Effects Of Neural Drives On Breathing In The Awake State In Humans
*Corresponding Author. Tel.: + 1-973-9727937; fax: +
1-973-9723585.
E-mail address cherniac@umdnj.edu
Abstract
We have developed a mathematical model of the regulation of ventilation that successfully simulates breathing in the awake as well as in sleeping states. In previous models, which were used to simulate Cheyne-Stokes breathing and respiration during sleep, the controller was only responsive to chemical stimuli, and allowed no ventilation at sub-normal carbon dioxide levels. The current model includes several new features. The chemical controller responds continuously to changes in PCO2 with a lower sensitivity during hypocapnia than in the hypercapnic ranges. Hypoxia interacts multiplicatively with PCO2 over the entire range of activity. The controller in the current model, besides the chemical drive, includes also a neural component. This neural drive increases and decreases as the level of alertness changes, and adds or subtracts from ventilation levels demanded by the chemical controller. The model also includes the effects of post-stimulus potentiation (PSP) and hypoxic ventilatory depression (HVD). While PSP eliminates apneas after a disturbance and also dampens the subsequent dynamics of the respiration, it is not a major factor in the damping of the response. Another finding is that HVD is destabilizing. The model is the first to reproduce results reported in conscious humans after hyperventilation and after acute and longer-term hypoxia. It also reproduces the effects of NREM sleep.
Besides occurring at sleep onset, cessation of breathing and cyclic variations in tidal volume and frequency are far more likely to occur when hypoxia or transient hyperventilation produces subnormal levels of PCO2 in NREM sleep than in awake subjects (Chapman et al., 1988; Datta et al., 1991; Meza et al., 1998b). In conscious humans, subnormal levels of PCO2 caused for example by a transient episode of increased breathing produce only occasional apneas or ventilatory oscillations (Meza et al., 1998b; Tawadrous and Eldridge, 1974; Fregosi, 1991; Meah and Gardner, 1994; Corfield et al., 1995). The ability of the awake subject to breathe spontaneously at levels of PCO2 considerably below resting seems to depend not just on chemical drives from central or peripheral chemoreceptors but rather on an interplay of chemical and neural or wakefulness drives (Asmussen, 1977; Fink, 1961).
Two broad categories of excitatory neural mechanisms seem to play significant roles in the persistence of ventilation in conscious humans at low levels of chemical stimulation and prevent the occurrence of apneas. The first arises from disturbances in the environment like noise and light and from mental activity that excites breathing by a direct central nervous system action without affecting any specific chemoreceptor. This factor, which we shall call the alertness factor, includes "wakefulness drive" (Fink, 1961; Shea et al., 1987; Nielsen and Smith, 1952; Mohan and Duffin, 1997).
The second mechanism, post-stimulus potentiation (after-discharge) results in an excitatory response that persists for a minute or so after the termination of a period of respiratory stimulation and helps prevent apnea even when the hyperventilation has resulted in hypocapnia (Eldridge, 1973, 1974). This stimulatory effect in humans can be offset by sufficiently severe hypocapnia and disappears if hypoxia is sustained for more than five minutes (Fregosi, 1991).
Our previous mathematical models of respiration that simulated Cheyne-Stokes breathing or sleep apnea (Longobardo et al., 1966, 1982) had no need to accommodate neurally stimulated ventilation. They have controllers that necessarily allow apneas to occur at sub-normal levels of PCO2. The ventilation/carbon dioxide relations for sub-normal values of CO2 in these models are extrapolations of the quasi-linear relationships found experimentally at normal and higher values of PCO2. Although these models are successful in duplicating the qualitative characteristics of the highly oscillatory breathing patterns of patients with Cheyne-Stokes breathing and that also occur in sleep, they are not adequate however to simulate the more stable breathing of awake humans.
Our current model focuses on breathing in conscious man. It is based on our earlier models of the chemical regulation of breathing but has several new features. Unlike the chemical controller in the previous models, that in the current model has no discrete CO2 thresholds at which apneas occur. Also the CO2 responses of the central and peripheral chemoreceptors are considered to be non-linear with activity even at very low levels of CO2. While the evidence for this is far from conclusive, there is experimental support for the idea that chemoreceptors can respond to PCO2 in the subnormal range albeit with a much diminished sensitivity (Patrick et al., 1995; Mohan and Duffin, 1997; Cummin et al., 1992). In addition, in this model we have added the effects of hypoxic depression, post-stimulus potentiation, and the alertness factor (Fink, 1961; Eldridge, 1974; Khamnei and Robbins, 1990).
The underlying concept of the model is that some minimum number of afferent impulses is required to give rise to ventilation. These impulses come from both neural and chemical sources. During deep sleep, chemical drives during hypocapnia may be too low to produce ventilation. But as sleep lightens additional impulses (increasing "wakefulness-like” drives) act on respiratory neurons so that their activity gradually becomes sufficient to produce ventilation.
Both wakefulness and sleep are considered to be graded in the model, the alertness factor falling as sleep deepens and decreasing even further in coma; but increasing in the awake state with excitement, and growing with heightening environmental disturbances, and intensity of emotions.
2. Model Description
Full details of the equations for the
controller are included in the Appendix.
Those for the dynamics of the gas stores have been published previously
(Longobardo et al., 1982). The
equations for the entire model and the values used for parameters are available
on web site http://www.oocities.org/respmodel
.
The basic structure
of the current model is the same as others and we have previously described (Longobardo et al., 1982; Khoo et al., 1991);
there is a “plant” consisting of
the body gas stores of CO2 and O2 and a controller, with
input from central and peripheral sensors.
Important changes to the previous model include a new concept for the
chemical controller, the effects on ventilation of excitatory neural inputs,
PSP and HVD. These are discussed below.
2.1. The Chemical Controller
The inputs to the
chemical controller are arterial PCO2 and arterial PO2
measured at the peripheral sensor, and brain PCO2 assumed to be the
tension of the venous blood leaving the brain.
The gas tension values at the chemical controller are delayed about 2
breaths in time from when they appeared at the lung, about 6-8 seconds, during
normal operation. The output of the
chemical controller is ventilation, in liters per minute. The constants
defining the controller were chosen so that when in equilibrium breathing
normal air, PaCO2 is approximately 39 mmHg, PaO2, 105
mmHg, and brain venous PCO2, 48 mmHg. Equilibrium ventilation is 6.3
liters/min. At this operating point the
controller CO2 gain is about 1.85 liters/minute/mmHg arterial PCO2
at constant saturation and O2 gain is 1 liter/min per % decrease in
saturation. It is slightly reduced in
terms of constant arterial PO2.
For the
Cheyne-Stokes model, these values would place the zero ventilation thresholds
for both the central receptor and the peripheral receptor at normoxia at close
to 36.25 mmHg PaCO2. In the
current model however there is no zero ventilation threshold for PCO2
for the chemical controller. Rather, we
assume that the chemical controller actions can be defined by two regions of
different CO2 slope, one above a transition PCO2, (TPCO2),
and the other below. Below TPCO2 ventilation is considered to
diminish linearly down to zero PCO2 (Fig 1 A). TPCO2 defines a change in slope
in the chemical controller from a higher value at above normal levels of PCO2
to one of the lower slope at subnormal PCO2 values. The value of TPCO2 is somewhere
between the zero ventilation threshold in the Cheyne-Stokes model for normoxia,
36.25 mm Hg and the equilibrium PCO2, 39 mmHg.
2.2. Alertness Factor
The alertness factor
consists of multiple elements and includes the “wakefulness drive” and all the
internal and external stimuli that affect ventilation independent of PCO2 and
PO2 (Asmussen, 1977; Shea et al., 1987; Mador and Tobin, 1991). As
the alertness factor increases, breathing at a specific ventilation
level requires less input from chemoreceptors. The opposite
is true when the alertness factor decreases as in sleep. We recognize that both during the alert
state and during sleep the magnitude of the alertness factor is not a single
value but rather varies over a range. During wakefulness the alertness factor
(AF) in the model can vary from slightly negative to positive values. When AF=0
ventilation disappears only at zero PCO2. On the other hand, during
quiet wakefulness, (an AF=–2) occasional apneas occur; and with a sufficiently
large decrease in the alertness drive as during deeper NREM sleep (AF=–11.5),
the model reverts to the Cheyne-Stokes model (Fig. 1 B). The nature of the irregular breathing in REM
sleep is unclear but seems complex involving more than changes in alertness
factor. We have not tried to simulate
apneas occurring in REM sleep.
2.3. Hypoxic
Ventilatory Depression
Hypoxic ventilatory
depression (HVD) is saturation and time dependent and is assumed to act
centrally. The data of Khamnei and Robbins (1990), and Easton et al. (1986)
were used as a base to quantify hypoxic depression with the general principle
that beginning after 5 minutes of hypoxia ventilation decreases gradually and
reaches a steady value in 20 to 30 minutes. Their data show that at 80%
saturation hypoxic depression results in a decrease of about 55% from the
initial peak response when hypoxia is begun. To describe HVD a third order
response to hypoxia was used with three equal time constants of 2.5 minutes.
The half time is about 11 minutes. At 80% saturation steady state depression is
about 6.5 liters/minute.
2.4. Post-Stimulus
Potentiation
Post-stimulus
potentiation (PSP) is simulated by a module that acts like a 'respiratory
memory' (Eldridge, 1973, 1974, 1980; Fregosi, 1991; Wagner and Eldridge, 1991;
Badr et al., 1992). As a disturbance
increases ventilation, the module charges to a potential equal to the
incremental ventilation caused by the disturbance. This charging occurs exponentially in time, defined by a first
order differential equation. The model
is gated so that during charging there is no effect on ventilation. But if the controller asks for a sudden drop
in ventilation, the module "discharges”, again exponentially, allowing
ventilation to fall gradually. The time constants for charging and discharging
are 7 ˝ seconds and 22 ˝ seconds respectively.
In the model PSP is made to disappear after about five minutes of
hypoxia by introducing a threshold, described by a high order differential
response to the hypoxic level. The threshold is designed to increase slowly
during the first 2.5 minutes of hypoxia, and then rise rapidly during the next
several minutes so that PSP disappears by 5 minutes as experimentally observed
(Fregosi, 1991; Georgopoulos et al., 1990).
2.5. The Body Stores
The body stores of
carbon dioxide and oxygen are based on experiments on animals and humans and
are divided into three compartments: the brain, the muscle and the lung
compartment, which has an anatomical dead space. The equations for their
dynamics have been previously described (Longobardo et al., 1966, 1982). The
fall of arterial PO2 during apnea is 55 mmHg per minute in the first
minute, and the rise of arterial PCO2 during apnea is 6.4 mmHg/min,
as observed experimentally. Cerebral blood flow in the model is variable; a
linear function of arterial PCO2, and for constant PCO2 varies
inversely with the arterial oxygen saturation (Donegan et al., 1985).
This delivers a constant oxygen supply to the brain when arterial saturation
varies.
3. Results
3.1. Hyperventilation at Hyperoxic levels
Simulations of hyperventilation and its
off-transient response while breathing 37% oxygen were made varying the level
of alertness and the carbon dioxide gain in the hypocapnic region, and with PSP
except when noted. In all simulations
at the end of hyperventilation, arterial PCO2 was 20 mmHg and
arterial PO2 was 250 mm Hg.
3.1.1. The Effect of Increased Alertness
Factor and Stability
Figure 2A shows
the response to voluntary hyperventilation followed by normal breathing while
inhaling 37% oxygen during quiet wakefulness. The response is in accord with
the observations of Meah and Gardner (1994) who found that apneic periods
rarely occur immediately after voluntary over-breathing, but gradually increase
in number and length, the largest pauses occurring 2 minutes after the end of
the hyperventilation. Apneas in their
studies appeared with mean times between 0.8 and 5.6 minutes after the end of
hyperventilation, and the end of the apneic period was associated with an end
tidal PCO2 of about 36 mmHg.
In the model, as in the experiment, the first apnea started 2 minutes
after hyperventilation, which reflects post-stimulus potentiation, and the
period during which apneas occur ends after about 5 minutes. The arterial PCO2 is about 37
mmHg compared to Meah and Gardner's (1994) 36 mmHg end tidal PCO2.
If the alertness factor is increased as in Figure 2B and 2C, apneas disappear and oscillations are
greatly diminished Further increases
in AF completely eliminate oscillations. The higher ventilation due to the
alertness factor keeps oxygen higher and reducing controller gain changes that
might otherwise result from the hypoxia. This in turn keeps breathing stable.
3.1.2. The Effect of Variable Cerebral
Blood
The model includes variations of
cerebral blood flow with arterial PCO2 and arterial oxygen
saturation. Compared to simulations in which cerebral blood flow is kept
constant, brain PCO2 after hyperventilation is less reduced, the
higher brain PCO2 hastens the recovery to normal levels of
ventilation in the post-hyperventilation period. The response tends to be less oscillatory, because decreases in
arterial oxygen saturation are less severe.
3.1.3. The Effect of Increased TPCO2
and Stability
In the current model, increases in the
threshold PCO2, (TPCO2) increases controller
gain in the hypocapnic region. This increases stability as shown in Fig. 3, which compares responses for values of TPCO2
of 38.5 and 36.75 mmHg, during quiet wakefulness. Steeper hypocapnic slopes provide a more stable response because
increases in ventilation at low levels of PCO2, raising PO2
and diminishing the effects of O2 changes on controller gains.
As in previous models (Longobardo et al.,
1966; Khoo et al., 1982) increases in the gain of the CO2 response in the
hypercapnic range decrease stability.
3.1.4.
The Effect of Post-Stimulus Potentiation
The
previous simulations of ventilatory responses include the effects of PSP. Fig. 4 compares the
response to hyperventilation with and without PSP during quiet
wakefulness. In the absence of PSP an
apneic period of about two minutes ensues immediately after hyperventilation. After that the recovery of ventilation to
normal levels is about the same as when PSP is present.
3.2. Hypoxia
3.2.1. Short Term Hypoxia
Ventilatory responses were simulated to 8% O2
breathing for two minutes followed by breathing 37% O2. The principle
findings from these simulations are the same as from the hyperventilation
simulations; namely that higher alertness factors result in a more stable
ventilatory response post-hypoxia as shown in Fig. 5
and when post-stimulus potentiation is eliminated from the simulation the
stability characteristics are essentially unchanged, as with hyperventilation.
3.2.2. Long Term Hypoxia
If
hypoxia lasts for more than five minutes, HVD develops and PSP disappears
(Fregosi, 1991). Even though both of these effects tend to promote instability,
over a wide range of hypoxia oscillations in ventilation do not occur in
simulations during quiet wakefulness, but do during sleep. Fig.
6 shows the stable responses to 10% and 15% hypoxia during quiet
wakefulness with HVD present. But with
certain values of inspired oxygen which cause the arterial PCO2 to
be near TPCO2, for example during simulations of 14% O2,
breathing oscillations appear during hypoxia even in the alert state. This
occurs when there are sufficiently large increases in controller gain because
of the hypoxia, and the arterial PCO2 is in the region of the
transition PCO2. Hypoxic
depression raises PCO2 toward the transition PCO2 and
lowers oxygen levels.
The occurrence of oscillations during
hypoxia depends also on the magnitude of the slope at subnormal levels of PCO2
as it did in the post-hyperventilation period.
Others have shown that instabilities can
occur in the transition region where the two slopes meet (Duffin and McAvoy,
1988). Operation
at or about the transition PCO2 will be stable so long as the gain
is not driven to excessively high values by low oxygen tension.
To
determine whether the abruptness of the discontinuity at the TPCO2
threshold value contributes to the instability we smoothed the transition
between the lower and higher ventilation/CO2 slopes with a curve
tangent to the controller curve at plus or minus 1, 2 or 3 mmHg above and below
TPCO2 equal to 36.75 mm Hg. We found that the abruptness
does have an effect on the response, but it is quite small.
3.3 Sleep
The alertness factor was decreased by up to
-15 liters/minute to simulate different stages of NREM sleep. With sufficient decrease in alertness factor
the model becomes like our Cheyne-Stokes Model allowing cyclic variations in
ventilation occur during hypoxia and other ventilatory disturbances.
Ventilation while breathing 15% O2 during wakefulness is stable. As
shown in Fig. 7 instabilities start during the
transition to sleep and during sleep ventilation is unstable.
The
ventilatory response during the transition from wakefulness to sleep in the
current model can vary from steady to patently oscillatory, with apneas
depending on the speed of transition as shown previously (Khoo, 1999). In the
current model it also varies with change in the alertness factor so that
transition from wakefulness to deep NREM sleep is more oscillatory than
transition to light NREM sleep. Episodes of arousal followed by return to sleep
probably account for many of the intervals of periodic breathing seen in NREM
sleep.
4. Discussion
Healthy awake humans seldom become apneic or
breathe periodically. While apneas can occur in conscious healthy individuals,
after voluntary hyperventilation and with hypoxia, they are few in number and
rarely repetitive and appear at some times but not others even in the same
person. This contrasts with the common
appearance of apneas and periodic breathing during NREM sleep.
The
present study used mathematical models to evaluate potential mechanisms, which
might account for the scarcity of apneas and periodic breathing in the awake
state. We found that the simplest model
that allowed the essential features of breathing to be reproduced in both the
awake and sleeping states had a non-linear chemical controller, which was
active over a very wide range of PCO2 and PO2 and
included as well alertness factors with excitatory ventilatory effects.
In this model, stability also depended on the shape of the chemical controller curve; stability was greater when the PCO2 at which the high and low slope segments of the chemical controller met (TPCO2), was higher. While post-stimulus potentiation also helped stabilize responses and hypoxic depression had a destabilizing effect, their impact on the stability of breathing in awake subjects appeared to less than the other factors mentioned.
While the model presented deals with many of the mechanisms that may contribute to breathing in conscious humans, it is not complete. We have not included the effects of reflexes from the airways or muscles on breathing nor with the effects in producing periodicities interaction of such reflexes with a non-linear pattern generator on the regularity of breathing pattern or ventilation (Bruce, 1996; Lewis et al., 1992).
4.1. Comparison of Current With Previous
Model
Several previous studies have used mathematical models to simulate periodic breathing and examine the mechanisms, which potentially produce it (Longobardo et al., 1966; Khoo et al., 1982). The current model is the first to focus on breathing in conscious humans.
Longobardo et al. (1982) formulated a model, which simulated recurrent central, obstructive and mixed sleep apneas and showed that obstructive apneas could occur because of differences in responses of upper airway and chest wall muscles to chemical stimuli. Khoo et al. (1991, 1996) presented a model, which described the effects of state changes, arousal and airway obstruction on the occurrence of periodic breathing during NREM sleep. Khoo et al. (1991, 1996) showed that the faster the wake-sleep transition occurred, the more likely were periodic breathing and apneas to appear. We show in the present study that the magnitude of change in alertness is another factor.
4.2. The Excitatory Neural Drives
The excitatory neural drives, or alertness factor, which acts additively to the respiratory excitatory action of the central and peripheral chemoreceptors includes the wakefulness drive, described by Fink (1961) but comprises in addition excitatory environmental factors, cognition, and emotions. This is consistent with observations that show that in awake subjects ventilation falls even when just the eyes are shut, and rises with the performance of mental arithmetic (Shea et al., 1987; Mador and Tobin, 1991; Chin et al., 1996).
Although we have modeled the alertness factor simply as an additive term varying with sleep and alertness but unaffected by levels of carbon dioxide or oxygen, this may not be entirely correct. It seems possible that chemical stimuli do alter neural drives that make up AF since both may impinge at the same time on the same sets of neurons. If, for example, AF increased with CO2, the frequently observed steeper slope of the ventilatory response to CO2 that occurs with wakefulness would be explained. The results from the Nielsen and Smith (1952) might be interpreted to show an excitatory effect of hypoxia on AF but this idea is not supported by Mohan and Duffin (1997).
We understand that we have grouped into our alertness factor several components that may be differently affected by chemical drives and other background conditions. Certain types of neural drives may even affect specific components of ventilation. For example, anxiety has been shown to increase respiratory frequency by decreasing expiratory time (Masoka and Homma, 1999). Some mental activities such as intense concentration may actually favor the occurrence of post-hyperventilation apnea. Also, these drives probably do not disappear completely in sleep since even in deep sleep arousal is relatively easy. Hypoxia, itself, seems to have a direct excitatory effect centrally on blood pressure and to a degree on ventilation.
Peripherally chemodenervated animals display a weak excitatory ventilatory response with exposure to hypoxia but only when they are awake. In conscious goats made hypoxic, ventilation shows small increases even when the carotid bodies are maintained normoxic (Smith et al., 1997) However, during anesthesia, animals with sectioned carotid body nerves show only continuous depression of breathing when they are made hypoxic.
Recent studies in which cyanide has been microinjected into the ventral medullary surface suggest that there may be a centrally located chemoreceptor that can increase vasomotor activity (Solomon et al., 2000; Mitra et al.,1993).
Since the non-linear chemical response is evident in terms of ventilation, mainly if not exclusively during wakefulness and depends on the presence of a neural drive, it is difficult to say whether the chemical or the neural component is more important in preventing oscillations in ventilation. In fact, a model in which the controller responded linearly to chemical stimuli and as well to a neural component, which itself was dependent on CO2 and O2 levels would have resulted in essentially the same results. We chose the first possibility only because it seemed simpler conceptually. However there is some evidence that ventilation persists even in peripherally chemodenervated animals with a cooled ventral medullary surface to eliminate CO2 responses if the animal is awake which suggests that neural drives can act even when known chemoreceptors are suppressed (Forster et al., 1997).
4.3. Sensory and Ventilatory Activity at
Sub-Normal CO2 Values
We see neural drives as building on tonic activity produced by otherwise sub- threshold levels of PCO2 so as to produce breathing. There is considerable support for the idea that changes in PCO2 even in the hypocapnic range can affect respiration. Cummin et al. (1992) has shown in voluntary hyperventilation experiments in normal humans that CO2 boluses injected into the inspired air can alter ventilation even after PCO2 has been reduced 5 to 10 mmHg below its usual normal value. Patrick et al. (1995) using a volume cycle respirator in a cleverly designed study showed that humans respond to CO2 changes in the hypocapnic range. However in individuals who have periodic breathing there are rather sharp CO2 thresholds (Xie et al., 1997). Skatrud and Dempsey (1983) decreased below normal the PCO2 of blood perfusing the carotid body of conscious goats and found that this reduced the ventilation response to hypoxia and to hypercapnia. Smith et al. (1997) found similar results in conscious dogs.
Even in anesthetized animals, hypocapnia of increasing severity has a progressive inhibitory effect on breathing, increasing the level of hypoxia needed to reinitiate previously absent carotid body activity and ventilation. In an animal preparation in which the brain could be perfused independently of the rest of the body, Berkenbosh et al. (1984) found that changes in brain PCO2 in the range of 10 mmHg continued to influence respiration. Further, Eldridge (1980) observed that the after discharge produced by carotid sinus nerve stimulation was diminished in apneic animals by making them even more hypocapnic.
While in the current model we suggest that there could be responses to changes in CO2 even at extremely low levels of PCO2, it may be that individual CO2 chemoreceptors are not active over such a wide range. A non-linearity of the Ventilation /CO2 response could thus arise from heterogeneity in the response ranges of CO2 receptors, as has been shown for other receptors, so that some CO2 receptors are active at low levels of CO2 and others over a range of higher CO2 levels (Li et al., 1999; Forster et al., 1997) active over such a wide range. Li et al. (1999) studies in cats suggest the wake/sleep state alters the ability of specific central chemoreceptors to affect ventilation suggesting that different chemoreceptors may have different ranges of response to CO2.
4.4. Sleep
Alertness factors are recognized to decrease in NREM sleep. The idea that sleep is a state of sensory deafferentation is supported by experiments that show sensory deprivation leads to somnolence. Sleep weakens the sensory effects of stimuli of diverse origin which influence breathing but whose main action is on other systems (Velluti, 1997). State changes have been shown to affect the number of neurons displaying respiratory modulated activity (Orem et al., 1985; Orem and Vidruk, 1998). There are fewer of them during sleep compared to wakefulness. The residual tonic drive remaining in many brain neurons after mechanical hyperventilation eliminates phasic activity is also greater in wakefulness than sleep (Foutz et al., 1987). Nesland and Plum (1965) considered this tonic activity to be the substrate out of which phasic breathing ultimately results.
We have not attempted to model breathing during REM sleep. Its clear that the irregular breathing found in REM sleep involves excitatory inputs as well as inhibitory ones. However, despite their differences, Meza et al. (1998a) has found that in both NREM and REM sleep ventilation is primarily chemically controlled. We also recognize that both NREM and REM sleep probably come about from much more than a simple withdrawal of non-respiratory drives and probably include inhibitory mechanisms arising in part from changes in cerebral blood flow.
.
While simulations here show a stabilizing effect of cerebral blood flow changes produced by PO2 and PCO2 and the increase in cerebral blood flow with low oxygen might alleviate brain hypoxia and forestall hypoxic depression, in the goat surges in cerebral blood flow that occur in REM sleep seem to cause apnea. But experiments in humans show only small reductions in cerebral blood flow in NREM sleep and small increases or no change in REM sleep (Parisi et al., 1988; Braun et al., 1997).
Metabolic activity increases slightly with wakefulness (probably about 10%). While this change was not included in the present model, our previous studies show that this would tend to stabilize ventilation (Cherniack and Longobardo, 1990).
With respect to sleep/wake transitions, the current model behaves the same as that of Khoo, (1991) (Khoo et al., 1999). More extreme and more rapid transitions tend to cause more periodicity. In general, enhanced arousals tend to increase instabilities in breathing, but the effect may depend on whether the arousal occurs in REM or NREM sleep (Orem et al.,1980).
4.5. Hypoxic Ventilatory Depression
The time course of HVD in our model simulates the experimental results of Easton et al. (1986) and Khamnei and Robbins (1990). In the model it reduces total ventilation which is consistent with the idea that the depression acts mainly on the brain and the integration of central and peripheral chemoreceptor drives rather than at the peripheral chemoreceptors themselves (Neubauer et al., 1990). Robbins (1995) however has proposed that in conscious animals and humans, peripheral chemoreceptor activity is also depressed with hypoxia. While this agrees with the experimental finding that in conscious creatures after peripheral chemoreceptor denervation, hypoxia causes a small (15-20 percent) increase in ventilation, we have not included in our model a specific effect of hypoxia depression on peripheral chemoreceptors activity. This would reduce its net effects and diminish its destabilizing action.
4.7. Post-Stimulus Potentiation
Post-stimulus potentiation probably explains the difference in response produced by active and passive hyperventilation. Active hyperventilation usually fails to cause apneas in conscious humans while passive hyperventilation sometimes does; although differences in respiratory excitatory effects produced by increased metabolic activity and from muscle afferents probably also contributes to the disparity (Berkenbosch et al., 1984; Eldridge, 1973). Since post-stimulus potentiation has been described in anesthetized decerebrate cats following carotid sinus nerve and peripheral sensory nerve stimulation, it is not surprising that it should be seen in sleeping as well as conscious humans (Eldridge, 1974). However, studies suggest that its strength depends on the level of other non-respiratory drives so that it is weaker in sleep, and absent in patients in coma or with strokes (Daristotle et al., 1990). Its effectiveness as a stabilizing mechanism during wakefulness is also reduced because as hypoxia is prolonged post-stimulus potentiation diminishes (Georgopoulos et al., 1990).
4.8. Variability in Responses in Conscious
Humans
The present model deals with the occurrence of apneas and periodic variations in ventilation in the awake state. Differences in gain and in the curvature of the ventilation /PCO2 response curve and in the intensity of excitatory neural drives may largely account for variability among individuals in ventilation levels and the occurrence of apneas in the awake state.
The current model does not attempt to simulate variability in breathing patterns or to include the many factors that contribute to breath-to-breath variability in humans that are non-periodic. The interaction of afferent stimuli arising from mechanoreceptors in the airways and the respiratory muscles with the non-linear oscillator that generates the respiratory rhythm seems to a major cause of these variations and in certain cases may cause transient disturbance in the regularity of breathing that appear periodic (Lewis et al., 1992; Bruce, 1996). While this mechanism may account for some of the apparently periodic variability in ventilation seen in conscious humans, the mechanisms related to the behavior of the neurochemical controller which are included in the current model we believe play at least as important role.
Apneas have been observed after voluntary hyperventilation after some but not after all trials even in the same person. We attribute most of this intra-individual variability to at least two factors. First, alertness factors can change fairly quickly in intensity. Also the awake state seems not to be a single state but has different levels and different components which can alter not just the magnitude of the wakefulness drive and ventilation (Horner et al., 1997) but may affect mainly specific components of the respiratory pattern such as expiratory time.
Despite variability in intensity, the excitatory effect of alertness is stabilizing and should be and is most powerful during wakefulness when a variety of disturbances such as posture and speech commonly disrupt the automatic rhythm of breathing and could lead to the occurrence of apneas with consequent upset to oxygen supplies.
We thank Dr. Gerald Goertzel for his insight and rigor in the mathematical modeling of physiological systems. We also thank Dr. Nanduri Prabhakar for his assistance in preparing this paper and his thoughtful critique of the model.
APPENDIX
System Equations
The Controller
Nomenclature
Symbol Value
AF Alertness Factor, lit/minute
DIST Incremental ventilation above
normal after a disturbance, lit/min
Dp Peripheral ventilatory
drive, lit/min
Dc Central ventilatory drive,
lit/min
Dchem Chemical drive, Dp+Dc, lit/min
HVD Hypoxic
Ventilatory Depression, lit/min
HVDEQ HVD equilibrium value, lit/min
PSPP PSP
equilibrium value, lit/min
PSP_Th PSP Threshold, lit/min
PSP Post-stimulus potential,
lit/min
PaCO2 Partial
pressure of CO2 in the arterial blood, mm Hg
PvBCO2 Partial pressure of CO2 in
and leaving the brain, mm Hg
SaO2 Arterial
oxygen saturation, %
tauHVD Hypoxic
Ventilatory Depression time constant, min 2.5 tauPSPC PSP module charging time constant,
min 0.125
tauPSPD PSP module discharging time constant,
min 0.25
TPCO2 Threshold
for arterial PCO2, mm Hg
TPCO2,B Threshold
for brain PCO2, PvBCO2, mm Hg
A.1.1 The Chemical Controller
The
equations immediately following define the chemical controller characteristic,
the steady state ventilatory characteristic for chemical ventilation as a
function of carbon dioxide tensions and oxygen saturation.
The
responses of the chemical controller are defined in two regions separated by a
“transition” PCO2 threshold, TPCO2. Controller carbon
dioxide and oxygen gains are higher above the transition threshold and lower
below the threshold. See Figure 1a.
For
PaCO2 > TPCO2,
Dp, the peripheral ventilatory drive is
Dp=0.124*(101.72-SaO2)*(PaCO2-31.123)-1.43
liters per minute
Dc the
central ventilatory drive is
Dc=1.573*(PvBCO2-44.35)
liters/minute
For
PaCO2 <TPCO2,
Dp, the
peripheral ventilatory drive is
Dp=[(0.124*(101.72-SaO2)*(TPCO2
-31.123)-1.43)/ TPCO2]*PaCO2<
Dc, the
central drive is
Dc=[1.57*(TPCO2,B-44.35)/ TPCO2,B]*PvBCO2
TPCO2,B
is the brain carbon dioxide tension at TPCO2 in the normoxic steady
state.
The total
chemical ventilatory drive, Dchem is
Dchem=Dp+Dc
Above TPCO2
the controller gain for carbon dioxide at constant SaO2 is
CO2_Gain=0.124*(101.72-SaO2)+1.57
liters/minute/mm Hg increase in PaCO2
Below TPCO2
the controller gain for carbon dioxide is
CO2_Gain=0.124*(101.72-SaO2)*(TPCO2
-31.123)-1.43)/ TPCO2 +
1.57*(TPCO2 -44.35)/ TPCO2
A.1.2 Hypoxic Ventilatory Depression
The
magnitude of hypoxic ventilatory depression (HVD) is saturation and time
dependent.
HVD is described by a third order response to
hypoxia with three equal time constants of 2.5 minutes, with a final value of
HVDEQ=35* (normoxic_saturation-SaO2). For normoxic saturation values
of 99.3%, and saturation during hypoxia of 78 % this amounts to an equilibrium
depression of about 7.5 liters/minute. In this model,
with 10% fiO2, saturation was 78%, PaO2 was 37.5 mm Hg and PaCO2,
29 mmHg the loss is 55% of the initial increase.
The
equations for the development of HVD are
Dhvd1=(1/(tau))*((HVDEQ)-hvd1);
hvd1=hvd1+Dhvd1;
Dhvd2=(1/(tau))*(hvd1-hvd2);
hvd2=hvd2+Dhvd2;
DHVD=delt*(1/(tau))*(hvd2-HVD);
D
signifies the time derivative, hvd1 and hvd2 are local variables.
A.1.3 Post-Stimulus Potentiation
Post-stimulus potentiation, PSP is simulated using the
equations for an R-C circuit. As a disturbance increases ventilation, the
module charges toward an equilibrium potential equal to the incremental
ventilation over normal caused by the disturbance. This charging occurs
exponentially in time. During charging there is no effect on ventilation. The module is gated however so that if there
is a sudden drop in ventilation, the module "discharges”, again
exponentially, allowing ventilation to fall gradually instead.
The
equilibrium potential for PSP at any time is, during charging
DPSPP=
(1/tauPSPC)*(DIST-PSPP)
and during
discharging is
DPSPP=(1/tauPSPD)*(-PSPP)
PSP is made to disappear after about five minutes of
hypoxia by the introduction of a PSP threshold, which increases with hypoxia
and time. The threshold increases slowly during the first 2.5 minutes of
hypoxia, and then rises rapidly during the next several minutes so that the PSP
disappears by about 5 minutes.
PSP=PSPP-PSP_Th
A.1.4 Total Ventilation
Total ventilation is the sum of the
chemical drives, alertness factor, post stimulus potentiation less hypoxic
ventilatory depression.
Total Ventilation=Vchem+AF+PSP-HVD
A.2 Cerebral Blood Flow
Cerebral
blood flow is
QdotB=0.038*PaBCO2+1/SaO2-1.42
This formulation delivers a constant supply of oxygen to the brain
when arterial saturation varies. At normal conditions cerebral blood flow is
1.096 liters per minute.
The complete equations for the mathematical model, including
parameters used in the simulation are on the web site http://www.oocities.org/respmodel
.
References
Asmussen, E., 1977. Regulation of respiration: "The Black Box". Acta Physiol. Scand. 99 (1), 85-90.
Badr, M.S., Skatrud, J.B., Dempsey, J.A., 1992. Determinants of poststimulus potentiation in humans during NREM sleep. J. Appl. Physiol. 73 (5), 1958-1571.
Berkenbosch, A., van Beek, J.H., Olievier, C.N., De Goede, J., Quanjer, P.H., 1984. Central respiratory CO2 sensitivity at extreme hypocapnia. Respir. Physiol. 55 (1), 95-102.
Braun, A.R., Balkin, T.J., Wesenten, N.J., Carson, R.E., Varga, M., Baldwin, P., Selbie, S., Belenky, G., Herscovitch, P., 1997. Regional cerebral blood flow throughout the sleep-wake cycle. An H2(15)O PET study. Brain 120 (Pt 7), 1173-1197.
Bruce, E.N., 1996. Temporal variations in the pattern of breathing. J. Appl. Physiol.80, 1079-87
Chapman, K.R., Bruce, E.N., Gothe, B., Cherniack, N.S., 1988. Possible mechanisms of periodic breathing during sleep. J. Appl. Physiol. 64 (3), 1000-1008.
Cherniack, N.S., Longobardo, G.S., 1990. Effect of metabolic rate on the occurrence of periodic breathing. In: Issa, F.G., Suratt, P.M., and Remmers, J.E. (Eds.). Sleep and Respiration, Progress in Clinical and Biological Research, Vol. 345. Wiley-Liss, New York, pp. 167-176.
Chin, K., Ohi, M., Fukui, M., Kita, H., Tsuboi, T., Noguchi, T., Otsuka, N., Hirata, H., Mishima, M., Kuno, K., 1996. Inhibitory effect of an intellectual task on breathing after voluntary hyperventilation. J. Appl. Physiol. 81 (3), 1379-1387.
Corfield, D.R., Morrell, M.J., Guz, A., 1995. The nature of breathing during hypocapnia in awake man [published erratum appears in Respir. Physiol. 1996 Apr-May, 104 (1), 89]. Resp. Physiol. 101 (2), 145-159.
Cummin, A.R., Sidhu, V.S., Telford, R.J., Saunders, K.B., 1992. Ventilatory responsiveness to carbon dioxide below the normal control point in conscious normoxic humans. Eur. Respir. J. 5 (5), 512-516.
Daristotle, L., Berssenbrugge, A.D., Engwall, M.J., Bisgard, G.E., 1990. The effects of carotid body hypocapnia on ventilation in goats. Respir. Physiol. 79 (2), 123-135.
Datta, A.K., Shea, S.A., Horner, R.L., Guz, A., 1991. The influence of induced hypocapnia and sleep on the endogenous respiratory rhythm in humans [published erratum appears in J. Physiol.,London, Dec., 1991, 444, 778]. J. Physiol. London, 440, 17-33.
Donegan, J.H., Traystman, R.J., Koehler, R.C., Jones, M.D., Jr., Rogers, M.C., 1985. Cerebrovascular hypoxic and autoregulatory responses during reduced brain metabolism. Am. J. Physiol. 249, H-421-429.
Duffin, J., McAvoy, G.V., 1988. The peripheral-chemoreceptor threshold to carbon dioxide in man. J. Physiol. (London) 406, 15-26.
Easton, P.A., Slykerman, L.J., Anthonisen, N.R., 1986. Ventilatory response to sustained hypoxia in normal adults. J. Appl. Physiol. 61, 906-911.
Eldridge, F.L., 1973. Posthyperventilation breathing: different effects of active and passive hyperventilation. J. Appl. Physiol. 34 (4), 422-430.
Eldridge, F.L., 1974. Central neural respiratory stimulatory effect of active respiration. J. Appl. Physiol. 37 (5), 723-735.
Eldridge, F.L., 1980. Subthreshold central neural respiratory activity and afterdischarge. Respir. Physiol. 39 (3), 327-343.
Fink, R.B., 1961. Influence of cerebral activity in wakefulness on regulation of breathing. J. Appl. Physiol 16,15-20.
Forster, H.V., Ohtake, P.J., Pan, L.G., Lowry, T.F., 1997. Effect on breathing of surface ventrolateral medullary cooling in awake, anesthetized and asleep goats. Respir. Physiol. 110 (2-3), 187-197.
Foutz, A.S., Boudinot, E., Morin-Surun, M.P., Champagnat, J., Gonsalves, S.F., Denavit-Saubie, M., 1987. Excitability of 'silent' respiratory neurons during sleep-waking states: an iontophoretic study in undrugged chronic cats. Brain Res. 404 (1-2), 10-20.
Fregosi, R.F., 1991. Short-term potentiation of breathing in humans. J. Appl. Physiol. 71 (3), 892-899.
Georgopoulos, D., Bshouty, Z., Younes, M., Anthonisen, N.R., 1990. Hypoxic exposure and activation of the afterdischarge mechanism in conscious humans. J. Appl. Physiol. 69 (3), 1159-1164.
Horner, R.L., Sanford, L.D., Pack, A.I., Morrison, A.R., 1997. Activation of a distinct arousal state immediately after spontaneous awakening from sleep. Brain Res. 778, 127-134.
Khamnei, S., Robbins, P.A., 1990. Hypoxic depression of ventilation in humans: alternative models for the chemoreflexes. Respir. Physiol. 81 (1), 117-134.
Khoo, M.C., Kronauer, R.E., Strohl, K.P., Slutsky, A.S., 1982. Factors inducing periodic breathing in humans: a general model. J. Appl. Physiol. 53 (3), 644-659.
Khoo, M.C., Gottschalk, A., Pack, A.I., 1991. Sleep-induced periodic breathing and apnea: a theoretical study. J. Appl. Physiol. 70 (5), 2014-2024.
Khoo, M.C., Anholm, J.D., Ko, S.W., Downey, R. 3rd, Powles, A.C., Sutton, J.R., Houston, C.S., 1996. Dynamics of periodic breathing and arousal during sleep at extreme altitude. Respir. Physiol. 103 (1), 33-43.
Khoo, M.C., 1999. Periodic breathing and central apnea, In: Altose, M.D., Kawamaki, Y. (Eds.), Control of breathing in health and disease, Marcel Dekker, New York. pp. 203-250.
Lewis, J.E., Glass, L., Bachoo, M., Polossa, C., 1992. Phase resetting and fixed- delay stimulation of a simple model of respiratory rhythm generation. J. Theor. Biol.159, 491-506.
Li, A., Randall, M., Nattie, E.E., 1999. CO2 microdialysis in retrotrapezoid nucleus of the rat increases breathing in wakefulness but not in sleep. J. Appl. Physiol. 87 (3), 910-919.
Longobardo, G.S., Cherniack, N.S., Fishman, A.P., 1966. Cheyne-Stokes breathing produced by a model of the human respiratory system. J. Appl. Physiol. 21 (6), 1839-1846.
Longobardo, G.S., Gothe, B., Goldman, M.D., Cherniack, N.S., 1982. Sleep apnea considered as a control system instability. Respir. Physiol. 50 (3), 311-333.
Mador,
M.J., Tobin, M.J.,
1991. Effect of alterations in mental activity on the breathing pattern in
healthy subjects. Am. Rev. Resp. Dis.
144 (3 Pt 1), 481-487.
Masoka, Y., Homma, I., 1999. Expiratory time determined by individual anxiety levels in human. J. Appl. Physiol. 86, 1329-1336.
Meah, M.S., Gardner, W.N., 1994. Post-hyperventilation apnea in conscious humans. J. Physiol ,London, 477 (3), 527-538.
Meza, S., Giannouli, E., Younes, M., 1998a. Control of breathing during sleep assessed by proportional assist ventilation. J. Appl. Physiol. 84 (1), 3-12.
Meza, S., Mendez, M., Ostrowski, M., Younes, M., 1998b. Susceptibility to periodic breathing with assisted ventilation during sleep in normal subjects. J. Appl. Physiol. 85 (5), 1929-1940.
Mitra, J., Dev, N.B., Trivedi, R., Amini, S., Ernsberger, P., Cherniack, N.S., 1993. Intramedullary sodium cyanide injection on respiratory and vasomotor responses in cats. Respir. Physiol. 93, 71-82.
Mohan, R., Duffin, J., 1997. The effect of hypoxia on the ventilatory response to carbon dioxide in man. Respir. Physiol. 108 (2), 101-115.
Nesland, R., Plum, F., 1965. Subtypes of medullary respiratory neurons. Exp. Neurol. 12, 337-348.
Neubauer, J.A., Melton, J.E., Edelman, N.H., 1990. Modulation of respiration during brain hypoxia. J. Appl. Physiol. 68 (2), 441-451.
Nielsen, M., Smith, H., 1952. Studies on the regulation of respiration in acute hypoxia. Acta Physiol. Scand. 24, 293-313.
Orem, J., Dick, T., Norris, P., 1980. Laryngeal and diaphragmatic responses to airway occlusion in sleep and wakefulness. Electroencephalogr Clin Neurophysiol. 50, 151-164.
Orem, J., Osorio, I., Brooks, E., Dick, T., 1985. Activity of respiratory neurons during NREM sleep. J. Neurophysiol. 54 (5), 1144-1156.
Orem, J., Vidruk, E.H., 1998. Activity of medullary respiratory neurons during ventilator-induced apnea in sleep and wakefulness. J. Appl. Physiol. 84 (3), 922-932.
Parisi, R.A., Neubauer, J.A.,
Frank, H.H., Santiago, T.V., Edelman, N.H., 1988. Linkage between brain blood
flow and respiratory drive during sleep. J. Appl. Physiol. 64, 1457-1465.
Patrick, W., Webster, K., Puddy, A., Sanii, R., Younes, M., 1995. Respiratory response to CO2 in the hypocapnic range in awake humans. J. Appl. Physiol. 79 (6), 2058-2068.
Robbins, P.A., 1995. Hypoxic ventilatory decline: site of action. J. Appl. Physiol. 79 (2), 373-374.
Shea,
S.A., Walter, J., Pelley, C., Murphy, K., Guz, A., 1987. The effect of visual and auditory stimuli upon resting
ventilation in man. Respir. Physiol. 68 (3), 345-357.
Skatrud, J.B., Dempsey, J.A., 1983. Interaction sleep state and chemical stimuli in sustaining rhythmic ventilation. J. Appl. Physiol. 55 (3), 813-822.
Smith, C.A., Harms, C.A., Henderson, K.S., Dempsey, J.A., 1997. Ventilatory effects of specific carotid body hypocapnia and hypoxia in awake dogs. J. Appl. Physiol. 82 (3), 791-798.
Solomon, I.C., Edelman, N.H., Neubauer, J., 2000. Pre-Botzinger complex functions a central hypoxia chemosensor for respiration in vivo. J. Neurophysiol. 83, 2854-2868.
Tawadrous, F.D., Eldridge, F.L., 1974. Posthyperventilation breathing patterns after active hyperventilation in man. J. Appl. Physiol. 37 (3), 353-356.
Velluti, R.A., 1997. Interactions between sleep and sensory physiology. J. Sleep Research 6, 61-77.
Xie, A., Rankin, F., Rutherford, R., Bradley, T.D., 1997. Effects of inhaled CO2 and added dead space on idiopathic central sleep apnea. J. Appl. Physiol. 82 (3), 918-926.
Wagner, P.G., Eldridge, F.L., 1991. Development of short-term potentiation of respiration. Resp. Physiol. 83 (1), 129-139.
Table
1
EQUILIBRIUM VALUES FOR DIFFERENT LEVELS OF
ALERTNESS FACTORS
State Alertness Drives Tensions
Saturation
Dp DC HVD
Total PaCO2 PaO2 %
|
Very Alert |
+2 |
|
0.4 |
4.0 |
0 |
6.4 |
|
38 |
106.8 |
|
99.5 |
|
Alert |
0 |
|
0.9 |
5.4 |
0 |
6.3 |
|
39 |
105.5 |
|
99.4 |
|
Quiet Wakefulness |
-2 |
|
1.4 |
6.8 |
0 |
6.2 |
|
40.2 |
104.3 |
|
99.2 |
|
NREM Sleep |
-11.5 |
|
4.2 |
13.2 |
0.2 |
5.7 |
|
45.0 |
98.7 |
|
98.6 |
Alertness
and Drives are in liters/minute and Tensions are in mmHg.