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HIGHLIGHTED TOPICS
Physiology and Pathophysiology of Sleep Apnea

Transition from acute to chronic hypercapnia in patients with periodic breathing: predictions from a computer model

¹Divisions of Pulmonary and Critical Care Medicine and ²Nephrology, Department of Medicine, New York University School of Medicine/Bellevue Medical Center, New York, New York

Submitted 2 May 2005 ; accepted in final form 26 December 2005

	ABSTRACT

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Acute hypercapnia may develop during periodic breathing from an imbalance between abnormal ventilatory patterns during apnea and/or hypopnea and compensatory ventilatory response in the interevent periods. However, transition of this acute hypercapnia into chronic sustained hypercapnia during wakefulness remains unexplained. We hypothesized that respiratory-renal interactions would play a critical role in this transition. Because this transition cannot be readily addressed clinically, we modified a previously published model of whole-body CO₂ kinetics by adding respiratory control and renal bicarbonate kinetics. We enforced a pattern of 8 h of periodic breathing (sleep) and 16 h of regular ventilation (wakefulness) repeated for 20 days. Interventions included varying the initial awake respiratory CO₂ response and varying the rate of renal bicarbonate excretion within the physiological range. The results showed that acute hypercapnia during periodic breathing could transition into chronic sustained hypercapnia during wakefulness. Although acute hypercapnia could be attributed to periodic breathing alone, transition from acute to chronic hypercapnia required either slowing of renal bicarbonate kinetics, reduction of ventilatory CO₂ responsiveness, or both. Thus the model showed that the interaction between the time constant for bicarbonate excretion and respiratory control results in both failure of bicarbonate concentration to fully normalize before the next period of sleep and persistence of hypercapnia through blunting of ventilatory drive. These respiratory-renal interactions create a cumulative effect over subsequent periods of sleep that eventually results in a self-perpetuating state of chronic hypercapnia.

acute hypercapnia; respiratory-renal interaction; bicarbonate retention; computer model

Prior studies investigating the mechanisms of chronic hypercapnia were limited to patients with established chronic hypercapnia, and therefore the transition from acute to chronic hypercapnia could only be inferred. Mechanisms reported to contribute to the chronic hypercapnia include central hypoventilation manifested by a decrease in minute ventilation during wakefulness and/or sleep (29, 39), mass loading due to obesity induced abnormalities of pulmonary mechanics (26, 35), and ventilation-perfusion mismatch and/or abnormal mechanics due to associated cardiopulmonary disease (6, 8). However, these derangements are not altered by treatment of OSAHS and therefore cannot explain the reversal of hypercapnia after tracheostomy or application of nasal CPAP (15, 31, 40).

Previous studies have suggested a role for elevated bicarbonate concentration in sustaining a chronic hypercapnic state once established. Tenney (42) suggested that elevated bicarbonate concentration represents a "compromise adaptation" for hypercapnia. A role for an elevated bicarbonate concentration per se as a mechanism of generating a chronic hypercapnic state was suggested by Goldring et al. (17, 19) during experimentally induced metabolic alkalosis in normal subjects. Elevated bicarbonate concentration would blunt the change in hydrogen ion concentration for a given change in PCO₂, in accord with the Henderson-Hasselbalch relationship, thereby blunting ventilatory CO₂ drive. This alteration of ventilatory CO₂ drive was demonstrated in patients with chronic hypoventilation syndromes under experimentally altered changes in serum bicarbonate concentration (18).

These findings suggest a potential mechanism for the transition from acute nocturnal to chronic sustained hypercapnia in patients with OSAHS. Acute hypercapnia during periodic breathing would initiate bicarbonate retention. Although the magnitude of the bicarbonate retention during a single night is likely to be small, the time constant for bicarbonate excretion is longer than that for PCO₂ (28); therefore, this small increase may not be fully excreted before the next period of sleep (recurring periodic breathing). Because these considerations cannot be addressed clinically, a model was constructed to address this hypothesis that respiratory-renal interactions may play a critical role in the transition from acute to chronic hypercapnia.

	METHODS

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Model.   A computational model was constructed to investigate the transition from acute to chronic hypercapnia under conditions of repetitive apneas simulating OSAHS followed by periods of regular breathing simulating wakefulness. Our laboratory (30) previously developed a model of whole-body CO₂ kinetics on the basis of work by Farhi and Rahn (11), Longobardo et al. (25), and Khoo et al. (21–23) by incorporating pattern of breathing and periodicity. For the present study, we expanded this model to include a respiratory control center and a renal bicarbonate controller. A schema of this new model is illustrated in Fig. 1, and model parameters are presented in Table 1. The model was developed in C and executed on an IBM-compatible personal computer.

View larger version (19K): [in this window] [in a new window]   Fig. 1. Schematic of the model used in the simulations. Briefly, CO2 produced in the tissues is circulated to the lung on the basis of partial pressures and storage capacities of the various compartments. In the lung, CO2 is removed by ventilation, which is controlled by the respiratory controller responding to the pH of the brain compartment. Arterialized blood leaves the lung and returns to the tissue and the kidney, where bicarbonate (HCO3–) transfer occurs. HCO3– is transferred on the basis of a target pH and the current PCO2 according to a specified time course. FRC, functional residual capacity.

Whole-body CO₂ kinetics (previously published model).   The present study expands a previously published and validated model of whole-body CO₂ kinetics (30). Briefly, in this prior model iterative calculations are performed that describe CO₂ transfers within the model (30). During each iteration interval (1/64 s), aliquots of metabolic CO₂ production are added to two body tissue compartments (muscle and other tissues) at constant rates as determined by the specified CO₂ production for that compartment. Blood flow through these tissues results in movement of an aliquot of blood from the arterial to the venous pool, along with an amount of CO₂ determined by the gradient of CO₂ from tissue to blood and by the CO₂ content equations for blood and tissue. After equilibration in the venous blood pool, the same size aliquot of blood is moved into contact with the lung. The lung is represented by a single gas compartment with a small tissue and capillary blood volume, all equilibrated to the same PCO₂. The volume of this compartment changes from the specified functional residual capacity during each iteration according to respiratory phase. CO₂ flows along the lung-to-capillary blood gradient and is washed out of the lung during exhalation. An aliquot of "arterialized" blood is next moved into the arterial blood pool. Finally, an aliquot of arterial blood is distributed to the tissues along with the CO₂ it contains. This entire cycle of calculations is repeated for each iteration interval. These compartments and input model parameters can be seen in the expanded schema of the new model in Fig. 1 and Table 1.

Ventilatory controller.   A ventilatory controller has been added to this model within a brain compartment consisting of a specified volume and receiving a specified blood flow. The ventilatory controller determines the change in tidal volume from the eupneic level on the basis of a user-specified ventilatory gain. Before the initiation of each breath, the model determines the hydrogen ion concentration within the brain compartment on the basis of the partial pressure of carbon dioxide and the bicarbonate concentration of the blood in the brain compartment. The blood-brain barrier is modeled by allowing for different rates of change in bicarbonate concentration in blood perfusing the brain compared with arterial blood; thus the hydrogen ion concentration obtained is analogous to the value present in cerebrospinal fluid. The PCO₂ in the brain compartment is assumed to fully equilibrate, during each iteration, to the value in the arterial blood pool.

The ventilatory controller responds to deviations in hydrogen ion concentration from normal (i.e., that present at pH = 7.4) using the user-defined ventilatory response slope, which is linear down to an apneic threshold (27, 38). The ventilatory response slope is entered by the user as the change in minute ventilation per change in PCO₂ in the blood. This ventilatory response is reexpressed by the model by using the Henderson-Hasselbalch equation as the change in minute ventilation per change in hydrogen ion concentration (assuming a bicarbonate concentration of 24 meq/l) and held constant throughout each simulation. Modeling of the controller in this fashion allows the ventilatory response to PCO₂ to vary as serum bicarbonate concentration changes. This approach simulates empiric observations of the effects of metabolic acid-base disorders on ventilatory control (17, 19). Equations implementing the ventilatory response are given in the APPENDIX.

Although an apneic threshold is present in the model, it is not relevant to simulations of obstructive apnea in which arterial PCO₂ (Pa_CO2) remains either equal to or greater than 40 Torr during all simulations.

Renal bicarbonate controller.   A renal bicarbonate controller has also been added to the model to simulate metabolic compensation for changes in acid-base status induced by the respiratory system. Prior data have demonstrated effects of blood PCO₂ on renal bicarbonate reabsorption independent of any effect of blood pH (7, 9, 32–34). On the basis of these observations, the renal bicarbonate controller was modeled to change the base excess in the arterial blood pool based on the deviation of Pa_CO2 from 40 Torr (7, 9, 33, 34). The metabolic compensation is modeled by using base excess rather than bicarbonate concentration to exclude the bicarbonate generated from mass action because of acute changes in Pa_CO2. Use of base excess in the model assumes that the nonbicarbonate buffers are normal and remain unchanged during all simulations (12–14).

The Pa_CO2 is recorded after each breath and is used to calculate the base excess that would completely compensate for that PCO₂ as described by Schlichtig and Severinghaus (36, 37). A change in base excess is then applied to the blood on the basis of the current base excess, the base excess that would fully compensate for the current Pa_CO2, and the time course specified for the kidney to effect a change in blood bicarbonate concentration. This time course includes the time constant for renal bicarbonate excretion and the resulting concentration change in blood. The time course was fixed for a given simulation, and the effects of differing time courses were evaluated in additional simulations. Equations implementing bicarbonate retention and excretion are given in the APPENDIX.

Model assumptions.   Important assumptions of the model include the following: 1) Within each compartment of the model, mixing is assumed to be ideal and CO₂ equilibrates completely during each iteration interval when blood, gas, and tissue are in contact (30). 2) The lung is a single uniform compartment (30). 3) The CO₂ storage capacity of the blood and tissue compartments (11) is constant over time. The CO₂ storage capacity of the lung compartment changes with time but only because of the changes in gas volume due to respiratory pattern (30). 4) The lung volume does not change during breath hold (30). 5) The time required for the renal controller to fully compensate for a given chronic PCO₂ level is constant for all PCO₂ values.

Model validation.   To validate the behavior of the respiratory and renal bicarbonate controllers and their interactions, simulation runs of the model were performed to confirm that the controllers, when unconstrained, defended an existing eucapnia or returned to eucapnia from a noneucapnic state to produce a normal blood acid-base status. First, simulations consisted of unconstrained, regular (nonperiodic) breathing starting from eucapnic, hypercapnic, or hypocapnic conditions. Acute and chronic respiratory disturbances were simulated by starting with bicarbonate concentration ([HCO₃^–]) values consistent with presence or absence of renal compensation. Second, simulations were performed under sustained periodic breathing with no limitations on either interapnea duration or tidal volume (beyond the normal inspiratory capacity). Each run used default values for parameters for awake ventilatory response (2.0 l·min^–1·Torr^–1) and the bicarbonate time constants for retention and excretion. Results are shown in Table 2. The data indicate that the model does not spontaneously develop hypercapnia or sustain a preexisting hypercapnia when the controllers are unconstrained.

View larger version (14K): [in this window] [in a new window]   Fig. 2. The model's time course of HCO3– kinetics is compared with experimentally obtained values published in the literature. The x-axis plots days from either the onset of hypercapnia or its removal (left and right graphs, respectively). The y-axis shows the change in HCO3– concentration at the end of each day expressed as a percentage of the final change. Heavy line represents the empirical data obtained in dogs; thin line represents data obtained from the model. Time courses for HCO3– retention and excretion of the model closely match the empirical results.

Outcome data.   The primary outcome data analyzed were the Pa_CO2 and blood bicarbonate concentration at the end of each 16-h period of wakefulness and the evolution of ventilatory responsiveness during wakefulness and during sleep over the 20-day simulations. The ventilatory CO₂ response during wakefulness was determined at the end of each simulated day as follows. The initial CO₂ response slope, which was held constant in terms of hydrogen ion concentration, was reexpressed as ventilatory response to PCO₂ by using the existing bicarbonate and the Henderson-Hasselbalch relationship. Ventilatory responsiveness during sleep was quantified as the ventilatory response to the volume of CO₂ loaded during the preceding apnea as previously published (3). For each apnea, the CO₂ load during the apnea and the postapnea ventilation for breaths initiated during the first 10 s of the interapnea period were calculated. From these data, the postapnea ventilatory response was derived and expressed as milliliters of ventilation per 10 s per milliliter CO₂ load. The postapnea ventilatory response was averaged over all events during each night, yielding a single value for each 8-h sleep period.

	RESULTS

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Evolution of acute hypercapnia.   Figure 3 shows the arterial PCO₂ obtained from the model during a single 24-h period consisting of 8 h of sleep (repetitive apneas) followed by 16 h of wake (regular breathing), starting from an eucapnic baseline. The CO₂ response was set to 2.0 l·min^–1·Torr^–1 and bicarbonate time courses matched those illustrated in Fig. 2. Figure 3A shows 2 min of regular breathing with a stable normal value for Pa_CO2 before the onset of periodic breathing. Figure 3, B and C, shows the 8 h of periodic breathing representing sleep. Pa_CO2 is forced to accumulate during the periodic breathing through limitation of the interevent period, thus mimicking patients who awake with acute hypercapnia. There is an immediate increase in bicarbonate concentration that occurs at the onset of periodic breathing due to mass action (Fig. 3B), which is followed by a progressive further increase over the course of the night, reflecting renal bicarbonate retention (Fig. 3C). At the end of the 8-h sleep period, wakefulness ensues with unconstrained regular breathing determined by the ventilatory controller (Fig. 3D). Persistence of elevated Pa_CO2 and [HCO₃^–] levels at the end of this period of wakefulness may, over time, lead to a transition from acute to chronic hypercapnia.

View larger version (29K): [in this window] [in a new window]   Fig. 3. Arterial PCO2 (PaCO2) and HCO3– concentration ([HCO3–]) obtained from the model during a single 24-h period consisting of 8 h of sleep (repetitive apneas) followed by 16 h of wake (regular breathing). A: 2 min of regular breathing during wakefulness before the onset of periodic breathing. Middle and bottom graphs illustrate stable normal values for PaCO2 and [HCO3–]. B: first 5 min of periodic breathing (top). Middle: development of acute hypercapnia with oscillating values for PaCO2. Note, PaCO2 does not return to normal because the interevent period is limited to 12 s (2 breaths). Bottom: immediate increase in [HCO3–] that occurs owing to mass action. C: similar data for the remaining sleep period. Although individual oscillations are not visible on the compressed time scale, a trend toward increasing PaCO2 and [HCO3–] is apparent. D: ensuing 16-h period of wakefulness with regular breathing. PaCO2 and [HCO3–] rapidly fall but do not return to the starting values of 40 Torr and 24 meq/l.

View larger version (16K): [in this window] [in a new window]   Fig. 4. PaCO2 (left) and [HCO3–] (right) trends over the 20-day simulations. With isolated reduction in either renal HCO3– excretion or reduced ventilatory response, increases in PaCO2 and [HCO3–] occurred. In contrast, the relatively small effects of blunted respiratory control alone and reduced renal HCO3– excretion alone show marked synergism when both occur simultaneously.

View larger version (21K): [in this window] [in a new window]   Fig. 5. Final PCO2 at the end of 20-day simulations is plotted as a function of the initial awake ventilatory response to CO2. Data are shown for the default value for renal HCO3– excretion (bottom line) and for reduced renal HCO3– excretion (top line). When renal HCO3– excretion is normal, awake PaCO2 is maintained at normal levels except when ventilatory control is markedly abnormal (awake response of 0.1 mm·min–1·Torr–1). However, when renal excretion of HCO3– is reduced, an increase in PaCO2 occurs even at normal ventilatory response slopes and any reduction in awake respiratory response results in a further increase in PaCO2. Shaded area reflects the PaCO2 associated with intermediate values of ventilatory drive and HCO3– excretion rates.

View larger version (15K): [in this window] [in a new window]   Fig. 6. Evolution of ventilatory response and HCO3– levels are shown. Left: awake ventilatory response results over a 20-day simulation. , Blood [HCO3–] values at the end of each wake period; , daily value for the awake ventilatory CO2 response. As HCO3– concentration increased, the awake ventilatory response decreases from 0.5 to 0.4 l·min–1·Torr–1. Right: effect of HCO3– on the postapnea ventilatory response. As with the awake ventilatory response, increases in HCO3– concentration were associated with decreases in postapnea ventilatory response.

View larger version (18K): [in this window] [in a new window]   Fig. 7. Awake ventilatory response to CO2, expressed as a percentage of the value obtained at a HCO3– concentration of 24 meq/l, is plotted as a function of increased blood HCO3– levels. A hyperbolic relationship between ventilatory response and HCO3– exists, indicating blunting of the ventilatory response to CO2 at elevated HCO3– levels.

	DISCUSSION

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The present study utilizes a model to address the role of bicarbonate kinetics in the transition from acute to chronic hypercapnia. The model demonstrates that 1) acute transient hypercapnia during periodic breathing can transition into chronic sustained hypercapnia during wakefulness; 2) this transition requires persistence of elevated bicarbonate concentration during the periods of wakefulness; 3) persistence of elevated bicarbonate concentration can be induced in the model by either alteration of renal bicarbonate kinetics, reduction of ventilatory drive, or both; and 4) elevated bicarbonate concentration blunts ventilatory CO₂ responsiveness from its initial value yielding higher Pa_CO2 values on awakening, which further reduces bicarbonate excretion. These respiratory-renal interactions create a cumulative effect over subsequent periods of sleep that eventually results in a self-perpetuating state of chronic hypercapnia. Although this paper modeled obstructive sleep apnea, this mechanism is potentially applicable to all states of repetitive acute hypercapnia with or without underlying lung disease.

The validity of the model's predictions requires justification. The present model was derived from a previously validated model of whole-body CO₂ kinetics (30) to which ventilatory and bicarbonate control were added. The present model was shown to defend eucapnia despite repetitive apneas when interapnea duration was unconstrained, allowing Pa_CO2 to return to 40 Torr before subsequent apneic periods. In addition, the model can be shown to return to a eucapnic state after a single acute perturbation of the acid-base state. For simulations that resulted in development of chronic hypercapnia, the values for both Pa_CO2 and [HCO₃^–] and postevent ventilatory responsiveness match published observations in hypercapnic patients with OSAHS (3, 5, 15, 24). Furthermore, experimentally derived data from humans and dogs under normal and chloride-depleted conditions were utilized to set the range of bicarbonate retention and excretion used in the model (16, 28). Thus the effect of bicarbonate retention on the generation of chronic hypercapnia as shown in the model can be considered relevant to the generation of chronic hypercapnia in clinical states.

There are additional factors that would attenuate or augment the development of chronic hypercapnia in the clinical setting. Hypoxia and the wakefulness drive to breathe would attenuate the accumulation of CO₂ during periodic breathing. The effects of these factors on ventilatory drive can be approximated in the model (Fig. 5) by increasing the set ventilatory drive to CO₂. The net effect of these factors on ventilatory responsiveness will determine whether chronic hypercapnia ensues. Diuretic-induced chloride depletion and the use of sedatives or oxygen may contribute to development of hypercapnia through effects on renal bicarbonate kinetics and respiratory control even in the absence of preexisting hypercapnia. In addition, hypercapnic patients with OSAHS tend to have reduced CO₂ response, and obese hypercapnic patients with OSAHS are often in a state of salt and water retention due to cardiorespiratory failure and/or the metabolic syndrome (2, 5, 10, 15, 20). These factors provide additional mechanisms for altered bicarbonate kinetics.

The results obtained in the present study were based on simulations of obstructive sleep apnea in which other causes of hypercapnia were excluded. Although the results indicate that respiratory-renal interactions alone may generate a chronic hypercapnic state, this mechanism would still contribute in the presence of underlying diseases such as obesity and chronic lung disease. These considerations may help explain the observations that chronic hypercapnia in patients with OSAHS is frequently associated with either no evidence or relatively mild degrees of underlying obstructive airway disease and that chronic hypercapnia in patients with the obesity hypoventilation syndrome does not require the presence of extreme obesity (6, 8, 24, 26).

In summary, we propose the following as a mechanism for the generation of chronic hypercapnia in patients with ventilatory sleep disorders in the absence of intrinsic cardiopulmonary disease on the basis of our previous studies and on the present model (1–4, 15, 29–31). An inciting acute ventilatory event, such as apnea or hypopnea, causes a transient increase in Pa_CO2. Patients with an adequate and immediate ventilatory response sufficient to maintain the average Pa_CO2 at 40 Torr will show no net change in total tissue CO₂ stores and will therefore remain eucapnic (4). In contrast, patients with inadequate interapnea unloading of CO₂, due either to blunting of the interapnea ventilatory response (3) or to limitation of the interapnea duration relative to duration of apnea (1), will demonstrate a progressive rise in Pa_CO2 over subsequent events with compensatory renal bicarbonate retention. Although this increase in total body CO₂ stores represents an acute hypercapnia at the onset of wakefulness, the maintenance of chronic hypercapnia is dependent on an individual's inability to unload this increase in both PCO₂ and bicarbonate during the waking period. The ability to accomplish unloading during wakefulness is determined not only by the magnitude of the load but also by the ventilatory response to CO₂ and by renal handling of bicarbonate. Thus persistence of elevated bicarbonate level not only defines the state of chronic hypercapnia but also provides a mechanism for the development and perpetuation of this state.

	APPENDIX

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Conversion of Ventilatory Response Slope from l·min^–1·Torr^–1 to l·min^–1·[H⁺]^–1

where Response is the ventilatory response slope to hydrogen ion at baseline, and Response is ventilatory response slope to CO₂ at baseline.

is hydrogen ion change ([]) with 1-Torr PCO₂ change at bicarbonate of 24 meq/l.

Calculation of Tidal Volume of Breath (Fixed Frequency = 10)

where V_T is the tidal volume produced by the respiratory controller.

is change in tidal volume (Drive_VT) induced by a difference between the current hydrogen ion concentration in brain () and the basal concentration ([H_Basal⁺]).

where PCO_{2 Current} is the current brain PCO₂ and [HCO₃^– _Current] is the current brain bicarbonate concentration.

is the basal concentration of hydrogen ion at pH 7.4 and a bicarbonate concentration of 24.

is the predicted tidal volume (Basal_VT) from the Bohr equation based on CO₂ production (CO₂).

Factors of 100 and 76 convert to a tidal volume expressed in milliliters at a respiratory rate of 10 breaths per minute. Note: all volumes in model are STPD.

Base Excess Calculation

where SBE is base excess (from Severinghaus, Ref. 37).

Determination of Base Excess Target for Renal Compensation to Alterations in PCO₂

where SBE_Target is target base excess and PCO_{2 Current} is the current PCO₂ in the blood (from Schlictig et al., Ref. 36).

Determination of Base Excess Change per 6-s Interval

where SBE_New is the new base excess to be produced, SBE_Current is the existing base excess, SBE_Delta is the change in base excess for this 6-s period, and 600 is a factor to convert response rates in hours to a rate per breath.

As the model recalculates the change in base excess after each 6-s interval, the linear time course described by the above equation is transformed into an exponential time course.

	GRANTS

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This research was supported by National Heart, Lung, and Blood Institute Grant 5 F32 HL-09686 and National Institute of Environmental Health Sciences Grant 3P30ES00260-40S1.

	ACKNOWLEDGMENTS

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The authors thank Drs. Neil S. Cherniack and Guy S. Longobardo for thoughtful comments and suggestions with regards to the implementation of this model.

	FOOTNOTES

 

Address for reprint requests and other correspondence: R. Norman, Division of Pulmonary and Critical Care Medicine, Dept. of Medicine, New York Univ. School of Medicine, 550 First Ave., New York, NY 10016 (e-mail: robert.norman{at}med.nyu.edu)

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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