VD r. V < 0 (4.3.4e)

Transcription

1 234 where V i = inspiratory flow rate, m 3 /sec N i = neural output, neural pulses (V V r ) = lung volume above resting volume, m 3 p mus(e) = pressure generated by expiratory muscles, N/m 2 C = respiratory compliance, m 5 /N R = respiratory resistance, N sec/m 5 η = conversion of neural output to muscle isometric pressure at FRC, N/m 2 /neural pulses v = muscle force-length and geometric effects, N/m 5 φ = muscle force-velocity effect, N sec/m 5 If v(v V r ) > ηn i, then the muscle cannot generate an inspiratory pressure because of its mechanical disadvantage. In this case, which occurs in the early part of inspiration when lung volume is above the resting volume V r, flow is still in the exhalation direction, and V V VD r e = RC (4.3.4a) where V D e = expiratory flow rate, m 3 /sec If [v(v V r ) (V V r )/C p mus(e) ] > ηn i, flow is also in the exhalation direction. This situation is encountered when V > V r and ηn i has not become sufficiently strong to overcome elastic recoil: V D ηni v( V Vr ) ( V Vr )/ C e = (4.3.4b) R If (V V r )/C < 0, then inspiratory flow is both passive and active. Flow is calculated in two steps, with passive flow calculated from and active flow from V ipassive = ( V ) Vr C p mus( e) R (4.3.4c) and V iactive = ηn i v( V Vr ) φv ipassive φ R (4.3.4d) V i = V i = V ipassive if iactive V ipassive iactive V < 0 (4.3.4e) V if V iactive > 0 (4.3.4f) Volume is obtained by integrating flow rate. Coefficient values were obtained from the literature: ηn i was chosen to give a peak isometric pressure of 1470 N/m 2 (15.0 cm H 2 O) with a neural input of 15.0 arbitrary units (η = N/m 2 /arbitrary unit). Compliance C was taken to be 1.3 x 10-6 m 5 /N (0.13 L/cm H 2 O) and two values of resistance R used were 196 kn sec/m 5 (2.0 cm H 2 O sec/l) and 588 kn sec/m 5. The muscle length tension effects represent the difference between passive elastance 64 and effective elastance obtained in normal human subjects during electrophrenic 64 Elastance is the inverse of compliance.

2 235 stimulation. The value for v thus becomes 5.4 x 10 5 N/m 5 (5.4 cm H 2 O/L). Although taken to be a constant, the actual value of v probably varies with level of inspiratory activity (Younes and Remmers, 1981). The value for muscle force velocity effect φ is taken from human subject data at a lung volume close to FRC. Its value is 573 kn sec/m 5 (5.85 cm H 2 O sec/l), and, again, it would probably be more correct not assumed constant. Younes and Remmers (1981) report that inspiration, as determined by flow rate, is different from inspiration from a neural standpoint. Inspiratory flow rate is delayed from the onset of neural output if beginning lung volume is above resting lung volume: expiration continues until the neural output overcomes opposite elastic tendencies. If beginning lung volume is below resting lung volume, then inspiratory flow may precede neural output. The amount of delay or anticipation depends on the rate of rise of the neural output as well as resistance and compliance of the respiratory system. The end of inspiratory flow is always delayed beyond the peak of neural output. The extent of delay depends on rate of decline of neural output and respiratory resistance and compliance (Younes and Remmers, 1981). Changes in the shape with time of the neural output can overcome large increases in respiratory resistance and compliance. Inspiratory duration appears to be determined by the respiratory controller. Although the exact mechanism of inhalation time control is unknown, it appears that inhalation can be ended abruptly in a manner similar to a switch (Younes and Remmers, 1981). This switch appears to have a variable threshold to such input factors as lung volume, chest wall motion, blood gases, muscular exercise, body temperature, sleep, disease, and drugs. Figure Figure Relation between intensity of inspiratory terminating influences and inspiratory duration in the cat. As each stimulus (clockwise from upper right: lung volume, electrical stimulus to the rostral pons, electrical stimulus to the intercostal nerves, and body temperature) increases in magnitude, inspiratory time shortens. Conversely, as inspiratory time accumulates, a lower stimulus is necessary to halt inspiration. No lung volume feedback was present for voltage and temperature stimuli. (Adapted and used with permission from Younes and Remmers, 1981.)

3 236 shows that the threshold to terminate inspiration decreases with inspiratory time. For instance, the longer inspiration progresses, the smaller the lung volume must be in order to conclude inspiration. Sustained lung volume changes have little or no effect (Younes and Remmers, 1981). Similarly, electrical stimuli to intercostal nerves will shorten inspiration with a timevarying threshold. It would be expected that this effect would be analogous to the effect produced by intercostal muscle mechanoreceptors operating naturally within a feedback loop. It has been reported that airway occlusion, chest wall distortion, and vibration all cause shortening of inspiration (Younes and Remmers, 1981). Stimulation of the rostral pons area (in the region of the pneumotaxic: center) of the brain can decrease inspiratory duration, as can body temperature. Hypercapnia decreases inspiratory duration, and at least part of this may be due to increased participation of chest wall reflexes as the result of more vigorous inspiration. Many of the preceding factors seem to interact to reduce inspiration discontinuance threshold below the level that would exist if several factors were not present (Younes and Remmers, 1981). This effect of body temperature on inspiratory time is clearly of importance to an animal that pants when overheated, like a cat. Although humans are not known to rely on this same heat loss mechanism, an effect such as this would give rise to a respiratory thermal exercise limitation interaction as discussed in Section 1.5. Control of expiratory time is somewhat different from that of inspiratory time. Unlike inspiration, which is always actively initiated by muscular action, exhalation is considered to be passive at rest and active during exercise. Control of expiration appears to differ, therefore, in the dependence of expiratory duration on the previous inspiratory time, and in the active control of expiratory flow by respiratory resistance regulation (Martin et al., 1982; Younes and Remmers, 1981). The transition from exhalation to inhalation also exhibits switching behavior with variable threshold (Figure ). 65 The switch characteristic can be determined by stimulus of the rostral pons area (nucleus parabrachialis medialis) and by chemical stimulation of the carotid bodies. Subthreshold stimuli cause a translocation of the stimulus time characteristic toward the left (Younes and Remmers, 1981). Because of this, repetitive subthreshold stimuli can have a cumulative effect and change the overall shape of the stimulus time switching characteristic. Hence static lung volume changes (as stimuli) do affect the exhalation switching characteristic (Figure ), unlike the inhalation switch where static lung volume did not affect inhalation time (Younes and Remmers, 1981). Exhalation time is essentially linked to the preceding inhalation time (Grunstein et al., 1973; Younes and Remmers, 1981). Evidence shows a central neural linkage between these two times, which probably acts through the central expiratory excitation threshold illustrated in Figure Since expiratory time and lung volume are interrelated, it should not be surprising to note that expiratory reserve volume (ERV; see Section 4.2.2) also appears to be under respiratory control. An increase in exhalation time would be expected to increase ERV because of the curve in Figure Changes in ERV are minimized by active resistance changes, to be discussed later, but decreases in ERV have been reported in humans with hypercapnia (Younes and Remmers, 1981). Evidence from cats indicates that an important expiratory flow rate regulating mechanism, called expiratory braking, is due to contraction of the inspiratory musculature during exhalation and due to active regulation of upper airway resistance (Younes and Remmers, 1981). The role of each of these in humans is not clear, but it is likely that expiratory braking does occur, 66 probably by inspiratory muscular action. Vagal discharge to upper airway muscles causes changes in glottal opening. Rapid changes in resistance, as 65 Although this evidence was obtained from resting animals, there is no reason to believe it is not true during exercise. 66 For instance, there appears to be an optimal resistance to exhalation in humans, and switching from nose breathing at rest to mouth breathing during exercise occurs when nasal resistance exceeds mouth resistance.

4 237 Figure Stimulus strength required to terminate expiration and initiate inspiration as related to expiratory time. The stimulus was current applied to the rostral pons area of the brain. As current increases, expiratory time shortens. (Used with permission from Younes and Remmers, 1981.) Figure Effect of lung volume on the stimulus strength (electrical current to the rostral pons) required to terminate expiration and initiate inspiration. As lung volume increases, so does expiratory time (lower plot). A series of splayed curves of the type found in Figure (upper plot) will result in exhalation time varying with lung volume. Thus stimulus strength must also be influenced by lung volume. For higher volumes a larger amount of current is required to terminate exhalation at any specific time. (Adapted and used with permission from Younes and Remmers, 1981.)

5 238 through opening and closing of a tracheostomy tube, result in rapid and continuous changes in generated muscle pressure. Expiratory flow rate thus appears to have a regulated level. Hypercapnia seems to decrease expiratory braking. Control Signals. Most models to be considered later use as the controlled variable a level of some chemical component such as arterial or venous pco 2.Yamamoto (1960) has suggested, however, that the magnitude of oscillations of pco 2 throughout the respiratory cycle may be involved in respiratory control. We have seen that there are discernible oscillations in blood gas levels during respiration (Section 4.2.2) and that peripheral chemoreceptor outputs follow these oscillations (Section 4.3.1). We have also noted that cardiovascular control is influenced by pulse pressure (Section 3.3.1). It would therefore not be surprising if respiratory-produced blood gas fluctuations had a role in respiratory regulation. Because this fluctuation would dampen more severely by mixing as distance from the pulmonary circulation increases, it is suggested that it is detected by peripheral chemoreceptors (Jacquez, 1979). Some authors have suggested that, instead of the excursion of the oscillation, the meaningful input is the derivative, or rate of change, of arterial pco Effector Organs Many actions are associated with respiration, and there are interfaces between things internal to the body and external, between cardiovascular and respiratory systems, and between various and often contradictory functions such as swallowing, smelling, and breathing. It is no wonder, then, that respiratory regulation is so complex and deals with so many effector organs. Respiratory Muscles. The most obvious effector organs are the respiratory muscles, consisting of the diaphragm and external intercostals for inspiration and the abdominals and internal intercostals for expiration. These muscles are responsible for causing the rhythmic mechanical movement of air. Respiratory function of these muscles is superimposed on their functioning to maintain correct posture of the thoracic cage. Respiratory muscles, like all other skeletal muscles, react by contraction to a neural input discharge. In general, the force of contraction varies with degree of neural input (both firing rate and number of fibers firing). However, the degree of reaction varies with geometrical configuration of the muscles. There is a length tension relationship, whereby force generated by the contracting muscle is directly related to its length: the longer the respiratory muscle, the greater the force that can be produced (see Section 5.2.5). Thus the smaller the thoracic volume, the more vigorous is the inspiratory drive. There is also a force velocity relationship, whereby contractile force is maximum when the velocity of shortening of the muscle is zero (see Section 5.2.5). At any given lung volume the generated inspiratory pressure is greatest for the lowest inspiratory flow rate. It is clear, then, that inspiratory and expiratory muscle pressures are not simple translations of neural output. Inspiratory muscles, which actively pull against the force of expiration, and expiratory muscles, which pull against inspiration, help to stabilize respiratory control and can be important in expiratory braking. It frequently happens during respiration that muscles are pulled by other muscles against their developed forces. When a muscle length is increasing while it is actively developing a force tending to shorten itself, the muscle is said to be developing negative work (see Section 5.2.5). All of the energy expended by a muscle undergoing negative work becomes heat. Airway Muscles. Airway muscles must be coordinated in their actions with the major respiratory muscles in order to perform the actions of swallowing, sneezing, coughing, and smelling. The muscles of the pharynx are used to prevent the passage of food and gastric materials into the lungs (Comroe, 1965). When specific chemical irritants pass below the larynx, there is a pulmonary chemoreflex consisting of apnea, bradycardia, and hypotension

6 239 often followed by a cough (Comroe, 1965). Bronchoconstriction also occurs in response to chemical irritants such as sulfur dioxide (SO 2 ), ammonia (NH 3 ), high levels of carbon dioxide (CO 2 ), inert dusts, and smokes. The degree of response adapts rapidly to repeated stimuli and becomes weaker with age (Comroe, 1965). Smoking a cigarette induces an immediate twofold to threefold increase in airway resistance which lasts from 10 to 30 minutes (Comroe, 1965). Local Effectors. Many other local effector organs are used to deal with specific respiratory problems and operate within the overall context of respiratory control and coordination. We have already mentioned the reflex control of ventilation and perfusion in local areas of the lung (see Section 4.2.2). There is also a local control of mucus secretion and movement of cilia to remove dust particles from the lower reaches of the lung and move them toward the throat, where they can be swallowed Exercise Although a great deal of research has been performed investigating the nature of ventilatory responses to exercise, at this time there is no final explanation for experimental observations. This is not due to a lack of ingenious or elegant experiments; enough of these appear to have been performed to possibly elucidate respiratory controller details [see especially the results of Kao (1963) and Casaburi et al. (1977)]. Rather, the difficulty appears to lie in the complex nature of respiratory control and the multitude of possible inputs and outputs. Because of these, details of respiratory responses are difficult to reproduce, and there appear to be significant influences of the degree of sophistication of the subjects, prior work history, ages of the subjects, and individual variation (Briscoe and DuBois, 1958; Whipp, 1981). Responses to be described in this section are, therefore, to be considered to be responses of normal, healthy, young adult males, with cautious application to any one particular individual. Application of these ideas to young females can probably be made without much reservation -fine details may vary-and application to older adults must take into account changes of mechanical properties and responsiveness that occur with age (Berger et al., 1977). A schematic representation of the ventilatory response with time during exercise appears Figure Schematic representation of the ventilatory response to exercise. The immediate rise is probably due to muscular stimulation, and the plateau value will depend on the level of exercise. When exercise stops, the immediate fall probably indicates that the muscles have ceased moving. Residual carbon dioxide production keeps ventilation above resting levels at least until the oxygen debt is repaid. 67 To be sure that the upper airway cilia are not overwhelmed by the larger amounts of mucus received from the lower airways, upper airway cilia beat (move repetitively) at a higher frequency than lower airway cilia (Iravani and Melville, 1976).

7 240 in Figure Immediately after the onset of exercise there is a sudden rise of minute volume, followed by a slower rise to some steady-state value. When exercise ceases, there is an abrupt fall in minute volume, followed by a recovery period. Initial Rise. The immediate rise is thought by most researchers to be neurogenic (Tobin et al., 1986), possibly arising from the exercising muscles themselves (Adams et al., 1984) and possibly involving the rapid transient increase in blood flow (Weiler Ravell et al., 1983). There are several reasons for this view: first, the response occurs too abruptly to allow for the carriage of metabolites from exercising muscles to known chemoreceptor sites; and, second, passive stimulation of the muscles will also induce hyperpnea. There is typically no change seen in end-tidal CO 2 (and, by inference, no change in arterial pco 2 or ph) or respiratory exchange ratio (R) at the onset of exercise. Yet there is a sudden and significant rise in ventilation, the magnitude of which has been found to sometimes, but not always, depend on the severity of exercise (Miyamoto et al., 1981; Whipp, 1981). Passive limb movement (limbs moved by other than the muscles of the person himself) will also result in this immediate ventilatory response (Jacquez, 1979). There has been no convincing confirmation of the muscular sensors or neural pathways that induce this immediate rise. Also, for work increments imposed on prior work, no additional abrupt change is observed; that is, the sudden hyperpnea occurs only upon the transition from rest to exercise despite the fact that, when it occurs, its magnitude appears to vary with exercise level. Also, this immediate hyperpnea can be abolished by prior hyperventilation (Whipp, 1981). Nevertheless, it is generally conceded that muscular movement induces an immediate exercise hyperpnea that remains constant for seconds after the onset of exercise. 68 Sudden cessation of exercise is accompanied by a similar abrupt fall in ventilation. Transient Increase. Following the first phase of exercise response, there is an exponential increase in ventilation toward a new, higher level, which occurs with a time constant of sec (Whipp, 1981). There is a very similar time constant for carbon dioxide production, as measured at the mouth. The time constant for oxygen uptake, however, is only about 45 sec (Whipp, 1981). Thus there appears to be a much higher correlation between V D and VD E V D O 2 and VD E. This implies the importance of carbon dioxide in respiratory than between control. Whipp (1981) notes, however, that CO 2 V D CO 2 as measured at the mouth, differs considerably from V D CO 2 as produced by the muscles. There is a large capacity for CO 2 storage in the muscles and blood. 69 Thus the high correlation between VD E and V D CO 2 involves CO 2 delivery to the lungs and not CO 2 production by exercising muscles. Carotid body function is essential for this close association to take place. Figure shows measured responses to sinusoidally varying exercise level in a healthy subject. Minute volume, oxygen uptake, carbon dioxide production, and end-tidal CO 2 partial pressure (and pco 2 ) all show sinusoidal variations. Minute volume is highest when arterial pco 2 is the highest, but the ratio between VD E and V D CO 2 does not remain constant and can be seen to decrease when VD E increases. The reason for this is that V E is not zero when V CO 2 is zero; thus the effect of the initial constant value for VD E is made smaller as increases. Whipp (1981) unequivocally states that the transient increase in ventilation appears to have a first-order linear response. That is, the increase in minute volume obeys the characteristic differential equation dvc E τ VC E = 0 (4.3.5) d( t t ) d 68 See Saunders (1980) for an alternative explanation of the immediate ventilatory rise based on the time rate of change of CO 2 at the carotid bodies. An increase in heart rate at the beginning of exercise changes this rate of rise almost immediately. 69 There is very little oxygen storage capacity compared to oxygen needs. VD E

8 241 Figure Average responses to sinusoidal exercise in a healthy subject. Phase lags are evident. Those responses with no phase lag are assumed to be directly related to the exercise stimulus. (Adapted and used with permission from Whipp, 1981.) where τ = time constant of the response, sec t d = delay time, sec The value for τ, as mentioned before, is about sec. The solution to Equation will be found from both complementary and particular solutions. For instance, if, at the beginning of time, a step change in work rate is incurred, the solution to Equation is VD ( )(1 ( t td )/ τ E = VD E VD E e ) (4.3.6) o where V D E = steady-state minute volume after the step change, m 3 /sec V D E o = steady-state minute volume before the step change, m 3 /sec Jacquez (1979) cites evidence that the transient response to increasing concentrations of CO 2 in the inspired breath does not appear to come from a linear system (Figure ). As the magnitude of the steady-state response increases, so does the time constant (Table 4.3.1). Steady State. If the work rate performed is not too high (less than the anaerobic threshold), a steady state is finally reached wherein minute volume does not change appreciably. Relationships between respiratory ventilation and percentage of inhaled CO 2, percentage of 70 Whippet al. (1982) state that this equation can also be used for caffeine slows the response. V D and V O D. Powers et al.( 1985) give evidence that 2 CO 2

9 242 Figure The response of one individual to different percentages of inhaled carbon dioxide. As the steady-state response increases, so does the apparent time constant. (Adapted and used with permission from Padget, 1927.) TABLE Approximate Time Constant Values Taken from the Curves of Figure Percent Final V D E, Time Constant, CO 2 m 3 /sec (L/min) sec x 10-4 (26.3) x 10-4 (22.2) x 10-4 (16.6) x 10-4 (12.8) 50 Initial V D E, = 1.25 x 10-4 (7.50 L/min) inhaled O 2, and blood ph are seen in Figure Since normal percentages of carbon dioxide in the exhaled breath are % (Tables and 4.2.8), the large increase in minute volume with carbon dioxide increase occurs at percentages very close to normal values. On the other hand, the range of percentage of oxygen in the exhaled and inhaled air is 15 21%, but minute volume does not begin to respond to oxygen lack until the 6 8% level. Therefore, carbon dioxide appears to be a much more potent stimulus for respiratory adjustments than is oxygen. One reason for this may be the dramatically adverse psychophysiological effects of increased atmospheric carbon dioxide content (Figure 4.3,2). As little as 2 4% can cause measurable changes in perception, and 20 30% CO 2 in the inhaled gas can cause coma (Jacquez, 1979). Oxygen concentration of inhaled air would have to be reduced to 10% or less for any noticeable effect, and normally the only feeling that is described is one of euphoria. Opinion on the driving input for ventilatory response has been divided for a number of years. Jacquez (1979) summarized experimental data which relate minute volume to alveolar

10 243 Figure The responses of healthy men to increasing inhaled carbon dioxide levels, decreasing blood ph levels, and decreasing oxygen levels. The response to carbon dioxide is linear over a wide range beyond the threshold value of 3.5%. Above 10% CO 2 the respiratory system can no longer compensate by increased ventilation. Responses to ph and O 2 are, in general, smaller and nonlinear. (Adapted and used with permission from Comroe, 1965.) partial pressure of carbon dioxide (arterial pco 2 is strongly related). Whipp (1981) maintains, however, that the true driving input is carbon dioxide evolution at the lungs, not arterial pco 2. We will return to Whipp's formulation after a while. Both authors agree that there is a linear relationship between V D E and either arterial pco 2 or V D CO 2 for the normal control range above some threshold value and below an upper extreme. To be clearer about this, we note that slope of the response graph relating V D E to some measure of carbon dioxide production is linear, but the value of the ratio between V D E and the carbon dioxide measure diminishes because of the initial value for V D E. Figures and show this linear relationship between alveolar partial pressure of CO 2 and minute volume. Above a threshold value called the "dog-leg," or "hockey-stick," portion, ventilation is seen to be a linear function of arterial pco The family of curves results from different values of arterial po 2. Since the slopes of these curves change, the interaction between carbon dioxide and oxygen appears to be multiplicative. Within a small amount of error, all curves above the dog-leg intersect the abscissa at a common point. Jacquez (1979) presents the form for carbon dioxide control of ventilation above the dog-leg as V E = κ(p A CO 2 β) 1 α γ p A O 2 (4.3.7) wherev E = minute volume, m 3 /sec p A CO 2 = alveolar partial pressure of carbon dioxide, N/m 2 p A O 2 = alveolar partial pressure of oxygen N/m 2 α,β,γ,κ = constants which vary between individuals, α,β,γ, N/m 2 ; κ, m 5 /(N sec) 71 Cunningham (1974) reports that in the hypoxia of exercise the E V D vs. pco 2 curves are displaced greatly to the left and upward, may no longer be linear, may have slopes less than those of the curves at rest, and show no sign of a dog-leg.

11 244 Figure Ventilatory responses to alveolar levels of carbon dioxide for four levels of alveolar oxygen. In this plot is shown the abrupt change in sensitivity that occurs at some threshold value called the dog-leg. (Adapted and used with permission from Nielsen and Smith, 1952.) Changes in blood ph also affect minute ventilation, and, because of the relation between pco 2 and ph (Equation 3.2.3), ph effects are difficult to separate from CO 2 effects. Somewhat slower transient response of ventilation to ph compared to pco 2 indicates that ph effects are not identical to pco 2 effects (Jacquez, 1979). This is not surprising in view of the chemoreceptor mechanisms discussed earlier (Section 4.3.1). If a steady-state response is reached, Cunningham et al. (1961) showed that the ventilatory response to pco 2 in ammonium chloride acidosis is shifted toward increased alveolar pco 2 with no significant change in slope. In metabolic acidosis, 72 they concluded, there is only a minor change in the parameters α, κ, γ in Equation but the parameter β 72 Metabolic acidosis occurs whenever blood ph is lowered by natural metabolic or pathogenic means. Inhaling air enriched in CO 2 produces metabolic acidosis; blood bicarbonate movement to replace chloride lost in vomiting produces metabolic acidosis; metabolizing large quantities of protein containing sulfur (metabolized into sulfuric acid) produces metabolic acidosis; excessive ketone production during lipolysis and fatty acid liberation in diabetes can produce metabolic acidosis: incomplete oxidation of glycogen into lactic acid causes metabolic acidosis.

12 245 Figure Ventilatory responses to alveolar levels of carbon dioxide for six levels of alveolar oxygen partial pressures in N/m 2 (mm Hg). All curves intersect roughly at the same point. Note also the highly nonlinear interaction between CO 2 and O 2. (Adapted and used with permission from Comroe, 1965.) changes significantly. Data by Cunningham et al. (1961) show β = β 0 β 1 c (4.3.8) HCO 3 where β = parameter in Equation 4.3.5, N/m 2 β 0 = intercept of β sensitivity, N/m 2 β 1 = sensitivity of β to bicarbonate concentration changes, N m/kg c = bicarbonate concentration, 73 kg/m 3 HCO 3 Average values for β 0 and β 1 for five subjects are 2400 N/m 2 and 1.75 N m/kg, respectively. The term (p A CO 2 β) in Equation now becomes (p A CO 2 β 0 β 1 c ); in this sense 3 HCO the effects of CO 2 and ph are additive (Jacquez, 1979). One main difficulty with Equation is that it does not predict the ventilatory response to exercise (Jacquez, 1979). In fact, the response to increased carbon dioxide in the blood caused as a result of metabolism is an almost imperceptible change in arterial pco 2 but a large 73 Plasma and urine concentrations are frequently expressed in terms of milligrams percent (mg of the species/100ml solution) or milliequivalents per liter (millimoles of the species times electrical charge/volume of solution in liters). The value for β 1 was originally expressed as 0.8 mm Hg L/meq.

13 246 Figure The ventilatory response to carbon dioxide depends on its source. Inhaled CO 2 causes an increase in ventilation with a concomitant increases in arterial partial pressure of CO 2. Metabolic CO 2 produced within the working muscles results in an isocapnic increase of ventilation. The difference between these two sources of CO 2 may be due to the remoteness of the CO 2 respiratory sensor. increase in ventilation. The response to inhaled carbon dioxide is a much larger change in arterial pco 2 and a smaller increase in ventilation (Figure ). Swanson (1979) gives a possible controller equation for ventilation as V e = K 1 p a CO 2 K 2 CO2 V K 2 (4.3.9) wherev CO 2 = the rate of carbon dioxide production, m 3 /sec p a CO 2 = arterial partial pressure of carbon dioxide, N/m 2 K 1, K 2, K 3 = coefficients, m 5 /(N sec), unitless, and m 3 /sec, respectively The first term related to arterial pco 2 is a feedback term, which indicates to the system that ideal levels have not been maintained and that ventilation must be increased proportionately to the error which appears in p a CO 2. The second term is a feedforward term which indicates to the system that a ventilatory adjustment must be made to anticipate future changes in p a CO 2 (see also Section for further discussion of feedback and feedforward control applied to stepping motion). The K 2 coefficient must be very much larger than K 1 if the situation illustrated in Figure is to hold true. During exercise, there are both an increased level of metabolic CO 2 and an increased level of inhaled CO 2 due to respiratory dead volume. Below the dog-leg, carbon dioxide sensitivity is drastically reduced. The reason for this is not now known, but several hypotheses have been offered (Jacquez, 1979). One possibility involves the estimate that 80% of the CO 2 response results from central receptors and the remaining 20% from peripheral receptors. It may be that below the dog-leg, central receptors are not contributing to CO 2 response. Anot6r possibility is that the low arterial pco 2 below the dog-leg causes constriction of the cerebral blood vessels so that local cerebral pco 2 depends on local CO 2 production and not on arterial pco 2. Similarly, the interaction between hypercapnia and hypoxia illustrated in Figure has been postulated to arise in peripheral chemoreceptors (Cunningham, 1974). Outputs from these receptors then sum with outputs from central receptors in the final determination of

14 247 minute volume. Lloyd's (Cunningham, 1974) formulation of this activity takes the form V D E a = γ 0 γ H log(h a / H ( p O γ ) A 2 a0 ) (4.3.10a) where If H a < V D E a = minute volume contribution due to arterial chemoreceptors, m 3 /sec λ 0 = hypoxia threshold, m 5 sec/n λ H = hypoxia sensitivity, m 5 sec/n γ = constant, N/m 2 (see Equation 4.3.7) H a = arterial hydrogen ion concentration, kg/ m 3 H a0 = arterial threshold hydrogen ion concentration, kg/ m 3 H a0, then V D E a = λ0 ( p A O2 γ ) (4.3.10b) The use of hydrogen ion concentration rather than carbon dioxide partial pressure merely indicates the normally close relationship between them. This use treats these receptors as the same whether or not they respond separately to arterial pco 2 or H. Response to central (brain) receptors is given by where If H c < V D E c c 0 = µ 0 µ v log( H / H c ) (4.3.11a) V D E c = intracranial receptor contribution to minute volume, m 3 /sec µ 0 = central receptor response independent of H, m 3 /sec µ v = central receptor sensitivity to H, m 3 /sec H c = central hydrogen ion concentration, kg/m 3 H c = central threshold hydrogen ion concentration, kg/m 3 0 H c 0, then V D E c = µ 0 (4.3.11b) Total minute ventilation is the sum of V D E a V D E c : V D E = V D E a V D E c (4.3.12) Whipp (1981) argues strongly for considering minute ventilation to be related to carbon dioxide production 74 rather than to arterial pco 2. Any change in arterial pco 2 "is a consequence of the ventilatory change, not the cause of it." Mean arterial pco 2 and H during moderate exercise are typically unchanged from control values; therefore, there must be a different control mechanism in this instance compared to CO 2 inhalation studies where arterial pco 2 and H increase (Whipp, 1981). Most investigators have indicated that arterial pco 2 does not change during exercise from its normal value of 5.33 kn/m 2 (40 mm Hg; Comroe, 1965). Berger et al. (1977), however, report on a study that shows small but measurable increases in pco 2 accompanied 74 Whipp (1981) reviews evidence that the type of metabolized food is important in determining ventilation. When fats are metabolized, with a respiratory exchange ratio of 0.7, about 7 molecules of CO 2 are produced for every 10 molecules of O 2 utilized. When carbohydrates are used, R = 1.0, and 10 molecules of CO 2 are produced for each 10 molecules of O 2 utilized. The CO 2 output is considerably higher for a given metabolic load when carbohydrates are the predominant fuel source. It has been demonstrated that minute volume is proportionately higher for larger proportions of carbohydrate metabolized.

15 248 by increased oxygen uptake. Martin et al. (1978) and Filley et al. (1978) suggest an increased sensitivity to pco 2 during exercise. Mahler (1979) presents the view that muscular exercise and other neural influences shift the intercept of the CO 2 response curve without shifting the slope. Therefore, the basic control of ventilation during exercise is through these shifts in CO 2 sensitivity. Response to severe oxygen lack is difficult to elicit from humans without changes in ventilation, which, in turn, decrease arterial partial pressure of carbon dioxide. When care is taken to assure constant arterial pco 2, curves similar to those in Figure result. For constant alveolar pco 2, the ventilatory response is nonlinear and shows the multiplicative interaction discussed earlier. When plotted against arterial hemoglobin saturation percentage, minute ventilation response curves become linear (Figure ). Oxygen sensitivity is wholly a result of peripheral chemoreceptors. From the instant a subject is given a breath of pure oxygen, a decrease in ventilation is seen after a short delay of about 5 sec ( sec for different individuals, longer delays for older subjects; Jacquez, 1979). This is equivalent to respiratory cycles and is the appropriate amount of time for the circulating blood to reach the peripheral chemoreceptors. Maximum response occurs after sec. Hypoxic sensitivity is somewhat more variable than hypercapnic sensitivity in normal subjects (Berger et al., 1974). The change in respiratory minute volume can be expressed as (Cunningham, 1974) V D E = α V D E (4.3.13) 0 p λ ao 2 Figure Steady-state ventilatory response to alveolar oxygen partial pressure for three fixed levels of alveolar carbon dioxide partial pressure given in N/m 2 (mm Hg). The oxygen ventilatory response is nonlinear and interrelated to carbon dioxide response. (Adapted and used with permission from Lloyd and Cunningham, 1963.)

16 249 Figure Steady-state ventilatory response to arterial oxygen saturation of hemoglobin. For each of the three different levels of alveolar carbon dioxide partial pressure, the oxygen ventilation response is linear. (Adapted and used with permission from Rebuck and Woodley, 1975.) where V D E o = minute volume in response to a very high p a O 2, m 3 /sec p a O 2 = arterial partial pressure of oxygen, N/m 2 α = constant, N m/sec γ = threshold value, N/m 2 (see Equation 4.3.7) The value for γ is approximately 4.27 kn/m 2 (or 32 mm Hg; Cunningham, 1974) and the value for α has been found to range from to N m/sec ( mm Hg L/min) with an average value of N m/sec (Berger et al., 1974). Martin et al. (1978) found an almost tenfold increase in the value of α between rest and exercise. Although minute volume is not a linear function of oxygen partial pressure, it is often considered to be linearly related to oxygen uptake below the anaerobic threshold (Figure ). Arterial pco 2 is not maintained at set levels during these exercise tests. Other inputs have been found to influence the steady-state level of ventilation. Ammonia has been found to produce hyperventilation, and significant amounts of ammonia are found in the blood during exercise and some pathological states (Jacquez, 1979). Body temperature, which increases during exercise, is known to affect ventilation mainly through an increase in sensitivity to alveolar pco 2 (Jacquez, 1979; Whipp, 1981). This increased sensitivity appears as an increase in parameter κ in Equation Emotion and stress can induce hyperpnea. Increased catecholamine concentrations, which often accompany high levels of emotion, have been shown to increase ventilation by increasing hypoxic sensitivity. In Equation 4.3.7, the effect is seen mainly in a change in parameter α (Whipp, 1981). Sleep, high blood pressure, anesthetics, and some drugs decrease ventilation levels (Jacquez, 1979; Whipp, 1981). Other drugs, such as aspirin, increase CO 2 sensitivity and thus increase ventilation (Jacquez, 1979). Acclimatization can modify ventilatory responses to CO 2, O 2, and ph. Figure

17 250 Figure Average ventilatory response of three subjects to inhalation of carbon dioxide as they acclimatize to 3800 m altitude. As with many bodily functions, response to change is greatest immediately after the imposition of the change, and the response slows with time. (Adapted and used with permission from Severinghaus et al., 1963). presents carbon dioxide sensitivity curves as they change over the course of eight days at 3800 m altitude (hypoxic conditions). It is also known that patients with chronic obstructive pulmonary disease (COPD) usually exhibit abnormally low carbon dioxide sensitivities (Anthonisen and Cherniack, 1981), but there is a question whether existing low CO 2 sensitivity predisposes humans to suffer from COPD (Forster and Dempsey, 1981). Age appears to decrease CO 2 sensitivity (Altose et al., 1977) and the practice of yoga breathing exercise has also been found to reduce CO 2 sensitivity (Stǎnescu et al., 1981). Cessation of Exercise. When exercise ceases, there is often an immediate fall in minute ventilation (Figure ), although this may be masked by a long, gradual decline. Ventilation rates remain elevated because carbon dioxide and lactate are not removed immediately from the blood (see Section 1.3.3). For subjects recovering from maximal exercise (90 100% V D O 2 max ), breathing is typically more rapid and shallow than for lower exercise rates. Younes and Burks (1985) attribute this to pulmonary interstitial edema (fluid in the lung tissue) occurring only at very severe exercise rates, but Martin et al. (1979) assert that the rise in rectal temperature associated with exercise reduces tidal volume compared to its value without heating. Anaerobic Ventilation. During very heavy exercise there is an additional respiratory drive caused by increased blood lactate (see Section 1.3.5). 75 Incomplete oxidation of glucose results in lactic acid, which then produces increased arterial pco 2 through the buffering reaction: H La Na HCO 3 Na La H 2 CO 3 Na La CO 2 H 2 O (4.3.14) where La = lactate anion = CH 3 CHOH COO Bicarbonate levels are reduced and carbon dioxide production is increased beyond that 75 Cunningham (1974) reports negligible steady-state changes in blood lactate at work intensities below 60 75% of aerobic capacity (60 75% of V D O 2 max ), but lactate concentration increases more than tenfold in severe exercise. In mild exercise, blood lactate concentrations increase transiently and reach a significant peak 5 10 min after the start.

18 251 Figure Pulmonary ventilation for various levels of oxygen consumption during rest and exercise. There is a linear portion until the aerobic threshold is reached. Four individual curves show the scatter to be expected between individuals. (Adapted and used with permission from Astrand and Rodahl, 1970.) predicted by the respiratory quotient (see Section 3.2.2). 76 During this phase, the respiratory exchange ratio will exceed the respiratory quotient. There is a narrow range of work rates over which nearly complete ventilatory compensation can be made for the increased levels of CO 2 produced (Figure ). The relationship between oxygen uptake and work rate will still appear to be linear, but the relationship between minute volume and oxygen uptake will become nonlinear in this region. If a steady state can be reached, end-tidal pco 2, decreases, but the blood ph level appears to be regulated at its previous normal value. At even higher work rates (see Section 1.3.5), ventilation increases ever more rapidly, arterial pco 2 falls even more, and blood ph declines (Whipp, 1981). This condition cannot be maintained. Kinetics of this process are very poorly understood. Aside from the practical problems of pushing test subjects to their limits to obtain meaningful data, many aspects of the problem cannot be easily measured. With a reduction in arterial pco 2, one would expect, on the basis of information in Figure , that a decrease in ventilation would result. Instead, minute volume appears to be related to the rate of CO 2 evolution. In addition, the blood-brain barrier is much more permeable to CO 2 relative to H and HCO 3 -. Therefore, while the peripheral chemoreceptors are reacting to increased blood H (metabolic acidosis) and carbon dioxide production, the cerebrospinal fluid (and thus fluid surrounding the central chemoreceptors) becomes alkaline. These conditions are sure to produce conflicting regulatory tendencies. 76 Approximately 4 x 10-7 m 3 (400 ml) of CO 2 is produced as a result of a decrease of 61 g/m 3 (1 meq/l) of HCO - 3 in the extracellular fluid (Whipp, 1981).

19 252 Figure Respiratory measures with progressive work rate. Minute volume increases linearly with work rate up to the anaerobic threshold, when it begins increasing disproportionately. Tidal volume can be seen to reach a limit after the anaerobic threshold, but respiration rate increases greatly. (Adapted and used with permission from Martin and Weil, 1979.) If work rate increases at a rate too high for equilibrium to be established, blood ph no longer appears to be regulated but instead falls (Whipp, 1981). Respiration is much less efficient, and the respiratory muscles begin to require much more oxygen to perform the work of breathing than they require below the anaerobic threshold. It has been reported that at a ventilation rate of m 3 /sec (140 L/min) a small increase in ventilation requires an increment of oxygen utilization greater than that which can be provided by the increase in ventilation (Abbrecht, 1973). Figure illustrates another interesting facet: below the anaerobic threshold, increased minute volume comes as a result mainly of tidal volume increase; above the anaerobic threshold, tidal volume remains nearly constant, and the increase of minute volume is supplied by an increase in respiration rate. Ventilatory Loading. It has been stated, and commonly assumed, that exercise performance is not limited by respiration in healthy subjects (Astrand and Rodahl, 1970). The same cannot be said for humans suffering the effects of respiratory disease, or those who are wearing