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Themed Issue Papers |
1 New Jersey Medical School, University of Medicine and Dentistry of New Jersey, NJ, USA
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(Received 14 September 2005;
accepted after revision 7 November 2005; first published online 10 November 2005)
Corresponding author N. S. Cherniack: New Jersey Medical School UMDNJ, 185 South Orange Avenue, PO Box 1709, Newark NJ07101-1709 USA. Email: cherniac{at}umdnj.edu
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Introduction |
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Probably because of the linkages that exist among physiological systems and the pervasive action of the respiratory rhythm on the activity of brain neurones, the swings in ventilation are often accompanied by fluctuations of blood gases, heart rate, blood pressure, EEG, sympathetic activity and the diameter of the pupil of the eye (McNaughton, 1998).
Periodic breathing has been reported in several diseases but is especially associated with cerebrovascular and cardiovascular diseases. However, it also occurs in normal asleep (Pryor, 1951; Hoff & Beckenbridge, 1954; Karp et al. 1960; Lange & Hecht, 1962; Lanfranchi et al. 1999; Thalhofer et al. 2000; Nopmaneejumruslers et al. 2005). Both central and obstructive sleep apnoea can give rise to patterns of breathing identical to CSR (Lyons et al. 1958). It almost always occurs in states of decreased awareness. Its form may vary even in the same person in different cycles. There even seems to be a kind of preperiodic breathing in which the oscillations in minute ventilation require spectral analysis for detection (Pack et al. 1988).
While it is likely that not all periodic breathing has the same aetiology, its resemblance to the oscillations of the output in man-made feedback control systems operating unstably has naturally led to the idea that this odd form of breathing might be caused by instability in the regulation of breathing. With regard to the respiratory system, this has been interpreted to mean that increases in the ventilatory response to hypoxia and/or hypercapnia (controller gain) or increases in the circulation time between lungs and chemoreceptors (delays in information transfer on the level of O2 and CO2 tensions, PO2 and PCO2) cause instability. Engineers have used mathematical modelling to predict the boundaries of stable control in the systems they design. This has led to the construction of analogous mathematical models of the respiratory control system to simulate periodic breathing, and to the use of these models to predict its occurrence (Longobardo et al. 1966, 1982, 2002; Khoo et al. 1982). These efforts have been very helpful in evaluating possible causes of periodic breathing, identifying gaps in our knowledge of respiratory neurophysiology, and even in suggesting treatment options. However, not all instances of periodic breathing are easily explained as control system instability by current models.
Control system instability
Instability in control theory is a well-defined state with a very specific meaning, namely, the loss of the ability to maintain constant output despite constant input, so that output becomes cyclic or, even worse, the output cycles grow, leading ultimately to the destruction of the system (Khoo et al. 1982; Khoo, 2000).
The primary purpose of feedback in the respiratory system seems to be to reduce excursions in blood gases from normal when internal or external disturbances occur that stimulate or inhibit breathing. It is generally thought that the respiratory controller behaves as a proportional regulator producing, in response to changes in PCO2 and PO2 from a physiological desirable value (set point), proportional counteracting changes in ventilation. The body may, however, employ additional forms of control of respiration during exercise and the transition to sleep. A direct consequence of feedback is that the system response after being disturbed will be quicker but more accurate so that the final excursion of the controlled variables from the desired value will be less than if there were no control, but the system in reaching the final value will be more oscillatory; i.e. the system behaves as if it had less damping. With higher gains the error caused by a disturbance is still further reduced but damping falls further. Both controller properties and the properties of the controlled system, e.g. lungs, muscles and blood flow, determine whether the system will become unstable when disturbed. Primary among system properties are: (a) the ‘controller gain’, or sensitivity, of the controller, which is its response to a change in ventilation per change in unit PCO2 or PO2; (b) the gain of the controlled system, also called the ‘plant gain’, which can be expressed as the change in PCO2 or PO2 per unit change in ventilation; (c) the circulation time; and (d) the degree of alertness as it varies during wakefulness or sleep.
Loop gain is the product of controller gain and plant gain. Loop gain is easily defined mathematically for linear systems and is a measure of system damping when disturbances result in small variations of system variables. The respiratory system is non-linear, and the determination of loop gain and its relationship to damping is more complicated. As yet there is no definitive relationship established between loop gain and the occurrence of periodic breathing.
Controller and plant gains. Controller responses to CO2 and O2 are different. Unlike the response to CO2, which is linear (constant controller gain), at least in the hypercapnic range, the response to O2 is hyperbolic, so that controller gain increases as hypoxia becomes more severe. Plant gain is the effect of ventilation on PCO2, the inverse of the slope of the metabolic hyperbola, the steady-state equilibrium relationship between ventilation and PCO2, and so is determined by where on the metabolic hyperbola the body is operating. Steady-state plant gain increases at higher PCO2 levels when CO2-free air is breathed but not if higher levels of CO2 are caused by inhaling a gas containing some CO2. Like controller gain, the higher the plant gain, the faster and more oscillatory is the response (see Fig. 1). Operating at higher PCO2 is a significant cause of instability during sleep.
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PCO2 in the brain, where the central chemoreceptors are located, changes more slowly than arterial PCO2, helping to stabilize breathing. The time constant of the change is inversely related to cerebral blood flow (Poulin & Robbins, 1998; Banaji et al. 2005). Subnormal cerebral blood flow (which is fixed and unaltered by changes in the level of oxygen or carbon dioxide) makes the changes in gas tensions at central chemoreceptors slower than if blood flow were normal. This has a stabilizing effect on breathing, but has the adverse effect of reducing the supply of oxygen. Normally hypercapnia and hypoxia increase cerebral blood flow, while hypocapnia reduces blood flow and thus counters the effects on central chemoreceptors of changes in arterial blood gases so that gas tensions at those receptors change less than those in the arterial blood. The more responsive cerebral blood flow is to hypercapnia and hypoxia, the more stable breathing, as shown in Fig. 2.
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Apnoeas. Apnoeas can occur reflexly, when the respiratory pattern generator is defective, or when the level of chemical drive is insufficient to initiate ventilation. This threshold level is sometimes present during wakefulness, but occurs far more commonly with sleep, coma and anaesthesia (Dempsey & Skatrud, 1986; Longobardo et al. 2002; Dempsey et al. 2004). The size of the O2 and CO2 gas stores (the volume and chemical form of oxygen and carbon dioxide in the body) determines how soon PCO2 will reach the apnoea threshold with hyperventilation; and how quickly PO2 will plummet during apnoea and PCO2 rise, which will have a strong influence on whether apnoea will recur.
At the apnoeic threshold, controller gain abruptly changes to zero. In conscious individuals, a neural drive, ‘wakefulness’ or ‘alertness drive’, sustains breathing at subnormal levels of chemical drive (Fink, 1961; Shea, 1996). Not just the apnoeic threshold but any point at which ventilation abruptly changes as, for example, the intersection of the wakefulness drive with the ventilatory response line, can give rise to oscillations in breathing, but while ventilation oscillates there is no apnoea.
There is also a difference in the effects of active versus passive hyperventilation. In passively hyperventilated test subjects, breathing abruptly decreases when hyperventilation stops (Dempsey et al. 2004). However, in conscious voluntarily hyperventilating individuals, as well as in anaesthetized animals in which excessive ventilation is produced by stimulation of afferent nerves, breathing decreases gradually to a lower level when stimulation stops. This phenomenon, known as short-term or postsynaptic potentiation (PSP), would seem to prevent instability, but is attenuated by hypoxia (Georgopoulos et al. 1995). It is absent in many patients with periodic breathing. The physiological processes that produce it are not known in any detail, making it difficult to know at what step of controller processing to place PSP. When it has been included in mathematical models, its stabilizing effects are small.
Experimentally produced periodic breathing
Studies in animals and humans have been largely limited to examining the role of increased controller gain and increased circulation time in producing periodic breathing. In general, they have supported the idea that feedback instability can cause periodic breathing, and their results have been used in mathematical models (Crowell et al. 1956; Cherniak et al. 1966, 1979; Cherniak and Longobardo, 1973).
Chapman et al. (1988) produced periodic breathing in five of 10 healthy sleeping humans by amplifying their usual respiratory responses. Subjects with periodic breathing had greater responses to hypercapnia under both normoxic and hypoxic conditions. Significant oscillations in breathing pattern could be detected by spectral analysis during sleep. The authors believed that these spontaneous oscillations could be converted to periodic breathing with apnoea when loop gain was increased. Meza et al. (1998) produced periodic breathing by assisted ventilation in normal subjects, which raised controller gains. Proportional assist breathing has been used to obtain an estimate of loop gain in patients with sleep apnoea, which showed that sleep apnoea patients have increased loop gains (Younes et al. 2001).
More recently, the effects of other factors on instability have been examined in animal experiments. The study by Han et al. (2002) of periodic breathing in mice suggested that short-term potentiation is an important factor that stabilizes breathing.
While hypoxia is destabilizing to respiratory control, theoretically periodic breathing can be produced even under hyperoxic conditions or if the peripheral chemoreceptors are denervated, and if the gain of the operating central chemoreceptors is sufficiently great. Periodic breathing can be produced in sleeping dogs even if peripheral chemoreceptors are blocked by dopamine (Cheneul et al. 2005).
Mathematical models of the respiratory control system
Earlier mathematical models using feedback attempted to simulate the dynamic effects of CO2 inhalation. They showed that feedback to a proportional controller approximately reproduced the on- and off-transients in blood gases and ventilation that were observed when humans inhaled a CO2-enriched gas mixture. Initially the CO2 sensor was represented as a proportional controller embedded in the body that consisted of a homogeneous pool of CO2 in dissolved and chemically combined forms (Grodins et al. 1954). Subsequent models put the CO2 sensor in a separate brain compartment connected to the rest of the body by the cerebral blood flow and, in some models, to a cerebrospinal fluid compartment as well (Grodins et al. 1967; Duffin, 1972; Middemdorf & Loeschcke, 1976). These models more precisely duplicated CO2 inhalation but were unable to reproduce periodic breathing unless quite unrealistic assumptions about controller gains or delays were made. Greater success in simulating periodic breathing was obtained with mathematical models that included oxygen sensors and oxygen stores, multiple body compartments in addition to the brain, and the effects on ventilation of simultaneous changes in PCO2 and PO2 (Longobardo et al. 1966).
As more was learned about respiratory control, the complexity of the mathematical models increased further (Longobardo et al. 1982; Khoo et al. 1982, 1991; Khoo & Berry, 1996; Longobardo et al. 2002, 2005; Topor et al. 2004). The more complex models include oxygen and carbon dioxide chemoreceptors, the effects of brain hypoxia, the effects of hypoxia and hypercapnia on cerebral blood flow in the controller, and a compartmentalized version of the body tissues connected to the controller by motor and sensory nerves and the circulation. The details of the model (Longobardo et al. 2002) that is used in the construction of figures in this paper can be found on the Internet (http://www.geocities.com/respmodel). This model has been used extensively to examine the effects of changing states of sleep and wakefulness on ventilatory stability. More recently the model has been expanded to include multiple five neurone pattern generator and pacemakers in order to simulate responses to elevated levels of CO2 (Longobardo et al. 2005). Figure 3 shows this model, which can serve as representative of the more recent models. In the model the chemical inputs, PbrainCO2 (brain carbon dioxide tension measured by centrally located chemoreceptors), and PaCO2 and PaO2 (arterial blood carbon dioxide and oxygen tension measured at the peripheral sensor), are joined by neural inputs that modulate alertness arising from higher brain centres. Then these inputs determine the ventilation that is required to bring the system into equilibrium. The brain CO2 stores are considered to be a single compartment in which the central CO2 receptor resides. The compartment is connected to the rest of the plant via the cerebral circulation, whose perfusion rate varies with the level of PCO2 and PO2. Ventilation drives the respiratory muscles and the lungs, and changes body gases. The gas values are fed back to the controller, which again adjusts the ventilation. The controller is a proportional controller, which generates a corrective ventilatory drive roughly linearly with deviations of brain and arterial PCO2 from the resting values. A representation of the steady-state characteristic of the controller is shown in the top panel of Fig. 3 as the graph of ventilatory drive as a function of PCO2. The corrective action is increased exponentially with hypoxia. The characteristic is raised by increases in alertness, and lowered by decreases as in sleep. The importance of a sleep–waking cycle as a mechanism for producing periodic breathing is a feature of other mathematical models (e.g. Khoo et al. 1991; Pack & Gottschalk, 1993).
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Clinical insights provided by mathematical models
One clear lesson from mathematical models is that periodic breathing is a ‘systems disorder’ produced by the interplay of multiple factors. The characteristics of disturbances to breathing and their interaction with the control system can be critical in determining ventilation responses and the occurrence of periodic breathing. Large abrupt changes in ventilation produced, for example, in the transition from waking to sleep and vice versa or by apnoeas, are potent factors causing periodic breathing. All of these factors contribute to the occurrence of periodic breathing in congestive heart failure and cerebrovascular disease.
The effects of sleep and level of arousal. Sleep promotes the occurrence of periodic breathing in several ways: by increasing plant gain; through shifts in sleep stages and to arousal; and by increasing the possibility of upper airway obstruction. The decrease in functional residual capacity that occurs in the supine position reduces oxygen stores. Topor et al. (2001) found threefold greater loop gains in patients with central sleep apnoea versus those without it. Fluctuation in arousal levels through their effects on chemosensitivity and airway patency can trigger periodic breathing or exacerbate its severity or duration (Khoo et al. 1991; Longobardo et al. 2002). The speedier the transition from wakefulness to sleep and vice versa, the more likely is periodic breathing to occur (Khoo et al. 1991; Longobardo et al. 2002).
Studies of sleep-disordered breathing have highlighted the importance of wakefulness drives in preventing apnoea. While breathing during wakefulness is determined by an amalgamation of signals arising from chemoreceptors and mechanoreceptors and signals from supramedullarly brain centres (that affect alertness or are volitional or behavioural), breathing asleep is determined largely in a reflex manner, with chemoreceptors playing the major role. Although chemoreceptors protect well against hypercapnia and hypoxia, they offer no protection against the intermittent hypoxia resulting from hypocapnia-induced apnoea.
The upper airway muscles, like the muscles of the chest wall, respond to hypoxia and hypercapnia, and to neural inputs but with differences in thresholds and sensitivity (Longobardo et al. 1982). It is possible that the control of the upper airway muscles as well as the chest wall muscles can become unstable, leading to periodic breathing with an obstructive component (Onal et al. 1986; Younes et al. 2001). Hudgel et al. (1993) found cyclic variations in breathing and in upper airway resistance in elderly subjects. Upper airway muscle responses to CO2 and O2 can also alter the characteristics of periodic breathing. Oxygen ameliorates periodic breathing but sometimes converts central to obstructive apnoea, while inhalation of CO2 abolishes it, as mathematical models with upper airway muscles predict (Longobardo et al. 1982). Alternatively, severe hypoxia as predicted by models may convert obstructive to central apnoeas (Longobardo et al. 1982; Warner et al. 1987).
Congestive heart failure (CHF). Periodic breathing occurs in almost half of patients with congestive heart failure (Quaranta et al. 1997). Mathematical models indicate that prolongation of the circulation time is a major factor in the induction of periodic breathing in patients with CHF, and this will lead to longer cycles of hyperpnoea and apnoea. Periodic breathing cycles in patients with CHF are longer than those seen in healthy individuals at altitude (Pinn et al. 2000; Pryor, 1951).
Although the destabilizing action of a long circulation delay is obvious in mathematical models, the length of circulation time is reported not to predict the occurrence of periodic breathing in congestive heart failure (Hall et al. 1996). In these models, the delay is usually treated as a dead time, during which there is no information transfer at all. But the circulation may not transmit information in discrete chunks, but rather in a more graded way. The cardiac dilatation and increases in central blood volume that occur in CHF increase oxygen stores and improve stability, partly offsetting the effects of delays. Also, the reduction in cardiac output may alter the distribution of perfusion to the tissues and may change the dynamics of the ventilatory response. There may be different distributions in patients with similar circulation times. But this has not been examined much either experimentally or in mathematical models. Perhaps even more importantly, many of the patients with periodic breathing also have increased controller gains and this, as shown in Fig. 4, interacts with circulation time in producing periodic breathing (Wilcox et al. 1998).
Besides circulation time, CHF also alters stability in other ways that could modify the effects of circulation time prolongation. Congestion of the lung and atelectasis stimulate vagally mediated reflexes, which increase controller gains. They also decrease lung volume, thus reducing the O2 stored in lung gas.
Relatively little is known about the effects of CHF and reduced cardiac output on cerebral blood flow or its control. As shown in Fig. 2, mathematical models predict the effects to be considerable. CNS dysfunction altering awareness may, for example, contribute to periodic breathing in patients with CHF. Central effects of hypoxia and the decrease in grey matter seen in CHF patients may be important in causing periodic breathing by reducing alertness (Woo et al. 2003). There might, for example, be inadequate circulation to the brain in patients with CHF. Some patients who have had heart transplants continue to experience CSR even though cardiac function is improved, and this has been attributed to residual CNS damage (Thalhofer et al. 2000).
Periodic breathing without apnoea has been reported in individuals in the waking state and is said to indicate quite a poor prognosis. Mathematical models suggest that periodic breathing might occur at the abrupt change in slope that occurs at subnormal levels of PCO2 in conscious people (Rapanos & Duffin, 1997). It can develop after exercise that worsens heart failure and produces increased lung water (Agostoni et al. 2003). However, periodic breathing occurs predominantly during sleep in CHF (Ahmed et al. 1994).
Cerebrovascular disease. Periodic breathing occurs with diseases of the brain, such as tumours and encephalitis, but is seen more often with strokes, particularly after the period of acute injury (Hoff & Beckenbridge, 1954; Plum & Brown, 1961; Nopmaneejumruslers et al. 2005). Like the periodic breathing seen in CHF, it is more common during sleep and may have an obstructive component (Yaggi & Mohsenin, 2004). Periodic breathing in stroke patients sometimes occurs together with heart failure. Bilateral cortical injury frequently leads to periodic breathing, perhaps by loss of the inhibitory action of the cortex on chemosensitivity (controller gain). In some cases, chemosensitivity seems depressed in periodic breathers, but this is usually associated with hypercapnia that elevates plant gains. Studies by Lange & Hecht (1962) in stroke patients showed in general higher controller gains. They also found that patients with CSR were more likely than normal subjects to develop apnoea after voluntary hyperventilation.
The occurrence of periodic breathing does not help to localize brain injury (Autret et al. 2001). Respiratory neurones communicate with wide areas of the brain, so that injury in different areas of the brain may have the same effect on breathing. In addition, changes in sleep structure commonly occur with strokes. As discussed earlier, altered regulation of cerebral blood flow and changes in the distribution of the brain perfusion influence respiratory system stability through effects on central chemoreceptors.
The responses to brain hypoxia may depend on the specific areas affected, but are complex theoretically even when the hypoxia is considered to be global. Hypoxia has a central depressive effect on breathing, and it can alter postsynaptic potentiation (Georgopoulos et al. 1995).
Studies using spectral analysis of breathing have found a kind of preperiodic breathing in conscious older patients. Pack et al. (1988) showed, using digital comb filtering of breathing in the elderly, that those who demonstrated greater oscillations when awake were more likely to have periodic breathing when asleep. Older patients are more likely to have both cerebrovascular and cardiovascular disease.
Mathematical models support the idea that the system instability that gives rise to periodic breathing can originate in changes in either the nervous or cardiovascular systems. In patients with disease in either system, periodic breathing is far more frequent during sleep. Since periodic breathing itself can have detrimental effects on health, it is now recommended that periodic breathing when it is present be treated specifically. The diversity of treatments recommended illustrates the finding of mathematical models that small changes in different parts of the system can stabilize breathing (Thalhofer et al. 2000; Hu et al. 2003).
Problems to be solved
Mathematical models help to assemble complex data and allow the analysis of possible interrelationships among the multiple factors that may have an impact on pathophysiology. While one major function of models is to generate hypotheses, another important aim is to reveal areas in which more information is required.
Models of periodic breathing involve simulations of ventilation at subnormal levels of respiratory stimulation. Not much is known about the interaction of chemical and neural stimuli in this range. The PCO2 at which breathing stops (apnoea threshold) depends on thresholds of multiple chemoreceptors. Whether the stimulus to the central chemoreceptors is intracellular hydrogen ion, extracellular hydrogen ion, or transmembrane hydrogen ion gradients is not known, but in large part it is perfusion dependent and for the most part it is only indirectly related to arterial PCO2 (Nattie, 2001; Richerson et al. 2005). There are also no data on whether these receptors have the same sensing mechanism or how many of these receptors are needed for spontaneous breathing.
The behaviour of breathing and the circulation over the entire subnormal PCO2 range affects control system stability and not just the points at which breathing stops and resumes. For example, changes in cerebral blood flow with hypoxia and hypercapnia are non-linear; alter the dynamics of changes and the steady-state relationships between brain and arterial PCO2 and the dynamics of ventilation changes (Ide et al. 2003; Banaji et al. 2005).
What is meant by ‘being awake’ and the impact of wakefulness on reflex responses is poorly understood. There seem to be gradations between unconsciousness and consciousness that could affect the apnoeic thresholds and breathing at subnormal chemical drives. So-called autonomic or subcortical arousals can affect the cardiovascular system without producing classical EEG changes of arousal (Sforza et al. 2000), but their effects on respiratory control remain to be determined.
Spontaneous breathing resumes in passively hyperventilated conscious humans at a lower PCO2 by decreasing tidal volume than by adding CO2 to the inspired air to increase PCO2 with tidal volume and rate left unchanged (Altose et al. 1986). Whether this inhibiting effect of rhythmic lung excursions is a manifestation of a vagal reflex or originates more from the conscious perception of chest wall movement is unclear.
Although there are mathematical models that simulate respiratory neurone activity, most models that simulate ventilation responses treat the respiratory controller as a black box (Longobardo et al. 2005). The neuronal circuits that generate the respiratory rhythm are quite complex. Both oscillating networks and pacemaker neurones seem to be involved, though the relative importance of each may vary with maturation. The participating neurones are not the same and probably have different thresholds of activation. Some of the pattern-generating neurones may be chemosensitive and also have different susceptibilities to hypoxic stimulation and depression. These controller complexities may be involved in the periodic breathing that occurs in premature infants and in the elderly. McKay et al. (2005) partially destroyed NeuroKinin-1 (NK-1) neurones in the pre-Botzinger complex in the medulla of adult rats, which then developed recurrent apnoeas during sleep and then while awake. There were abrupt transitions in the sleep–waking cycle. The authors believed that destruction of pattern-generating neurones might underlie central apnoeas occurring in the elderly and might be a cause of sudden death. Chemosensitivity was not measured in these animals.
The respiratory controller is not a static element. In addition to the delays in the response of the respiratory pattern generator to changes in ventilatory demand, there are dynamic shifts in the operational points of the system, e.g. during sleep along the metabolic hyperbola to higher operational levels of CO2, and during exercise, to higher ventilation at about the same resting CO2 level as during normal wakefulness. From an engineering perspective, these shifts and the subsequent systems behaviour appear as ‘integral plus proportional’ control, which minimizes errors to set-point changes, as in sleep transition, or tries to maintain the set point under load changes, as in exercise. There have been models of the ventilatory response during exercise using the mathematics of integral control (Yamamoto, 1978, 1980).
There is some evidence that during sleep an integral type operation of the respiratory controller might help respiration to adapt to the changes in metabolic rate and neural drive that accompany the sleep–waking cycle. This is supported by the fact that the mathematics of integral control predicts less stability the faster the changes in controller position, as with faster transitions to sleep from wakefullness. Sudden arousals, and higher frequency sleep–arousal–sleep cycles would be expected to be more oscillatory than slower state changes. What signals might allow for integral control during sleep are unknown.
The responses of the respiratory controller to afferent signals are gated, having different effects in different parts of the respiratory cycle. Cunningham (1975) presented the novel idea that the timing of chemoreceptor signals within the respiratory cycle of inspiration and expiration could have a significant effect on ventilation and so on whether on not periodic breathing occurred. This interesting idea has not so far been pursued further.
Finally, the effects of linkages of the respiratory to other physiological systems on stability require further exploration. Cyclic changes in blood pressure believed to arise from unstable circulatory control can give rise to periodic breathing (Preiss et al. 1975). Cycling between sleep and wakefulness produced by hypoxia and by hypercapnia also may cause periodic breathing. The destabilizing effects of arousal are well known and the propensity to arousal has been shown to cycle in NREM sleep (Sforza et al. 2000). Saunders & Stradling (1993) used a mathematical model to show that cycling between sleep and wakefulness during hypoxia was able to produce periodic breathing despite having assumed a two-thirds reduction in controller gain during sleep.
Hopefully these uncertainties will be resolved with improved research techniques. Even better, this research will allow simplifying principles to be uncovered about breathing and its relationship to the brain and the circulation.
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