INTRODUCTION

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION RESULTS DISCUSSION APPENDIX REFERENCES

CARBON DIOXIDE is known to have a significant impact on the cardiovascular system. Experimental studies in animals suggest that hypocapnia causes a depression of the central vasomotor neurons (34, 35, 38) and abates the peripheral chemoreflex response (4, 20, 30-32); the opposite effects occur during hypercapnia (16, 34, 35, 38). Moreover, CO₂ is known to be a vasodilator of many peripheral vascular beds (including the brain, heart, and skeletal muscle) (6, 15, 18, 28, 44, 53). Furthermore, in conditions when ventilation is free to change, hypercapnia provokes an increase in lung inflation, thus stimulating slowly adapting pulmonary-stretch receptors with myelinated A fibers; the latter cause tachycardia and vasodilation in the vascular beds under sympathetic reflex control (10, 11). Finally, changes in systemic arterial pressure (SAP), which often accompany hypercapnia or hypocapnia, modulate the action of the baroreflex control system, which, in turn, exerts a powerful control on several cardiovascular parameters.

Even though the main mechanisms involved in the cardiovascular response to CO₂ changes have been familiar for many years, their final effects on cardiovascular quantities are far from being completely recognized. Although several experiments indicate that hypercapnia causes an increase in total peripheral resistance (TPR), tachycardia, and an increase in mean SAP, others report a significant decrease in total systemic resistance and a decrease in heart rate (HR) (5, 25, 48, 50, 54, 61). Moreover, changes in cardiac output (CO) exhibit an almost equal dispersion in both directions during both increasing and decreasing PCO₂.

These apparent contradictions of experimental data can ensue from the extreme complexity of the entire cardiovascular control system, characterized by the nonlinear superimposition among multiple mechanisms operating simultaneously. Individual variability, differences in the experimental setup (for instance free vs. artificial ventilation), or a variance in hemodynamic conditions (for instance in the SAP level or in metabolism) may bring about a different balance between regulatory actions, thus resulting in opposing final changes of the same regulated quantities.

A further aspect that requires particular attention is that changes in blood PCO₂ almost always occur together with O₂ pressure changes (for instance during hypocapnic hypoxia or asphyxia). Because the regulatory actions triggered by changes in PO₂ and PCO₂ share several common afferent pathways and utilize the same effectors, the level of nonlinear superimposition becomes exceedingly complex (1).

Mathematical modeling and computer simulation techniques have often been advocated as important tools to investigate the complexity of physiological control systems in rigorous quantitative terms. In recent years, we formulated a mathematical model of the short-term cardiovascular regulatory response to acute isocapnic hypoxia (59). The model includes the arterial baroreflex, the peripheral chemoreflex, the lung-stretch receptors, the hypoxic response of the central neural system (CNS), and the local O₂ effect on the vascular beds with a higher metabolic requirement. With that model, we were able to summarize several different experimental results concerning acute hypoxia into a single theoretical setting (60).

The main limitation of the previous model was the absence of CO₂ mechanisms, i.e., the model could be used to investigate hypoxia in isocapnic conditions only. The aim of the present subsequent study is to include the effect of blood PCO₂ into the previous mathematical model in accordance with present physiological knowledge. This may be important 1) to provide a theoretical framework for the analysis of physiological experiments characterized by changes in PCO₂; and 2) to provide possible explanations for the differences observed among experimental results. In particular, we aspire to analyze the putative role of each mechanism in the cardiovascular response to CO₂.

This paper is structured as follows. First, the mathematical model is briefly described in qualitative terms, laying stress on the new aspects only. Second, physiological results concerning normoxic hypercapnia, hypocapnic hypoxia, and hypercapnic hypoxia are simulated. Finally, a sensitivity analysis on the main mechanisms is performed to gain a deeper understanding on the possible rationale for experimental differences.

Glossary

Cvb,O2	Oxygen gas concentration in venous (v) blood leaving brain (b), ml O2/ml blood
Cvb,O2n	Oxygen gas concentration in venous blood leaving brain under normal (n) conditions, ml O2/ml blood
Cvj,O2 j = h, m	Oxygen gas concentration in venous blood leaving heart (h) and skeletal muscle (m), respectively, ml O2/ml blood
DVp	Time delay of ventilatory response to peripheral chemoreceptors (p), s
DVc	Time delay of ventilatory response to central chemoreceptors (c), s
fab	Baroreceptor afferent (ab) activity, spikes/s
fac	Afferent chemoreceptor (ac) activity, spikes/s
fap	Afferent activity from lung-stretch receptors, spikes/s
fsj j = h, p, v	Activity in the efferent sympathetic (s) fibers to heart, peripheral resistances, and veins, respectively, spikes/s
f, KH	Parameter related with the strength of the afferent chemoreceptor response to CO2, dimensionless
gccsj j = h, p, v	Gains of the central chemoreceptor sympathetic (ccs) response to CO2 acting on heart, peripheral resistances, and veins, respectively, s1 mmHg1
gj,O2 j = h, m, b	Gain of the local O2 response on the coronary (h), muscular (m), and cerebral (b) vascular beds, respectively, ml blood/ml O2
gVp	Gain of ventilatory response to peripheral chemoreceptors, l/min · s
gVc,h,gVc,l	Gain of ventilatory response to central chemoreceptors (h during hypercapnia, l during hypocapnia), l/min · mmHg1
Gbp	Cerebral peripheral hydraulic conductance, ml/mmHg1 · s1
Gbpm	Basal (n) value of cerebral peripheral hydraulic conductance, ml/mmHg1 · s1
kj,CO2 j = h, m	Parameter related to the central gain of the CO2 effect, coronary and muscular bed, respectively, mmHg
kisc,sj j = h, p, v	Parameter related to the central gain of the hypoxic (ischemic) response, mmHg
kac	Parameter related to the central gain of the afferent chemoreceptor response, mmHg
PaCO2n	PCO2 basal value (n), mmHg
O2,ac	Oxygen pressure at the central point of the afferent chemoreceptor response, mmHg
O2,sj	Oxygen pressure at the central point of the hypoxic (ischemic) response, mmHg
Rjp j = h, m	Coronary and skeletal muscle resistance (hydraulic), respectively, mmHg · s · ml1
Rjpn j = h, m	Normal coronary and skeletal muscle resistance (hydraulic), respectively, mmHg · s · ml1
RR	Respiratory rate, breaths/min
	Ventilation, l/min
p	Change in ventilation induced by activation of peripheral chemoreceptors, l/min
c	Change in ventilation induced by activation of central chemoreceptors, l/min
VT	Tidal volume, l
Wc,sj j = h, p, v	Synaptic weights from chemoreceptors acting on heart peripheral resistances and veins, respectively, dimensionless
Wp,sj j = h, p, v	Synaptic weights from pulmonary (lung)-stretch receptors acting on heart, peripheral resistances, and veins, respectively, dimensionless
Wb,sj j = h, p, v	Synaptic weights from baroreceptors acting on heart peripheral resistances and veins, respectively, dimensionless
xb,O2	State variable representing the effect of O2 on the cerebrovascular bed, dimensionless
xb,CO2	State variable representing the effect of CO2 on cerebrovascular bed, dimensionless
xj,O2 j = h, m	State variable representing the effect of O2 on coronary and muscular bed, respectively, dimensionless
xj,CO2 j = h, m	State variable representing the effect of CO2 on coronary and muscular bed, respectively, dimensionless
sj j = h, p, v	Offset terms for the sympathetic response, describing the effect of gas alterations in the central neural system on efferent sympathetic activity to heart, peripheral resistances, and veins, respectively, s1
sj j = h, p, v	Upper saturation level of the hypoxic (ischemic) response, s1
ac	Time constant of the afferent chemoreceptor response, s
cc	Time constant of the central chemoreceptors response, s
isc	Time constant of the hypoxic (ischemic) response, s
O2	Time constant of the peripheral O2 response, s
CO2	Time constant of the peripheral CO2 responses
Vp	Time constant of ventilatory response to peripheral chemoreceptors, s
Vc	Time constant of ventilatory response to central chemoreceptors, s
A, B, C, D	Parameters describing the cerebral blood flow response to CO2 (from Ref. 45)

	MODEL DESCRIPTION

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION RESULTS DISCUSSION APPENDIX REFERENCES

The model includes the pulsating heart, the vascular system, and various regulatory actions. Description of the regulatory mechanisms, in turn, distinguishes between the afferent information from several groups of receptors (arterial baroreceptors, peripheral chemoreceptors, and lung-stretch receptors), the response of the CNS to changes in PO₂ and PCO₂, the activity of the efferent sympathetic fibers directed to the heart and peripheral vessels, the vagus activity, the response of various effectors to the efferent activity of neural fibers, the local effect of O₂ and CO₂ on peripheral resistances, and the ventilation response to peripheral and central chemoreceptor drive. A block diagram summarizing the main aspects of the regulatory actions is shown in Fig. 1.

View larger version (25K): [in this window] [in a new window]   Fig. 1.   Block diagram describing the interactions among regulatory mechanisms according to the present model. CNS, central neural system.

The description of the pulsating heart and of the entire vascular system is unchanged compared with that used in previous studies (57, 59), where all details can be found. Hence, these parts of the model are not described again for the sake of brevity.

Afferent information. The arterial baroreceptors respond to changes in both the instant value of SAP and its rate of change; slowly adapting lung-stretch receptors respond to changes in VT. Both responses include a static characteristic and a first-order dynamic. The response of both groups of receptors is the same as that used in the previous paper (59).

View larger version (28K): [in this window] [in a new window]   Fig. 2.   Steady-state activity in the afferent chemoreceptor fibers (fac) vs. arterial PCO2 (PaCO2), plotted at different levels of arterial PO2 (PaO2) ranging from deep hypoxia (top left) to hyperoxia (bottom right). Continuous lines are model simulation curves obtained at different levels of PaO2. Experimental data are from Fitzgerald and Parks (20) (, + , *, ×, ) and from Lahiri and Delaney (31) () in cats, at corresponding levels of PaO2.

Efferent neural pathways. The efferent pathways in the model comprise both sympathetic and parasympathetic (vagal) neural fibers. The activity in these efferent fibers is a nonlinear monotonic function of the weighted sum of activities from baroreceptors, chemoreceptors, and lung-stretch receptors, where the weights may be positive or negative. Moreover, afferent information is compared with an offset term; in the case of sympathetic activity, the latter is modulated by hypoxia in the CNS and by CO₂ changes in the medulla (see CNS response).

CNS response. The model assumes that changes of PO₂ and PCO₂ affect the sympathetic activity directly by modifying the offset term in the equation linking sympathetic response to the afferent information (Eqs. 4-7 in APPENDIX). Both mechanisms include a static characteristic and a first-order, low-pass dynamic.

Cardiovascular effectors for the reflex control. As explained above, in the present work the sympathetic activity is subdivided into three distinct branches. The first is directed to systemic arterioles in the splanchnic, muscular, and nonautoregulated extrasplanchnic vascular beds and modifies the peripheral resistance. The second is directed to the peripheral veins and modifies venous unstressed volumes in the same vascular beds. Finally, sympathetic activity to the heart affects heart period and the end-systolic elastance in the right and left ventricles. The vagal activity works on the heart only by modulating heart period. Each effector response includes a pure delay, a monotonic static function, and a first-order, low-pass dynamic. Equations are formally identical to those used in a previous work (59) and hence are not repeated for briefness.

Local effect of O₂ and CO₂. We assume that hypoxia in the coronary, brain, and skeletal muscle circulation causes vasodilation through a local mechanism. It is well known that the local O₂ effect can be ascribed to two concurrent mechanisms, i.e., a direct effect of O₂ on smooth muscle tension in the arteriolar wall and an indirect effect mediated by the release of vasodilatory metabolites (adenosine, pH, etc.) by the hypoxic tissue. Because the aim of this model is not to analyze the synergic action of these mechanisms in detail and to assess their individual role, but just to simulate the overall O₂ effect on peripheral resistances, we used a single empirical equation for each compartment. In this equation, we assumed that the controlled quantity for the local O₂ regulation is O₂ concentration in the venous blood leaving the compartment. This choice is appropriate because venous O₂ concentration is influenced by both the arterial O₂ content and local blood flow, as well as by tissue O₂ consumption rate; hence, its changes reflect all stimuli (direct and indirect) affecting the vascular bed.

View larger version (24K): [in this window] [in a new window]   Fig. 3.   Percent changes of peripheral muscle resistance (Rmp) in the skeletal muscle vascular bed vs. local (PCO2) measured by Refs. 28, 44, and 53 in conditions where only the local mechanism is active. Continuous line represents model results simulated by giving a value for the local vasodilatory effect of CO2 as in Table 1 (km,CO2 = 142.8 mmHg). The large dispersion among experimental data is remarkable.

Control of and VT. is regulated by both central and peripheral chemoreceptors. Because both effects are largely additive in most physiological conditions (7), we can write (Eq. 16 in APPENDIX)
where represents ventilation and the three terms on the right-hand side of the previous equation denote the normal level of ventilation (i.e., ventilation during normoxia and normocapnia, _n), and the changes in ventilation induced by stimulation of peripheral (_p) and central chemoreceptors (_c), respectively. The effect of each group of chemoreceptors has been simulated using a simple first-order linear differential equation with a pure delay (Eqs. 17 and 18 in APPENDIX) (3, 8, 9, 55).

View larger version (20K): [in this window] [in a new window]   Fig. 4.   Time pattern of minute ventilation (, top) and tidal volume (VT, bottom) simulated with the model (left) and measured by Reynolds and Milhorn (46) (right) in response to a 10-min step isocapnic hypoxia (PaO2 = 40 mmHg). Clinical data are means ± SE for 10 subjects.

1

1

View larger version (20K): [in this window] [in a new window]   Fig. 5.   Time pattern of minute (top) and VT (bottom) simulated with the model (left) and measured by Reynolds et al. (47) (right) in response to a 25-min step hypercapnia (PaCO2 = 56 mmHg). Clinical data are means ± SE for 14 subjects.

View larger version (23K): [in this window] [in a new window]   Fig. 6.   Plot of the steady-state relationship between VT and minute according to the present model (continuous line). Clinical data are from Dripps and Comroe (17), Hey et al. (23), and Reynolds and Milhorn (46).

	RESULTS

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION RESULTS DISCUSSION APPENDIX REFERENCES

In all subsequent figures, experimental data taken from the literature are presented as means ± SE. Just in a few cases, SE are not presented because they could not be acquired from the original publication. Moreover, to quantitatively assess the adequacy of fitting, a statistical Student's t-test has been performed between the model prediction and the corresponding experimental data in all cases where the experimental SE was available. Three levels of statistical significance are used as the following: *P < 0.1, **P < 0.05, and ***P < 0.01.

CO₂ response of the CNS. A preliminary group of simulations was performed to give a numerical value to the parameters characterizing the CNS response to local CO₂ changes. To this end, the action of baroreceptors, peripheral chemoreceptors, and lung-stretch receptors was excluded from the model to simulate conditions occurring in artificially ventilated animals after the vagi, carotid sinus, and aortic nerves were cut (34). Exclusion of these mechanisms was achieved by artificially maintaining the input quantities of these groups of receptors at their basal value throughout the simulations, i.e., these receptors work in open-loop conditions with an input quantity different from that used in the rest of the cardiovascular model. Pa_CO2 was then changed from 20 to 50 mmHg. The parameter affecting HR (g_ccsj in Eq. 6 on APPENDIX) was assigned to reproduce the HR increase measured by Downing et al. (16) in dogs (~40 beats/min increase if PCO₂ of the CNS superfusate is increased by ~80 mmHg). The parameters affecting peripheral resistance and CO (g_ccsp and g_ccsv) were given to reproduce the changes in the main hemodynamic quantities observed by Lioy et al. (34) in the rat. A comparison between model predictions and experimental results is shown in Fig. 7 for two different values of parameter g_ccsp. It is worth noting that experimental data can be reproduced reasonably well assuming that the CNS response to CO₂ does not significantly affect the venous unstressed volume. This assumption, however, will be removed when simulating other experiments (see Normoxic hypercapnia). Significant statistical differences between simulated and real data are evident only during severe hypocapnia.

View larger version (20K): [in this window] [in a new window]   Fig. 7.   Percent changes in mean systemic arterial pressure (SAP), skeletal muscle resistance (Rmus), total peripheral resistance (TPR), cardiac output (CO), and absolute values of heart rate (HR) vs. PaCO2, simulated with the model in steady-state conditions after elimination of all reflex mechanisms (i.e., baroreflex, peripheral chemoreflex and lung-stretch receptor reflex). In this condition, only the central neural system (CNS) response to CO2 and the local mechanisms are operative. Continuous lines have been obtained by using the parameter values for the CNS response as in Table 1 (i.e., gccsp = 1.5 mmHg1 · s1, gccsv = 0 mmHg1 · s1, gccsh = 1 mmHg1 · s1 , see Eq. 6 in APPENDIX). Dotted lines have been obtained using a lower value for parameter gccsp = 1.0 mmHg1 · s1. The latter change does not appreciably affect HR. Diamonds, mean values ± SE from Lioy et al. (34). * and ×, presence of significant statistical differences between the model prediction and the corresponding experimental data for the two different simulations (*, gccsp = 1.5 mmHg1 · s1; ×, gccsp = 1.0 mmHg1 · s1). HR changes (~0.5 beats · min1 · mmHg1) agree with experimental results by Downing et al. (16).

Normoxic hypercapnia. Figure 8 shows the percent changes in the main hemodynamic quantities simulated with the model in response to an acute +10-mmHg increase in Pa_CO2, performed at constant PO₂ = 80 mmHg, i.e., the same basal value as in Ref. 25. This simulation was performed with all mechanisms working in closed-loop conditions. Results are compared with those computed from data reported in Koehler et al. (25). The agreement is satisfactory with no significant statistical difference.

View larger version (15K): [in this window] [in a new window]   Fig. 8.   Steady-state percent changes in mean SAP, CO, HR, and TPR simulated with the model in response to a 10-mmHg increase in PaCO2 at constant PaO2 = 80 mmHg (normoxic hypercapnia). All parameters for feedback mechanisms are as in Table 1. Experimental mean values ± SE are from Koehler et al. (25). No significant statistical difference is evident between model predictions and experimental data (P > 0.1 for all quantities).

View larger version (11K): [in this window] [in a new window]   Fig. 9.   A: steady-state percent changes in mean SAP, CO, HR, and TPR simulated with the model in response to an acute increase in PaCO2 up to 58.5 mmHg at constant PaO2 (95 mmHg) (normoxic hypercapnia). Experimental data are mean values ± SE from Richardson et al. (48). SE for SAP was not available. Two examples of model simulations are shown. In the first (basal), all parameters were given the same values as in Table 1. However, this choice leads to significant statistical differences in the prediction of HR, CO, and TPR. To overcome these differences, we had to modify the CNS response to CO2 (gccsp = 0 mmHg1 · s1, gccsv = 1.7 mmHg1 · s1, gccsh = 0 mmHg1 · s1; these changes signify a greater CNS control on venous unstressed volume, with negligible CNS control on peripheral resistance and HR) and assume a greater local vasodilatory effect of CO2 on the skeletal muscle vascular bed (km,CO2 = 8.3 mmHg). B: steady-state percent changes in HR, skeletal muscle blood flow (m), and skeletal muscle peripheral resistance (Rmp), measured by Richardson et al. (48). in the forearm after local sympathetic blockade. This experiment was simulated with the model by excluding all sympathetic effects on the skeletal muscle vascular bed and using the same parameter sets as in A.

Hypercapnia during controlled ventilation. Several authors analyzed the effect of hypercapnia on cardiovascular variables in anesthetized animals with controlled ventilation plus hyperoxia. In these experiments, owing to artificial ventilation, lung-stretch receptors have no role in the regulation, hence their input was maintained constant throughout the simulations. Two different examples are shown in Fig. 10 (50, 61) and compared with model predictions. In the experiments by Wendling et al. (61), TPR increases during hypercapnia, whereas CO decreases. This result can be reproduced by using the basal set of parameters, but just assuming a reduction in the strength of the CNS response on HR and on TPR. The last changes may reflect the use of anesthesia during the experiment.

View larger version (15K): [in this window] [in a new window]   Fig. 10.   Percent changes in the main hemodynamic quantities measured at different levels of PaCO2 in anesthetized artificially ventilated dogs. Continuous lines are model simulation results obtained using the following parameters for CO2 response: gccsp = 0 mmHg1 · s1, gccsv = 0.4 mmHg1 · s1, gccsh = 0 mmHg1 · s1, km,CO2 = 12.5 mmHg, kh,CO2 = 7.7 mmHg. Dashed lines have been obtained using gccsp = 0.5 mmHg1 · s1 and gccsh = 0.2 mmHg1 · s1. In all these simulations the input of lung-stretch receptors was maintained constant to mimic artificial ventilation, and moderate hyperoxia was adopted (as in the original experiments).

Hypocapnic hypoxia. Figure 11 shows the percent changes in the main hemodynamic quantities simulated in response to an acute hypoxia, with a concomitant decrease in PCO₂. Two different examples are reported and compared with data obtained by Krasney and Koehler (29) in dogs and Kontos et al. (27) on human volunteers. The agreement between model simulation results and data by Krasney and Koehler (29) is satisfactory, using the basal parameter set without statistical differences. In contrast, very significant statistical differences are evident to mean SAP and TPR if model predictions are compared with data by Kontos et al. (27). However, these differences can be overcome if the strength of the peripheral chemoreceptor response to CO₂ is just moderately increased (from K_H = 3 to K_H = 4.7, see Eq. 1 in APPENDIX).

View larger version (14K): [in this window] [in a new window]   Fig. 11.   Steady-state percent changes in mean SAP, CO, HR, and TPR simulated with the model in response to acute hypoxia associated with hypocapnia (hypocapnic hypoxia). Final levels of hypoxia and hypocapnia used in these simulations are shown in the corresponding panels. A: mean values ± SE from Krasney and Koehler (29); B: mean values ± SE from Kontos et al. (27). In the second experiment, the starting level of PaO2 was as low as 75 mmHg. All model parameters used to simulate the first experiment are as in Table 1. Two simulations have been performed for the second experiment. The first simulation used the same parameter values as in Table 1. However, significant statistical differences are evident as to SAP and TPR. These differences can be overcome using a higher strength for the peripheral chemoreceptor response to CO2 (KH = 4.7 instead of KH = 3.0 in Eq. 1 in APPENDIX). ***P < 0.01.

Hypercapnic hypoxia. Figure 12 shows the percent changes in the main hemodynamic quantities simulated in response to acute hypercapnia + acute hypoxia. Comparison is performed with two different experimental results in dogs (25, 49). Figure 12A shows that the model is able to reproduce the experimental results by Koehler et al. (25) fairly well using the basal set of parameters. However, we can observe that HR and so CO are overestimated. In contrast, the results by Rose et al. (49) (see Fig. 12B) exhibit a significant decrease in TPR during hypercapnia + hypoxia. The model can approximately simulate this behavior only assuming that the CNS response to CO₂ has scarce effect on resistance and HR and assuming a stronger vasodilatory effect of CO₂ on peripheral vascular beds. It is interesting to observe that the latter changes conform to those already hypothesized to simulate data by Richardson et al. (48) and Rothe et al. (50).

View larger version (15K): [in this window] [in a new window]   Fig. 12.   A: steady-state percent changes in mean SAP, CO, HR, and TPR simulated with the model in response to an acute 10-mmHg increase in PaCO2 associated with a simultaneous reduction in PaO2 (from 80 to 40 mmHg) (hypoxic hypercapnia). All parameters for feedback mechanisms are as in Table 1. Experimental data are mean values from Koehler et al. (25). SE are not shown because they were not reported in the original paper at this level of hypoxia. B: percent changes in the same quantities measured by Rose et al. (49) (mean values ± SE) at a greater level of hypoxia. These changes can be roughly simulated with the model assuming a poor CNS response to CO2 (gccsp = 0 mmHg1 · s1, gccsv = 0 mmHg1 · s1, gccsh = 0 mmHg1 · s1) and a strong local vasodilatory effect (km,CO2= 8.3 mmHg, kh,CO2= 7.7 mmHg). However, it is still worth noting the existence of a great overestimation of HR by the model, which is reflected in overestimation of CO and mean SAP, too.

Sensitivity analysis. Because the cardiovascular responses to CO₂ pressure changes reported in the literature show striking differences from one case to another (5, 25, 38, 48, 50, 54, 61), we found it useful to perform a sensitivity analysis on the role of the individual mechanisms. To this end, Fig. 13 shows the percent changes in the main hemodynamic quantities simulated with the model in response to a Pa_CO2 increase from 40 to 60 mmHg during normoxia (Pa_O2 = 95 mmHg) first when all mechanisms are intact and then after selective exclusion of a single mechanism. The individual mechanism was eliminated by opening the corresponding feedback loop and maintaining the input quantity at the basal level, thus excluding the corresponding regulatory action. However, when excluding the CNS response to CO₂, we also excluded the action of central chemoreceptors on ventilation, i.e., all central influences are simultaneously withdrawn.

View larger version (28K): [in this window] [in a new window]   Fig. 13.   Sensitivity analysis on the role of the individual reflex mechanisms to the response to an acute 20-mmHg increase in PaCO2, performed at constant PaO2 (95 mmHg). Solid bars, steady-state percent changes in mean SAP, CO, HR, and TPR simulated with the model in basal conditions (i.e., with all parameters as in Table 1). Other bars represent simulation results after selective elimination of a feedback mechanism. It is remarkable that the CNS response and the central chemoreceptor response to ventilation have been excluded together to mimic the absence of all central receptors.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION RESULTS DISCUSSION APPENDIX REFERENCES

The major aim of the present work was to extend a previous model of short-term cardiovascular regulation to account for the effect of PCO₂ changes on cardiovascular parameters. The new aspects incorporated include the nonlinear O₂-CO₂ interaction at the peripheral chemoreceptors, the direct CNS response to CO₂ changes, the role of central chemoreceptors on ventilation, and the local CO₂ effect on peripheral resistances. The parameter values characterizing these individual mechanisms have been given on the basis of specific physiological experiments in which the contribution of each mechanism could be adequately assessed independently of the others. Subsequently, we verified that the integrated action of all these mechanisms joined with the regulatory actions described in the previous work (i.e., the baroreflex response, the hypoxic CNS response, the action of lung-stretch receptors, and the local oxygen effect) is able to reproduce experimental results reasonably well in a variety of experimental conditions (normoxic hypercapnia, hypercapnia with artificial ventilation, hypoxic hypercapnia, and hypocapnic hypoxia). At present, we are not aware of other models able to summarize all these regulatory actions into a single theoretical structure. In fact, although various models of the baroreflex control have been presented in previous years (21, 22, 42), no one describes the effect of changes in gas tension on cardiovascular parameters in accurate quantitative terms.

The present model may have several important implications: it may be useful to summarize present physiological knowledge, it may help the rational interpretation of physiological data, and it may constitute the core of future software packages of didactic value. In perspective, the model may also be of value in the clinical practice, especially in the analysis of physiopathological conditions characterized by acute changes in blood gas content. In addition, it might be combined with other models describing lung mechanics, gas exchange processes, pharmakinetics, and/or electrolyte disorders. These areas of explorations may permit deeper comprehension of the interaction between the cardiovascular system and other physiological systems, often studied separately. For instance, the model may be useful to study the effect of respiratory pathologies on cardiovascular quantities and/or to analyze the transport of various substances (not only O₂, but also drugs or anesthetics) in different hemodynamic conditions. To this end, however, the model should be enriched with other aspects, not considered presently, such as equations for gas exchange at the alveoli, lung mechanics, pH balance, and capillary exchange.

In the following, the main results obtained with the present simulations are critically discussed.

Normoxic hypercapnia. When arterial O₂ content is maintained at its basal level, the model furnishes a typical cardiovascular response to hypercapnia. This is characterized by a significant ventilation increase (Fig. 5) and a moderate increase in mean SAP, HR, and TPR, whereas CO exhibits insubstantial changes (Fig. 8). As clarified by the sensitivity analysis reported in Fig. 13, this response is the result of the complex superimposition among the various mechanisms simultaneously operative. In particular, according to Fig. 13, the model ascribes the increase in total systemic resistance to the synergistic action of the peripheral chemoreceptors and of the CNS response to CO₂. Selective elimination of these mechanisms, in fact, attenuates the rise in TPR during hypercapnia. Conversely, the increase in HR results from the CNS response and the simultaneous stimulation of lung-stretch receptors (secondary to the ventilation increase). Finally, it is worth noting the pivotal role played by the baroreflex control in buffering excessive cardiovascular derangement. In the absence of this mechanism, in fact, even a moderate hypercapnia would result in large increases in mean SAP and HR.

Hypercapnia with artificial ventilation. The significant differences in the response to CO₂ visible between Figs. 8 and 9 are not exceptional but correspond to other findings in the physiological literature. For instance, as shown in Fig. 10, comparable differences can be also observed in experiments performed in artificially ventilated dogs, i.e., without lung-stretch receptors. According to some authors, the main consequence of hypercapnia is a moderate arterial hypertension with an increase in TPR, whereas CO exhibits either inconclusive changes (54) or moderate reduction (61). The model can reproduce this scenario fairly well using the basal parameter set (but just assuming a weakening of central chemoreceptors, which can be due to anesthesia). Conversely, Rothe et al. (50) observed a progressive decrease in total resistance when increasing the hypercapnic level up to 90 mmHg; moreover, these authors observed a progressive increase in central blood volume and mean filling pressure, indicating active venoconstriction through sympathetic activation. Results by Rothe et al. can be reproduced quite well assuming a strong local vasodilatory effect of CO₂ on peripheral resistances and the existence of sympathetic venoconstriction from the CNS response. According to this idea, Rothe et al. suggested that about 30% of the observed increase in mean filling pressure arises from receptors in the brain. The latter scenario is similar to that hypothesized when simulating the experimental results by Richardson (48), revealing remarkable analogies between the two cases.

Hypercapnic hypoxia. Similar differences in the response to CO₂ can also be noticed by comparing the experimental results by Koehler et al. (25) and Rose et al. (49) during hypercapnic hypoxia in conscious dogs. According to experimental results by Koehler et al., the model suggests that moderate hypoxia (40 mmHg) with hypercapnia results in a significant increase in SAP, CO, and HR, whereas total systemic resistance exhibits only an inconsistent change. The model explains these results ascribing the increase in HR to activation of lung-stretch receptors and to the CNS response (stimulated both by hypoxia and hypercapnia) and the increase in CO to the increase in mean filling pressure, caused by peripheral chemoreceptor activation. Meanwhile, TPR remains almost unchanged because it depends on various antagonistic actions. In fact, the CNS response and the peripheral chemoreceptor activation work to increase resistance in reflexly regulated vascular beds, whereas the strong stimulation of lung-stretch receptors and the local vasodilatory effect of CO₂ and O₂ conspire to reduce systemic resistance in the reflexly and the metabolic regulated vascular beds, respectively.

Hypocapnic hypoxia. The model is able to reproduce the cardiovascular response to hypocapnic hypoxia reasonably well, both in awake dogs (29) and human volunteers (27), even though the second simulation may benefit from a moderate change in the peripheral chemoreceptor sensitivity to CO₂.