INTRODUCTION

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THE SYMPATHETIC LIMB of the arterial baroreflex is the most important negative feedback control system functioning physiologically to attenuate the effects of rapid daily perturbations in arterial pressure (3, 5, 6, 10, 27). For example, the change in arterial pressure induced by a postural change from lying to standing is sensed by arterial baroreceptors located within the walls of the aortic arch and internal carotid arteries. This fall in pressure is neurally encoded and relayed via afferent pathways to a brain stem vasomotor center, and it then immediately causes an appropriate degree of compensatory vasoconstriction through activation of efferent sympathetic pathways. Without such compensation, the simple act of standing would cause a fall in arterial pressure responsible for perfusing the brain, potentially resulting in loss of consciousness (5, 11, 13, 30).

A series of experimental studies by Guyton and colleagues (6) developed an open-loop approach for analytically characterizing a physiological system with a feedback loop and established important concepts such as Guyton's equilibrium diagram for right atrial pressure, venous return, and cardiac output. This diagram enables us to quantitatively and analytically understand how the unique value of the cardiac output is determined by the cardiovascular system. Similarly, the arterial baroreflex system has been extensively studied by the open-loop approach (14, 15, 24). Many earlier studies revealed the baroreceptor-mediated control of sympathetic nerve activity (SNA) (4, 8, 9, 16, 19, 23) and the sympathetic control of heart rate and cardiovascular mechanics (2, 7, 18, 26, 29). However, an analytic approach for identifying an operating point of the arterial baroreflex has not been developed. Such an approach is needed for an integrative understanding of the mechanism by which the arterial pressure at the operating point is determined under the closed-loop conditions of the feedback system. The purpose of this investigation was to develop a new analytic framework for the sympathetic arterial baroreflex. The results indicate that the decomposition of the baroreflex loop into mechanoneural and neuromechanical arcs allows us to analytically determine the operating point by equilibrating respective function curves.

	METHODS

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Theoretical Consideration: Coupling of Mechanoneural and Neuromechanical Arcs

View larger version (20K): [in this window] [in a new window]   Fig. 1.   Sympathetic arterial baroreflex system in closed-loop (A) and open-loop (B) conditions. Pd indicates external disturbance to arterial pressure (AP). In open-loop conditions, relationship between baroreceptor pressure (BRP) and sympathetic nerve activity (SNA) and that between SNA and systemic arterial pressure (SAP) can be quantitatively measured. When the 2 curves characterizing the 2 relationships are plotted on an equilibrium diagram, intersection of the 2 curves is supposed to be operating point of AP and SNA under closed-loop conditions of feedback system (C).

Animals and Surgical Procedures

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To open the feedback loop of the arterial baroreflex system, we cut the vagi and the aortic depressor nerves and isolated the carotid sinus baroreceptor regions by our previously described method (24). Briefly, the external carotid artery was ligated at the root of the bifurcation of the common carotid artery, and then the internal carotid and pterygopalatine arteries were embolized with two ball bearings of 0.8-mm diameter (Fig. 2). Two short polyethylene tubes (PE-50) were placed into both carotid sinuses and connected to a fluid-filled transducer (DX-200; Viggo-Spectramed, Singapore) and to a custom-made servo-controlled pump system (24, 25) based on an electromagnetic shaker and power amplifier (ARB-126; AR Brown, Osaka, Japan). We used the servo-controlled pump to impose various pressures on the carotid sinus baroreceptor regions.

View larger version (22K): [in this window] [in a new window]   Fig. 2.   Scheme for an experimental setting. To characterize relationship between carotid sinus pressure (CSP) and SNA and that between SNA and SAP under open-loop conditions of arterial baroreflex system, we made a computer command a power amplifier to drive an electromagnetic shaker so that CSP changed stepwise between 80 and 160 mmHg. To close feedback loop of carotid sinus baroreflex system with carotid sinuses isolated vascularly, in real time we imposed instantaneous SAP on carotid sinus baroreceptor regions. Inset, example of original tracings of CSP, SNA, and SAP during closed-loop conditions.

To record SNA, we identified the left renal nerve branch from the aorticorenal ganglion via a retroperitoneal approach through a left flank incision. The nerve branch was isolated and carefully dissected free. A pair of Teflon-coated platinum wires (7720; A-M Systems, Everett, WA) was looped around and fixed on the nerve branch. The implantation site of the wires was embedded in silicone rubber (Sil-Gel 604; Wacker, Munich, Germany). Finally, the flank incision was closed in layers. The nerve activity was amplified and band-pass filtered in the frequency range between 150 and 3,000 Hz (JB-610J and AB-610J; Nihon Kohden). The root mean square (RMS) waveform of SNA was generated through a custom-made RMS-DC converter with a cutoff frequency of 100 Hz.

Data Recording

Protocol 1: Characterization of two arcs under open-loop conditions. To characterize the mechanoneural and neuromechanical arcs, we examined the relationship between carotid sinus pressure (CSP) and SNA and that between SNA and SAP under open-loop conditions of the arterial baroreflex system. After a stabilization period during which CSP was kept at 100 mmHg for 30 min, we altered CSP sequentially in 10-mmHg step increments from 80 to 160 mmHg, and then in 10-mmHg decrements from 160 to 80 mmHg by the servo-controlled pump. Each step was maintained for 1 min. The command signal to the servo-controlled pump was generated by a dedicated laboratory computer (PC-9801RA21; NEC, Tokyo, Japan) through a digital-to-analog converter (DA12-4-98; Contec, Osaka, Japan). The same cycle of sequential changes in CSP was repeated three times over a 1-h period. The electrical signals of CSP, SNA, and SAP were first low-pass filtered with antialiasing filters having a cutoff frequency of 50 Hz (3 dB) and an attenuation slope of 80 dB/decade (ASIP-0260L; Canopus, Kobe, Japan) and then digitized at a rate of 2 kHz by means of an analog-to-digital converter (AD12-16D-98H; Contec).

Protocol 2: Measurement of operating points under closed-loop conditions. To measure the operating points under the closed-loop conditions of the arterial baroreflex system, we closed the feedback loop of the system with our servo-controlled pump system. As shown in Fig. 2, while digitizing SAP at a rate of 2 kHz through the analog-to-digital converter, the computer in real time commanded the power amplifier to make CSP identical with SAP. Using this technique, we were able to impose the same pressure waveform as SAP on the carotid sinus baroreceptor in the frequency range up to 10 Hz. CSP, SNA, and SAP were recorded for 3 min under the closed-loop conditions.

Protocol 3: Effects of hemorrhage on two arcs and operating points. To examine the effects of loss of blood on the two arcs and the operating point, we also characterized the two arcs and measured the operating points in various hemorrhagic states. We randomly allocated any two volumes of blood loss to each rat in the range of 0.5-2% of body weight by drawing and returning blood through the polyethylene tubing placed into the left common carotid artery.

Data Analysis

To parametrically characterize the relationship between the input and output, we analyzed the data using a four-parameter logistic equation model (15) where y is the output and x is the input. The four parameters are defined as follows: p₁ is the range of change in y (i.e., maximum minus minimum values of y); p₂ is the coefficient for calculation of gain; p₃ is the value of x corresponding to the midpoint over the range of y; and p₄ is the minimum value of y. The instantaneous gain is also calculated from the first derivative of the logistic function, and the maximum gain is p₁p₂/4 at x = p₃. After the parametric characterization, we identified the intersection of the two curves as the estimated operating point on the equilibrium diagram (Fig. 1C).

We obtained the actual operating points under the closed-loop conditions of the arterial baroreflex in baseline and various hemorrhagic states as means of a 3-min data period during which CSP was controlled to be identical with SAP.

Statistical Analysis

	RESULTS

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Shown in Fig. 3A is a representative example of original tracings of CSP, SNA, and SAP during the open-loop carotid sinus baroreflex control of SNA and SAP in the baseline state. The responses of SNA and SAP to a given level of CSP were consistent and reproducible throughout the 1-h recording protocol. The fact that SAP appears to be a mirror image of CSP indicates that the arterial baroreflex is a negative feedback system. Figure 3, B and C, displays the relationship between CSP and SNA and that between SNA and SAP of the example. Both of the curves characterizing the mechanoneural and neuromechanical arcs were sigmoidal and could be well described by the four-parameter logistic equation models; the RMS error of estimate for the mechanoneural arc was 1.8% and that for the neuromechanical arc was 0.3%.

View larger version (28K): [in this window] [in a new window]   Fig. 3.   Original tracings of CSP, SNA, and SAP in baseline state (A) and graphs showing relationship between CSP and SNA (B) and between SNA and SAP (C). Values in B and C are means ± SD of steady-state responses at same level of CSP. For mechanoneural (MN) arc curve characterizing CSP-SNA relationship, 4 parameters for curve fitting were estimated as follows: p1 = 1.13; p2 = 0.0751; p3 = 123; p4 = 0.078. For neuromechanical (NM) arc curve characterizing SNA-SAP relationship, 4 parameters were estimated as follows: p1 = 152; p2 = 2.86; p3 = 0.575; p4 = 56. See METHODS for detailed explanation of procedure for normalization of value of SNA and definition of parameters. a.u., Arbitrary units.

Figure 4 demonstrates the effect of severe hemorrhage on the two arcs in the rat for which baseline data were presented in Fig. 3. As can be seen in Fig. 4A, severe hemorrhage did not affect the SNA response but attenuated the SAP response to CSP; severe hemorrhage seemed to affect only the neuromechanical arc. The differential effect of hemorrhage becomes even clearer if we draw the function curves of the two arcs as shown in Fig. 4, B and C. The blood loss markedly reduced the slope of the neuromechanical arc curve and shifted the curve downward, whereas the mechanoneural arc curve was similar to that in the baseline state.

View larger version (25K): [in this window] [in a new window]   Fig. 4.   Original tracings of CSP, SNA, and SAP in a severe hemorrhagic state (A) of animal whose baseline data were presented in Fig. 3 and graphs showing relationship between CSP and SNA (B) and between SNA and SAP (C). Values in B and C are means ± SD of steady-state responses at same level of CSP. For MN arc curve characterizing CSP-SNA relationship, 4 parameters for curve fitting were estimated as follows: p1 = 1.11; p2 = 0.0790; p3 = 123; p4 = 0.059. For NM arc curve characterizing SNA-SAP relationship, 4 parameters were estimated as follows: p1 = 78; p2 = 1.52; p3 = 0.501; p4 = 15.

To show how the operating point estimated from the two arc curves moved after severe hemorrhage, we plotted the two curves of Fig. 3 or Fig. 4 on the equilibrium diagram (Fig. 5). The pressure and SNA at the intersection in the baseline state (Fig. 5A) were computed to be 123 mmHg and 0.501 arbitrary units (a.u.), respectively, whereas the measured pressure and SNA at the true operating point under the closed-loop conditions of the arterial baroreflex were 122 mmHg and 0.502 a.u., respectively. On the other hand, pressure and SNA at the intersection after severe hemorrhage (Fig. 5B) were calculated to be 69 mmHg and 1.02 a.u., respectively, whereas the measured pressure and SNA at the true operating point were 68 mmHg and 1.02 a.u., respectively. A good agreement between the operating points estimated and measured was observed even after severe hemorrhage. In the baseline state, the two arc curves appeared to intersect each other near the midpoint, i.e., p₃, of each arc where each arc gain was maximum by definition (see METHODS). After severe hemorrhage, on the other hand, the intersection was located on the outlying portion of both curves.

View larger version (12K): [in this window] [in a new window]   Fig. 5.   Equilibrium diagrams of MN (solid line) and NM (dotted line) arcs in baseline (A) and severe hemorrhagic state (B). , Intersections that are assumed to be operating points of closed-loop conditions of arterial baroreflex system in respective states. See text for detailed explanation.

The relationships between the operating points estimated by the equilibrium diagram analysis and those measured for 48 cases in 16 rats are illustrated in Fig. 6. For both arterial pressure and SNA, the estimated values are very close to the measured ones. The RMS error of estimate for arterial pressure was 2% and that for SNA was 3%.

View larger version (16K): [in this window] [in a new window]   Fig. 6.   Relationships between values analytically estimated and actually measured for arterial pressure (A) and SNA (B) at operating points of closed-loop conditions of arterial baroreflex among 48 cases in 16 rats. RMS, root mean square.

The multiple-comparison test indicated that hemorrhage significantly reduced arterial pressure and significantly increased SNA under the closed-loop conditions of the arterial baroreflex according to the severity of blood loss (Table 1). Hemorrhage did not affect any of the four parameters characterizing the mechanoneural arc curve, but reduced p₁, p₂, and p₄ of the neuromechanical arc curve.

	DISCUSSION

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We have shown that the operating point of the sympathetic arterial baroreflex estimated from the open-loop operational curves of the mechanoneural and neuromechanical arcs was in good agreement with that measured under the closed-loop conditions in various hemorrhagic states. These results indicate the validity of our framework for the analytic estimation of the operating point of the sympathetic baroreflex control of arterial pressure.

Importance of Analytic Approach in Estimating Operating Point of Feedback System

The proposed framework made it possible to describe the integrative behavior of the sympathetic arterial baroreflex system. As shown in Fig. 7A, the controlled variable of the system, arterial pressure, is fed back into the mechanoneural arc. For the sake of simplicity, we linearized both functional curves. In the mechanoneural arc, a set-point pressure is displayed as reference. The functional meaning of the set-point pressure is the pressure that nullifies SNA on the mechanoneural arc curve (Fig. 7B). The manipulated variable SNA, then, affects the characteristics of the neuromechanical arc. In the neuromechanical arc, we assume an offset value of pressure as P₀. The functional meaning of P₀ is shown as the pressure that is generated by the cardiovascular system at the null SNA (Fig. 7B). Under the closed-loop conditions of the feedback system, the controlled and manipulated variables should converge on their respective values at the operating point. This framework allows us to explain analytically and show graphically the effect of hemorrhage on the arterial pressure and SNA under closed-loop conditions. Loss of blood volume, the external disturbance that we used in the present study, reduced both the gain and the offset of the neuromechanical arc curve and lowered the operating pressure and increased the operating SNA simultaneously (Fig. 7B).

View larger version (22K): [in this window] [in a new window]   Fig. 7.   Carotid sinus baroreflex system composed of MN and NM arcs based on our framework (A). For simplicity, we linearized both functional curves. A set-point value (Pset) for a controlled variable, AP, could be supposed as pressure at which SNA becomes minimal (B). Gain factor of MN arc is expressed as G. Characteristics of NM arc could be described by gain factor H and offset pressure P0; P0 is pressure that cardiovascular system generates at minimum SNA. Loss of blood volume (BV), therefore, could be considered to lower gain and offset of NM arc (dotted line) and then to reduce AP and increase SNA at operating point of closed-loop conditions of system. If MN arc has an infinite gain, AP at operating point (Poperating) matches with value at set point (Pset). Note that hemorrhage did not affect Pset but lowered Poperating. In contrast to our framework, an earlier diagram (C) proposed by Kent et al. (15) described operating point as "set point." They reported that intersection of CSP-SAP curve (solid line) and line of identity (dashed line) was termed "set point." See text for detailed explanation.

As shown in Fig. 7B, the set-point pressure and operating-point pressure are obviously different. The operating-point pressure is always lower than the set-point pressure. From Fig. 7A, according to the feedback control theory (6), ignoring P₀ yields the operating-point pressure as where P_set is the set-point pressure, G is the gain of the mechanoneural arc, and H is the gain of the neuromechanical arc. The operating-point and set-point pressures match only when the open-loop gain, i.e., GH, is infinitely large. The fact that the loop gain of the carotid sinus baroreflex is on average ~2-3 (6, 10, 15, 24) suggests that the operating-point pressure should be ~65-75% of the set-point pressure. Kent et al. (15) estimated the carotid sinus baroreflex characteristics in terms of the CSP-SAP relation and defined the set-point pressure as the pressure at which CSP equals SAP (Fig. 7C). However, this pressure is the operating-point pressure and thus should not be confused with the set-point pressure in our definition. The importance of the distinction between the operating-point and set-point pressures is supported by the fact that hemorrhage greatly affected the operating-point pressure but did not affect the mechanoneural arc and, thereby, the set-point pressure. Although such an argument may seem a matter of semantics, we believe that clear distinction between the set-point and operating-point pressures in the framework of control theory is crucial for in-depth understanding of the physiological mechanism determining arterial pressure through the baroreflex system.

Baroreflex Gain and Function

Three cases are simulated, in which the effect of the external disturbance is assumed to shift the neuromechanical arc only downward by 40 mmHg. In the first case (Fig. 8A), the two curves of the mechanoneural and neuromechanical arcs before the imposition of the external disturbance are assumed to be similar to those of the baseline state shown in Fig. 5A. In such a case, the two curves intersect each other at the point at which the instantaneous gain of each arc is peaked, and thus the instantaneous gain of the total baroreflex loop becomes maximal at the operating point of the closed-loop conditions. These factors determine the operating point after the imposition of the external disturbance and thus contribute toward attenuating the effect of external disturbance to 10 mmHg. In the second case (Fig. 8B), the neuromechanical arc before the external disturbance is assumed to be shifted at the lower left on the equilibrium diagram, whereas the characteristics of the mechanoneural arc are the same as those of Fig. 8A. Although the maximum gain of each arc is the same as that of Fig. 8A, the external disturbance could result in a pressure fall by 23 mmHg. In the third case (Fig. 8C), we suppose that the mechanoneural arc curve is shifted upward and that the neuromechanical arc curve is shifted as much as that of Fig. 8B. These conditions deviate the operating point toward the outlying portion of both curves. The effect of external disturbance, therefore, could not be reduced at all by such an ill-conditioned baroreflex system, even if the maximum gain of each arc remained unchanged. Thus it is fair to say that the arterial baroreflex system displays its role to the full if the instantaneous gain of each arc is peaked at the operating point of the closed-loop conditions.

View larger version (12K): [in this window] [in a new window]   Fig. 8.   Equilibrium diagrams between 1 MN arc (solid line) and 2 NM arcs before (dotted line) and after (dashed line) imposition of external disturbance to NM arc. Effects of external disturbance that shifts NM arc only downward by 40 mmHg are simulated in 3 conditions of baroreflex system. , , Operating points before and after external disturbance, respectively. In normal conditions similar to Fig. 5A, effect of external disturbance is attenuated to 10 mmHg (A). If NM arc curve before external disturbance is shifted at lower left (B), effect of external disturbance results in a pressure fall by 23 mmHg despite same MN arc curve and value of maximum gain of NM arc as those in A. If NM arc curve is shifted at lower left and MN arc curve is shifted upward before the external disturbance (C), effect of external disturbance is not attenuated at all, even if values of maximum gains of two arcs should be same as those in A.

To examine whether the actual baroreflex system is optimized in terms of the gain, we reanalyzed the baroreflex gain of the experimental data obtained during the baseline states. Here we define an optimization index for a total-loop gain of the baroreflex system as follows where G_{Total,operating} is the total-loop gain at the operating point of the closed-loop conditions, G_MN,max is the maximum gain (G_max) of the mechanoneural arc, and G_NM,max is G_max of the neuromechanical arc. As illustrated in Fig. 9A, if the gains of both arcs were not maximal at the operating point, the total-loop gain should not be maximal at the operating point. In such a case, the optimization index should not attain 100%. Interestingly, in the baseline state, the optimization index was >90% (96 ± 2%) for all of the animals studied (Fig. 9B), indicating that the gain at the operating point is well optimized.

View larger version (12K): [in this window] [in a new window]   Fig. 9.   A: equilibrium diagram of MN (solid line) and NM (dotted line) arcs and graph showing instantaneous gains of MN arc (SNA/CSP) at various levels of CSP and NM arc (SAP/SNA) at various levels of SAP. In example simulated, arterial pressure at operating point () is 130 mmHg and total-loop gain at operating point is product of gain of MN arc at 130 mmHg of CSP (0.017 a.u./mmHg, ) and gain of NM arc at 130 mmHg of SAP (90 mmHg/a.u., ). On other hand, maximum gain (Gmax) of MN arc is given at 140 mmHg of CSP (0.02 a.u./mmHg, ×), and Gmax of NM arc is given at 100 mmHg of SAP (120 mmHg/a.u., ×). Therefore, optimization index is calculated to be 64%. B: frequency distribution of optimization index of arterial baroreflex in baseline states for 16 rats. In every animal, optimization index was >90%. See text for definition of optimization index.

Many experimental studies of the sympathetic arterial baroreflex system with a variety of hypertensive (16, 20) or heart failure (4, 19) animal models and clinical studies of hypertension (22) and heart failure (17, 21) conclude that "baroreflex dysfunction" plays an important role in hypertension or heart failure. However, most of the studies did not strictly or accurately define what baroreflex dysfunction was. For example, some studies interpreted the low value of the baroreflex sensitivity (BRS) as baroreflex dysfunction and then concluded that this dysfunction contributed to a high level of arterial pressure in hypertensive patients (22) or an increased SNA in heart failure animals (19). On the basis of our framework, the BRS is equivalent to the maximum gain of the mechanoneural arc (G_MN,max). However, even if the animal model has a low value of G_MN,max, if it has a high value of G_NM,max and the normal value of G_{Total,operating}, the animal should display a normal baroreflex function to attenuate the effect of external disturbance on arterial pressure. Moreover, as discussed in Importance of Analytic Approach in Estimating Operating Point of Feedback System, the arterial pressure and SNA at the operating point depend not only on the maximum gain of the mechanoneural arc but also on many other factors such as the set-point pressure and the characteristics of the neuromechanical arc (Fig. 7). Therefore, the low value of BRS is not directly linked to baroreflex dysfunction or a high level of arterial pressure or SNA. We should carefully interpret the experimental and clinical findings of the baroreflex studies and consider their functional meanings on the basis of an integrative framework. Our framework would be useful for a comprehensive understanding of baroreflex function.

Clinical Implications

View larger version (14K): [in this window] [in a new window]   Fig. 10.   Simulation results of effects of postural tilting on AP and SNA in a normal subject (A) and a patient with central baroreflex failure (B). Solid lines, MN arc curves; dotted lines, NM arc curves at supine position; dashed lines, NM arc curves during standing. , Operating points in supine position; , operating points during standing. Note that level of SNA unresponsive to postural tilting determines magnitude of AP fall as well as level of supine AP in central baroreflex failure. See text for detailed explanation.

Limitations

In summary, we propose an analytic framework for understanding the sympathetic baroreflex control of arterial pressure. We divided the feedback system into two arcs, mechanoneural and neuromechanical. We characterized the mechanoneural arc by the response of SNA to baroreceptor pressure and the neuromechanical arc by the response of SAP to SNA. The intersection between the two functional curves on the equilibrium diagram gives the operating arterial pressure. Such an approach could help us analytically understand the integrative function of the sympathetic baroreflex system.