What type of feedback loop is hypertension

ANP causes, among other effects, vasodilation by relaxing vascular smooth muscle [ 31 ]. The effect is most pronounced in the presence of elevated plasma concentrations of vasoconstrictor hormones, such as in advanced cardiac failure, since plasma angiotensin, AVP and other vasoconstrictors are elevated in that setting [ 32 ]. Renin is produced by juxtaglomerular cells of the kidneys, which reside in the afferent arterioles of glomeruli.

The release of renin is regulated by three primary mechanisms, a renal vascular baroreceptor, which responds to changes in renal perfusion pressure within the afferent arteriole, a tubular, macula densa-dependent sensor that measures distal tubular salt concentration in the filtrate, and renal sympathetic nerves.

Low blood pressure in the afferent arteriole and low sodium chloride concentration in the tubule at the macula densa both stimulate renin release [ 33 , 34 ]. This mechanism mediates different ANGII effects, including among others, vascular smooth muscle contraction leading to blood pressure rise, and increased production of aldosterone from the adrenal zona glomerulosa [ 36 ]. Aldosterone mainly acts on distal nephron components, viz. This latter phosphorylates myosin light chain MLC , thus enhancing myosin activity and initiating actomyosin interaction [ 44 ].

On the other side, activated CaM also binds to the caldesmon peptide, thus removing its hindering effect on actomyosin interaction in relaxed smooth muscle, due to caldesmon binding to actin-tropomyosin [ 45 ]. Hence, different CaM actions coordinately result in promoting smooth muscle contraction.

The extent of actomyosin interaction and ensuing smooth muscle contraction is determined by the balance between the activities of CaM-activated MLCK on one side, and MLCP on the other side [ 48 ]. We built a model that describes dynamic control loops regulating the vasomotor tone of vascular smooth muscle, blood volume, and mean arterial pressure.

The key players and their interactions are visually represented by the diagram of Fig 1. Labels for functional agents are the following.

Labels for effect mediators are the following. Lines with arrow ending indicate activation; lines with butt ending indicate inhibition. The system is a completely-closed one, i.

The activity and connections of baroreceptor stretch receptors and osmoreceptors are also included. The diagram consists of nodes, representing body systems producing physiological variations, and arcs connecting nodes, representing the mediators of these variations, viz. In the loop analysis of control systems, time constants and delays are essential parameters in the mathematical description of the system behaviour.

Time constants are associated with the time intervals spanning between the stimulation and the activation of a functional agent at a given node. Delays correspond to the time intervals spanning between the activation of a functional agent at one node, and the stimulation of another functional agent at the downstream node. In the herein presented systems, the different processes can be grouped into four time-scale ranges: endocrine signals; mechanical effects operating on stretch receptors; nerve signal conduction; and intracellular signal transduction pathways.

The time response for endocrine signals is not always known with precision, but a wide complex of evidence on endocrine axes suggests that the time spanning from the secretion of a hormone to the response of its target cells should range between min [ 54 — 56 ]. Data about the herein considered hormones are scarce, but pulsatile ANP secretion with a median frequency of 36 min has been found in healthy human subjects, thus being in line with the above estimates [ 57 ].

Also, an estimate for the time responses of stretch receptors to mechanical stimuli can be inferred from a study in the dog, where ANP secretion has been found to increase within 2. These responses appear to be one order of magnitude faster than those of endocrine signals.

The time response along the nervous tracts of the system, depending on nerve signal conduction and synaptic interaction, can be estimated at below 1. The presence of different processes characterised by time responses that differ of orders of magnitude enables mathematical simplifications relying on time-scale separation, which allowed us to rigorously analyse the complex interplay of interactions in the AAR systems.

Consider the system represented in Fig 1. A structural loop analysis was performed to achieve the following main result: the overall control scheme can be functionally split into two redundant control systems, based on negative loops, which operate in parallel and qualitatively perform the same control action.

The schemes describing the two coexisting regulation systems which can be achieved from Fig 1 through the mathematical processing outlined in the three steps above—see also the Models and methods section below are reported in Fig 2. It is important to stress that each of the two systems in Fig 2 , the one including DTC and the one including VSM, is a candidate oscillator according to the results in [ 15 , 16 ], since it is the negative feedback of a monotone system see the Models and methods section for details; [ 60 — 65 ].

Being a candidate oscillator, each of these systems admits a single equilibrium point for each given choice of the parameter values , corresponding to all the variables being at steady state homeostatic conditions ; if the equilibrium becomes unstable, then persistent oscillations occur. An influence analysis showed that the two separate, but coexisting, regulation systems have the same qualitative behaviour and execute the same function, although the two schemes are structurally different.

Indeed there is no one-to-one correspondence between the arcs. Remarkably, the influence matrices associated with the two systems are structurally consistent, as shown next. The entry M ij of the influence matrix M [ 66 — 68 ] see also [ 20 , 69 — 71 ] expresses the sign of the steady-state variation of the i th variable of a dynamical system due to a persistent positive excitation caused by an external input applied to the dynamic equation of the j th variable.

In our structural parameter-free analysis [ 66 , 71 ], each entry of the influence matrix can assume the following values. The structural influence matrices corresponding to the systems in Fig 2 are. Also, the two schemes are weakly consistent, because there is no contradiction between corresponding entries in the two structural influence matrices, apart from the first column, which is different because ACO does not affect any other key player in the VSM system, while in the DTC system it directly activates DTC, and thus indirectly affects all other key players.

After having examined the complete system, consisting of nodes acting at the systemic level, we made an attempt at combining the systemic and cellular levels. The nodes of the loops of our complete system see Fig 1 represent cells that transfer signals from upstream to downstream elements by intracellular signal transduction pathways. Therefore, we analysed a system consisting of a subset of the above one, including ANP and AVP stimulation of vascular smooth muscle, a complex of crosstalks between AVP- and ANP-dependent signal transduction pathways operating within vascular smooth muscle cells, and stretch receptors closing loops onto AVP and ANP secretory systems.

The system representation is shown in Fig 3. Labels for effect mediators and anatomical districts are the following. Other labels and line endings as in Fig 1. The choice for selecting vascular smooth muscle cells derives from the rather good knowledge of the interplay between AVP- and ANP-elicited pathways within these cells.

Moreover, the choice of the AVP and ANP endocrine systems resides in their antagonistic effects, and the presumable similarity of their delays, since both involve only one slow endocrine step time-limiting step , and a series of rapid intracellular processes, receptor responses, and nerve signal conduction steps.

A structural loop analysis allowed us to obtain the following results, derived in the Models and Methods section:. Hence, also this system is a candidate oscillator, as defined above [ 15 , 16 ]. The system corresponds to the following dynamic model, associated with the graph in Fig 4.

In particular, to study its oscillatory properties, we analysed the linearised version of the system around an equilibrium point:.

To investigate the problem from a mathematical standpoint, we introduced a suitable oscillation-propensity index. As discussed in [ 19 ], for oscillations to occur:. Therefore, we took as oscillation-propensity index the minimum loop gain that is necessary for the onset of oscillations.

The smaller this value, the more the system is prone to oscillations. Through our delay analysis we showed that, when all the loops have approximately the same delay, so that they can be regarded as a single negative loop with delay, the system is prone to oscillations. Conversely, when the loops can have different delay, oscillations may be ruled out, because the resulting gain stability margin is larger when the delays are non-homogeneous.

Then, the system of Eqs 6 — 9 becomes. For small values of the gains p and q , the system is stable and does not oscillate. If we increase the gains above a certain threshold, oscillations will appear. The critical condition for the onset of oscillations is given by the equation.

In general, we can measure the oscillation propensity as follows. The oscillation propensity is defined as. Therefore, the smaller the radius the closer the curve is to the origin , the larger the oscillation propensity. The radius of the blue circle centered in the origin and tangent to the curve is inversely proportional to the oscillation propensity. Hence, we can normalise the gains to get. An important consequence is the following: assuming that all the loops have approximately the same delay in normal conditions, then altering one of them by artificially changing its delay will hinder the oscillatory behaviour of the system.

Control loops are ubiquitous in biology at all scales, from individual cells to entire organisms, and are fundamental to rule the dynamic behaviour of living processes and to ensure homeostasis [ 72 , 73 ]. Hence, living beings can be seen as fully integrated complexes of control systems, operating by loop dynamics. Biological and physiological mechanisms result from an extremely complex interplay of interactions; this complexity has been given theoretical interpretations in the framework of organisational closure [ 74 , 75 ] and has been successfully analysed using system-theoretic and control-theoretic approaches [ 72 , 73 ].

In complex biological networks, the presence of network motifs [ 76 , 77 ] is fundamental to explain important behaviours; one of the most recurrent network motifs is the so-called feed-forward loop [ 73 , 78 ]. Such a network analysis has been carried out not only at the cellular level, but also at the organismal level, leading to network physiology [ 79 — 81 ], which aims at explaining physiological functions based on the topology of the network of interactions. In particular, the loop structures that can be found in the complex networks of dynamical interactions ruling life seem crucial to enable life-preserving dynamic behaviours in biology and physiology, and the functioning of each organism appears in fact as the result of complex aggregations and interactions of functional loops.

The well-documented AVP-ANP-RAAS endocrine control of body fluids and blood pressure was therefore analysed using mathematical tools, to highlight the loop arrangement and its dynamic function. The loop analysis of the whole system AAR shows that it can be split into two coexisting dynamic systems, which contain alternatively the VSM and DTC functional agents as loop nodes , thereby exerting their effects on blood pressure and blood volume, respectively.

The influence matrix analysis shows that the two systems are qualitatively equivalent in that they perform the same control function, even though the physiological mechanisms are different. Moreover, the loop analysis shows that both the VSM and the DTC loop systems are candidate oscillators having a single equilibrium point, which can be either stable or yield persistent oscillations under instability conditions. Also the AAV subsystem, combining functional agents acting at cellular and systemic scales, can be described as a candidate oscillator, whose propensity to exhibiting actual sustained oscillations is higher when the delays of all the loops in the subsystem are comparable.

Hence, our mathematical analysis suggests that the physiological mechanisms regulating long-term homeostasis of blood hydraulic parameters are arranged into a complex of equivalent loop systems, consisting of candidate oscillators with a single equilibrium point. Also, the whole system can be split into two systems displaying essentially the same functioning, an apparent redundancy that could offer alternatives for coping with accidental defaults, similar to the well-known, alternative kidney-lung regulation of blood pH [ 82 ].

Of course, our model must be seen as functionally coupled to other body systems, like the sympathetic and parasympathetic neurovegetative branches [ 83 ], while the interaction of multiple negative loop systems could be at the basis of complex oscillatory behaviours, with stochastic flavour, detected in the time course of physiological processes [ 84 ].

It is worth stressing that all the results we derived are completely independent of the exact functional expressions associated with activating and inhibitory interactions in the loop dynamics, and of the exact function parameters.

Hence we can be sure that they hold for any system with this qualitative structure, even when we lack precise quantitative information. Future research will be oriented to understanding if other homeostasis and endocrine systems display the same features, in order to possibly formulate a general paradigm in terms of loop dynamics.

Two important control loops are found in the baroreceptor reflexes operating over the short term and the kidneys operating over the long term. The aortic and carotid baroreceptors stabilize pressure, preventing short-term fluctuations; when this control loop is surgically removed, lability increases with little change in the average pressure. Positive feedback is a mechanism in which an output is enhanced in order to maintain homeostasis.

Positive feedback mechanisms are designed to accelerate or enhance the output created by a stimulus that has already been activated. Positive feedback mechanisms are designed to push levels out of normal ranges. To achieve this, a series of events initiates a cascading process that builds to increase the effect of the stimulus. This process can be beneficial but is rarely used because it may become uncontrollable.

A positive feedback example is blood platelet accumulation and aggregation, which in turn causes blood clotting in response to an injury of the blood vessels. Negative feedback mechanisms reduce output or activity to return an organ or system to its normal range of functioning.

Regulation of blood pressure is an example of negative feedback. Blood vessels have sensors called baroreceptors that detect if blood pressure is too high or too low and send a signal to the hypothalamus. The hypothalamus then sends a message to the heart, blood vessels, and kidneys, which act as effectors in blood pressure regulation. If blood pressure is too high, the heart rate decreases as the blood vessels increase in diameter vasodilation , while the kidneys retain less water.

These changes would cause the blood pressure to return to its normal range. The process reverses when blood pressure decreases, causing blood vessels to constrict and the kidney to increase water retention. In turn, ACTH directs the adrenal cortex to secrete glucocorticoids, such as cortisol. Glucocorticoids not only perform their respective functions throughout the body but also prevent further stimulating secretions of both the hypothalamus and the pituitary gland.

Temperature control is another negative feedback mechanism. Nerve cells relay information about body temperature to the hypothalamus. The hypothalamus then signals several effectors to return the body temperature to 37 degrees Celsius the set point.

The effectors may signal the sweat glands to cool the skin and stimulate vasodilation so the body can give off more heat. Positive feedback mechanisms are designed to push levels out of normal ranges.

To achieve this, a series of events initiates a cascading process that builds to increase the effect of the stimulus. This process can be beneficial but is rarely used because it may become uncontrollable. A positive feedback example is blood platelet accumulation and aggregation, which in turn causes blood clotting in response to an injury of the blood vessels.

Negative feedback mechanisms reduce output or activity to return an organ or system to its normal range of functioning. Regulation of blood pressure is an example of negative feedback. Blood vessels have sensors called baroreceptors that detect if blood pressure is too high or too low and send a signal to the hypothalamus.

The hypothalamus then sends a message to the heart, blood vessels, and kidneys, which act as effectors in blood pressure regulation. If blood pressure is too high, the heart rate decreases as the blood vessels increase in diameter vasodilation , while the kidneys retain less water. These changes would cause the blood pressure to return to its normal range.

The process reverses when blood pressure decreases, causing blood vessels to constrict and the kidney to increase water retention.