum mechanics —provided we settle for modest degrees of precision, but surely enough to give us a qualitative idea of the dynamics and its basic patterns.

The other two modes are simply what moves and what is moved, but the articulation and coexistence of the three can be understood in very different ways: from a purely mechanical way to a more specifically semiotic one. Here again, the indistinction or ambiguity between kinetic, potential and internal energy, which we have already noticed in relational mechanics, might be of some relevance.

The principle of inertia is a possibility, that of force a brute fact, the action-reaction —the same act seen from two sides- is a relationship of mediation or continuity. We can put them on the same plane or put them on different planes, which constitute an ascending or descending gradation, as in fact are the modalities of the Samkya system.

Actually, it should not be too difficult to find the common ground that the Indian and Chinese semiologies of the pulse have, beyond the differences of terminology and categories; and to move from this common ground to the quantitative, but extremely fluid, language of continuum mechanics. Thus we would have a method to pass from qualitative to quantitative aspects, and vice versa; and to find dynamic patterns that now pass unnoticed. There are several issues here. One is the extent to which these qualitative descriptions can be made consistent.

Another question is to what extent the representation of a qualitative scale can be made intuitive. Let us think, for example, of biofeedback signals, which can be effective under the representation of forces, potentials, and many other more indirect relationships. What is interesting is that these types of assisted feedback do not aim at control and manipulation, but at tuning in to the organizing principle of the dynamics.

From our perspective, as we have already said repeatedly, all physical systems, from galaxies to atoms, have feedback. But what are the physical limits of, let us say a human being, to tune in to other entities? The phase rhythmodynamics and its resonances, the time scale, the energy scale, strain-stress constitutive relations, the dependence on free energy? Or the capacity to align with the Pole that both systems have in common? Is there interference or is there rather a parallelism on the same background?

These are subjects for which science has not yet found even the minimum criteria, but which should help us to overcome the instrumental compulsion, the instrumentation syndrome that has guided human technology since the first tools, and which intensifies as the tools offers less resistance to the user.

One more question is whether this type of trimodal analysis, or even a bimodal one, has a recursive character, as the same feedback and the presence of the continuous proportion in the circulatory system suggest; and what type of recursion is involved.

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The characterization of the dynamic equilibrium should always indicate the Pole of the evolution of a system, if it has one. In the case of the Solar System and the planets this is obvious —and notwithstanding, it is still far from receiving the attention it deserves. But it turns out that the bilateral nasal cycle is also telling us about an axis even in a process where polarity does not look very relevant, from the biomechanical point of view, such as the compression and release of a gas in our own organism. This should be of great interest to us, and it provides a thread through which many other things can be revealed.

In fact, the Earth’s own climate or that of other planets, with its great complexity, is a more explicitly polar system than the respiratory regime of any mammal —and in this case the separating barrier would be the intertropical convergence zone. The point of interest here is that, if the analogy is sound, from a thermomechanical point of view the degree of separation that the barrier exerts, possibly associated with a topological torsion, could also be defining the degree of autonomy of the system with respect to the external conditions —let us call it the endogenous component. An endogenous view that would have to be duly complemented with appropriate sensors and observations of the so-called spatial time [36].

If we said before that the fact that an ellipse has in its interior two focuses does not mean that we only have to look inside it for the origin of the forces that determine its shape, the same is true for the disturbances that usually affect other organisms or systems, which does not prevent them from synthesizing in their behavior the product of external and internal factors, in the breath not less than in other balances that run in parallel.