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Role of acid-base balance in the chemoreflex control of breathing

Departments of Anaesthesia and Physiology, University of Toronto, Toronto, Ontario

Submitted 30 May 2005 ; accepted in final form 10 August 2005

	ABSTRACT

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

 
This paper uses a steady-state modeling approach to describe the effects of changes in acid-base balance on the chemoreflex control of breathing. First, a mathematical model is presented, which describes the control of breathing by the respiratory chemoreflexes; equations express the dependence of pulmonary ventilation on PCO₂ and PO₂ at the central and peripheral chemoreceptors. These equations, with PCO₂ values as inputs to the chemoreceptors, are transformed to equations with hydrogen ion concentrations [H⁺] in brain interstitial fluid and arterial blood as inputs, using the Stewart approach to acid-base balance. Examples illustrate the use of the model to explain the regulation of breathing during acid-base disturbances. They include diet-induced changes in sodium and chloride, altitude acclimatization, and respiratory disturbances of acid-base balance due to chronic hyperventilation and carbon dioxide retention. The examples demonstrate that the relationship between PCO₂ and [H⁺] should not be neglected when modeling the chemoreflex control of breathing. Because pulmonary ventilation controls PCO₂ rather than the actual stimulus to the chemoreceptors, [H⁺], changes in their relationship will alter the ventilatory recruitment threshold PCO₂, and thereby the steady-state resting ventilation and PCO₂.

computer modeling

View larger version (16K): [in this window] [in a new window]   Fig. 1. Simplified block diagram illustrating the respiratory chemoreflex control of ventilation. Pulmonary ventilation controls PCO2 and PO2, forward part of the loop. PCO2 and PO2 via the respiratory chemoreflexes control ventilation, feedback part of the loop. In addition, ventilation is also affected by drives to breathe independent of the chemoreflexes, here called the wakefulness drive.

Modelers of the chemoreflex control of breathing usually express the chemoreceptor stimuli in terms of PCO₂ and PO₂ and the resultant response in terms of pulmonary ventilation (6, 15, 27, 33, 53, 61, 64), although some early modelers used pH as the stimulus (31, 38). However, the latter modelers did not consider acid-base disturbances or any detailed models of the relation between pH and PCO₂.

Currently, breathing is assumed to be the sum of three components: central and peripheral chemoreflex drives to breathe and a ventilatory drive dependent on state, an approach introduced by Lloyd and Cunningham (32) that has come to be known as the "Oxford" model. The model uses linear relations between ventilation and PCO₂ above a threshold and a rectangular hyperbolic relation to describe the modulation of peripheral chemoreflex sensitivity to PCO₂ by PO₂. The effect of behavioral state (45, 55) is modeled as the addition of a "wakefulness drive" to breathe (34), a concept introduced by Fink (12) because the drive disappears during sleep.

Many laboratories have measured the ventilatory responses to carbon dioxide and hypoxia to establish parameters for the Oxford model, using a variety of methods. Early estimates used steady-state methods (32), and with the introduction of a convenient hyperoxic rebreathing technique by Read (49) many investigators have determined the central chemoreflex sensitivity to PCO₂, the peripheral chemoreflex presumed silenced by the hyperoxia (e.g., Ref. 37). However, neither of these methods measures the wakefulness ventilation drive or the ventilatory recruitment threshold of the response to PCO₂; the latter corresponds to the apneic threshold in sleep (36). Usually the ventilatory recruitment threshold has been taken as the extrapolation of the response to the PCO₂ axis, but this intersection point varies with the slope or sensitivity of the response as well as the strength of the wakefulness drive, unlike the actual threshold.

In 1987, I introduced a modified version of Read's rebreathing method that allowed direct determination of the ventilatory recruitment threshold. In addition, the method measures the ventilatory response to PCO₂ at a chosen isoxic PO₂ tension and the subthreshold ventilation, which is taken as a measure of the wakefulness or basal drive to breathe (2, 8). A number of studies using this method (e.g., Ref. 39) accumulated sufficient data on a large number for subjects to develop a model of the respiratory chemoreflexes (9). One major change of concept in this model is the rejection of hypoxia as an independent stimulus; hypoxia only acts to sensitize the peripheral response to carbon dioxide. This point is illustrated in Ref. 39, where the effects of hypoxia on the response to carbon dioxide clearly do not affect the subthreshold ventilation, and it was directly demonstrated in Ref. 48, where the response to hypoxia below the threshold was measured. These results clearly disagree with the classical view of hypoxia as an independent stimulus to breathe, as illustrated in Ref. 43, and argue against viewing PO₂ as the primary stimulus to the peripheral chemoreceptors (e.g., Ref. 63). In the present model, PO₂ only modulates the sensitivity of the peripheral chemoreceptor response to PCO₂.

In recent studies of the changes in the chemoreflexes induced by exposure to patterns of hypoxia (7), including altitude hypoxia (57), it became apparent that consideration must also be given to acid-base changes. These may alter the relationship between the actual stimulus to the chemoreceptors, [H⁺], and the measured stimulus, PCO₂, and so necessitated the development of a model of the respiratory chemoreflex control of breathing in terms of the actual stimulus [H⁺] rather than the measured stimulus PCO₂. This paper presents such a model, and it is used to illustrate how changes in acid-base variables affect the regulation of breathing. Although the predictions are based on a quantitative model, comparisons with experimental data are of necessity qualitative, because measures of the requisite acid-base variables in humans are lacking. The presentation of the model is therefore essentially as a "proof of concept," and my aim is to stimulate debate about traditional approaches to the control of breathing and acid-base balance.

	METHODS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

 
The Chemoreflex Model in Terms of PCO₂

The model consists of mathematical relations between chemoreflex stimuli, PCO₂ and PO₂, and the resultant ventilation. As Dejours originally suggested (4), these relations describe chemoreflexes, with a reflex arc from the chemoreceptors to the outcome ventilation. The model presented here was developed from a previous model (9) that described the chemoreflex responses to hypoxia and carbon dioxide in terms of both tidal volume and breathing frequency. The model developed here expresses the response as ventilation only and was derived from the previous model by making the assumption that breathing frequency was constant at 12 breaths/min. The central and peripheral chemoreflex drives to breathe are assumed to be additive but do not actually affect pulmonary ventilation until a drive threshold is exceeded. They then add to the wakefulness drive to breathe. The following sections detail these relations in turn, presenting them in both graphical and algebraic forms (APPENDIX A).

Central chemoreflex.   Figure 2A shows the central chemoreflex alone as a linear relation between central PCO₂ input and the central chemoreflex drive to breathe output, and it assumes an aggregate response of all central chemoreceptors. The drive to breathe can be thought of as the signal transmitted from the central chemoreceptors to the medullary respiratory neurons measured in terms of pulmonary ventilation, with the slope of the response indicating the sensitivity of the chemoreflex. In addition, there is a central chemoreceptor threshold: the PCO₂ above which the central chemoreceptors generate a drive signal. The response to carbon dioxide is therefore determined by both sensitivity and threshold parameters according to Eq. A1.

View larger version (23K): [in this window] [in a new window]   Fig. 2. Central (A) and peripheral (B) chemoreceptor responses to PCO2 and PO2 in terms of the drives to ventilation that they produce. Each chemoreceptor has a threshold PCO2 below which no drive is produced and above which the drive to ventilation is linearly related to PCO2 with a slope defined as the sensitivity. For the peripheral chemoreceptor the latter depends on PO2 as shown in the inset.

Central and peripheral chemoreflex drives sum.   Currently the prevailing view is that the central and peripheral drive signals sum centrally to produce an overall drive to breathe without a more complex interaction (28). However, the summed signals must increase beyond a drive threshold before pulmonary ventilation is affected, as illustrated in Fig. 3. In other words, even though the central and peripheral chemoreceptors are generating signals, ventilation is unaffected until their summed signal strength is large enough to exceed the drive threshold of 18.5 l/min and produce an increase in pulmonary ventilation. As a result, when measuring the central chemoreflex ventilation response to carbon dioxide, there is another threshold created: the ventilatory recruitment threshold is the PCO₂ below which ventilation is unaffected by carbon dioxide and above which the response is linearly related to PCO₂. This ventilatory recruitment threshold is equivalent to the apneic threshold when the wakefulness drive is absent during sleep (36).

View larger version (26K): [in this window] [in a new window]   Fig. 3. Central plus peripheral chemoreflex ventilatory responses to PCO2 add to produce a chemoreflex drive to ventilation (left axis) depending on the PO2 (solid, dotted, and dashed lines). A difference of 6 Torr was assumed between arterial and central PCO2. However, this drive must exceed a chemoreflex drive threshold before ventilation (right axis) is affected. This requirement produces a ventilatory recruitment threshold, a PCO2 below which there is no ventilation and above which ventilation increases linearly with PCO2.

A complete graphical picture of the control of breathing in a resting individual may be developed by assuming a difference between central and arterial PCO₂ of 6 Torr. This value was chosen partly as a compromise between the measured differences between cerebrospinal fluid (CSF) and arterial PCO₂ of 10 Torr and suggestions that the actual medullary PCO₂ in the region of the central chemoreceptors may be only a few Torr above arterial due to their differential perfusion (23). An estimate can also be made from the differences steady-state and rebreathing ventilatory responses to carbon dioxide. The steady-state responses are plotted against end-tidal estimates of arterial PCO₂, whereas the rebreathing responses are plotted against end-tidal estimates of central PCO₂. In our laboratory's previous study comparing steady-state and rebreathing responses (40) they were parallel and separated by a mean of 7 Torr PCO₂.

This assumption has the effect of displacing the central chemoreceptor threshold downward by that amount, because central PCO₂ is assumed to be 6 Torr above arterial. It therefore affects the model predictions quantitatively but not qualitatively. Then, adding the chemoreflex and wakefulness drives to breathe produces a graph of the dependence of ventilation on PCO₂ shown in Fig. 4.

View larger version (23K): [in this window] [in a new window]   Fig. 4. Combining the wakefulness drive to breathe with the chemoreflex mediated ventilation (feedback part of control loop) yields the ventilation that results from any combination of PCO2 and PO2 (solid, dotted, and dashed lines). The metabolic hyperbola (gray line) describes how PCO2 is affected by ventilation (forward part of control loop). The control system equilibrium point (sometimes incorrectly called the set point) is the intersection of these relationships and predicts resting ventilation and PCO2.

Modeling Acid-Base Relations

Traditional model.   The traditional model of acid-base describes the equilibrium reaction of carbon dioxide and water expressed by the Henderson-Hasselbach equation, which defines pH. This approach leads to a simplistic understanding of acid-base balance, especially easy to understand when the linear form of the equation (44) is used:

where [H⁺] is hydrogen ion concentration (40 nM/l); PCO₂ is partial pressure of carbon dioxide (40 Torr); and [HCO₃^–] is bicarbonate ion concentration (24 mM/l).

An increase in PCO₂ due to decreased pulmonary ventilation, or a reduction in [HCO₃^–] due to a presumed increase in kidney excretion, will cause an increase in [H⁺], and the inverse changes will cause a decrease in [H⁺].

However, phosphate and proteins that contain histidine residues, like hemoglobin, also act as buffers within the body, so Siggaard-Andersen (56), recognizing the importance of these noncarbonic buffers, introduced the concept of "base excess," the amount of bicarbonate required to return plasma pH to 7.4 under standard conditions in vitro. Other modifications such as the concept of "anion gap" followed. This empirical approach provides insight into the classification, magnitude, and the nature of clinical acid-base disturbances, but the model breaks down at physiological extremes (10, 11). Furthermore, it uses transformed variables like pH and artificial concepts like base excess and anion gap, and it fails to identify the dependent and independent variables.

Stewart model.   Peter Stewart (58) suggested that a more rigorous physicochemical approach was feasible for clinical practice, because the complex equations of such an approach could easily be solved by modern computers. The Stewart approach considers PCO₂ and two other variables, SID (strong ion difference; the concentration difference of strongly dissociated positive and negative ions in solution) and [A_tot] (the total concentration of weakly dissociated anions in solution) to be the independent variables that determine the dependent variables [H⁺] and [HCO₃^–]. The six equations he developed are listed in APPENDIX B.

Modified Stewart model.   One weakness of the Stewart model was the assumption of a single dissociation constant for all plasma proteins to determine the contribution of weakly dissociated anions. The model does not therefore readily account for changes in phosphate or albumin that are often relevant in critically ill patients, chronic renal failure, and altitude acclimatization. In a modified version of the Stewart model developed by Figge et al. (10, 11), phosphate and albumin are substituted for total protein.

These investigators showed that globulins have a negligible role in acid-base equilibrium and quantified the role of phosphate and albumin, the latter the protein of greatest significance. Subsequently, Watson (62) simplified their approach by pointing out that only the histidine component of proteins can buffer hydrogen ion in the concentration range compatible with life and that although phosphoric acid has three dissociation constants only one is within the physiological range of [H⁺]. The resulting modified Stewart model equations are listed in APPENDIX C.

Chemoreflex Model in Terms of [H⁺]

Model equations.   The chemoreflex equations with PCO₂ as the input variable were converted to use [H⁺] as an input variable. In this new model the forward part of the feedback loop remains the metabolic hyperbola but the feedback part now contains an additional function to transform PCO₂ into [H⁺] as the block diagram in Fig. 5 illustrates. The [H⁺] is assumed to be that of the interstitial fluid in the vicinity of the central chemoreceptors, an extracellular stimulus. The model is therefore not valid in its present form if the actual stimulus is an intracellular one (47).

View larger version (17K): [in this window] [in a new window]   Fig. 5. Simplified block diagram illustrating the respiratory chemoreflex control of ventilation. Pulmonary ventilation controls PCO2 and PO2; the forward part of the loop. Arterial and central hydrogen ion concentration ([H+]) are determined by their respective PCO2, strong ion difference (SID), albumin concentration ([Alb]), and phosphate concentration ([PO4–]) by using the modified Stewart model equations. [H+] and PO2 control ventilation via the respiratory chemoreflexes, the feedback part of the loop. In addition, ventilation is also affected by drives to breathe independent of the chemoreflexes, here called the wakefulness drive.

	RESULTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

 
Dietary Acid-Base Disturbances

Measurements of the ventilatory response to carbon dioxide during dietary acid-base disturbances show that the response is displaced leftward during metabolic acidosis produced by ingesting ammonium chloride and rightward during metabolic alkalosis produced by ingesting sodium bicarbonate (30, 46). These dietary inputs produce changes in SID, and in a series of investigations Jennings and colleagues (reviewed in Refs. 25, 26) examined the control of breathing in dogs using diet to control SID and therefore disturb acid-base balance. They too found that there was a change in the chemoreflex threshold for PCO₂ and noted that it counterbalanced the effects of SID on [H⁺] such as to restore [H⁺] to normal.

To simulate the effects of dietary acid-base disturbances, alterations in SID were applied to the chemoreflex model, and the model equations were used to predict the resting ventilation, arterial [H⁺], and PCO₂ from the intersection of the ventilatory response to carbon dioxide and the metabolic hyperbola, i.e., the equilibrium point. First, the changes were equally applied to both arterial and central SID, which were displaced from their normal values, 5 mM/l above and 5 mM/l below. Then, because Jennings (26) found that the dietary changes in central SID were about half those of arterial SID, changes of 10 mM/l above and below normal were applied to arterial SID while central SID varied by 5 mM/l from normal. For all these simulations it was assumed that central PCO₂ was 6 Torr higher than arterial PCO₂ and that this difference remained constant. In addition, a carbon dioxide production of 0.3 l/min and a wakefulness drive of 7 l/min were assumed, and PO₂ remained constant at 100 Torr. The chemoreflex responses to [H⁺] were assumed to be unaltered throughout.

The resulting simulation equilibrium values and assumed parameters are detailed in Table 1. Figure 6 shows the resulting ventilation vs. PCO₂ graphs, for the arterial and central SID changes 5 mM/l above and below normal. The changes were exaggerated when the arterial SID was varied by 10 mM/l from normal rather than 5 mM/l (shown in gray in Fig. 6). Inset: mean steady-state ventilatory responses to carbon dioxide in humans from Ref. 30 during acid-base changes induced by diet that produced base excesses of –7.1 and +4.5.

View larger version (27K): [in this window] [in a new window]   Fig. 6. Chemoreflex control of breathing model predicts changes in the ventilatory recruitment threshold of the ventilatory response to PCO2, as well as in the resting ventilation and PCO2 resulting from changes in arterial and central SID of plus 5 mM/l (dotted lines) and minus 5 mM/l (dashed lines) produced by dietary intake of sodium bicarbonate and ammonium chloride, respectively. Gray lines show the response if the arterial SID changed by plus and minus 10 mM/l and the central SID changed by plus and minus 5 mM/l. It was assumed that there were no changes in the chemoreflexes or the metabolic hyperbola (thick gray line). Circles show the equilibrium points predicting resting ventilation and PCO2. Inset: mean steady-state ventilatory responses to CO2 during acid-base changes induced by diet (base excess acidosis = –7.1; alkalosis = +4.5; redrawn from Ref. 30).

View larger version (19K): [in this window] [in a new window]   Fig. 7. Chemoreflex control of breathing model predicts changes in central PCO2 (, left scale) and [H+] (, right scale) resulting from changes in arterial and central SID of plus and minus 5 mM/l. Other model assumptions are as for Fig. 6. Inset: mean data from Ref. 23 during diet-induced changes in acid-base balance, where, using the assumption made by Jennings (25) that central bicarbonate ion concentration ([HCO3–]) changes are similar to those of central SID, they can be qualitatively compared with the model predictions.

Ascent to altitude produces hypoxic induced changes in the chemoreflex regulation of breathing that lead to increasing ventilation and a reduction in PCO₂ (54). However, central [H⁺] returns to normal after acclimatization (5). In his review Jennings (26) examined the case for the adjustment of central SID so as to maintain central [H⁺] during altitude acclimatization, using data from Ref. 5 and estimating CSF SID from measures of CSF [HCO3–]. Similar to the acid-base disturbances induced by dietary alterations in SID, Jennings found that, for the altitude acid-base disturbances, CSF PCO₂ was directly related to CSF SID, and he argued that central [H⁺] was maintained by regulating central SID to compensate for the reduction in PCO₂ (26).

Recently, we measured the ventilatory responses to carbon dioxide as well as blood acid-base variables at sea level and compared them to those after 5 days at an altitude of 3,480 m (57). Resting end-tidal PCO₂ decreased by an average of 8.5 Torr, and resting PO₂ at altitude was an average of 64 Torr. The pH of blood samples was not significantly different, and neither was the SID. However, [Alb] and phosphate concentration ([PO4–]) were significantly elevated by an average of 1.12 g/dl and 0.38 mM/l, respectively, a finding in agreement with another study (22).

To simulate the effects of altitude acclimatization, these changes in PO₂, [Alb], and [PO4–] were applied to the chemoreflex model, and the equations used to predict the steady-state resting ventilation, arterial [H⁺], and PCO₂ from the intersection of the ventilatory response to carbon dioxide and the metabolic hyperbola, i.e., the equilibrium point. It was assumed that central PCO₂ was 6 Torr higher than arterial PCO₂ and that this difference remained constant because cerebral blood flow and metabolism were unchanged (41). In addition, a carbon dioxide production of 0.3 l/min and a wakefulness drive of 7 l/min were assumed, and PO₂ was 100 Torr at sea level and 64 Torr at altitude. The chemoreflex responses to [H⁺] were assumed to remain unaltered. In keeping with the experimental findings of a normal central [H⁺] (5), central SID was altered at altitude so as to maintain central [H⁺] at its sea level value as illustrated in Fig. 5 of Ref. 26. Additionally, the simulation was also performed without assuming a compensatory change in central SID to show the effects of the arterial blood changes alone.

The results of the simulation in terms of the steady-state equilibrium points and assumed parameters are listed in Table 1. Figure 8 shows the ventilation vs. PCO₂ graphs with arterial changes only (altitude 1 line) and with both arterial and central changes (altitude 2 line). The inset shows example rebreathing responses from Ref. 57 illustrating the leftward shift in the ventilatory responses to carbon dioxide without a significant change in slope. For these rebreathing responses, end-tidal PCO₂ corresponds to central PCO₂, and so the response lines are shifted right relative to the model's responses, which are plotted against arterial PCO₂.

View larger version (23K): [in this window] [in a new window]   Fig. 8. Chemoreflex control of breathing model predicts the decrease in the ventilatory recruitment threshold PCO2, as well as the increase in resting ventilation and decrease of resting arterial PCO2 resulting from a 5-day sojourn at altitude. Solid line, normal ventilatory response to CO2 (sea level). It was assumed that plasma albumin and phosphate increased by 1.12 g/dl and 0.38 mM/l, respectively, and that end-tidal PO2 decreased to 64 Torr (57). If central pH was not defended by altering SID, the predicted CO2 response at altitude is shown by the dotted line (Altitude 1). If central [H+] was defended by altering central SID the response at altitude is shown by the dashed line (Altitude 2). It was also assumed that there were no changes in the chemoreflexes or the metabolic hyperbola (thick gray line). Circles show the equilibrium points, and crosses show data for resting PCO2 from Ref. 57. Inset: example rebreathing responses [isoxic at 150 Torr PO2 (A) and at 50 Torr PO2 (B); and , sea level; and , altitude] from study (57) illustrating the leftward shift in the ventilatory responses to carbon dioxide without a significant change in slope. (Note that the rebreathing end-tidal PCO2 corresponds to central PCO2 and so the response lines are shifted right relative to the model's responses plotted against arterial PCO2.)

During chronic hyperventilation hypocapnia (14), the ventilatory response to PCO₂ is shifted to the left (51), and, when chronic carbon dioxide retention producing hypercapnia occurs, the ventilatory response to PCO₂ is shifted to the right (1, 3). These two states were simulated by increasing the wakefulness drive from 7 to 10 l/min for the former condition, and increasing inspired PCO₂ from 0 to 10 Torr for the latter condition. In each case, arterial and central [Alb] and [PO4–] were assumed unaltered from normal, as were the chemoreflexes. Two compensatory scenarios were simulated. First, both arterial and central SID were adjusted to return arterial and central [H⁺] to normal values, simulating a complete renal and central compensation. Second, only a central compensation of SID to return central [H⁺] to normal was simulated.

Table 1 details the parameter settings and the resulting equilibrium values. The model predicted the steady-state ventilation vs. PCO₂ response lines and equilibrium points during these compensated respiratory disturbances of acid-base balance, and Fig. 9 shows the resulting graphs. The inset shows mean steady-state ventilatory responses to carbon dioxide in humans for similar disturbances: the hyperventilation responses are those before and after 6 h of hyperventilation so as to reduce resting PCO₂ by 10 Torr (51). The carbon dioxide retention response was derived by increasing the threshold of the control response line by 2.5 Torr, as the mean change reported to occur after 2 days when end-tidal PCO₂ was increased by 8 Torr (3).

View larger version (27K): [in this window] [in a new window]   Fig. 9. Chemoreflex control of breathing model predicts changes in the ventilatory recruitment threshold of the ventilatory response to PCO2, as well as in the resting ventilation and PCO2 resulting from long-term respiratory changes. In one case inspiratory PCO2 was raised to 10 Torr, resulting in a shift in the metabolic hyperbola (thick line) to the right (thick gray line) to mimic CO2 retention (dotted lines). In the other case the wakefulness drive was increased from 7 to 10 l/min to mimic a chronic hyperventilation syndrome (dashed lines). Arterial and central [H+] were defended by altering arterial and central SID. Gray lines show the response if only central [H+] was defended by altering central SID. Inset shows mean steady-state ventilatory responses to CO2 during respiratory induced acid-base changes redrawn from Refs. 3 and 30; the control and hyperventilation responses shown are those before and after 6 h of hyperventilation so as to reduce resting PCO2 by 10 Torr (51), and the CO2 retention response shown was after 2 days of increasing end-tidal PCO2 by 8 Torr (3).

	DISCUSSION

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

As for all models, the success of predictions depends on the model parameter values chosen and the assumed changes in response to challenges. The parameters used for this model were derived as much as possible from experimental data obtained from the literature, as were the assumptions of the changes in these parameters for the simulations. However, they are still vulnerable to criticism as to the particular values chosen for the model, especially because there are large variations between individuals, and so the quantitative predictions of the model may differ from observations. In particular, there is a lack of data on central acid-base variables during the disturbances modeled here, and so comparisons of model predictions with experimental data are of necessity qualitative. Nevertheless, if the correctness of the general premises applied to the simulations (reviewed below) is accepted, then changes in the model parameter values will not alter the qualitative conclusions drawn from these simulations. These are as follows:

First, the primary effect of acid-base disturbances on the chemoreflex control of breathing is to change the partial pressure of carbon dioxide at which carbon dioxide begins to stimulate breathing, i.e., the ventilatory recruitment threshold PCO₂, even though the threshold in terms of [H⁺] remains unchanged. Second, the model simulations demonstrate the importance of central SID in the regulation of breathing, as originally suggested by Jennings (25, 26). Third, changes in plasma phosphate or albumin will also produce changes in the ventilatory recruitment threshold. Finally, it should also be pointed out that, as the figures and tabled data show, the changes in the ventilatory response to carbon dioxide were dominated by changes in threshold, and changes in slope or sensitivity, although present, were minor in comparison.

Dietary Acid-Base Disturbances

For the dietary changes in acid-base balance it was assumed that only SID changed and that there was no change in the chemoreflex responses to [H⁺]. These simulations are therefore the simplest in terms of premise and are supported by experimental observations in dogs (25, 26). That the model provides a qualitative prediction of the ventilatory recruitment threshold shifts observed in humans (23, 30, 46) argues for the correctness of the assumptions.

As the model also illustrates, alterations in the degree of change in arterial vs. central SID did not change the pattern of the results to any significant degree, primarily because of the dominance of central chemoreflex control at normal oxygen tensions, and so knowledge of central acid-base status is essential if the model is to be quantitatively assessed. Therefore, comparing the model prediction to the experimental responses (30) shown in the Fig. 6 inset, it appears that either the central changes in SID produced by the experimental diet were smaller than those assumed in the model or the model simulation is an overprediction of the threshold changes. These two possibilities cannot be distinguished, because experimental data describing the degree of central acid-base changes in SID are not available.

Similarly, the predictions shown in Fig. 7 illustrating the large changes in PCO₂ with dietary alterations of SID with little change in [H⁺] cannot be compared with direct measurements. Nevertheless, assuming that changes in central [HCO3–] reflect central SID, as Jennings has proposed (25, 26), the model prediction is qualitatively similar to experimental observations (23).

The model therefore demonstrates that the chemoreflex control of PCO₂ compensates for dietary disturbances in acid-base balance so as to regulate [H⁺] because the ventilatory recruitment threshold of the response to carbon dioxide is changed. This change occurs because of the altered relationship between PCO₂ and [H⁺], not because of any change in the chemoreflexes or change in any other stimulus to ventilation.

Respiratory Acid-Base Disturbances

The respiratory changes in acid-base balance produced by hyperventilation and carbon dioxide inhalation were also simple in terms of the assumed changes in model parameters; wakefulness drive and inspired PCO₂ were the only changes made in each model. However, both simulations assumed compensatory SID changes to correct central and arterial [H⁺]. Although the principle of defense of central [H⁺] is acknowledged (29), the complete correction of arterial [H⁺] by renal mechanisms may not be. Nevertheless, even if no renal arterial compensation is assumed, alterations in ventilatory recruitment threshold PCO₂ are still predicted by the model as long as central [H⁺] is defended, again primarily because of the dominance of central chemoreflex control at normal oxygen tensions.

Although there are no experimental data on the central acid-base changes during these respiratory disturbances, so that quantitative comparisons cannot be made, nevertheless qualitative comparisons can be made, comparing the experimental data in the Fig. 9, inset with the model predictions. The ventilatory recruitment threshold was shifted upward for carbon dioxide retention and downward for hyperventilation, more so when both central and arterial SID were adjusted than when central SID alone was adjusted. These changes are therefore qualitatively similar to those observed in experiments (1, 3, 51).

With respect to the hyperventilation experiment to reduce PCO₂ by 10 Torr (51), the reduction of arterial PCO₂ in the model was of similar magnitude. However, the leftward shift of the carbon dioxide response line predicted by the model, assuming both central and arterial [H⁺] compensation, was greater than the experimentally determined line and similar to the predicted response line for central [H⁺] compensation only. Whether this agreement occurred because the model assumption of a central-only [H⁺] compensation is correct, or because the compensation in the experiments was incomplete in 6 h, cannot be determined.

With respect to the experiments elevating end-tidal PCO₂ by 8 Torr (3), the model predictions of PCO₂ with central compensation alone and with both central and arterial compensation bracket the experimentally observed increase in PCO₂. It might therefore be expected that the model carbon dioxide response lines should also bracket the experimentally observed response line; however, as for the hyperventilation experiments, the model prediction is in closest agreement when only central [H⁺] compensation is assumed. Without central acid-base data this question cannot be resolved.

Altitude

The model provides a qualitative prediction of the decrease in the ventilatory recruitment threshold shift and the fall in resting PCO₂ observed in altitude experiments (21, 52, 57). However, there may be other parameter changes that were not modeled. Although the chemoreflex characteristics are likely to remain unaltered in acid-base disturbances produced by dietary changes, or respiratory induced changes in PCO₂ by hyperventilation and carbon dioxide retention, there is evidence from altitude studies that after long-term exposure to hypoxia the peripheral chemoreceptor response is enhanced (52), and laboratory studies of exposure to hypoxia show that over several hours ventilation increases, especially if normocapnia is maintained (e.g., Ref. 59). The increased ventilation appears to be due to a decrease in ventilatory recruitment threshold PCO₂ associated with the peripheral chemoreceptors (35). In the present simulation the chemoreflex responses were assumed to be unaltered and so this assumption may explain the underprediction of the decrease in the ventilatory recruitment threshold. If such an increase in responsiveness were to be applied to the model, there would be a further leftward shift of the ventilation vs. PCO₂ graph, again assuming an adjustment of central SID to correct central [H⁺].

The other major assumption for the model at altitude was that the arterial to central difference in PCO₂ remained unchanged. This difference is primarily determined by cerebral blood flow, and, although experimental evidence suggests that cerebral blood flow is unchanged at altitude (41), nevertheless it is of interest to speculate what would occur if it were increased and consequently the arterial to central difference in PCO₂ were decreased. Then central PCO₂ would be decreased and so would central [H⁺]. With a defense of central [H⁺] by decreasing SID, the ventilation vs. PCO₂ response line would be shifted still further to the left.

The simulated compensations for this respiratory induced hypocapnia included increases in [Alb] and [PO4–] and decreases in central SID. Both of these assumptions are supported by experimental evidence. However, as mentioned previously, although the principle of the regulation of central [H⁺] by altering central SID is acknowledged (29), that of the partial compensation of arterial [H⁺] by increased plasma anion buffering, although supported by one study (57), remains to be investigated further. Nevertheless, even without the assumed changes in plasma [Alb] and [PO4–], the model prediction is qualitatively similar to the changes in the ventilatory response to carbon dioxide observed between sea level and after altitude acclimatization (57).

Conclusion

The simulation scenarios chosen for illustration here are but a few of those possible using the model. The model can also be extended to other scenarios in which acid-base changes occur to examine how resting ventilation and PCO₂ are altered. Examples include the changes of SID during pregnancy and with progesterone over the menstrual cycle (18) and the acid-base disturbances occurring in renal failure (17). Further extensions to the model could include the incorporation of the dynamics involved in acid-base adjustments to predict the time course of respiratory and acid-base changes.

These model simulation experiments demonstrate that the relationship between PCO₂ and [H⁺] should not be neglected in modeling the chemoreflex control of breathing. They illustrate the perhaps obvious but neglected point that because pulmonary ventilation controls PCO₂ rather than [H⁺], the actual stimulus to the chemoreceptors, changes in their relationship will alter the ventilatory recruitment threshold PCO₂ and thereby the steady-state resting ventilation and PCO₂.

	APPENDIX A

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

 
Chemoreflex Model in Terms of PCO₂

Central chemoreceptor drive to breathe.  

(A1)

where Dc is the drive to breathe from the central chemoreceptors (l/min), PCO₂ is partial pressure of carbon dioxide at the central chemoreceptors (Torr), Tc is the threshold of the central chemoreceptors (34 Torr), and Sc is the sensitivity of the central chemoreceptors (1.6 l·min^–1·Torr^–1).

Peripheral chemoreceptor drive to breathe.  

(A2)

where Dp is the drive to breathe from the peripheral chemoreceptors (l/min), PCO₂ is the partial pressure of carbon dioxide at the peripheral chemoreceptors (Torr), Tp is the peripheral chemoreceptor threshold (34 Torr), and Sp is peripheral chemoreceptor sensitivity to PCO₂ (l·min^–1·Torr^–1).

The rectangular hyperbolic relation between Sp and PO₂ is described by the following equation:

(A3)

where Sp is peripheral chemoreceptor sensitivity to PCO₂ (l·min^–1·Torr^–1), S₀ is peripheral chemoreceptor sensitivity to PCO₂ in hyperoxia, i.e., the horizontal asymptote of the rectangular hyperbola (0 l·min^–1·Torr^–1), A is the area constant for the rectangular hyperbolic relation between Sp and PO₂ [16.7 l·min^–1·(Torr PO₂)^–1·(Torr PCO₂)^–1], P₀ is PO₂ for maximum sensitivity before failure, i.e., the vertical asymptote of the rectangular hyperbola [30 Torr (Ref. 60)].

Total drives to breathe.  

(A4)

where TD is chemoreflex drive threshold (18.5 l/min) and Dw is wakefulness drive to breathe (7 l/min).

Metabolic hyperbola.  

(A5)

where CO₂ is the metabolic production of carbon dioxide (ml/min), K is a proportionality constant (1.33), E is ventilation (l/min), PA_{CO2 is alveolar PCO2 = arterial PCO2 (Torr), and PICO2 is inspired PCO2 (Torr)}.

The proportionality constant, K, adjusts for the conversion of ventilation to alveolar ventilation and partial pressures to fractional concentrations and was arbitrarily calculated so that, at a resting metabolic production of 300 ml/min carbon dioxide and a resting arterial PCO₂ of 40 Torr, ventilation was 10 l/min.

	APPENDIX B

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

 
Stewart Equations for Acid-Base Balance

(B1)

(B2)

(B3)

(B4)

(B5)

(B6)

where [H⁺] is hydrogen ion concentration (M/l), [OH^–] is hydroxyl ion concentration (M/l), K'_W is the ion product for water (2.39 x 10^–14), [HCO3–] is bicarbonate ion concentration (M/l), [HA] is the undissociated protein concentration (M/l), [A^–] is the ionized protein concentration (M/l), K_A is the protein dissociation constant (1.74 x 10^–7), K_C combines equilibrium and solubility constants (2.45 x 10^–11), PCO₂ is partial pressure of carbon dioxide (Torr), K₃ is the dissociation constant for carbonate (1.16 x 10^–10), and SID = [Na⁺] + [K⁺] + [Ca²⁺] – [Cl^–] – [La^–] – [other anions] (M/l).

	APPENDIX C

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

 
Modified Stewart Equations for Acid-Base Balance

(C1)

(C2)

(C3)

(C4)

(C5)

(C6)

(C7)

(C8)

where [H⁺] is hydrogen ion concentration (M/l), [OH^–] is hydroxyl ion concentration (M/l), K'_W is the ion product for water (2.39 x 10^–14), K_C combines equilibrium and solubility constants (2.45 x 10^–11), PCO₂ is partial pressure of carbon dioxide (Torr), K₃ is the dissociation constant for carbonate (1.16 x 10^–10), [P_i,Tot] is the concentration of phosphate (M/l), K₂ is the phosphoric acid dissociation constant (2.19 x 10^–7), SID = [Na⁺]+[K⁺]+[Ca²⁺] – [Cl^–] – [La^–] – [other anions] (M/l), [Alb] is albumin concentration (g/dl), 66,500 is the molecular weight of albumin, [AFixed–] is the fixed negative charge concentration with 21 fixed negative charges per mol of albumin (M/l), [A_H,Tot] is the concentration of histidine residues with 16 residues per mole of albumin (M/l), [A^–] is the concentration of net charges on albumin (M/l), and K_H is the histidine dissociation constant (1.77 x 10^–7).

	APPENDIX D

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

 
Chemoreflex Model in Terms of [H⁺]

Central chemoreceptor drive to breathe.  

(D1)

where Dc is the drive to breathe from the central chemoreceptors (l/min), [H⁺] is hydrogen ion concentration at the central chemoreceptors (nM/l), Tc is central chemoreceptor threshold (31.8 nM/l), and Sc is central chemoreceptor sensitivity [1.78 l·min^–1 (nM·l^–1)^–1].

Peripheral chemoreceptor drive to breathe.  

(D2)

where Dp is the drive to breathe from the peripheral chemoreceptors (l/min), [H⁺] is hydrogen ion concentration at the peripheral chemoreceptors (nM/l), Tp is peripheral chemoreceptor threshold (34.6 nM/l), and Sp is peripheral chemoreceptor sensitivity to [H⁺] [l·min^–1 (nM·l^–1)^–1].

(D3)

where S₀ is peripheral chemoreceptor sensitivity to [H⁺] in hyperoxia [0 l·min^–1 (nM·l^–1)^–1], A is area constant for the rectangular hyperbolic relation between Sp and PO₂ [17.8 l·min^–1 (Torr·nM·l^–1)^–1], and P₀ is PO₂ for maximum sensitivity before failure (30 Torr).

Total drives to breathe.  

(D4)

where TD is chemoreflex drive threshold(18.5 l/min) and Dw is wakefulness drive to breathe (7 l/min).

	GRANTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

 
The Ontario Thoracic Society and The Heart and Stroke Foundation of Canada supported this work.

	ACKNOWLEDGMENTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C APPENDIX D GRANTS ACKNOWLEDGMENTS REFERENCES

 
I thank Dr. Donald Jennings and Dr. Harold Bell for thoughtful comments and suggestions that assisted the development of this model.

	FOOTNOTES

 

Address for reprint requests and other correspondence: J. Duffin, Depts. of Anaesthesia and Physiology, Univ. of Toronto, Medical Sciences Bldg., Rm. 3326, 1 King's College Circle, Toronto, Ontario, M5S 1A8 (e-mail: j.duffin{at}utoronto.ca)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

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