Effects of acetazolamide on control of breathing in sleep apnea patients: Mechanistic insights using meta‐analyses and physiological model simulations

Abstract Obstructive and central sleep apnea affects ~1 billion people globally and may lead to serious cardiovascular and neurocognitive consequences, but treatment options are limited. High loop gain (ventilatory instability) is a major pathophysiological mechanism underlying both types of sleep apnea and can be lowered pharmacologically with acetazolamide, thereby improving sleep apnea severity. However, individual responses vary and are strongly correlated with the loop gain reduction achieved by acetazolamide. To aid with patient selection for long‐term trials and clinical care, our goal was to understand better the factors that determine the change in loop gain following acetazolamide in human subjects with sleep apnea. Thus, we (i) performed several meta‐analyses to clarify how acetazolamide affects ventilatory control and loop gain (including its primary components controller/plant gain), and based on these results, we (ii) performed physiological model simulations to assess how different baseline conditions affect the change in loop gain. Our results suggest that (i) acetazolamide primarily causes a left shift of the chemosensitivity line thus lowering plant gain without substantially affecting controller gain; and (ii) higher controller gain, higher paCO2 at eupneic ventilation, and lower CO2 production at baseline result in a more pronounced loop gain reduction with acetazolamide. In summary, the combination of mechanistic meta‐analyses with model simulations provides a unified framework of acetazolamide’s effects on ventilatory control and revealed physiological predictors of response, which are consistent with empirical observations of acetazolamide's effects in different sleep apnea subgroups. Prospective studies are needed to validate these predictors and assess their value for patient selection.


| INTRODUCTION
Acetazolamide is a carbonic anhydrase inhibitor that causes bicarbonaturia, thereby producing metabolic acidosis and a concomitant increase in ventilation (Swenson, 1998). Acetazolamide reduces ventilatory instability or "high loop gain" (for more details, see the "Results of Meta-Analyses" section below Edwards et al., 2012, which is the pathophysiological mechanism underlying most types of central sleep apnea including high altitude periodic breathing and Cheyne Stokes respiration (CSA-CSR);  but loop gain is also a key contributor to obstructive sleep apnea (OSA) pathogenesis (Eckert et al., 2013;Orr et al., 2017). Based on comprehensive meta-analyses, we recently found that acetazolamide can substantially improve both OSA and CSA : Overall, based on study-level data, the apneahypopnea index (AHI) improved by 38% (95% CI: 31-45). AHI reductions were greater in studies administering higher doses of acetazolamide (at least up to ~500 mg/day) and tended to be more pronounced in studies focusing on CSA (especially high altitude and heart failure-related CSA). However, based on patient-level data, interindividual changes in AHI varied widely and were not well explained by dose or sleep apnea type. This heterogeneity in the efficacy of acetazolamide underscores the need to identify predictors of response in individuals.
Based on pathophysiological considerations, one would expect that for a given sleep apnea patient, the therapeutic response (change in AHI) is driven by: 1. How much does acetazolamide alter loop gain? 2. How high is loop gain at baseline? 3. Are there any other causes of sleep apnea (unaltered by acetazolamide)?
In fact, one study demonstrated a strong positive correlation between the change in loop gain and the change in AHI (r = 0.63, p = 0.001; Terrill et al., 2015) To aid with patient selection for long-term trials and clinical care, our objective for the current study was to understand better the factors that determine the change in loop gain following acetazolamide in human subjects with sleep apnea. Our recently published systematic review  focused on acetazolamide's effect on clinical outcomes (e.g., apnea-hypopnea index, blood pressure, etc.) in patients with sleep apnea, but in the process, we also collected data on acetazolamide's effect on control of breathing parameters (e.g., controller/plant gain, CO 2 production, etc.-for details see below). For the current study, we used these unpublished data to (i) perform meta-analyses clarifying the mechanisms through which acetazolamide lowers loop gain and, based on these results, (ii) to perform physiological model simulations to assess how different baseline conditions affect the relative change in loop gain (i.e., assess predictors of response).

| Conceptual framework
Loop gain is an engineering term that describes a negative feedback control system (Dempsey, 2019;Orr et al., 2017;Terrill et al., 2015;Younes, 2008). In the setting of ventilatory control, loop gain describes the interactions between the chemoreceptors (controller) and the lungs (plant) aiming to keep paCO 2 stable around ~40 mmHg.
Thus, if the controller and/or plant gain are elevated, then loop gain is high, which means that any minor perturbation in breathing (e.g., hypopnea due to upper airway collapse or hyperpnea following arousal from sleep) can lead to markedly fluctuating levels of paCO 2 , ventilation and upper airway dilator tone resulting in unstable breathing (Badr et al., 1995). In CSA, this instability can lead to periodic breathing and in OSA to repetitive obstructive events ("apnea begets apnea"). Conversely, lowering either loop gain component is expected to stabilize breathing and thus improve OSA/CSA as has been demonstrated in multiple studies .
The steady-state control of the breathing model is shown in Figure 1 that illustrates how these two loop gain components interact: (Dempsey, 2019).

| Controller gain
Chemosensitivity or "controller gain" describes the change in ventilation in response to changes in blood gases based on information from both central and peripheral chemoreceptors. In most (normoxic) conditions, the arterial paCO 2 is the primary stimulus for ventilation (Eckert & Butler, 2017). The ventilatory response to changes in CO 2 (VRCO 2 ) can be determined experimentally by measuring ventilation in response to varying paCO 2 levels in spontaneously breathing subjects (ΔVA/ ΔpaCO 2 ). Similarly, one can determine the ventilatory response to changes in arterial pO 2 (VRO 2 ; ΔVA/ΔpaO 2 ), but in general, oxygen increases ventilation only if hypoxia is severe (i.e., paO 2 < 50-60 mmHg), for example, at high altitude . In addition, hypoxia increases the VRCO 2 (O 2 -CO 2 interaction); (Lloyd et al., loop gain ∝ controller gain × plant Gain. 1958; West & KLuks, 2016). Thus, in normoxic conditions, the controller gain equals the VRCO 2 (i.e., ΔVA/ΔpaCO 2 ), but in hypoxic conditions, such as high altitude controller gain is higher because it is a function of both the VRCO 2 and the VRO 2 , plus hypoxia increases the VRCO 2 itself. Unless stated otherwise, in the following, we will assume normoxic conditions. Further, we assumed that the ventilatory response to varying levels of paCO 2 (i.e., VRCO 2 ) is the same above and below eupnea (Xie et al., 2013).

| Plant gain
The isometabolic curve reflects the relationship between alveolar ventilation (VA) and alveolar carbon dioxide (pACO 2 ) and is defined as: Note that the ventilation for a given pACO 2 depends on the metabolic CO 2 production, hence the name isometabolic curve. When plotted with ventilation as the dependent variable (i.e., on the y-axis as in Figure 1) then the reciprocal of the slope equals ΔpACO 2 /ΔVA. This ratio reflects how efficiently the lungs excrete CO 2 and is known as "plant gain." Given the hyperbolic shape of the isometabolic curve, plant gain varies depending on the level of steady-state ventilation: when VA is high, then plant gain is low which means for a given change in ventilation there will only be a small change in pACO 2 (i.e., pACO 2 fluctuations are dampened) and vice versa.
In the absence of upper airway obstruction, steadystate VA is determined by the intersection between the chemosensitivity line and the isometabolic curve (termed eupneic alveolar ventilation; VA eupnea ). The reciprocal slope of the tangent at this point thus reflects the (instantaneous) plant gain at VA eupnea . Note that the alveolar and arterial CO 2 are approximately equal, in the following, we used the term paCO 2 throughout for simplicity.

| Other parameters
The intersection between the chemosensitivity line and the x-axis (VA = 0) is termed apnea threshold (i.e., the paCO 2 at which ventilation stops), and the difference between the paCO 2 at VA eupnea and the paCO 2 at the apnea threshold is known as CO 2 reserve. Similarly, VA reserve denotes the change in ventilation from VA eupnea which will reduce the paCO 2 to the level at which ventilation ceases (i.e., paCO 2 at the apnea threshold). Note that the isometabolic curve and chemosensitivity line are the primary components that determine all these other parameters.

| Data collection and meta-analyses
For details, see . In brief, we queried MEDLINE, EMBASE, and clinicaltrials.gov for any study which assessed the effect of oral acetazolamide in adult OSA/CSA patients versus a control condition (e.g., no acetazolamide or placebo) prior to November 03, 2019. Two reviewers independently assessed eligibility and abstracted data from included studies. VA = CO 2 production × 0.863 ∕pACO 2 F I G U R E 1 Control of breathing model. Key parameters were defined based on data from the control groups shown in Table 1 (i.e., assuming CO 2 production = 206 ml/min, paCO 2 at VA eupnea = 38.2 mmHg, and paCO 2 at the apnea threshold = 33.5 mmHg)  To assess the effect of acetazolamide on parameters of breathing control as a relative change from the control conditions, we used meta-analyses based on ratio of means (ROM; results from sensitivity analyses based on absolute "weighted mean differences" were similar); Friedrich et al., 2008). Heterogeneity was quantified using I 2 which denotes the percentage of total variation across studies that is due to heterogeneity rather than chance (range: 0%-100%); (Higgins et al., 2003) For I 2 > 30%, we used random effects models and explored possible sources of heterogeneity (e.g., acetazolamide dose) via meta-regression and/or qualitative assessments depending on the number of studies.

| Model simulations
To identify potential predictors of response to acetazolamide, we created an Excel-based model of steady-state control of breathing ("ECOB-Model," available for free download at: https://tinyu rl.com/ECOB-Model) using results from the meta-analyses for CO 2 production, paCO 2 at VA eupnea and the apnea threshold as inputs and estimating the percent change in loop gain (%ΔLG 0 ) as the primary output: where CG, controller gain and PG, plant gain).
Varying one input parameter (i) at a time across a physiological range (i.e., controller gain 0.5-3 L/min/ mmHg, paCO 2 at VA eupnea 30-50 mmHg, CO 2 production 155-255 ml/min), we then assessed the effect of different baseline values (j) on the percent change in loop gain (%ΔLG i,j ). To assess the relative effect of different baseline conditions on the change in loop gain, results of these simulations were indexed to the change in loop gain under the initial conditions (%ΔLG 0 ) and plotted as a "relative reduction" (RR): where %ΔLG 0 was −21.8%, thus RR i,j > 1 denotes a greater reduction in LG, whereas 0 < RR i,j < 1 denotes a lesser reduction in LG (note: RR i,j < 0 would reflect an increase in LG but was not observed).

| Meta-analyses
whereas the other two studies (Fontana et al., 2011;Tojima et al., 1988) assessed VRO 2 under isocapnic conditions without accounting for body surface area (L/min/%SaO 2 ). When excluding the former study in a sensitivity analysis, then heterogeneity resolved and there was a reduction of VRO 2 by 24%, but results were nonsignificant with a wide confidence interval (ROM = 0.76, 95% CI: 0.48-1.20, I 2 = 0%, p = 0.24). c No clear cause of heterogeneity was identified: results were similar in studies using ABGs versus other tests to estimate paCO 2 as well as in studies that measured paCO 2 during wakefulness versus during sleep. Meta-regression suggested a dose-response relationship and the paCO 2 reduction was almost twice as large in studies administering ≥500 mg/day versus <500 mg/day (reduction by 13% vs. 7%) but these differences did not reach statistical significance (p > 0.18). d In sensitivity analyses, results were similar in studies that performed measurements during wakefulness versus sleep. e When using standardized mean differences, results were similar but heterogeneity resolved (SMD = −0.68, 95 CI −1.13 to −0.23 [corresponding to a loop gain reduction by 29%, 95% CI −48 to −10]; I 2 = 0%, p = 0.003) suggesting that heterogeneity was due to different measurement scales (mean loop gain across various frequencies ranging from 0.5 to 1.5/min 2 vs. loop gain at a frequency of 1 per minute (Wellman, 2018); results were also similar when using the static instead of dynamic loop gain reported by Edwards et al. (2012). f Heterogeneity was primarily due to one small study (Pranathiageswaran et al., 2014) (N control = 4, N AZM = 2) in which the acetazolamide-induced increase in CO 2 reserve was about two times larger as in other studies with a very small reported standard deviation. In sensitivity analyses, results were similar to minimal heterogeneity when excluding this study (1.25 [95% CI 1.04-1.5], I 2 = 0%, p = 0.01) or when assuming that this study erroneously reported standard errors instead of standard deviations (1.30 [95% CI 1.08-1.6], I 2 = 17%, p = 0.005). *denotes p < 0.05.

| Isometabolic curve
Acetazolamide increased CO 2 production by 9% (95% CI: −3 to +23; p = 0.13, N = 2 [Apostolo et al., 2014;Javaheri, 2006]), perhaps in part due to increased respiratory work, but the estimate is imprecise (Lederer et al., 2019). Based on the confidence interval, these results are compatible with no change, or an increase of the slope, of the isometabolic curve in response to acetazolamide (i.e., the same or lower plant gain for any given pACO 2 ).

| Loop/plant gain
Acetazolamide decreased plant gain by 32% (p < 0.001, N = 3 [Edwards et al., 2012;Ginter et al., 2020;Pranathiageswaran et al., 2014]) with a similar decrease in overall loop gain by 26% (p = 0.049, N = 2 [Edwards et al., 2012;Wellman, 2018]). Of note, the similar magnitude of change in plant and overall loop gain provides further indirect evidence that the slope of the chemosensitivity line (i.e., controller gain) does not change.

| Model simulations
As shown in Figure 1, we first modeled the isometabolic curve and the chemosensitivity line using pooled data from control conditions ( Table 2) as inputs for the ECOB-Model (i.e., assuming CO 2 production = 206 ml/min, paCO 2 at VA eupnea = 38.2 mmHg, and paCO 2 at the apnea threshold = 33.5 mmHg). Next, based on the results from meta-analyses, we modeled a left shift of the apnea threshold by 15% (i.e., −5 mmHg) without change in the slope of the chemosensitivity line (i.e., a left shift of the chemosensitivity line; Figure 2). The predicted changes in loop gain and other model output parameters were well within the range of the 95% CIs from meta-analyses providing face validity for this model simulation (see Table 3, Model 1). Alternative models assuming additionally an increase in CO 2 production by 9% and/or a reduction of controller gain by 11% showed similar results although the predicted reductions in loop gain were more pronounced (Table 3, Models 2-4).
Based on Model 1, we then assessed how the effect of acetazolamide on loop gain is modified by different baseline conditions (Figure 3): the loop gain reduction induced by acetazolamide was more pronounced with higher controller gain (up to ~20% greater reduction), higher paCO 2 at VA eupnea (up to ~10% greater reduction), and with lower CO 2 production at baseline (up to ~5% greater reduction). Importantly, the amount by which acetazolamide shifts the chemosensitivity line to the left is a major determinant of the resulting change in loop gain (Figure 4).

| DISCUSSION
Strengths of our study include the simultaneous examination of acetazolamide's effects on the different components of ventilatory control and the combination of meta-analyses and physiological model simulations to gain several, important mechanistic insights. First, to our knowledge, this is the first comprehensive, mechanistic meta-analysis of acetazolamide's effect on ventilatory control based on several small studies, thus providing a unified framework to explain how this drug stabilizes breathing (i.e., lowers loop gain) in patients with sleep apnea: our results suggest that acetazolamide primarily shifts the chemosensitivity line to the left. Thus, eupneic ventilation occurs at a steeper part of the isometabolic curve which results in a lower plant gain. Loop gain is proportional to controller and plant gain, thus under normoxic conditions (in which there appears to be no substantial change in controller gain), the relative reduction in plant gain is equal to the reduction in loop gain. Of note, we have previously shown that acetazolamide increases pO 2 on average by ~10 mmHg,  thus under hypoxic conditions, such as high altitude, one would additionally expect a reduction in controller gain (i.e., mitigation of the hypoxia-related increase in controller gain), and thus a more pronounced reduction in overall loop gain. Studies comparing acetazolamide's effect on controller/loop gain at different altitudes are lacking, but these theoretical considerations are supported by empirical data showing that acetazolamide improves sleep apnea more at high versus low altitude . The control of breathing model that we used provides another, perhaps more intuitive way to understand the effects of acetazolamide: because the isometabolic curve is hyperbolic, the left-shift of the chemosensitivity line lowers the apnea threshold more than the paCO 2 at eupneic ventilation (e.g., −5 mmHg vs. −4.4 mmHg, Figure 2) thus increasing the CO 2 and ventilatory reserves. In other words, a subject taking acetazolamide needs to increase ventilation and blow off more CO 2 to reach the apnea threshold than without acetazolamide, thus reducing the risk of developing central hypopneas and apneas which tend to also lead to upper airway collapse (i.e., can directly contribute to obstructive events; Badr et al., 1995).
Second, based on model simulations, we identified baseline controller gain and-to a lesser extent-baseline paCO 2 at eupneic ventilation as physiological predictors of the loop gain reduction achieved by acetazolamide. This may explain the pronounced improvement of sleep apnea in patients with heart failure (who tend to have a high controller gain) which appears to be less than the improvement of high altitude sleep apnea, but greater than other types of sleep apnea (see Figure 3 in Schmickl et al., [2020]). Further, given the linear relationship between loop gain reduction and reduction of the apnea-hypopnea index in small studies, (Terrill et al., 2015) these predictors may facilitate enrollment of likely responders into future trials. For example, paCO 2 at eupneic ventilation and controller gain can be estimated via end-tidal CO 2 measurements during a baseline study; (Edwards et al., 2012) using our online ECOB-calculator the expected reduction in loop gain can then be estimated (https://tinyu rl.com/ECOB-Model).
Third, our simulations also demonstrated that the amount of the left-shift of the chemosensitivity line is a critical determinant of the achieved loop gain reduction. Our meta-analyses suggested that the degree of left shift is dose dependent (there were insufficient studies to assess for dose effects on the apnea threshold, but the paCO 2 at VA eupnea decreased by 7% and 13% in studies administering <500 mg/day and ≥500 mg/day, respectively; Table  2). This left shift likely reflects the increased eupneic ventilation caused by the acetazolamide-induced metabolic acidosis acting on peripheral and central chemoreceptors (Swenson, 1998). The metabolic acidosis from acetazolamide that reaches its maximum within 24 h of administration is primarily due to an alkaline diuresis via renal carbonic anhydrase inhibition but local tissue acidification can contribute too (Swenson, 1998). Importantly, most of these effects are maximal at 250-500 mg, (Swenson, 1998), which likely explains the dose-response relationship between acetazolamide and the improvement of sleep apnea up to ~500 mg/day (after which the effects seem to plateau) in interventional studies .
A major limitation of our work is that the control of breathing model which we used assumes steady-state conditions (vs. the dynamic conditions typically observed during OSA/CSA) and that the concept of loop gain describes behaviors of linear systems, whereas nonlinearities exist in the respiratory control system (Dempsey, 2019). However, experimental studies in humans and animals have repeatedly demonstrated that alterations of overall loop gain or its components, even when measured under steady-state conditions, result in predictable changes in ventilatory stability and/or sleep apnea severity (Dempsey, 2019). Furthermore, in our analyses, we implicitly assumed that acetazolamide has no effect on the third component of loop gain, namely mixing gain which includes complex time constants and is rarely studied in the setting of acetazolamide. A major contributor to mixing gain is the time that it takes for the alveolar pACO 2 to be transmitted to the chemoreceptors in the carotid body which is primarily a function of cardiac output; the normal "circulatory delay" is about 7 s (Younes, 2014), but in the heart failure patients, this time may increase substantially, thus increasing mixing gain and overall loop gain (Stanchina et al., 2007). Given its mild diuretic effects acetazolamide may improve cardiac output and thus yield a greater reduction in overall loop gain in patients with heart failure, but one would not expect much effect of acetazolamide on cardiac output in patients without heart failure. Another component of mixing gain is the response speed of the different chemoreceptors which appears to be unaffected by acetazolamide based on experimental data (Teppema & Dahan, 1999). There were a few other noteworthy limitations: First, meta-analyses for the different ventilatory control components included different studies which had some methodological variability. But reassuringly most analyses revealed only a small amount of statistically detectable heterogeneity (i.e., I 2 < 30-50%), and results were overall consistent with patient-level data reported in many individual studies as well as with what is expected based on physiological models (Table 3). Second, by excluding studies in subjects without sleep apnea, we increased internal validity but reduced the sample size of studies included in meta-analyses and thus the precision of our results. However, confidence intervals for most results were F I G U R E 4 Model simulation: The impact of varying left shifts of the chemosensitivity line on the relative reduction of loop gain induced by acetazolamide sufficiently narrow to draw firm conclusions. Small sample sizes in most meta-analyses also limited our ability to assess for effect modification by study characteristics such as acetazolamide dose or duration of administration. A notable exception is the meta-analysis of paCO 2 at VA eupnea , which did suggest that doses ≥500 mg result in a greater left shift of the chemosensitivity line than doses <500 mg/day, which may explain the dose-response relationship between acetazolamide and the improvement of sleep apnea severity (up to ~500 mg/day) . Regarding the duration of administration, acetazolamide is expected to take full effect within 24 h (Swenson, 1998), and results were similar in sensitivity analyses excluding the three studies (Hackett et al., 1987;Rodway et al., 2011;Verbraecken et al., 2005) in which acetazolamide was administered for <2 days (data not shown). Similarly, in exploratory analyses, there was no apparent effect modification by sleep apnea type or percentage of women (data not shown) but results from one study (Caravita et al., 2015) did suggest a greater left shift in men than women. Thus, the low percentage of women in most prior studies limits the generalizability of our findings and we advocate for greater inclusion of women in future research. Finally, our data and analyses were performed with the objective of predicting change in loop gain with acetazolamide, not the change in OSA or CSA severity, which is affected by other endotypic traits as well Schmickl et al., 2018).
Prospective studies are needed to assess better the relationships between acetazolamide dose, the induced metabolic acidosis, and the achieved left shift of the chemosensitivity line. More research is also needed to assess how accurately the presented online calculator predicts changes in loop gain in individual patients and to validate baseline controller gain and paCO 2 at baseline as predictors of the loop gain reduction.

| CONCLUSION
Using a meta-analysis approach, we were able to demonstrate the impact of acetazolamide on the control of ventilation and more precisely estimate its impact: acetazolamide primarily causes a left shift of the chemosensitivity line but, in general, does not substantially affect CO 2 production or controller gain. An elevated baseline controller gain and paCO 2 at eupneic ventilation may predict greater reductions in loop gain from acetazolamide. Ultimately, the combination of physiological and other patient characteristics may allow highly accurate identification of patients responding to loop gain lowering interventions facilitating a personalized medicine approach.