KeywordsFiring Rate Sympathetic Nerve Activity Nucleus Tractus Solitarius Arterial Baroreceptor Nucleus Tractus Solitarius Neuron
Blood pressure is controlled by several feedback mechanisms. The fastest one baroreceptor reflex (baroreflex) can be defined as the biological neural control system responsible for the short-term blood pressure regulation.
The afferent part where the arterial pressure is being read out, transduced, and supplied
The central nervous system (CNS) where this input is processed and converted to the sympathetic and parasympathetic nerve activities
The effector organs that respond to sympathetic and parasympathetic tones by adjusting heart rate, contractility, vascular resistance, and a number of other physiological parameters
The afferent part is represented by baroreceptors, mechanoreceptors located in the great arteries, heart, and pulmonary vasculature, that transduce arterial pressure into action potential trains. Baroreceptors provide input to second-order neurons in nucleus tractus solitarius (NTS) located in the lower brainstem. Via a network of interneurons, the second-order barosensitive neurons provide an excitatory input to cardiac vagal motoneurons (CVM) in nucleus ambiguus (NA) and dorsal motor nucleus of vagus (DMNX) and inhibit the pre-sympathetic neurons in rostral ventrolateral medulla (RVLM). CVMs and pre-sympathetic RVLM neurons define parasympathetic (para-SNA) and sympathetic (SNA) nerve activities, respectively. Baroreflex models are aimed to quantify para-SNA and SNA reflex responses to sharp changes in arterial BP and, thus, attempt to describe the neural part of the system.
Deviations in blood pressure (BP) and blood volume are sensed in cardiovascular system by baroreceptors, mechanosensitive nerve endings activated by vascular or cardiac distension (Fig. 2). Arterial baroreceptors (located in the aortic arch and the carotid sinuses, see Fig. 1) increase their activity when BP rises, and reduce it if BP lowers. Cardiopulmonary baroreceptors in the heart, vena cava and pulmonary vasculature are aimed to sense central blood volume, and are sometimes called volume receptors or low-pressure receptors.
The afferent activity from arterial baroreceptors is sent to the medullary brainstem area called nucleus tractus solitarius (NTS) through glossopharyngeal nerve (from carotid sinus baroreceptors) and vagus nerve (from aortic arch) that together are known as the buffer nerves. In the NTS this information is processed by an intricate network of interneurons that control efferent parasympathetic (para-SNA) and sympathetic (SNA) nerve activities and release of antidiuretic peptide vasopressin (AVP) (see Fig. 1). All these mechanisms in response to changes in the arterial BP cause reflexes (Fig. 2) that ultimately push BP in the opposite direction providing a negative feedback control of arterial BP called arterial baroreflex. The CNS pathways of cardiopulmonary baroreceptors are similar to that of arterial ones except their activation has little effect on heart rate (HR) which is the fastest mechanism of BP control.
Due to complexity of the system, modeling studies usually focus on a particular aspect depending on phenomena considered while using simplified description of other compartments. Several integrative mathematical models were used to elucidate the role of baroreflex in cardiovascular instabilities, such as heart rate variability and spontaneous fluctuations of the arterial pressure (e.g., Mayer waves).
As a result of a change in arterial pressure, the cross-sectional area of the arteries changes leading to mechanical deformation of artery walls. Changes in the membrane strain resulting from the artery wall deformation lead to changes in the conductance of a variety of mechanosensitive ion channels in the sensory terminals of arterial baroreceptors. The cumulative effect of the opening of those channels in response to rise in pressure is an increased inward (depolarizing) current. If the resulting depolarization exceeds certain threshold, baroreceptors start firing action potentials with a rate defined by the magnitude of this current.
Rose et al. (1995) used a little different approach. Their baroreceptors had a pressure-dependent depolarizing current which was linear above a threshold pressure: I baro = K(P − P thr) if P > P thr and I baro = 0 otherwise.
Baroreceptor response to changes in arterial BP is very complex, nonlinear, and has multiple timescales. Rapid jumps in BP lead to much stronger changes of baroreceptor activity than gradual excursions of the same magnitude. Acute hypertension results in a sharp rise in the baroreceptor activity which, however, declines in time if hypertension is maintained. After acute withdrawal from the increased BP, baroreceptors first exhibit reduced activity (post-excitatory depression) which then adapts back to baseline.
Firing rate increases with BP.
The response exhibits threshold and saturation.
Sufficiently fast decreases in pressure cause firing rate to fall below the threshold.
A step change in pressure causes a step change in firing rate followed by a decay in firing rate (called adaptation or resetting depending on the timescale).
Response curves are sigmoidal and show asymmetric hysteresis-like behavior.
Conductance-Based Baroreceptor Model
Baroreceptor fibers are divided into two different types, A-type and C-type, depending on whether they are myelinated or not. Schild et al. (1994) performed a thorough study of their electrophysiological properties and developed a conductance-based model of A- and C-type cells based on voltage-clamp recordings in rat nodose sensory neurons (carotid sinus baroreceptors). Their model included two Na+ currents exhibiting fast and slow tetrodotoxin (TTX)-insensitive kinetics; low- and high-threshold Ca2+ currents exhibiting transient and long-lasting dynamics, respectively; and outward K+ currents consisting of a delayed-rectifier K+ current and Ca2+-activated K+ current. The model also includes extra- and intracellular C2+ dynamics.
Firing Rate-Based Baroreceptor Model
Nucleus Tractus Solitarius (NTS)
Baroreceptors map the spatial pressure distribution onto the inputs to the second-order neurons in the NTS. One of the puzzles of the identified baroreflex-related neurons in NTS is that in spite of receiving direct inputs from the first-order neurons, their activity does not have any frequency component corresponding to cardiac frequency. Somehow they do not respond to each heartbeat by performing a “low-pass filtration” of their inputs.
Rogers et al. (2000) suggested that this property can be concerned either with specific biophysical properties of NTS baroreceptors (Fig. 3) or with specific interactions in the NTS network of second-order interneurons (Fig. 4). By analyzing the responses of the second-order NTS neurons to induced blood pressure pulses, they have noticed that barosensitive second-order NTS neurons respond to blood pressure changes with a burst of activity whose frequency is much lower than the frequency of cardiac cycle, and the activity of these neurons is inhibited just before and after the bursts. Using these observations they developed a series of mathematical models of early stages of baroreflex based on the intrinsic cell properties and network mechanisms.
Intrinsic Properties-Based Model
Because of the different pressure thresholds, baroreceptors have a distributed sensitivity to BP and its rate of change. “Barotopic” organization hypothesis suggests that individual baroreceptors’ pressure thresholds (below which they are silent) are topically distributed in an interval of the pressures and that each second-order barosensitive neuron receives inputs from the first-order ones, whose thresholds lie in a definite small interval of pressure values.
In addition to basic spiking currents baroreceptors in their model included A-type potassium current responsible for rapid adaptation and a pressure-dependent depolarizing current which was linear above a threshold pressure (see section “Pressure-Electrical Transduction”). Each baroreceptor had its own threshold pressure P thr, and the thresholds had a sigmoidal distribution. Each NTS neuron received excitatory inputs from several baroreceptors with close thresholds and projected to several CVMs. The NTS neurons and CVMs had six conductances: sodium, delayed-rectifier potassium, A-type potassium, AHP-type potassium, l-type calcium, leakage conductances, and intracellular calcium dynamics including pumping and buffering. The CVMs projected to the sinoatrial (SA) node where their action potentials activated an acetylcholine (ACh)-activated inward rectifier K+ hyperpolarizing current which slowed the depolarization of the node and hence decreased the heart rate. The effect of vagal impulses on the hyperpolarizing current was greater for those arriving later in the cardiac cycle.
Sympathetic and Parasympathetic Activities
As mentioned, the classical baroreflex control of sympathetic nerve activity (SNA) operates via the second-order baroreceptor neurons that project to the caudal ventrolateral medulla region (CVLM). Through this path, the baroreceptor activation provides activation of CVLM neurons which in turn inhibit the pre-sympathetic rostral ventrolateral medulla (RVLM) neurons hence lowering both the RVLM activity and SNA. This pathway provides a direct negative SNA reflex response.
Sympathetic activity contains the respiratory modulation, which suggests that sympathetic and respiratory networks interact. Respiratory activity is also known to be modulated by the baroreceptor input. Together these facts imply that there may be another baroreflex pathway mediated by the respiratory neurons.
Baekey et al. (2010) have demonstrated that transient pressure pulses perturb the respiratory pattern in a phase-dependent manner, and those perturbations strongly depend on the integrity of the pons. The stimuli were delivered during inspiration, post-inspiration, or late expiration. With pons intact, the applied barostimulation had almost no effect on the amplitude and duration (i.e., inspiratory period) of the phrenic bursts even when stimuli were delivered during inspiration. At the same time, these stimuli suppressed or abolished inspiratory modulation of SNA. In contrast, the same stimuli delivered during post-inspiration or late expiration produced an increase in the expiration period and decreased SNA. The barostimulation-evoked prolongation of expiration was greater if stimulation was applied later during the expiratory phase. After pontine transection the barostimulation shortened the apneustic inspiratory burst. In all cases the sympathetic baroreflex-induced lowering of SNA persisted confirming the presence of a direct baroreflex pathway which bypasses the respiratory network.
Based on their experimental findings, Baekey et al. (2010) developed a mathematical model of baroreceptor-respiratory-sympathetic interactions that explained phase-dependent respiratory response to transient barostimulation. One of the implications of their model was that there is indeed a second pathway from baroreceptors to pre-sympathetic neurons in RVLM. This second pathway is mediated by respiratory circuits, specifically by the post-I neurons of BötC. This baroreflex pathway is strongly dependent on the respiratory-sympathetic interactions and needs pons to be intact.
The Role of Cardiopulmonary Baroreceptors
A majority of modeling studies only take into account arterial baroreceptors. However, under certain conditions blood volume regulation provided by cardiopulmonary baroreceptors plays a major role in blood pressure control. To understand the interplay between different mechanisms, Ursino (2000) developed a closed-loop mathematical model which included both arterial and cardiopulmonary baroreceptors and four effector components: heart period, systemic peripheral resistance, systemic venous unstressed volume, and heart contractility. He simulated the model to mimic the baroreflex response to mild and severe acute hemorrhages and found that the cardiopulmonary baroafferents play a significant role in the control of systemic arterial pressure during mild hemorrhages (lower than 3–4 % of the overall blood volume). Under these conditions arterial pressure could be maintained at its normal level solely by cardiopulmonary feedback loop without the intervention of the arterial baroreceptors. During more severe hemorrhages the latter take over the responsibility for pressure control, and the contribution of cardiopulmonary baroreceptors becomes negligible.
Ursino (2000) noticed that according to their model the stability region in the parameter space of the closed-loop system is quite narrow. For example, an increase in the static gain of the baroreceptors or a decrease in the rate-dependent component may lead to self-sustained oscillations similar to Mayer waves.
Baroreflex and Mayer Waves
Mayer waves are synchronous oscillations in SNA and arterial BP slower than respiratory rhythm. The origin and physiological mechanisms of these oscillations are currently unknown. The fact that Mayer waves are abolished by sinoaortic baroreceptor denervation strongly suggests the involvement of arterial baroreflex in this phenomenon. The baroreflex theory of Mayer waves explains the emergence of self-sustained oscillations in arterial pressure by the instability caused by fixed time delays in the baroreflex (presumably sympathetic) feedback loop (see the review by Julien (2006) and the literature therein cited). Since virtually any system with the delayed feedback is unstable for sufficiently large time delay values, many different models of dynamic arterial pressure control have succeeded in predicting Mayer waves (Julien 2006). The magnitude of the time delay is the determinant factor of the emerging oscillation frequency. Mayer wave frequency varies significantly between species which suggests that different species should have significantly different time delays in baroreflex feedback loop. In spite of numerous hypotheses suggested, no consistent explanation of this species-to-species variability was yet provided. Another challenge for the baroreceptor theory is the dependence of Mayer wave amplitude on the mean SNA level which the existing models fail to explain.
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