Blood pressure long term regulation: a neural network model of the set point development

Abstract

Background: The notion of the nucleus tractus solitarius (NTS) as a comparator evaluating the error signal between its rostral neural structures (RNS) and the cardiovascular receptor afferents into it has been recently presented. From this perspective, stress can cause hypertension via set point changes, so offering an answer to an old question. Even though the local blood flow to tissues is influenced by circulating vasoactive hormones and also by local factors, there is yet significant sympathetic control. It is well established that the state of maturation of sympathetic innervation of blood vessels at birth varies across animal species and it takes place mostly during the postnatal period. During ontogeny, chemoreceptors are functional; they discharge when the partial pressures of oxygen and carbon dioxide in the arterial blood are not normal.

Methods: The model is a simple biological plausible adaptative neural network to simulate the development of the sympathetic nervous control. It is hypothesized that during ontogeny, from the RNS afferents to the NTS, the optimal level of each sympathetic efferent discharge is learned through the chemoreceptors' feedback. Its mean discharge leads to normal oxygen and carbon dioxide levels in each tissue. Thus, the sympathetic efferent discharge sets at the optimal level if, despite maximal drift, the local blood flow is compensated for by autoregulation. Such optimal level produces minimum chemoreceptor output, which must be maintained by the nervous system. Since blood flow is controlled by arterial blood pressure, the long-term mean level is stabilized to regulate oxygen and carbon dioxide levels. After development, the cardiopulmonary reflexes play an important role in controlling efferent sympathetic nerve activity to the kidneys and modulating sodium and water excretion.

Results: Starting from fixed RNS afferents to the NTS and random synaptic weight values, the sympathetic efferents converged to the optimal values. When learning was completed, the output from the chemoreceptors became zero because the sympathetic efferents led to normal partial pressures of oxygen and carbon dioxide.

Conclusions: We introduce here a simple simulating computational theory to study, from a neurophysiologic point of view, the sympathetic development of cardiovascular regulation due to feedback signals sent off by cardiovascular receptors. The model simulates, too, how the NTS, as emergent property, acts as a comparator and how its rostral afferents behave as set point.

Figure 1

Baro-Cardiopulmonary-Chemoreceptor Negative Cardiovascular Feedback Loop. Med, medulla oblongata; CIC, CAC, VMC, cardioinhibitory, cardioaccelerator and vasomotor centers, respectively; Comp, comparator; neural reference R; error signal E after the difference against the outflow from the baro, cardiopulmonary and chemoreceptors (Ba, Ca ChR), respectively. BP, blood pressure = PRxCO; Mult, multipliers; PR, peripheral resistance; CO, cardiac output = HRxSV; HR, heart rate; SV, stroke volume. P, pacemaker; CE, myocardial contractile fibers; Trans, postulated transducers from neural section to CV side. Point C, output from the baro, cardiopulmonary and chemoreceptors; Point E_k, output from the vasomotor center VMC, in the medulla. Reproduced after Ref (1).

Figure 2

Cardiovascular System Nervous Control. The NTS receives afferents from its rostral nervous structures and send efferents to pre-sympathetic and pre-parasympathetic neurons. The same points C and E_k link, respectively, to NTS (the comparator) and to the blood vessels.

Figure 3

Neural network model of the simpathetic regulation. For each tissue (k), the sympathetic efferent discharge (E_k), the blood flow (F_k), the venous partial pressure of oxygen and carbon dioxide (pO₂v_k) and (pCO₂v_k), and the arterial partial pressure after the lung gases diffuse (pO₂a) and (pCO₂a) are shown. Finally chemoreceptors discharge (C) is depicted. R_k represents the rostral neural nuclei inputs from the NTS, and Wr_k and Wc_k represent the synaptic weights.

Figure 4

Arterial partial pressure of oxygen (pO₂a). Partial pressure evolves with fluctuations until the optimal value is achieved. The figure shows the dynamics of the first 200 iterations until the system adapts (when the discharge when the frequency of chemo receptors fall to zero). For each animal maturation takes place in a given time T, since 1,000 iterations were run, the unit is T/1,000. This comment applies to the rest of the figures.

Figure 5

Arterial partial pressure of carbon dioxide (pCO₂a). Partial pressure, before arriving at its maximum value, evolves like chemoreceptor discharge. Pressure converges to the optimal value.

Figure 6

Venous partial pressure of oxygen (pO₂v_k) of each tissue (k). The partial pressures start from random values and converge to the optimal values that provoke minimum chemoreceptor discharge.

Figure 7

Venous partial pressure of carbon dioxide (pCO₂v_k) of each tissue (k). Partial pressures start from random values and converge to the optimal values that provoke minimum chemoreceptor discharge.

Figure 8

Chemoreceptor discharge rate (C). When arterial partial pressures drift from the normal values, the chemoreceptors discharge, and do so until equilibrium is reestablished. The chemoreceptor discharge rate reaches a maximum value, then slowly and with fluctuations decays to zero when learning is finished. Measured in arbitrary values between 0 and 1.

Figure 9

Sympathetic efferent discharge rate (E_k) of each tissue (k). The discharge rate values evolve so that, after some fluctuations, all converge. Measured in arbitrary values between 0 and 1.