## Abstract

This is the first study able to examine and delineate the actual actions of the physiological mechanisms responsible for the dynamic couplings between cardiac output (CO), arterial pressure (P_{a}), right atrial pressure (P_{RA}), and total peripheral resistance (TPR) in an individual subject without altering the underlying regulatory mechanisms. Eight conscious male sheep were used, where both types of baroreceptors were independently exposed to simultaneous beat-to-beat pressure perturbations under intact closed-loop conditions while CO, P_{a}, P_{RA}, and TPR were measured. We applied the cardiovascular system identification method proposed in a companion paper (4) to quantitatively characterize the dynamic closed-loop transfer relations CO→P_{a}, P_{RA}→P_{a}, P_{a}→TPR, and P_{RA}→TPR from the measured signals. To validate the dynamic properties of the estimated transfer relations, the essential parts of the linear dynamics of the model were independently and comprehensively evaluated via error model cross-validation, and the overall model's steady-state behavior was compared with a separate random effects regression approach. In addition to numerous physiological findings, we found that the cardiovascular system identification results were exceptionally consistent with the analytically derived solutions previously discussed in Ref. 4. In conclusion, this study presents the first time validation of a cardiovascular system identification method by means of experimentally acquired animal data in the intact and conscious animal and offers a set of powerful quantitative tools essential to advancing our knowledge of cardiovascular regulatory physiology.

- cardiovascular regulatory physiology
- autonomic regulation
- arterial and cardiopulmonary baroreceptors
- local vascular autoregulation
- system identification

spaceflight alters autonomic regulation of arterial pressure (P_{a}) in humans (6, 12). About 20% of astronauts after short missions and 83% after long missions are not able to support P_{a} during upright posture for more than 10 min (35). Orthostatic hypotension is not exclusively bound to astronauts. Here on earth, endurance-trained individuals are predisposed to orthostatic hypotension or intolerance (7, 20, 29, 32). Furthermore, medications or even trivial events like taking a hot shower can produce an extensive decrease in total peripheral resistance (TPR) in ordinary individuals and likewise cause P_{a} to drop below the level necessary to maintain consciousness. Control of TPR is achieved by a complex closed-loop negative feedback system composed of the centrally mediated baroreflexes (5, 18, 24, 25, 27, 28, 38, 39) and the distally mediated local vascular autoregulation (9, 13, 17, 23, 38, 40, 46). Several studies have been conducted concerning the separate effects of the arterial and cardiopulmonary baroreceptors on the control of TPR (8, 15, 22, 41, 42, 45, 49) and the interaction between them (1, 14, 16, 30, 31, 33, 47, 48). Many have reported nonlinearities or interaction between baroreceptors (30, 47, 48). Others, however, have found no evidence of an interactive relationship, nor have they found evidence for a nonlinear effect of mean arterial pressure (P̅_{a̅}) and mean central venous pressure (CVP) as predictors of mean TPR (T̅P̅R̅) changes (33). To determine the effects of P̅_{a̅} and CVP or mean right atrial pressure (P̅_{R̅A̅}), acting through the arterial and cardiopulmonary baroreceptors to alter T̅P̅R̅, investigators open the feedback loop by surgically denervating or pharmacologically blocking one of the baroreceptors, whereas the other is exposed to pressure changes and T̅P̅R̅ is measured. This procedure, however, may not describe well the combined effects when both baroreceptors are functional and the feedback loop is intact. When the feedback loop is left intact, such as with lower body negative pressure (LBNP) in human subjects, for example (15, 30, 45, 48), even low pressures (0–20 mmHg) of LBNP produce changes in ascending and descending aortic and carotid sinus diameters such that selective unloading of the cardiopulmonary baroreceptors is not possible (19, 44). In 1989, researchers (33) examined for the first time the independent steady-state contributions of arterial and cardiopulmonary baroreceptors to TPR regulation in the intact and conscious animal when pressure changed at both groups of baroreceptors. They changed ventricular pacing rate and blood volume to vary P̅_{a̅} and CVP while T̅P̅R̅ was measured and analyzed them using a random effects regression approach. Despite its statistical validity, this type of analysis is not able to characterize the dynamic relationship between P_{a} and TPR or the dynamic relationship between CVP (or P_{RA}) and TPR. To the present day, we find no studies able to examine the independent dynamic contributions of P_{a} and P_{RA} to short-term TPR regulation by the arterial and cardiopulmonary baroreceptors when pressure changes at both groups of baroreceptors and the underlying control mechanisms are operating under intact closed-loop conditions. The aims of this study were as follows: *1*) to validate the cardiovascular system identification method proposed in the companion paper (4) against experimentally acquired animal data when the underlying physiological regulatory mechanisms are not altered either by opening the feedback loop or by the use of anesthesia, *2*) to examine for the first time the independent dynamic closed-loop contributions of cardiac output (CO) and P_{RA} on P_{a} directly via the systemic circulation and its underlying physiological control mechanisms in the intact and conscious animal, *3*) to examine for the first time the independent dynamic closed-loop contributions of P_{a} and P_{RA} to short-term closed-loop regulation of TPR by arterial and cardiopulmonary baroreceptors in the intact and conscious animal, and *4*) to compare the cardiovascular system identification results with the analytic solutions previously derived in the companion paper (4) for the physiological coupling mechanisms represented by the closed-loop transfer relations , , , and .

With these goals in mind, we designed and employed a conscious sheep model where both types of baroreceptors are simultaneously exposed to independent beat-to-beat pressure perturbations and the physiological control mechanisms are operating under intact close-loop conditions. We subsequently applied the proposed cardiovascular system identification method to quantitatively characterize the dynamics of the physiological coupling mechanisms of interest from the measured CO, P_{a}, P_{RA}, and TPR fluctuations. To obtain a complete characterization of the examined regulatory mechanisms, system identification requires the input signals to be poorly correlated and sufficiently broadband, so that all the modes of the system to be identified are excited and reliable (21, 43). For that purpose, we employed an orthogonal input design in which heart rate (HR) and venous return are independently varied with frequency band limited to 0.1 Hz about their mean values by two separate sources in a nearly uncorrelated fashion while the changes in CO, P_{a}, P_{RA}, and TPR are measured. To validate the dynamic properties of the estimated closed-loop transfer relations , , , and , the essential parts of the linear dynamics of the model are independently evaluated via error model cross-validation, and the overall model's steady-state behavior is compared with a separate random effects regression approach.

## METHODS

### Experimental Preparation

Fourteen young adult male 25- to 35-kg sheep were housed in an American Association for Accreditation of Laboratory Animal Care-accredited animal facility with controlled lighting, ventilation, temperature, and relative humidity. The animals were singly housed, and food was given twice daily. Water was provided ad libitum. The experimental protocol was approved by the Massachusetts Institute of Technology Committee on Animal Care. Four sheep were used in a pilot study where the proposed experiments were performed under anesthesia. From the remaining 10 animals, one animal did not survive the surgery and one animal died from infection 1 wk after cardiac instrumentation. Food was withheld for 24–48 h before surgery, and sheep were subsequently anesthetized with a 1:1 mixture of ketamine and diazepam used to effect sufficient anesthesia to allow endotracheal intubation. The left lateral thoracic surface was prepared aseptically for surgery, and aseptic techniques were employed throughout. A stomach tube was placed to evacuate ruminal contents, and the mouth and airways were periodically suctioned to maintain airway patency. The sheep were restrained in right lateral recumbency on a circulating hot water blanket, and anesthesia was maintained by 1–4% isoflurane. Positive pressure ventilation was initiated with respiratory rates of 8–12 breaths/min and tidal volumes of ∼600 ml. Lactated Ringer solution was administered via the saphenous vein at an approximate rate of 10 ml·kg^{−1}·h^{−1}.

A left rib resection thoracotomy was performed in which the fourth rib was removed. After pericardiotomy and creation of a pericardial cradle, pacing electrodes were applied to the surface of the right auricular appendage (Fig. 1). A right atrial catheter (Tygon, 3 mm inner diameter and 4 mm outer diameter) was placed using the Seldinger technique and fixed through use of a Tygon collar and finger trap of 4-0 silk. An ultrasonic flow probe (Transonic Systems, A series, 16- to 20-mm perivascular probes) was placed around the aortic root cardiac to the brachiocephalic trunk. An aortic catheter (Tygon, 3 mm inner diameter and 4 mm outer diameter) was placed using the Seldinger technique and fixed in place using a Tygon collar and finger trap of 2-0 silk. An intercostal thoracotomy was then performed in the sixth to seventh intercostal space, and an occluder cuff (In Vivo Metric, 14- to 20-mm perivascular occluders) was placed around the caudal vena cava through a mediastinal incision, as was a chest tube. All implants were tunneled subcutaneously to an interscapular position and fixed there with sutures of 2-0 nylon. Closure of each thoracotomy site was routine. Each sheep was fitted with a protective jacket with pockets to contain the catheters and wires. Analgesics including flunixin meglumine (Banamine; 1.1 mg/kg iv) were administered intraoperatively, and intercostal nerve blocks of 2% lidocaine or bupivicaine, and buprenorphine (Buprenex; 0.01 mg/kg bid) were administered postoperatively. The sheep were maintained on amoxicillin (20 mg/kg divided bid) or enrofloxacin (5 mg/kg divided bid) for 5–7 days postoperatively.

### Experimental Procedures

Experiments were performed on eight sheep after a 10-day recuperation period after cardiac instrumentation on the conscious animal while it rested in a custom-made sling. P_{a}, P_{RA}, and aortic flow (CO) were continuously monitored throughout the experiments as illustrated by schematic representation of the experimental setup depicted in Fig. 1. P_{a} and P_{RA} were measured by using calibrated strain-gauge-based pressure transducers (Transpac IV, Abbott Critical Care Systems) connected to the arterial and right atrial catheters. The frequency response of the utilized pressure transducers was comparable to the flow signal provided by Transonic Systems flowmeters. CO was measured from the flow probe on the ascending aorta. Atrial rate was set with a computer-controlled stimulator (Cardiac Stimulator, Nihon Kohden) connected to the atrial electrodes (Medtronic). Occlusion of venous blood flow was performed by a computer-controlled syringe pump (Harvard Apparatus, PHD2000 series) connected to the inflatable occluder cuff placed around the inferior vena cava. Data were continuously recorded and digitized using a Pentium-based computer and the Windaq data-acquisition package (Windaq, Dataq Instruments).

#### Experimental protocol 1: cardiovascular system identification.

This protocol was preceded by a 10-min control period where baseline values for HR were determined by averaging over the last 5 min of the control period. Immediately thereafter, a 5-min period of fixed rate pacing was initiated, where a new steady state was induced by pacing at a fixed rate 30% higher than baseline HR causing an increase in P_{a} and a fall in P_{RA}. Immediately after the initial 5-min period of fixed rate pacing, the venous occluder balloon was partially occluded to further decrease P_{RA} by ∼2 mmHg while fixed rate pacing continued for an additional 5-min period. Subsequently, a 20-min system identification period followed, in which a computer-controlled atrial pacing and venous occlusion algorithm independently perturb pacing rate and the degree of venous occlusion as to replicate an orthogonal two-input design where HR and venous return simultaneously vary with frequency bands limited to 0.1 Hz about their mean values in a nearly uncorrelated fashion.

#### Experimental protocol 2: multiple regression analysis.

After the conclusion of *protocol 1*, fixed rate pacing continued at a rate 30% higher than baseline HR and was kept unchanged until the end of the experimental protocol while the initial partial venous occlusion was initially maintained for the next 3–5 min. Subsequently, the degree of venous occlusion was increased for a 2-min period, after which the additional increment in venous occlusion was reversed for the following 3–5 min. The degree of venous occlusion was then further decreased for a 2-min period.

### Data Analysis

The recorded signals of CO, P_{a}, and P_{RA} were passed through a low-pass analog filter for antialiasing and sampled at 100 Hz. Data analysis of the filtered signals was completed using Matlab [Matlab version 6 (R12), MathWorks]. Short-term TPR fluctuations were determined from the measured CO, P_{a}, and P_{RA} signals using the mathematical method for TPR determination previously described in the companion paper (4) after P_{a}, P_{RA}, and CO were passed through a 10th-order digital FIR low-pass filter for antialiasing and resampled to a sampling frequency (*f*_{s}) = 0.5 Hz to filter out the high spectral content from the HR and respiratory frequency components. Please refer to the companion paper (4) for a detailed discussion of this issue. Consequently, the resulting effective time constant (τ_{eff}) = T̅P̅R̅·*C*_{a} (where *C*_{a} is arterial capacitance) provides an estimate for the effective time constant of the systemic circulation, which quantitatively characterizes the open-loop transfer relations , , and representing the immediate hydraulic effects of CO, P_{RA}, and TPR on P_{a}, respectively, directly via the systemic circulation as (1) where *s* represents the complex frequency. By calculating the standard deviations of the time-domain function representations of (*s*)·CO(*s*), (*s*)·P_{RA}(*s*), and (*s*)·TPR(*s*), respectively, as σ{}, σ{}, and σ{} for each individual subject, it was possible to roughly estimate the relative open-loop contributions of CO, P_{RA}, and TPR to dynamic changes in P_{a} during both experimental protocols in each of the eight animal subjects, respectively, as σ{}/σ, σ{}/σ, and σ{}/σ, where σstands for σ{} + σ{} + σ{}.

The cardiovascular system identification method proposed in the companion paper (4) as two separate autoregressive exogenous (ARX) model structures, referred to as hemodynamic (HSI) and regulatory system identifation (RSI), was applied to quantitatively characterize the physiological mechanisms in closed-loop responsible for the couplings among CO, P_{RA}, P_{a}, and TPR fluctuations in each of the eight animal subjects. Consequently, the closed-loop transfer relations (*s*), (*s*), (*s*), and (*s*) describing the dynamic input-output properties of these coupling mechanisms were modeled from fluctuations in CO, P_{RA}, P_{a}, and TPR acquired during *protocol 1* via HSI and RSI, and three of the most widely used model order selection criteria, Rissanen’s minimum description length principle (MDL) (36, 37), Akaike’s final prediction error (FPE) (2), and Akaike’s information theoretic criterion (AIC) (3), were evaluated in their overall ability to accurately compensate for the automatic decrease of the loss function as the flexibility *L* of the model structure increased. Finally, by calculating the standard deviation of the time-domain function representations of (*s*)·ΔCO(*s*)/C̅O̅ as σ{} and the standard deviation of (*s*)·ΔP_{RA}(*s*) as σ{}, it was possible to roughly estimate in each of the eight animal subjects the relative closed-loop contributions of CO and P_{RA} to the dynamic changes in P_{a} observed during both experimental protocols as σ{}/[σ{} + σ{}] and σ{}/(σ{} + σ{}), respectively. Likewise, by calculating the standard deviation of the time-domain function representations of (*s*)·ΔP_{a}(*s*)/P̅_{a̅} and (*s*)·ΔP_{RA}(*s*) as σ{} and σ{}, respectively, it was also possible to roughly estimate the relative closed-loop contributions of P_{a} and P_{RA} to the dynamic changes in TPR observed during both protocols, respectively, as σ{}/(σ{} + σ{}) and σ{}/(σ{} + σ{}).

### Validation

The most important validation for any given model is to test whether it is capable of describing fresh data sets that have not beenused to build the model. This can be done by direct evaluation of the essential parts of the linear dynamics of the model via error model cross-validation (21, 34): a quantitative test for the correctness of the estimated model structure. With this in mind, two nonoverlapping 10-min data segments from the 20-min system identification period in *protocol 1* were extracted and analyzed independently to give two sets of separate identification results for each animal, which could then be used for evaluation of consistency in the system identification procedure and for error model cross-validation. The residuals associated with the data and any given model have to be white and independent of the inputs for the model to correctly describe the system. Accordingly, to quantitatively test the hypothesis that the model error is independent of the inputs, the first 10 min of the 20-min system identification period in *protocol 1* were used to create the model, and the following 10 min were used to validate it. For a more elaborate description of error model cross-validation tests, the reader is referred to Refs. 21 and 34. In addition, to evaluate the model's steady-state behavior via an independent procedure, multiple regression analysis (MRA) was performed over all animals, and the results were compared with the group-average static gains determined via HSI and RSI. The ratios of estimated mean coefficients to estimates of their standard errors were used to judge the significance of the regression estimates.

## RESULTS

Figure 1 shows a typical 5-s example of the 100-Hz measured signals. Figure 2 displays a representative 10-min data segment collected during *protocol 1* (given in time and frequency) of measured CO, P_{a}, and P_{RA} signals resampled to 0.5 Hz and TPR determined from the measured signals using the mathematical method for TPR determination previously described in the companion paper (4). The resulting group-average standard deviations for CO, P_{a}, P_{RA}, and TPR during *protocol 1* were 8.5%, 5.3%, 1.5 mmHg, and 5.4%, respectively. Figure 3 displays the group-average results collected during *protocol 2* of measured CO, P_{a}, and P_{RA} signals resampled to 0.5 Hz and TPR determined from the measured signals using the mathematical method for TPR determination previously described in the companion paper (4). During partial venous occlusion, the resulting group-average steady-state changes in CO, P_{a}, P_{RA}, and TPR were −19.2%, −9.0%, −2.5 mmHg, and 10.8%, respectively, whereas during partial venous release they were 20.8%, 8.0%, 2.6 mmHg, and −13.7%, respectively. Figure 4 displays a representative graphical comparison between measured fluctuations in P_{a} depicted in red and P_{a} fluctuations predicted via *Eq. 1* depicted in blue. The measured input and output signals shown represent a 10-min data segment collected during *protocol 1*, whereas the couplings represent the estimated open-loop transfer relations , , and depicted in their time-domain form of step-response function representations. Table 1 displays results obtained by applying the method for TPR determination (4) to each of the eight individual animal subjects during both experimental protocols. Values denote mean estimates with standard errors. No statistically significant differences in values between protocols were found. Figure 5*A* displays the group-average results of estimated open-loop transfer relations and depicted in their time-domain form of step-response function representations together with the group-average system identification results for HSI depicted in squares. Group-average system identification results for RSI are shown in Fig. 5*B*. Group-average system identification results refer to the average model resulting from separately applying the cardiovascular system identification method (4) in conjunction with MDL to each of the eight individual animal subjects during *protocol 1*, each yielding a unique set of model parameters, which distinctly corresponds to that particular subject. Figure 6 displays the group-average results of optimal model orders and static gains determined via HSI (*A*) and RSI (*B*) in conjunction with MDL (squares), FPE (triangles), and AIC (circles) plotted against the initial maximal model order *L*. Group-average error model cross-validation results are displayed in Fig. 7*A* for the residual error (*k*) from HSI and in Fig. 7*B* for the residual error *e*_{TPR}(*k*) from RSI. The dotted lines correspond to the 99% confidence limits for the autocorrelation and cross-correlations, assuming that the error is indeed white and independent of the given inputs; thus the confidence limits become horizontal lines independent of time. Figure 8 displays the MRA results of predicted versus measured steady-state changes in P_{a} and TPR (*top*) as well as a statistical comparison between the static gains obtained via MRA and via cardiovascular system identification (*middle* and *bottom*). Specifically, Fig. 8*A* presents a statistical comparison between the static gains *G*{} and } obtained via MRA and via HSI (*middle*) as well as a statistical comparison between the static gains } and } obtained via MRA and HSI (*bottom*). Figure 8*B* displays a statistical comparison between the static gain } directly determined via MRA and RSI and indirectly obtained via HSI (*middle*) as well as a statistical comparison between the static gain } directly determined via MRA and RSI and indirectly obtained via HSI (*bottom*). Values denote mean estimates with 95% confidence intervals, and the symbols *, †, and ‡ below each value denote the significance level associated with that value. We found no statistically significant difference between MRA and cardiovascular system identification results, nor did we find any statistically significant difference between } or } indirectly determined via HSI and directly determined via MRA or RSI as graphically illustrated in Fig. 8*B*. Nonetheless, we found statistically significant differences between } and } as well as between } and } via MRA and HSI as graphically illustrated in Fig. 8*A*.

## DISCUSSION

In the companion paper (4), we demonstrated that the method for TPR determination was not only successful at tracking down short-term TPR fluctuations caused by short-term baroreflex and autoregulatory modulation but was also capable of effectively characterizing the dynamic input-output properties of the coupling mechanisms represented by the open-loop transfer relations , , and as described by *Eq. 1*. This study exhibits this method's ability to successfully and consistently explain the observed short-term P_{a} fluctuations almost in their entirety in the intact and conscious sheep when the contributions of ΔTPR to P_{a} fluctuations are taken into account as graphically illustrated in Fig. 4 by the impressive correlation (*r* = 0.99) between measured and predicted P_{a} fluctuations (see Table 1 for all animals). This method, however, does not provide any information regarding short-term baroreflex and autoregulatory modulation of TPR. Whereas in a previous publication by the same group, Mullen et al. (26) stress HR modulation by the arterial baroreflexes and respiration, but they do not account for the regulatory mechanisms responsible for short-term TPR fluctuations. With this in mind, we developed in the companion paper (4) a novel cardiovascular system identification method, referred to as HSI and RSI, which focuses on TPR modulation by the baroreflexes and autoregulation. In this study, we applied HSI and RSI to the data gathered from each individual animal subject during *protocol 1*. Accordingly, the data of each particular animal were used to build the model with a unique set of model parameters, which distinctly correspond to that same animal.

### Validation

Figure 6 demonstrates the robustness of MDL when applied in conjunction with HSI (*A*) and with RSI (*B*) to all animal subjects. FPE and AIC yielded overparameterized models, whereas MDL did not. FPE or the closely related AIC resulted in an almost linear relation between optimal model orders and the initial, maximal model order *L*, whereas MDL yielded on average optimal model orders *n* ≈ 4 in HSI and *p* ≈ 3 in RSI independent of *L* once *L* was large enough to allow for adequate determination of the optimal model orders *n* and *p*. Similarly, the group-average static gains determined in conjunction with MDL exposed values practically independent of *L* once *L* was large enough to allow for the adequate determination of *n* in HSI and *p* in RSI. The group-average error model cross-validation results presented in Fig. 7 demonstrate the correctness of the model structure obtained via HSI (*A*) and via RSI (*B*). The autocorrelation of the residual error (*k*) together with the cross-correlations between (*k*) and the inputs CO(*k*) and P_{RA}(*k*) depicted in Fig. 7*A* reveal that on average the residuals were white and did not contain shared information, thus confirming that the chosen model was able to pick up the essential parts of the linear dynamics from and demonstrating HSI's capability to describe fresh data sets that were not used to build the ARX model. The autocorrelation of the residual error *e*_{TPR}(*k*) and the cross-correlation between *e*_{TPR}(*k*) and P_{RA}(*k*) reveal that on average the residuals were white and did not contain shared information, whereas the cross-correlation between *e*_{TPR}(*k*) and P_{a}(*k*) exposes a consistent positive correlation at sample time *k* = 0 but no correlation otherwise, indicating an instantaneous positive effect of *e*_{TPR}(*k*) on P_{a}(*k*) but a clear independence at all other *k*. This observation reflects the strong and immediate positive hydraulic effects of TPR on P_{a} (not picked up by the chosen model, because the model delays *nk*_{1} = *nk*_{2} > 0) and is consistent with the fact that the estimated is not supposed to account for this hydraulically mediated effect at *k* = 0, because the model describes baroreflex and autoregulatory modulation of TPR by causal reflexes, which can only exist for *k* > 0. As a result, the test presented in Fig. 7*B* confirms that the chosen model was able to pick up the essential parts of the linear dynamics from and demonstrating RSI's capability to describe fresh data sets that were not used to build the ARX model. Furthermore, the model's steady-state behavior characterized by the static gains } and } determined via HSI and the static gains } and } determined via RSI does not differ significantly from the model's steady-state behavior characterized by the static gains determined via MRA as depicted in Fig. 8. In conclusion, the aforementioned results confirm that HSI and RSI were able to quantitatively characterize the examined dynamic closed-loop transfer relations , , , and and hence validate the proposed cardiovascular system identification method as a powerful quantitative tool to examine the dynamics of physiological coupling mechanisms when the physiological control mechanisms are operating under intact closed-loop conditions.

### Theoretical Versus Experimental Results

Particularly significant is the fact that the system identification results of , , , and are exceptionally consistent with the analytically defined step-response function representations previously derived in the companion paper (4). The dynamic properties of the closed-loop transfer relation , graphically illustrated with squares in Fig. 5*A*, reveal an immediate increase in P_{a}, given a positive step change in CO, exposing the direct positive hydraulic effects of CO on P_{a} mainly determined by the viscoelastic properties of the arteries. After a short delay of a few seconds, however, P_{a}'s rapid increase is truncated as a result of negative feedback regulation of TPR by the arterial baroreflex, which is graphically illustrated in Fig. 5*B*, where the dynamic properties of reveal a decrease in TPR after a short time delay of 2 s given a positive step change in P_{a}. Note that the static gain } indirectly determined from the estimated via HSI does not differ significantly from the static gain directly determined from the estimated via RSI or MRA as illustrated in Fig. 8*B*; thus the significant difference } − } can be explained by }. } is the static gain of the estimated open-loop transfer relation , which characterizes the direct positive hydraulic effects of CO on P_{a} determined by the effective viscoelastic properties of the systemic circulation. Similarly, the dynamic properties of the closed-loop transfer relation , graphically illustrated with squares in Fig. 5*A*, reveal an immediate increase in P_{a}, given a positive step change in P_{RA}, demonstrating the direct positive hydraulic effects of P_{RA} on P_{a} determined by the effective viscoelastic properties of the systemic circulation up to the time when the baroreflexes kick in to reverse the increase of P_{a} and quickly force P_{a} into negative values as a result of negative feedback regulation of the arterial baroreflex in addition to negative cardiopulmonary baroreflex regulation of TPR, which is graphically illustrated in Fig. 5*B*, where the dynamic properties of reveal a decrease in TPR after a short time delay of 2 s given a positive step change in P_{RA}. Note that the static gain } indirectly determined from the estimated and via HSI does not differ significantly from the static gain directly determined from the estimated via RSI or MRI as illustrated in Fig. 8*B*. In fact, the static gain of the cardiopulmonary baroreflex, }, explains why } is so small and yet significantly smaller than }. } is the static gain of the estimated open-loop transfer relation , which characterizes the direct positive hydraulic effects of P_{RA} on P_{a} determined by the effective viscoelastic properties of the systemic circulation. Even though the significant difference } − } can be explained by both arterial and cardiopulmonary baroreflexes, given the values determined for the arterial baroreflex, only cardiopulmonary baroreflex modulation of TPR can result in values for } close or smaller than zero. For a detailed discussion of this issue, please refer to the companion paper (4). In view of these results, we can conclude that the independent dynamic closed-loop short-term contributions of CO and P_{RA} on Pa, characterized by and , respectively, can indeed provide valuable quantitative information regarding the separate contributions of two physically isolated sensory regions (the arterial and cardiopulmonary baroreceptors) on a common effector region (TPR).

### Autonomic Control Versus Autoregulation

The ongoing conflicting effects between the centrally regulated arterial baroreflex and the distally controlled local vascular autoregulation are exposed in Fig. 9 by means of the group-average closed-loop transfer relation represented in its time-domain form of impulse-response function depicted in squares and sampled at 2 Hz as opposed to 0.5 Hz. With the higher resolution of 2 Hz, it becomes apparent how, given an impulse change in CO, the effects of local vascular autoregulation become evident at around 1 s when P_{a}'s natural time decay slows down as a result of the longer time constant of autoregulation. Up to that point in time, the viscoelastic properties of the systemic circulation determine for the most part P_{a}'s natural time decay. After 2 s, the arterial baroreflex kicks in to speed up P_{a}'s natural time decay and further force P_{a} into negative territory as a result of its negative feedback regulation. Thus, for illustrative purposes, the dashed curve exhibits a hypothetical extrapolation of P_{a}'s natural time decay had arterial baroreflex modulation of TPR not taken place. In addition to the results presented in Fig. 9, the presence of vascular autoregulation can also be inferred from the group-average ARX model order *p* > 3 (see Fig. 6*B*) determined by RSI (in conjunction with MDL), which is consistent with the analytic solutions previously derived in the companion paper (4), where we demonstrated that and must be characterized by at least third-order systems if vascular autoregulation plays an active role because in that case *p* = 3 + *f*_{s}*T*_{ar} with T_{ar} denoting the time delay of autoregulation. Nonetheless, we found that *G*{} < 0 (see Fig. 8*B*), thus still demonstrating dominance of the arterial baroreflex over vascular autoregulation. Please refer to the companion paper (4) for a detailed discussion on this issue regarding model order and dominance of one reflex over the other. As a result, the estimated closed-loop transfer relations and do not only describe the arterial and the cardiopulmonary baroreflexes, respectively, but they also characterize local vascular autoregulation of TPR. In conclusion, the independent dynamic contributions of P_{a} and P_{RA} to short-term closed-loop regulation of TPR by arterial and cardiopulmonary baroreceptors are also modulated by local vascular autoregulation.

### Dynamic Contributions

Autonomic baroreflex regulation and local vascular autoregulation account for only 50% of the dynamic changes in TPR during *protocol 1* and 69% during *protocol 2* as demonstrated by the resulting correlation coefficients between measured and predicted TPR fluctuations presented via RSI (see Table 2). Furthermore, P_{a} accounts for roughly 60% of the total explained dynamic changes in TPR, whereas the remaining 40% can be ascribed to P_{RA}, demonstrating that arterial baroreceptors are more important than cardiopulmonary baroreceptors in dynamic closed-loop control of TPR in the intact and conscious sheep. Raymundo et al. (33) concluded that arterial baroreceptors were more important than cardiopulmonary baroreceptors in steady-state P_{a} control in intact and conscious dogs. The fact that only 50–70% of TPR fluctuations can be accounted for by the baroreflexes and autoregulation provides an explanation for why no more than three-fourths of the observed dynamic changes (f < 0.25 hz) in P_{a} can be explained by HSI, which not only characterizes the combined viscoelastic properties of arteries and veins but also the physiological control mechanisms in closed loop responsible for short-term baroreflex and autoregulatory modulation of TPR. The unexplained one-fourth may very well reflect fluctuations due to other regulatory mechanisms like, e.g., the renin-angiotensin-aldosterone system. In contrast, the method for TPR determination explains 96% of the observed dynamic changes in P_{a} because this method takes into account all of the observed TPR fluctuations regardless of how they originated as demonstrated by the resulting correlation coefficients between measured and predicted P_{a} fluctuations (see Table 1). The unexplained 4% may be ascribed to the presence of nonlinear coupling mechanisms not accounted for and/or may simply be due to the disregarding of venous elasticity. In particular, TPR accounts for 40% of the total explained dynamic changes in P_{a}, whereas CO accounts for 50%, and P_{RA} takes care of the remaining 10%. These numbers reveal that even though CO and TPR account for the vast majority of explained P_{a} fluctuations, P_{RA} does, independently of CO, contribute to short-term Pa variability directly via the systemic circulation. Moreover, P_{RA} accounts for 18% of the explained changes in P_{a} during *protocol 1* and 15% during *protocol 2* when the contributions of P_{RA} to P_{a} directly via the systemic circulation and its underlying physiological regulatory mechanisms are determined in closed-loop via HSI, whereas CO accounts for 82–85% (see Table 2).

### Summary and Conclusions

This study presents the first time validation of a cardiovascular system identification method by means of experimentally acquired animal data in the intact and conscious animal and presents cardiovascular system identification results exceptionally consistent with the analytically defined impulse-response function representations previously derived in the companion paper (4). As a result, this study provides the necessary quantitative tools to explore and delineate the actual actions of the physiological mechanisms responsible for the dynamic couplings among CO, P_{a}, P_{RA}, and TPR in an individual subject without altering the underlying regulatory mechanisms.

The main physiological findings of this study in intact and conscious sheep are as follows: *1*) P_{RA} does, independently of CO, contribute to short-term P_{a} variability directly via the systemic circulation; *2*) almost all of the observed dynamic changes in P_{a} can be explained when the dynamic contributions of TPR to P_{a} fluctuations are taken into account, where TPR accounts for 40%, CO contributes 50%, and the remaining 10% is attributed to P_{RA}; *3*) 50–70% of TPR fluctuations can be explained by short-term autonomic and autoregulatory modulation; *4*) P_{a} accounts for roughly 60% of the total explained dynamic changes in TPR, whereas P_{RA} accounts for the remaining 40%; *5*) the independent dynamic contributions of P_{a} and P_{RA} to short-term closed-loop regulation of TPR by arterial and cardiopulmonary baroreceptors are also modulated by local vascular autoregulation; *6*) the centrally regulated arterial baroreflex exerts a dominant role over the distally controlled local vascular autoregulation; *7*) the independent dynamic closed-loop contributions of CO and P_{RA} on P_{a} provide valuable quantitative information regarding the separate contributions of two physically isolated sensory regions (the arterial and cardiopulmonary baroreceptors) on a common effector region (TPR); and *8*) about three-fourths of short-term P_{a} variability (f < 0.25 hz) can be accounted for by the systemic circulation and its underlying physiological control mechanisms of baroreflex and autoregulatory modulation of TPR, where CO accounts for 82–85% and P_{RA} takes care of the remaining 15–18%.

Furthermore, this study raises the following fundamental questions, which might be answered in a subsequent study by applying the method for TPR determination in conjunction with HSI and RSI to human data: *1*) How much of P_{a} variability observed in humans can be attributed to TPR? *2*) How much of TPR variability observed in humans can be attributed to short-term TPR modulation by the baroreflexes and autoregulation? *3*) It is not surprising for the centrally regulated arterial baroreflex in sheep to exert a dominant role over the distally controlled local vascular autoregulation; however, does the same occur in humans? *4*) In sheep, where 70% of blood volume is above or at heart level, it is not surprising that P_{a} accounts for the majority of the total explained dynamic changes in TPR; however, in humans, where 70% of blood volume is below heart level, should not P_{RA} play a major role or at least an equal role than P_{a} in the dynamic closed-loop control of TPR? *5*) Similarly, what are the independent dynamic contributions of CO and P_{RA} to short-term P_{a} variability directly via the systemic circulation and its underlying physiological regulatory mechanisms in humans?

In conclusion, the method for TPR determination, HSI and RSI offer a set of powerful quantitative tools essential to advancing our knowledge of cardiovascular regulatory physiology.

## GRANTS

This work was sponsored by the United States National Aeronautics and Space Administration through a grant from the National Space Biomedical Research Institute and by a grant from the Center for the Integration of Medicine and Innovative Technology.

## Footnotes

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- Copyright © 2004 by the American Physiological Society