The physiological control of respiration.

Molec. Aspects Meal. Vol. 13, pp. 445-567, 1992 Printed in Great Britain. All rights reserved.

0098 - 2997/92 $15.00 © 1993 Pergamon Press Ltd

THE PHYSIOLOGICAL CONTROL OF RESPIRATION Christopher B. Wolff*

Department of Physiology, King's College London, Campden Hill Road, Kensington, London W8 7AH, U. K.

Contents

CHAPTER 1 Introduction

447

CHAPTER 2 Ventilation

453

CHAPTER 3 Respiratory Pco2 Oscillations

463

CHAPTER 4 Respiratory Chemoreceptors

473

CHAPTER 5 Drives to Breathe

486

CHAPTER 6 Control Theory and Respiratory Models

504

CHAPTER 7 Long Term Respiratory Control--Chronic Hypoxia

517

CHAPTER 8 Long Term Respiratory Control--Metabolic Acidosis

529

CHAPTER 9 Respiratory Control--Towards an Integrated Theory

539

REFERENCES

546

*Also Consultant Clinical Physiologist, Guy's Hospital, London, U. K. 445

Table 1. Abbreviations

Main symbols V

9 b P F C

Volume Ventilation Flow Pressure, total or partial Fraction Concentration in a liquid e.g.

1

1min- i i min-

ml gas per 100 ml blood

H + [H +]

Gas exchange ratio Hydrogen ion, H " concentration

K+ [K+]

Potassium ion, K + concentration

[HCO3-I

Bicarbonate ion concentration Log I/[H +] o r - l o g (H +] Partial pressure (or tension) of Carbon dioxide (CO2) and Oxygen (02). Cardiac output, or other blood flow indicated by suffix

R

pH Pco2 Po2

0

'

mm Hg or kPa

usually nM (nano-mol) mmol or mM (milli-mol) mM pH units mm Hg or kPa 1min- i

Modifiers E A et a v, V Cv CSF CECF

Inspiratory Expiratory, Less commonly, I Alveolar Change in a quantity End-tidal Arterial venous, mixed venous (whole body) Cerebral venous Cerebrospinal fluid, Cerebral extracellular fluid

Combinations

fE

Expired ventilation (often 'ventilation') 1 min-l Alveolar ventilation 1 rain-1 CO2 production rate 1 rainVco2 Oxygen consumption rate 1 minVo, ACO 2 content, (venous - arterial) ml CO2/100 ml (dl) blood ACco2 Ratio of shunt to total blood flow through the lung QJQT mm Hg or kPa Paco2' Pao2' Petco:' Pvco_,, PPCO2, PACO2, PAO2 pH units pHcs v, PHcEcF etc.

W.A

FACO2, FAO2, Fxco: etc. mm Hg or kPa

PCECF.COz, PCSF,COzPcvco,_ HCO3-cs v etc.

mM

446

Chapter 1

Introduction

This review is concerned with understanding the physiological control of respiration, in particular with regard to the role of chemical control mechanisms. Apart from a general description of the functional properties of the components of the system and of the chemical control of respiration (macroscopic, rather than cellular), attention is drawn to ways in which knowledge of normal control and disease processes, at times, interact favourably. Knowledge of normal chemical values is constantly used diagnostically in medicine to expose disease abnormalities. On the other hand disease processes have sometimes been useful in revealing aspects of normal function. Such information may be obtained from disease states where ordinary laboratory experimentation is not possible. Finding out about normal function from disease, in this manner, has improved knowledge of the physiological control of respiration on several occasions. Examples found in the last three chapters concern chronic hypoxia and metabolic acidosis and the question as to whether their effects interact. The purpose of this chapter is to introduce respiratory control, mention being made of relevant chapters along the way. The first two sections deal with important paradoxes, concerning firstly respiratory sensitivity to oxygen and carbon dioxide (CO2) and secondly exercise and constant CO 2 tension/partial pressure (Pco2). During discussion of the second paradox mention is made of Chapters 2, 3, 5 and 6 (concerning, respectively, ventilation, respiratory oscillations, drives to breathe and control). The next section concerns the discovery and properties of the two main types of respiratory chemoreceptors (Chapter 4), essential as detectors of chemical respiratory control signals. Peripheral arterial chemoreceptors respond fast enough to detect respiratory oscillations in arterial Pco_,- Respiratory oscillations are the subject of the next section. After this is a section (concerning Chapters 7 and 8) on long term responses to hypoxia and metabolic acidosis where central chemoreceptors come into play. There is then a brief section in the last chapter of the review (Chapter 9) on long and short term respiratory control. Finally, it should be mentioned that basic aspects of ventilation are the subject matter of Chapter 2.

Absent or Slight Ventilatory Sensitivity to Low Oxygen Tension (Hypoxia) but High Sensitivity to Carbon Dioxide (C02) Oxygen is crucial to tissue respiration. "The body supplies the tissues with practically all the oxygen they require immediately it is wanted and to a degree which is proportional to 447

448

C.B. Wolff

the level of activity" (Wright, 1952). Carbon dioxide, generated simultaneously by tissue respiration, has to be transported from the tissues to the lungs for elimination. Oxygen is supplied via the lungs and arterial blood stream and this requires that ventilation should change in proportion to the changes in oxygen requirement. One might therefore expect that lowering of the oxygen concentration in the inspired 'air' would be met with increased ventilation and yet, with modest reduction in the inspired oxygen concentration, there is n o increase in ventilation (at least in the short term). Even with fairly severe h.ypoxia ventilatory increases are modest (unless CO, is added to the inspirate). Carbon dioxide (CO2) appears to be much more important in its effect on breathing than does oxygen. There is a vastly greater effect (increase in breathing) caused by adding CO 2 to the inspirate. This was realized over 100 years ago by Miescher-Rusch (1885). He wrote "carbonic acid spreads out its protecting wings over the oxygen needs of the body" (English translation from German).

High CO 2 Sensitivity yet no Pco= Rise in Exercise A natural tendency (which, fallaciously, has seemed at times to be supported by measurement) has been to assume that the CO 2 tension in alveolar gas (PAco2) and arterial blood (P~co:) will increase in exercise and provide the required increased stimulus to breathe. Although this appeared to be the case earlier this century it has since been proved incorrect. It has been found that Paco2 remains constant or even falls slightly, for example Forster etal. (1986). (At the most severe levels of exercise P~co2 falls considerably.) Rather suprisingly, the conclusion that Paco2 remains constant or even falls slightly in exercise had already been reached over 100 years ago by Geppert and Zuntz (1888) from their studies on dogs. Some of the reasons for this apparent anomaly will be discussed in Chapter 3, where respiratory oscillations in PAco2 and P~co2 are discussed. The most fundamental problem, misleading people into attributing some of the exercise stimulus to a rise in Pco2, results from a rise in Petco2 (end-tidal Pco2) in exercise even though Paco2 is not rising. It means that one cannot use Petco2 as a guide to the Paco2 stimulus level in exercise even though it is much easier to measure. There are formulae available to derive a probable Paco2 value from Petco2 (Jones et al., 1979) though this is not nearly as accurate as measured P~co2. It is now possible to obtain a reliable guide to Paco2 by drawing venous blood from the dorsum of the hand which has been 'arterialized'. Arterialization is undertaken by heating the hand and forearm to 43°C for 10-15 rain prior to withdrawal of blood samples (McLoughlin et al., 1992). Ventilatory sensitivity to increases in PACO2 and Paco:at rest is about 2 1 min -1 per mm Hg; 14 1 min-t per kPa. This is measured by means of a CO 2 response curve in which the subject is given CO 2 enriched gas mixtures to breathe. We are left with a problem which has yet to be solved satisfactorily. While there are undoubtedly large and appropriate increases in ventilation in exercise there is not an obvious drive from Paco2" The sensitivity shown by means of CO 2 response curves cannot operate for CO 2 to drive breathing because Pac02 does not increase. There are some papers showing increases but overall the story is of no increase. Paco,_ is kept remarkably constant, especially where the metabolic rate is increased (see later for references). Pac02 and PAC02 are

The Physiological Control of Respiration

449

also remarkably constant in the longer term at rest (Cunningham et al., 1986; Fitzgerald and Haldane, 1905). The decrease in Paco2 in heavy exercise is thought to result from metabolic acidosis, where tissue oxygenation can no longer keep pace adequately with tissue metabolism and lactic acid is a by-product of anaerobic metabolism. There is now some discussion as to whether increases in arterial potassium ion (Ka +) which occur in exercise contribute to the excess ventilation which lowers P~co: in heavy exercise. This will be discussed further in Chapter 5 (drives to breathe). It is apparent that the mean level of PaCO,. cannot be a major drive to breathing in exercise. However, other respiratory drives to breathe are discussed in Chapter 5. Several of these drives appear to be able to support adequate ventilation in exercise on their own. They would therefore, if anything, overdo the intensity of ventilation in exercise as they normally act together, so that the PACO2(and Paco2) would be low if their effects were simply additive. It is therefore important to consider a somewhat more sophisticated system as the putative mechanism. In order to get the right, constant, PACO2and Paco2 value the increase in ventilation has to be precisely related to the increase in metabolic rate. The physical requirement for alveolar ventilation (IkA, less than total ventilation) to change with the metabolic rate (specifically CO 2 production rate--l/CO2) is discussed in Chapter 2 and embodied in the equation given here, Pc02 = PB. 17c02/I2A(Pc02 = PACO2 or Pac02),

(1)

where PB is barometric pressure and Paco2 is the mean value over the respiratory cycle (see later). For Pco2 to remain constant alveolar ventilation must increase or decrease precisely in proportion to the increases and decreases of metabolic rate. This is achieved by the respiratory control system. Our problem is to understand how it is done. Constancy of Pco2, like constancy of other aspects of the internal environment, is very important. It means that the cells are independent of the external environment. Keeping the internal environment constant in the face of changes in the external environment requires the operation of very sophisticated (in human terms) control systems. The concept that the processes keeping the internal environmental constant free the animal to live in a wide range of external environments, originated with Claude Bernard (Bernard, 1878) and was developed by Cannon (1932) who coined the term 'homeostasis'. Homeostasis was used to mean "all the processes concerned in controlling the physical and chemical properties of the internal environment" (Bayliss, 1966). Control systems require 'feedback' where information as to the important variable (the one which is to be kept constant) is fed back to the 'controller' (usually the brain). Control theory will be discussed in Chapter 6 with models of the respiratory, system. Arterial Pco2 oscillates with a respiratory frequency (as will be discussed shortly). A new computer model, incorporating these respiratory Pco2 oscillations has been described at the end of Chapter 6.

450

C.B. Wolff

Peripheral and Central Arterial Chemoreceptors Receptors are a prerequisite for control, acting as detectors for the feedback element. Peripheral and central arterial chemoreceptors are discussed in Chapter 4. Until the peripheral arterial chemoreceptors were discovered shortly before 1930 (De Castro, 1926, 1928; Heymans and Heymans, 1927) it was thought that all respiratory chemical stimulation acted on respiratory centers via the arterial blood stream. De Castro's discovery of the carotid body was of an anatomical structure which he thought from his knowledge of structure/function relationships was likely to "taste the blood'. The discovery of peripheral arterial chemoreceptors, the aortic and carotid bodies, by Heymans and Heymans (1927) appears to have been genuinely independent though this has been disputed. It was made on a functional basis. They experimented on dogs in which the only connections between head and body were neural (the head was independently perfused) and discovered respiratory sensitivity to hypoxia and to increases in PCO2of the trunk. The response consisted of vigorous movements of the alae nasae, normally accompanying vigorous respiration. This demonstrated chemoreceptor function in the trunk. This was a result of stimulation of aortic chemoreceptors. In an extension of one such experiment hypoxic blood was injected into one of the artificially perfused carotid arteries. Much to their suprise vigorous movements of the alae nasae again occurred. This carotid artery chemosensitivity was due to the carotid body. Other aspects of carotid body sensitivity (to metabolic acid, fast CO, change and to potassium ion--K + will also be discussed in Chapter 4. Prior to this the term 'respiratory center' was the name given to a putative site of neural respiratory mechanisms and the site of action of any chemical with respiratory stimulating effects. For about 15 years this terminology remained in place apart from those chemoreceptive functions found to belong to the peripheral arterial chemoreceptors. Then, another site of chemical action, distinct from other neural respiratory mechanisms, was discovered by Leusen during a series of experiments involving the stimulating effects of a variety of substances applied to the surface of the brainstem by a technique known as ventriculo-cisternal perfusion (Leusen, 1950, 1954a,b). This site appears to be deep to the ventro-lateral surface of the brainstem (about 200 Ixm) and specifically sensitive to local acidity, though there is now argument about this specificity (there is probably also some independent sensitivity to Pco2)- This is the central chemoreceptor. The ways in which respiratory stimuli in the blood affect it require clarification, though its well defined ventilatory response to increased PaC02seems clear (but see Chapter 5). The long term effects of hypoxia and metabolic acidosis will be considered shortly, but first let us return to short term changes in respiratory gases, namely, respiratory oscillations in alveolar and arterial Pco,_and Po2"

Respiratory Oscillations During inspiration alveolar Pco2 falls as a result of its dilution with air, whereas during due to the arrival of CO 2 from pulmonary arterial (mixed venous) blood. Since these changes are repeated with every breath, in normal subjects, PAco2 oscillates at respiratory frequency. Similar PA.O, oscillations are generated, with their

expiration PACO2 rises


451

rise during inspiration and fall in expiration. Their changes are therefore opposite in direction to those of PACO:oscillations. Alveolar and arterial Pco: and Po: oscillations are described in Chapter 3 and it is also shown how their slopes can be calculated both for inspiration and expiration. The adequacy, or otherwise, of transport of respiratory oscillations between the lungs and peripheral arteries is also discussed. Chapter 5 (drives to breathe) puts forward the view of Yamamoto, originally proposed in 1960, that Paco,_ oscillations, derived from PAco2 oscillations, are a potential candidate as the main mediator of information about Vco 2 in exercise. At that stage it was not known that there are Paco2 oscillations in the arterial blood. The idea that Paco,_ oscillations may be important in respiratory control is carefully considered in this review. Control theory and models are discussed in Chapter 6 where a new model is described which incorporates P~co2 oscillations.

Chronic Responses to Hypoxia and Metabolic Acidosis To return to long term adjustments, the central chemoreceptors are critically involved in both acclimatization and in adaptation to metabolic acidosis. Chapters 7 and 8 provide descriptions of what can be regarded as chronic sensitivity for hypoxia (Chapter 7) and acidosis (Chapter 8). Sensitivity is expressed in terms of the degree to which Paco,_ is depressed by hypoxia or metabolic acidosis. The sensitivities are therefore the gradients of a Paco2/PaO2relationship and a Paco2/PH relationship. An attempt is made to work out the transition from the acute state to the chronic one for each of these stimuli and is more successful with hypoxia than with acidosis. It is argued that changes in cerebral blood flow are important for hypoxia but not for metabolic acidosis. The reasons for the difficulty, in explaining the transition (from the acute to the chronic state) with acidosis, is due to differences in the reported rates at which Paco2 changes after exposure to metabolic acid and uncertainty, until recently, as to whether arterial H + acted on central or peripheral arterial chemoreceptors.

Long Term and Short Term Respiratory Control Chapter 9 describes two new hypotheses, one concerned with long term changes and the other with short term respiratory control. For long term changes the hypothesis combines the relationships between Paco2 and Pao2 and between Paco2 and pH a from Chapters 7 and 8 and shows that the effects of PaQ and pH a on Paco, are additive. The change in PaCO2 probably represents a change in what is known as 'the set point'. In the area of acute respiratory control (keeping Paco2 constant) the hypothesis is based on the need for a high open loop gain (Chapter 6) in exercise. The idea is that this is provided by oscillations in afferent chemoreceptor discharge frequency and that the way these act gives rise to negative feedback (Chapter 6).

452

C.B. Wolff

Basic Points on Ventilation (Chapter 2) The next chapter outlines basic points on ventilation, which will help in the understanding of later discussions concerning respiratory control. Those sufficiently familiar with these basic points may wish to move on immediately to Chapter 3 which is on respiratory oscillations.

Chapter 2

Ventilation

It is important to examine any differences between alveolar and arterial gas tensions which may occur before analyzing the effects on them of ventilation and metabolic rate. This is because such differences would greatly complicate interpretation of arterial blood gas results measured in vitro in case they differed from in vivo values.

Gas Tensions in the Lung and in Arterial Blood It was realised before the turn of the century that arterial blood chemical changes in oxygen (02) and CO 2 result from changes in alveolar gas partial pressure (PAo2 and PACOz). There were, however, problems which mainly concerned instrumentation, which led Haldane to still believe in 1935 that arterial Po2 (Pao2) was higher than alveolar (PAo2) (Haldane and Priestley, 1935). This was referred to as the oxygen secretion theory because, for it to be true, oxygen had to be moved from alveoli to blood against a tension gradient. Although Haldane quoted that oxygen secretion occurs in fish (Biot, 1807) studies have since condemned the theory. Oxygen movement is reliably assumed to depend on the presence of a diffusion gradient favouring movement from alveoli to pulmonary capillary. Although the diffusibility of oxygen is less than that of CO 2 the tension gradient for oxygen is much higher than it is for CO_,. Equilibrium is reached for both gases well within the pulmonary capillary. This is believed to be the case in normal lungs but it is just possible that there is not always diffusion equilibrium for CO 2 in disease. Doubt as to whether chemical equilibrium for CO 2 was reached in normal lungs (Filley, 1976) was raised prior to the discovery of carbonic anhydrase in the capillary endothelium in 1978--see Klocke (1987). Carbonic anhydrase speeds up the heavily buffered reaction between CO 2 and water inside red cells and yet there is no carbonic anhydrase in the plasma (Maren, 1967; Roughton, 1964). If the endothelial carbonic anhydrase were to be missing in the lungs of patients with respiratory disease there could be an equilibration problem with continuation of the CO2/H20 reaction during the passage of blood from the lungs to the peripheral arteries, The respiratory gases could still be in chemical disequilibrium on arrival at the arterial chemoreceptors. If the time taken to withdraw arterial blood and measure gas tensions were sufficient to allow full chemical equilibration the assessed (measured) values would 453

454

C.B. Wolff

differ from those operative in the patient. However, Klocke suggests that the effect of the missing carbonic anyhydrase would not be significant (Klocke, 1987). Shunts and shunt effect (see later) cause differences between alveolar and arterial P Q (called the A-a gradient) though such A - a gradients are small for Pco:, End tidal Pco2 (Pe~co2) is a good estimate of Paco~ in resting subjects and is used, for example, in assessing CO 2 sensitivity by means of-CO 2 response curves. In exercise, however, Petco2 increases as exercise intensity increases (McLoughlin et al., 1986) whereas mean arterial Pco2 does not (Wasserman et al., 1975). This is analysed in some detail at the end of Chapter 3. It results from the way Pco: oscillations change in exercise. We can now consider the basic relationships between ventilation, respiratory gases and metabolic rate since, under most circumstance there is full chemical and diffusion equilibrium for them at the lung. The main simplification this allows is that alveolar and arterial tensions are approximately equal. It can be important to note when this is not the case.

Ventilation The term ventilation is used on its own even though it strictly represents a rate, or flow of gas (i.e. a volume of gas per minute). This terminology has become orthodox and avoids the potential confusion with respiratory rate. Since we breathe in and out we have both inspiratory and expiratory ventilation. The inspiratory version is the amount of external gas drawn in past our lips, usually air, whilst expiratory ventilation is the amount of gas passing outward to the atmosphere. The expiratory gas used to be refered to as expired 'air' though the gas mixture is low in oxygen and rich in carbon dioxide. Inspiratory and expiratory ventilations differ slightly because of the inequality of carbon dioxide output and oxygen uptake. At rest about 6% of the atmospheric air (oxygen) is removed from the fresh air drawn into the alveolar compartment (gas exchange area) of the lung while the corresponding addition of CO2 is about 5%. For these values the respiratory quotient (R) is 0.83 (CO2 added/Oz subtracted) and the shrinkage in volume between inspiration and expiration is therefore 1%. (It is not only much more convenient but can be more accurate to assume that inspiratory and expiratory ventilation are equal rather than to to use different instruments to measure inspiratory and expiratory volumes. The error between them is likely to exceed 1%.) Expiratory ventilation is often obtained by collection in a Douglas bag. It is suggested that initial calculations be made from measurements made under ambient conditions, only applying precise temperature and pressure corrections later. It is then straightforward to derive the various relationships and handle them intuitively, while still obtaining results close to those which are strictly correct.

Alveolar Ventilation (I/A) and Dead Space (VD) The term alveolar volume and the symbol Va are used differently by non-clinical and clinical respiratory physiologists. In clinical respiratory physiology the term and symbol are used to mean the total volume of alveolar gas. Non-clinical respiratory physiologists


455

and sometimes (confusingly) clinical respiratory physiologists use them totally differently: they are taken to mean a volume of gas which constitutes part of the tidal volume (VT): V T = V A q- V D.

(2)

VA is one of the few respiratory symbols which is ambiguous. VA in Eq. (2) is the part of the breath which is involved in gas exchange. VD in the equation is the dead space gas, the volume of gas coming from the dead space in the lung, so called because it fails to exchange respiratory gases. The 'anatomical' dead space, refers to the conducting airways (mouth trachea, bronchi etc.). Since the airways do not exchange gas ( 0 2 and CO2) one will, on inspiration, breathe in a volume of air VT; only the volume VA will reach the alveolar compartment (exchange area) of the lung, leaving the volume VD behind in the airways. The airway gas (volume VD) will re-emerge unchanged in expiration. Expiration therefore results in a dead space volume of air emerging into the atmosphere. A total volume Vv of alveolar gas is expelled from the alveolar compartment but at the end of the expiration only a volume VA will have reached the atmosphere leaving a volume VD of alveolar gas in the airways (dead space). Hence, there is an expiratory and an inspiratory version of VA (and for that matter also of VD). To return to ~ventilation', where there is a flow of gas (hence a dot over each of the symbols), since we have both inspiratory and expiratory versions of alveolar ventilation

(vA); '~"Z = ~'AE or- ~"D

(3)

15"I = 12al + 1/D

(4)

where 12E and I/AE represent expiratory ventilation and alveolar ventilation and 121 and 12AI represent inspiratory ventilation and alveolar ventilation. We can also see that when VT = VA + VD are multiplied by respiratory frequency we obtain IV" = ~/A q- ~/'D"

(5)

Alveolar ventilation therefore has two definitions according to whether it is inspiratory or expiratory. Inspiratory alveolar ventilation is the amount of fresh air reaching the alveolar compartment of the lung per minute. This is the usual definition given. Expiratory alveolar ventilation is the amount of alveolar gas reaching the atmosphere per minute. Although far less often given as a definition it is much more helpful in understanding respiratory control. From the definition of expiratory alveolar ventilation: I/A X F A,cOz = I)'co2

(6)

where FA.co 2 represents the concentration (fraction) of CO 2 in the alveolar compartment of the lung. From Dalton's law of partial pressures (effectively the proportion by pressure is the same as the proportion by volume):

Facoe = PAcoJPB

(7)

456

C.B. Wolff

where PB is the ambient barometric pressure. (There is often confusion about whether water vapour pressure should be subtracted. In the present context it is the true fraction as above which is required. Subtraction of water vapour gives a special fraction refered to as the 'dry fraction' which is the proportion which the gas of interest constitutes of all gases other than water vapour. This may explain the low Pe,.co: values in Fig. 7.) Equations 6 and 7 can be thought out from first principles. From them, by substitution (of PACo2/PB for FACO2):

(/A.PAco2/PB =

%0._

(8)

PACO2 = I?Co2'PB/VA

(9)

and hence:

The alternative form at rest where Paco2 -- PACO2 is:

Paco, =

%o.PB/C,

(10)

This is the same as Eq. 1 (Chapter 1). It is considered preferable to consider it in this form, rather than the form commonly quoted in which gas volume corrections are given. Although there are strictly three variables in Eq. 10 it is worth considering only two of them changing at any one time (while the third is constant). Two such versions are particularly useful; one, where l/co2iS kept constant, producing the so called 'metabolic hyperbola'; the other, where P~co2 is constant, in which case we can consider the way 17A varies with changes in l?co._, as in exercise. With constant l/co: (metabolic hyperbola) for example in a resting subject breathing air, changes in alveolar ventilation (I/A) result in reciprocal changes in Paco2" There is a whole family of metabolic hyperbolae (iso-metabolic lines) each at a different metabolic rate (.I?cQ). At any given metabolic rate doubling of 12A will result in halving Pcoz; increasing VA to 1.5 times the original value will result in Pco2 being reduced in the same proportion, i.e. 2/3. Although total ventilation does not necessarily change in direct proportion to alveolar ventilation a similar relationship applies. In exercise with constant .Pcoz we can consider the effect of increasing ventilation as Vco , increases. Since 12A and Vco: go hand in hand (see Eq. 9 above) and ventilation chang.es very similarly 1/E will increase in proportion to 17co 2. Figure 1 shows how ~'E and V A increase with increasing I/co e. The slope of the 12A/I?CO., line, from the rearranged form of Eq. 9 (1/A = (/co2.PJPaco:), is PB/Paco: or 1/FAco2. The slope of the 9"Uco2 line also largely reflects PB/Paco2. For a P,co2 of 40 mm Hg (5.3 kPa) and barometric pressure of 760 mm Hg (101 kPa) PB/Paco2 is 19. For hyperventilation with a P~co2 of 30 mm Hg (4 kPa) it is 25.3. I)'E/I/CO2 therefore re-expresses Paco: in another form (hyperbolically) rather than being of any importance in its own right.


457

.jv

~0

Ventilation [l_/min. 30 BTPS} 20 10 ,,

.

.

.

.

,

0.5

.

.

.

.

J

1,0 VC02 {ml min-I)

Fig. 1. The relationships are shown for both total ventilation (V..E) and alveolar ventilation (~'A) to the CO2 production rate (r~co:). Both are linear, ~'z versus Vco~, showing an intercept on the y axis, ~'A versus Vco z giving a line through the origin. Since VA = VcoJFAco2 the slope of the VA versus l~'co2 line is 1/FAco2. The slope therefore simply reflects P¢o2. The slope of the ~'E versus Vco 2 line is a little bit greater as it reflects an increase in dead space ventilation in addition to Pco._.

Implications of

Pco2Constancy

It is apparent that if P¢o,_ is constant in the face of changes in ~'¢o:then l?A has to change in proportion to Vco2- The crucial question in considering chemical control is: "How does the respiratory control system match f'A changes to I?co 2 changes and thereby sustain a constant Pco2 ?''. It has been argued that this is not a critical relationship by Bennett and Fordyce (1985). They suggest that uncoupling of the relationship between ventilation and metabolic rate by 25% only alters Pco2 by 2 mm Hg. However, according to Eq. 1 the deviation from the isocapnic value of 40 mm Hg will be to 40/1.25 = 32 mm Hg (4.3 kPa), a deviation of 8 mm Hg (1.1 kPa). It seemed that Bennett et al. (1985) meant something different by "coupling between ventilation and metabolism" than the change in ratio described here. They described a mathematical model of the respiratory system in which ventilation was driven by ]/co_,and Paco2 each with a scaling coefficient such that: l/Z = Gco2 Paco2 + Gex l?co, - B.

(11)

This is what is known as a controller equation (see Chapter 6). Gc% was the slope of the CO 2 response curve and Gex was chosen so that Paco2 remained constant when lPco 2 increased. B was changed "to preserve the normal operating point". This meant that isocapnia was mathematically determined by Gex. These authors referred to percentage changes in Gex as "changes in the degree of coupling between ventilation and metabolism" and clearly showed that Paco2 was only altered by small amounts. Their paper simply shows that the respiratory system can hypothetically do very well as regards the matching required (keeping alveolar ventilation at a constant ratio to f'co_-) if it 'knows' the precise value of l/co 2. We still do not know whether and if so how, the respiratory system 'knows' the ~'¢o2" Since alveolar ventilation is significantly less than total ventilation it is hard to understand how alveolar ventilation normally varies in precisely the same proportion as does metabolic rate. One might imagine there to be some mechanism whereby the body

458

C.B. Wolff

can allow for the difference between total ventilation and alveolar ventilation (dead space ventilation). The control mechanism is not thought to calculate dead space ventilation but one's total ventilation is, nevertheless, somehow adjusted appropriately. In the early stages of mild to moderate exercise the rate of CO 2 delivery to the lungs increases in an approximately exponential manner. The fact that ventilation also increases in similar proportion results in Pcozremaining constant. This requires a respiratory control system with a response rate faster than a fraction of a breath. It is often assumed, incorrectly, that the ventilatory response rate is slow and represented by the slowly changing CO 2 excretion. However, ventilation follows CO~ excretion so accurately that PAco~, remains constant. The response of the system is therefore fast. It is likely that if the speed of delivery of CO, was to vary then ventilation would change fast enough to follow and keep Pco: constant. It would be useful to confirm this experimentally.

Dead Space

Practical Considerations

If either dead space or the alveolar volume ventilated per breath (VA--non-clinical) is estimated, an error in that estimate will affect the other variable in the opposite direction (see Eq. 2). We usually want to know I~'A (effective ventilation) rather than VA or VD. This is a multi-breath estimate rather than single breath estimate. We can readily obtain k'A in the steady state from ~'co~ and FAco: (FAcoz = PAcoz/PB).

9A = 9coJG, co2

or 9A =

f/E.FEco:/FAc02

(12)

It is often assumed that PACO2 = Petco2, is a reasonable assumption for most purposes in resting subjects. However, we shall see in Chapter 3 .(respiratory Pco,_ oscillations) that this is likely to be progressively more inaccurate as Vco 2 increases. The true value of mean PAco2 required is half way between end-tidal Pco2 and the lowest value of alveolar PcQreaching the atmosphere. This is the mean of the PACO2which reaches the atmosphere (mean expired alveolar Pco2) rather than the mean PacQ in the alveolar compartment--mean of the PAco_, oscillation--see Chapter 3. (This is mean intra-alveolar Pco2.) Mean expired alveolar Pco~_ and end-tidal Pco2 are very similar at rest but become progressively different with exercise. Furthermore, it is very difficult to be sure of the lowest value of alveolar Pco2 reaching the atmosphere (because of mixing), though the principles by which it may be calculated will be outlined later. An alternative approach to finding space (and respiratory rate):

~'A is to first find the average, single breath, dead l/A = l / E - f VD

(13)

where f is respiratory rate (frequency). To find the dead space for every breath one can use a fast 0 2 or CO 2 analyzer. If airway gas tension (concentration) is monitored this will produce a trace on a pen recorder which first shows ambient air values in the early part of expiration. This is due, as expiration starts, to the passage of air from the dead space to the atmosphere. The next part of the record consists of alveolar gas with a recording of alveolar Po, or Pco2. It is usual to relate the alveolar gas concentration to the volume record (Krogh and Lindhard, 1914) e.g. for CO 2 --see Fig. 2.


459

6 FACO 2 s (%) 3

v

2 1

0 0

Vo

i i I , 0.5 1.0VT Expired Volume (litres)

Fig. 2. This is a plot of FAco: against volume expired for one breath to explain the Fowler method of obtaining dead space (VD). The linear sloping section, the plateau, is extended to the left to the point V which is a corner of an area V, ET, VT, V D which is the same as the area under the original FACO2/ volume curve. Mean expired alveolar FACO2 is the average of VV D (trough value of respiratory oscillation) and ETVT (end-tidal). (Wolff and Paddon, unpublished.)

The area under this curve is the volume of CO 2 produced in the breath (Fowler, 1948). The plateau of the PcoJVT or Po~_/VT plot is usually linear. If, for a Pco,_/Vx plot the linear segment is extrapolated; a vertical (V, VD) can be dropped to the volume axis which intersects the extrapolated plateau (at 1/). This forms the rectilinear shape (V, ET, VT, VD) with an area equal to the area under the curve. The dead space VD is then the volume of air returned to the atmosphere and VA (non-clinical) is the volume of alveolar gas expired. This would be very satisfactory except for an instrumentation problem. There is a degree of mixing of the gas sample as it is drawn continuously from the airway and passes down the sampling pipe to the gas analyzer (Wolff and Paddon, 1991). This means that the abrupt fall in airway CO 2 at the onset of inspiration/end of expiration is not faithfully recorded. True end-tidal gas is diluted with air; the apparent end-tidal Pco2 (where airway CO 2 begins to fall) therefore occurs earlier than it should. This makes it impossible to align the airway CO2 and volume records correctly without some independent means of assessing the effective delay between real events at the tip of the gas analyzer sampling pipe and the corresponding recordings. When this is done (Wolff and Paddon, 1991) it shows that the end of expiration/start of inspiration corresponds to a point at least half way down the descent from the plateau of the airway CO 2 record. There is then also a little bit of the end of the airway CO 2 plateau missing which has to be allowed for. It is hoped that it will soon be possible to produce an accurate system for (anatomical) dead space measurement. This will do much to correct estimates of alveolar ventilation. In patients whose lung function is disorganized the alveolar plateau may not bear the linear relationship to expired volume found in normal subjects. Indeed, there are likely to be several functional anatomical dead spaces. It is therefore impossible to obtain meaningful single breath dead space values. A solution is to use arterial P¢o2 rather than alveolar Pco2 in Bohr's equation for calculating the (multi-breath) dead space (Bohr, 1891, 1909). This is derived as follows:

460

C.B. Wolff

~/E'FEco: = I/A'FAco:

(14)

substituting for l/A(i.e. IPE--IPD):

9E, FEco= = 9z. FAco:-- 9~. FACO:

(15)

9D = 9E(FAco:-- FECO:) / FACO:

(16)

VD = ~'E(PAcoe-- PECO2) / PACO:'

(17)

therefore,

this is equivalent to,

When alveolar Pco2 or Fco 2 is replaced with P, cozWe obtain the Bohr equation, VD = VE(Paco: -- PECOz) / P~co2

(18)

VD = VT(P~coz-PEcoz) / P~co:.

(19)

The calculated value for V D ( l / d r ) is known as the physiological dead space.

Dead Space Effect The physiological dead space takes into account impaired perfusion of a significant number of alveoli where local ventilating gas undergoes inadequate exchange with pulmonary capillary blood. This kind of dead space, at alveolar level (alveolar dead space), is also referred to as parallel dead space and constitutes a 'dead space effect'. It is commonly found in patients with lung disease (Hughes, 1990) and is distinct from the dead space which results from the presence of non-exchanging airways, the well known 'anatomical dead space' described above. The airways are said to function as 'series' dead space. The difference between physiological (series and parallel--alveolar) and anatomical (just series) dead space values is therefore the parallel or alveolar dead space and signifies patches of poorly perfused lung. The value obtained is equivalent to pure alveolar dead space (no perfusion) which is not the real situation. It is nevertheless a useful guide to the extent of underperfusion or 'dead space effect'. Although errors in measurement can produce large errors in the calculated value of the dead space it is generally assumed that, for practical purposes, the ratio V J V T is 20-30 % (Bohr, 1891, 1909). This flies in the face of the older assumption that dead space is fixed and is about 150 ml. It is probably much larger when tidal volume is large and further studies should show whether or not the magnitude of such changes is a convenient percentage of tidal volume. The greater slope of the 12E versus Vc.o2 than the 1/A versus 12co 2 plot (Fig. 1) suggests that I/D (and VD) increase more with Vco 2 than I/A (or VA). Hence, the percentage, IOOVD/VT will increase with l?co :. Values of physiological dead space which are greater than 30% of V x are generally taken clinically to indicate maldistribution of pulmonary' blood flow (Hughes, 1990).


461

Shunt and 'Shunt Effect'--Venous Admixture When there is passage of blood from the right side of the heart to the left, without going through the lungs, there is a true shunt. There is no oxygenation of the desaturated (shunted) blood. This occurs, for example, with the congenital heart disease Fallot's tetralogy. The extent of the shunt is expressed as Q]OT% where 0 represents flow and Q]QT is the proportion which the shunt flow (Q~) contributes to total flow (cardiac output, QT). The difference (QT-Qs), the pulmonary blood flow, is called Qc (pulmonary capillary flow). Multiplying flow by 0 2 content (Co2) gives net O, flow per minute in each pathway. The shunt flow of oxygen and pulmonary arterial flow of oxygen must add up to the arterial flow. Hence:

G + Cvo:G = Go,O-

(20)

where Coo2 is end capillary O 2 content (effective content in the pulmonary arterial blood), Cvo," is the 0 2 content in pulmonary arterial (and shunt) blood and Cao 2 is the 0 2 content in the arterial blood. C~o2 is taken to be the content of blood with alveolar Po2, arterial content is calculated from measured Pad2 and Q o : is often assumed, unless a pulmonary arterial catheter is in place for direct sampling. From Eq. 20 and Oc = (QT-Qs):

O]OT = ( Cc02- Cao2)/(Ccoe- Cvo2).

(21)

This is the extent of venous admixture. Where patches of disorganized lung with low ventilation/perfusion ratios are present in diseased lungs there is relative overperfusion compared with the local alveolar ventilation. This will behave like a partial shunt. It is convenient to use the equation for venous admixture to work out the value of the pure shunt which would give the same effect as the existing partial situation. Suppose, for example, the venous admixture calculation gave a supposed pure shunt which was 10% of cardiac output. The real situation might be that 20% of the vasculature went to areas of lung with a low (//Q. Partial, but incomplete, oxygenation of 20% of the pulmonary capillary flow could behave much as if 10% was totally unventilated. This adoption of the concept of an equivalent pure shunt is referred to as 'shunt effect'. It can then be used for the lungs concerned and in the above instance the shunt effect would be 10%. It is a convenient measure of the extent to which underventilated areas interfere with oxygenation. Shunt effect and pure shunt can be distinguised by administration of pure oxygen. This wilt overcome the reduced supply of oxygen to the underventilated areas (shunt effect) and increase P~o: significantly, whereas this does not happen with pure (true) shunts. In spite of these problems we can, for most p~Tactical purposes, assume that PAco2and Paco, are equal, especially at rest. For arterial Po2 (Pao,_) there is a difference (or A - a gradient) due to a small shunt effect even in normal subjects. A small amount of venous blood comes through to mix with the majority from the alveolar capillary drainage. Since the O,/Hb dissociation curve is very shallow even the very small amount of venous admixture lowers the P~o,_ of the arterial blood by an estimated 7 mm Hg (0.93 kPa) (Cruz et al., 1975; Wolff, 1980) or, 5 mm Hg (0.67 kPa) according to West

462

C.B. Wolff

(1970). It is Pao2 which is most affected in lung disease. Hyperventilation of normally (or underperfused) alveoli can increase oxygen tension but does not have much effect on oxygen content as this is close to saturation anyway. On the other hand underventilation of normally perfused alveoli leads to a hypoxic perfusate. The mixture is hypoxic. For CO 2 hyperventilated alveoli compensate for underventilated ones with an average outflow closer to normal. It is probably less confusing to use the measurable concepts of dead space effect (under perfused alveoli) and shunt effect (under ventilated areas of perfused lung) in patients with lung disease, than to use the generalized concept of ventilation/perfusion imbalance ((//Q). Both dead space effect and shunt effect involve ventilation/perfusion imbalance but in one there is under ventilation (shunt effect) and in the other under perfusion (dead space effect). It is regional inhomogeneity (non-generalized change) which gives rise to the problems. For example, in exercise ventilation increases faster than cardiac output so (//O for the whole lung increases well above the value of unity which it normally adopts at rest. Shunt effect calculations have considerable usefulness in assessing hypoxia in patients as will be illustrated in Chapter 7. Respiratory oscillations have been touched on in this chapter. They are analyzed in some detail in the next (Chapter 3).

Chapter 3

Respiratory Pco2 Oscillations

General Aspects As mentioned in Chapter 1 the recurring inspiratory fall and expiratory rise in PACO2 means that PACO2 oscillates with every respiratory cycle. These changes are therefore referred to as respiratory PACO2 oscillations. As will be discussed later these changes, which are also equilibrated in pulmonary capillary blood, are normally carried from the lung to the systemic arteries, where they become respiratory PACO,_oscillations. PACO2 rises during expiration at rest at a rate of 1 mm Hg per sec (0.133 kPa sec-~). With a respiratory period of approximately 3 sec the whole rising ramp is unlikely to exceed 2 mm Hg (0.267 kPa). The amplitude of resting PACO2oscillations is therefore also about 2ram Hg (0.267 kPa). These seemingly trivial resting oscillations are however at the lowest end of the range. The whole rise occupies the time from the start of expiration to the time in the next inspiration when atmospheric air reaches the alveolar compartment of the lung, i.e. when the airways (or anatomical dead space has been cleared of alveolar gas (which has returned to the alveoli). The part of the cycle, during which PACO2rises therefore lasts longer than the PACO2falling phase (of alveolar dilution with air). Since the rate of rise of PACO2in expiration is proportional to ~'co2 and this can easily increase 15 fold with exercise, the expiratory ramp may show a rate of rise of at least 15 mm Hg sec -1 (2 kPa sec-1). Admittedly the expiratory phase of the oscillation will last for a shorter time in heavy exercise than it does at rest but the oscillations are still much too large to be regarded as trivial. Furthermore, rather than their amplitude, it seems their rate of change component is more important. This is because of the nature of the peripheral arterial chemoreceptor response which will be discussed irt Chapters 4 and 5. It is important to point out here that there is good evidence that the alveolar gas oscillations (Pco2 and Po,_) are carried to the arterial chemoreceptors from the lungs with very little smoothing despite passage through the pulmonary veins, heart and systemic arteries. The evidence includes recordings of the oscillations in arterial pH (Fig. 3) which result from equilibration (diffusion and chemical) of PACO2 oscillations with blood in the pulmonary capillaries prior to transportation to the systemic arteries. 463

464

C.B.

Wolff

rAlk'a I ine

IApH 0,03% , . , , . , .,., ~ , ~, A / " Fll-V L - A c i d - ~,r X / ~ V ~ "~ r

ill

~

IIIIIIIIIIIIIIIIIIIIIit1111

Time

II

Iseconds)

Fig. 3. The recordings from above downwards are arterial pH, inspiratory tidal volume and airway CO 2 in a normal resting subject (DMB). Alveolar oscillations result from rising CO, in expiration followed by dilution during inspiration. Alveolar oscillations generate pulmonary capillary blood oscillations. These are carried with little attenuation to become Paco: oscillations. The recorded pH oscillations act as an indirect monitor of Paco,_ oscillations. The time shift between lung and systemic arterial pH (and P~co2) is usually about 2 breaths duration in man (as in this record) and one breath duration in cats.

Secondary evidence comes from studies which have shown that flow in large vessels presents a 'blunt velocity profile' (Caro et al., 1978). This means that unlike Poiseuille flow where the blood at the center of the vessel moves much faster than blood near the walls, the blood, apart from a small stationary layer at the surface of the vessel wall, all moves at much the same speed. This sustains the variations in concentration generated at the lung despite the fact that the blood flows through the pulmonary veins, left heart, aorta and smaller branch arteries. So it keeps blood with a tow Paco2 (oscillation trough) together at one point in the stream and oscillation peak blood together at another. There is probably a small amount of smoothing since, if one considers arterial pH recordings, there is a little rounding of the recorded pH oscillations and a little more curvature of their falling limb than would be expected from the corresponding (virtually linear) rising phase of PACO2generated in expiration (DuBois, Britt and Fenn, 1952). There is no significant lag or attenuation from the pH electrode which has a 90% response time under the recording conditions of about 10 msec. (Band and Semple, 1967). The ripples on the pH record are due to the heart beat avid may be a result of the first blood entering in diastole being the last to leave in systole.

Generation of Alveolar Pco= Oscillations Respiratory oscillations in Paco2 are of theoreIical importance partly because of a potential direct role in the control of breathing but also because their presence can mislead the investigator as to the mean value of PACO2 and Paco2 which are certainly required in the investigation of respiratory control. One of several ways in which Pco2 oscillations may cause misunderstanding is discussed in the last section in this chapter. The oscillations also have some bearing on the Fowler method of calculating anatomical dead space (Chapter 2). Calculation of the oscillation in PACO2 resembles derivation of the common Fick equation which is used for calculating cardiac output and, similarly, is a statement of the conservation of matter. The model used here for calculation of the oscillation


465

in PACO: is a version of the 'single alveolus' lung model of DuBois et aL (1952). 'Alveolus' is taken to mean all the alveolar gas itself plus a volume of blood equivalent to alveolar gas. This was called by the name "equivalent lung volume', abbreviated to ELV by DuBois et al. (1952). It is bounded (Fig. 4) at: (1) the blood inlet (pulmonary arterial/pulmonary capillary) junction; (2) the blood outlet (pulmonary capillary/pulmonary venous) junction; (3) the alveolar/airway (dead space) junction.

3_)-kA3i rway

1,/,/

.N--Lung , ....Blood

,.

s

i

t

2

Fig. 4. ELV (the equivalent lung volume) consists of alveolar gas plus the volume of gas which would be required to hold the CO z present in alveolar capillary blood. (1) Blood inlet (pulmonary arterial / pulmonary capillary) junction. (2) Blood outlet (pulmonary capillary / pulmonary venous) junction. (3) Alveolar / airway (dead space) junction.

The amount of C O 2 in the ELV will be ELV.FAco,- and its rate of change: dCO2/dt = dELV/dt.FAco: + dFAco2/dt.ELV.

(22)

If Oco: is the rate of CO 2 gain from blood, at junction 1 (equal in the long term to Vco2) and FACO2 is airway Fco 2 we can work out that the rate of CO, increase in the ELV due to arrival 'from' blood and airways is: dCO2/dt = ~'co, + dELV/dt'FAco2.

(23)

Hence:

dELV/dt'FAco~ + dFAcoJdt'ELV = /'co~ + dELV/dt'F~,co .* -

-

•

2

(24)

In expiration where FAC02* is actual f A c o : (dELV/dt.FAco~)_ disappears from both sides leaving:

dFAcoJdt.ELV = /eco~

(25)

dFAcojdt = /~co2/ELV

(26)

from which:

466

G.B. Wolff

dP Aco:/dt = PB-/,coz/ELV.

(27)

This is applicable breath-by-breath; the longer term steady-state relationship is:

dFAcoJdt = I ) c o J E L V

(28)

dPAco2/dt = PB'I/co2/ELV

(29)

as described in Cochrane et al. (1982) and Edwards et al. (1983). A conceptual analogy is constant water flow into a parallel sided container. The rate at which the water level rises will be proportional to the flow of water (analogy, l/co:) and inversely proportional to the capacity of the container (analogy, ELV). For the latter part of inspiration, after the dead space has filled with air so that alveolar dilution occurs, the situation is complicated by the fact that air is crossing the lung/dead space interface (junction 2). The term previously referred to as FAco2* becomes zero, so from Eq. 24:

dELV/dt'FAco2 + dFAco2/dt'ELV = ~;'co2"

(30)

Dilution with alveolar gas only occurs for a fraction of the respiratory cycle, say ilk. Alveolar ventilation which is averaged over the whole respiratory cycle is therefore Ilk of dELV/dt, so: I/A = d E L V / d t / k

(31)

but I/A = iecoz/FAco2, so k./,co z = dELV/dt.FAc Q. We can now substitute k. ~co2 for dELV/dt. FAco:in Eq. 30 to get:

k't;'co-, + dFAco2 Idt'ELV = /'co,.

(32)

Hence:

d F a c o J d t = /,CO_,(1--k)/ELV

(33)

or

dPAco2 ~dr = PB" i'co2(1-k)/ELV.

(34)

The steady state relationship is of the same form:

dPAco2/dr = PB" I)co2(1-k)/ELV

(35)

where k is the ratio of the respiratory period to the dilution period with air. These equations can be used to calculate expiratory and inspiratory (dilutional) values. of dPAcoJdt. For example dPAco2/dt in expiration at rest is 1 mm Hg sec -1 for a Vco 2 of 237 ml m-1 and ELV of 3 1. At the same l/co 2, inspiratory (dilutional) rate of 'rise' of PACO2 is,

dPAco2/dt = 760x0.237/60 ( l - k ) / 3 mm Hg sec -1, or


467

dPacoz/dt = 101 x 0.237/60( 1 - k)/3 kPa sec- t. For a dilutional period which is 1/3 respiratory cycle, k = 3 and dPaco:/dt = - 2 mm Hg sec -1 (----0.267 kPa sec-t). For exercise with Vco: ten times greater (i.e. 2.37 1 min - t ) the P~co: slopes are ten times greater, being 10 mm Hg sec-t (1.33 kPa sec -~) in expiration and - 2 0 mm Hg sec - t ( - 2 . 6 7 kPa sec - t ) during the dilutional period of inspiration. The directly proportional relationships between rates of change and IPco~- have lent the oscillations an appeal as potential purveyors of information about the metabolic rate in exercise and as a link between metabolism and the brain via the intervening bloodstream and the peripheral arterial chemoreceptors (Chapter 4), An important difficulty in such a scheme resides in the fact that larger breaths than average in a (quasi) steady state will generate oscillations with larger rates of change and vice versa. If ventilation follows rate of change and there is some evidence that it does, it becomes difficult to see how positive feedback will be avoided. It is possible that positive feedback is present (see a new model for CO 2 in Chapter 6) without the expected instability (see control theory, also Chapter 6). Summers and Ward (1985) produced a simple electrical analog of CO_, transport including a tissue supply, a lung and experimental (exponential) transport lags (tissue to lung; lung to tissue). This generated respiratory oscillations in precise agreement with these equations. The new model for CO2 discussed in Chapter 6 also incorporates peripheral arterial and central chemoreceptors and a circulation with real time delays as well as control elements. The equations derived here are incorporated as essential algorithms.

Constant Flow Expiration and Alveolar

CO 2

Calculation

It is possible to train normal healthy subjects to undertake every individual expiration at reasonably constant flow. This was done by Cochrane et al. (1982) in order to obtain

.Alveolar C02

....z

I

i

ins~)iration.,

Expiration

Fig. 5. Shows a diagrammatic representation of a PACO2 oscillation. In expiration it is a linear rising ramp, which lasts throughout expiration and then continues during the time taken to clear the dead space at the beginning of inspiration. PACO: then falls, continuing to do so until the end of inspiration. Airway CO 2 is the same as alveolar CO, after the delay t and only represents values from the oscillation trough up to end-tidal Pco, which is a little above the mean intra-alveolar value.

468

C.B. Wolff

an airway CO z profile for each breath with a plateau consisting purely of alveolar gas delayed in its arrival at the mouth by a fixed time interval (Fig. 5). Although this assumed a constant volume dead space during expiration the plateaux were linear. The slope of each plateau was assumed to be that of the alveolar gas and the breath-by-breath values (dPcoJdt) were averaged for each of a number of steady states (at different metabolic rates). On the basis of the steady state expiratory Eq. 29, dPAco2/dt = PBf/c.oJELV, one would expect mean dPAco:/dt to vary in direct proportion (y = rex) with Vco 2. This was found to be the case. Nevertheless, if the dead space changes during each expiration dPAco:/dt values could have been incorrect. A second method used in this paper, with near normal breathing (slightly slower than normal), utilised back-calculation, from airway' CO, and volume, of a small segment of expiratory PACO2.by taking into account the time taken to expire alveolar gas through the dead space. VI) had to be found for each breath then subtracted from the volume corresponding to a given airway CO 2 to give another volume and hence the time, at which that airway CO,_ had started out, through the airways, as alveolar CO z. Again it was found, as with the square breathing method, that mean dPAcoJdt correlated with l/co z as a y = m x relationship. In a separate study (Edwards et al., 1983) the mean value of dPAco:/dt was first obtained for two or three different steady states, The subject was then asked to breathe at high lung volume, in the expectation that this would increase ELV. This was expected to give a reduced mean dPAcoz/dt compared with the value expected at normal lung volume. This was confirmed and independently assessed with a whole body plethysmograph which showed agreement with the values derived from the formula for ELV (from Eqs 28 and 29; i.e. ELV = PB.f/co21(dPAcoz/dt). This study therefore suggested that the formula is compatible with real changes in the variables and that lung volume can be derived from dPAcoJdt and Ikco_,.

Relationship to Pulmonary Blood Flow The equations for dPAcoz/dt imply linearity (constant rate of change). Though this is reasonable for practical purposes, an illuminating relationship can be obtained if the CO 2 flux to the lung is expressed as the product of the arteriovenous content difference and pulmonary blood flow. This leads to the expression:

PACO2 = Pvco: (1-eO("P~mcv)o

(36)

where u is the slope of the in vivo CO 2 dissociation curve and Q is the pulmonary blood flow ( = cardiac output). This is equivalent to an expression derived by DuBois et al. (1952). It is a saturating exponential, the saturating value for PACO2 being PvcQ. It can be seen that the alternative form:

dPAco:ldt = (u.PB/ELV)Q( Pvco:-P Aco2)

(37)

will give alveolar Pco,changes in expiration which are close to linear because the PACO2 changes are small relative to the gap between P,.co2 and PAco:, It is possible from measured dPAcoz/dt and PACO,_values tO obtain a theoretical value for P, co2(Wolff,


469

1985), ELV (Edwards et al., 1983) and mean PAco,_ (average of measured values). Hence, it is possible to obtain cardiac output (pulmona U blood flow). As might be expected the curve (PAco. against time, described by Eq. 36) will rise most quickly when PACO: is lOW, with small lung volumes and when pulmonary blood flow is high. The time constant for the rising PAco: exponential is about 7 sec at rest and as little as 1 sec in heavy exercise. It can be seen that the expiratory PACO2rate of change, breath-by-breath is affected by lung volume, (within breath) blood flow to the lung as well as the instantaneous value of Paco2' This is not so different from the steady state: dPaco2/dt = P B ' f / c o z l E L V (Eqs 28 and 29) since the CO, flux to the lung in these equations is Vco2 = u.Q (Pvco2--PAco2). Equation 37 can therefore be reduced to dPAcoz/dt = (PB/ELV) x Vco2, virtually the same as Eqs 28 and 29. In both the transient and the steady state dPAco2/dt therefore depends on the CO 2 flux to the lung. It will however depend on pulmonary blood flow during transients but will be independent of pulmonary blood flow in the steady-state.

Oscillations in Arterial pH, Pco2 and Po2 Early recordings of respiratory oscillations in P~o~_ were made by Yokota and Kreuzer (1973). It was thought these were attenuated by comparison with theoretical alveolar gas Po2 oscillations (Chilton et al., 1954). This attenuation does not seem to have been borne out. One would expect PAO2tO be related closely to PAcQ oscillations, though of opposite sign, because similar theoretical considerations apply to their calculation. Using the same principles to derive an equation for their expiratory slope we obtain: dPAo2/dt = -- PB'I2oJELV"

(38)

Since the respiratory exchange ratio, R = Ikcoe/t?o, it is therefore apparent that: dP Aco21dt = - R . d P AO2/dt.

(39)

Derivation of both kinds of oscillations suggest an expected modest extent to which PAO2 oscillations exceed Paco2 oscillations - - i.e. approximately in the ratio (1/R):I or (1/0.83):1 = 1.2:1. Oxygen electrode monitoring has improved enough to give stable records with sufficient speed of response to record P~o2 oscillations. It may therefore be worth considering its use, in some circumstances, as an indirect monitor of CO, oscillations, since fast CO 2 monitoring still is not possible. In order to monitor Paco2 oscillations, Band et al. and others have employed fast response pH electrodes (Band and Semple, 1967). The electrodes were initially made of glass but are now plastic and of various formats including catheter tip electrodes. Arterial pH records uniformly show respiratory swings, reproducing the expected Paco2 oscillations (generated earlier at the lungs as Paco2 oscillations). The magnitude of pH change is that which would be predicted by in vitro buffering of PAcQ oscillations. There is a linear relationship between log Pco2 and pH, where each doubling of P c Q produces a change of approximately 0.2 pH units. Hence, ApH/Alog Pco2 is about 0.667. This means that at

470

C.B. Wolff

40 mm Hg (5.3 kPa), 1 mm Hg (0.133 kPa) PaCO-, change is equivalent to a pH change of 0.0071 units, at 30 mm Hg (4.0 kPa) 0.0095 pH units and at 80 mm Hg (10.7 kPa) 0.0036 pH units. In cats (Band et al., 1969a, b) the oscillations are a little under 0.02 pH units in amplitude and at a P~co: of 30 mm Hg (7.5 kPa) this amounts to Paco~_ oscillations of 2 mm Hg (0.27 kPa) amplitude. In a study on man (Band et al., 1980) at rest oscillation rate of change was 4.41x10-3pH units sec -l and in mild exercise 11.95×10 -3 pH units sec-~(Fig. 6). These correspond to 0.6 mm Hg sec-l (0.082 kPa sec -I) at rest and 1.7 mm Hg sec-~ (0.225 kPa sec-1) in exercise (Band et al., 1980). The ratio of d P ~ c o J d t was 2.7 (between exercise and rest) in this study and this, as .predicted (from Eqs 28 and 29 for Paco~), was the same as the exercise to rest ratio for V c o 2.

(Alkl') ApH 0.02

units I i Insp. vT (Acid ~) (L) I-3 C02 L 0 (%)

/%J~./V~j~

~,,~ , , , ~ , , , ~ , , . W h , ~ ,

,

r-

~

Ii

I

/

~W H i~W. i ~ im H ~W H J~, ~m lH ~ H m-A iir-r.-i H m H n-m ~

Inset of

exercise

TIME in seconds

Fig. 6. The figure shows arterial pH oscillations in normal man (the author) at rest and in exercise. Inspiratory tidal volume and airway CO2 are also shown. For details see text. Adapted from Band et al. (1980).

It is possible to obtain more accurate assessments of the conversion from pH~ change to P~co, change using Siggard Andersen's nomograms and tables (Siggaard Andersen, 1962, 1963)-, as outlined in Prior et al. (1985). These incorporate Hb and take into account the effect of the base excess. Alternatively the Severinghaus slide rule gives the same answer (Severinghaus, 1966). Recent comprehensive equations are available from Siggaard Andersen et al. (1988).

Paco= and Pet,CO= differ in Exercise We know that end-tidal PcO2 (Petco2) differs theoretically from mean (intra-alveolar) Pco, even at rest, though the difference is small. Mean intra-atveolar Pc02 is a 'best guess' of Pac02 so Petc02 and Pac02 are also likely to differ from one another. Petc02 appears to represent a sample from a little above the middle of the expiratory PACO2ramp (mean intra-alveolar Pco2)--see Fig. 5. This ramp lasts from the onset of expiration until soon after the beginning of the next inspiration. The extent to which P~tco2 exceeds Paco2 will depend on the rise from mid-ramp to PetcO2 sampling time (see Fig. 5). The extent to which Petco2 exceeds mean intra-alveolar Pco2 (and ?mean Paco~?) will vary in direct proportion to the CO, flux to the lungs (mean value !/co2). If, as has been established (Forster et al., 1986; Holmgren and Mcllroy, 1964; Wasserman mean PaCO2 remains constant and PetcO2 is representative of alveolar gas at

et al., 1975),


471

a reasonably constant small time interval after the middle of the expiratory PAco.:ramp, there will inevitably be an increase in P e t c o : in exercise which is proportional to Vco,_. It is hardly surprising that such correlations have been found; Jones et al. (1979). Jones and Campbell (1975), McLoughlin et al. (1986) and Scruple (1993) showed that, in exercise as well as at rest, arterial Pco:could be estimated from P~tco~_ and tidal volume (VT). Where Paco: and P~co,_ are in mm Hg and VT is in 1 min-l: Paco_, = 5.5 + 0.9 Pe,coz

(40)

This can be rearranged to predict what Pet,co2 will do if P~co,_ remains constant at 40 mm Hg in exercise:

(4t)

Pc,co:= 38.33 + 2.33 VT

This predicts 5 or 6 mm Hg rise in Petco-, (0.67 - 0.8 kPa) without any change in Paco2 for exercise of about 100 W work rate. It is apparent that without any increase in Paco~ (a putative signal) there is a very significant rise in P+tco:. P+tco2 changes are not therefore indicative of a change in the Pco,. signgl in exercise. One should only invoke changes in signals which play upon receptors (Moran Campbell, personal communication). A very clear example of an increased P~tco: (labelled PAco,) in exercise without any such rise in Paco2 is given in Fig. 3 of Wasserman et al. (1975) and see Fig. 7.

Pa CO 2 co (ram Hg)

. . . . . . .

-49

35

z.5

PetC02 (mm Hg)

f

L.o - -

f+.,.,....+~ ÷ ~ + ~ ÷-

35

REST

EXERCISE I

01

I

I

I

J

234 5 minutes

Fig. 7. The figure shows P+co2and Petco2 monitored over the same period in normal subjects, first at rest and then during the first five rains of exercise. The data, has,been extracted from Fig. 3 of Wasserman et al. (1975). There is a rise in P+,coz in exercise which is not matched by P, co.,-

The importance of using Paco2 r a t h e r than PetcO2 in exercise to assess the respiratory control status cannot be over-emphasized. As mentioned in Chapter 1, it is now possible to obtain mean P~co,_ from arterialized venous blood (McLoughlin et al., 1992). Heating the forearm and hand causes faster blood flow. The blood is little affected by tissue

472

C.B. Wolff

metabolism and yields Pco2 and pH values close to arterial. Po~_ values are affected too much by tissue uptake. Sometimes the results obtained in this way for P~co2 are more reliable than those obtained by direct arterial puncture. This is because a direct arterial sample may not give a good mean value of Paco: if the sample does not include a whole number of respiratory oscillations. Passage of blood through the arterialized capillary bed before it is sampled will smooth respiratory oscillations, probably eliminating them and thereby giving a good mean value.

Chapter 4

Respiratory Chemoreceptors

Discovery of arterial and central (brainstem) detectors of arterial blood gas and pH changes transformed our understanding of mechanisms operative in respiratory control. We still do not have a complete description of their sensitivities but are in a far stronger position to propose realistic models of the whole system than previously, when everything was attributed to a unique respiratory center. The peripheral arterial chemoreceptors were discovered first, both anatomically by De Castro (1926) and functionally by Heymans and Heymans (father and son) (1927). De Castro suspected a chemoreceptor role, suggesting the chemoreceptors 'tasted' the blood. Sensitivity was found to both CO, and hypoxia. Ten to fifteen years later Leusen (1950, 1954a, b) found that ventriculo-cisternal perfusion of the brain with acidic fluids stimulated respiration. This was the (functional) discovery of the central (brainstem) chemoreceptor.

Peripheral Arterial Chemoreceptors The peripheral arterial chemoreceptors (carotid and aortic bodies) are the only 'physiological' receptors for hypoxia. (There are also 'pharmacological' receptors for hypoxia which affect vascular resistance. For example alveolar hypoxia causes pulmonary arteriolar constriction, while cerebro-vascular resistance is reduced by arterial hypoxia.) The afferent chemoreceptor discharge frequency (in nerves from the carotid and aortic bodies) is increased by hypoxia. In the steady state the arterial chemoreceptor response to hypoxia is hyperbolic and has been well shown both with multi-fiber (Hornbein, 1968) and single fiber (Biscoe et al., 1970) preparations (see also Fidone and Gonzalez, (1986). The advantages of single fiber preparations (Biscoe, 1971) include the knowledge that the fiber monitored is of pure chemoreceptor type and does not include baro-receptors. It has been said that multifiber and single unit preparations each have non-representative features. It now seems likely that for steady state measurements the overall response is reasonably representative for both single and multi-fiber preparations. Single unit preparations combined with averaging have been particularly informative for fast changes. Figure 8 shows steady-state response curves from two different single chemoreceptor units. 473

474

C.B. Wolff

_E2 ....

0

I

I

I

200

I°,, 400

i 600

Pa,o~ (mm Hg) Fig. 8. Two single units (afferent carotid chemoreceptor fibers) were monitored to give these approximately hyperbolic Pao2 response curves. From Biscoe et al. (1970).

They illustrate the fact that such responses have a significant slope well into high oxygen. This is important as it is not the case for the acute ventilatory response to hypoxia which is flat over the mild hypoxia/hyperoxia range (see Chapter 7). Aortic chemoreceptor responses have been reported ranging from non-contributory to being a moderate fraction of those due to carotid chemoreceptors (Lahiri et al., 1981). Discussion from here on will concentrate on carotid arterial chemoreceptors (i.e. carotid body function). The response to CO e is definite but modest compared with central sensitivity, though steady state hypoxia and CO~ act multiplicatively on peripheral arterial chemoreceptor discharge (Lahiri and DeLaney, 1975). This is similar to steady state ventilatory responses (see Chapter 5). By contrast the peripheral arterial chemoreceptor response to acid is large, consistent with constituting much of the drive to ventilation in metabolic acidosis (Schuitmaker et al., 1987). Until recently reports on mechanisms of the ventilatory response to metabolic acidosis were incompatible with one another. This is discussed in some detail in Chapter 8. An example of normal afferent peripheral arterial chemoreceptor discharge and the response to increased Pco2 is shown in Fig. 9. The normal, unstimulated, record illustrates an important feature of the firing pattern of single units. At least in the quiescent state (with normal gas tensions, perfusion and pH), firing shows an apparently random pattern, which obeys the mathematical rules of the Poisson distribution (Biscoe and Taylor, 1963). There has been considerable interest in the mechanisms involved at the receptor which result in this peculiarity (Biscoe, 1971; Fidone and Gonzalez, 1986). The likelihood is that despite a very slow average resting discharge rate (1-2 impulses sec -1) the presence of 300--400 parallel chemoreceptor units in the sinus nerve (Fidone and Sato, 1969) will result in a high resolution, smooth signal at the central projection areas.

The Physiological Control of Respiration l

1

I

,J.,

I sec

i

~

475 ~

I

Fig. 9. Afferent chemoreceptor discharge in cut sinus nerve chemoreceptor fiber. Single unit preparation. Lower record shows response to increased Pco2: [(t) Pco: = 40, pH = 7.40, Po, = 150; (2) P¢o- = 80, pH = 7.40, Po2 = 150. Gas tensions in mm Hg; for kPa divide by 7.5]. From Joels (1960).

Chemosensitivity to respiratory Paco2 oscillations One of the earliest records of averaged afferent chemoreceptor discharge, showing an oscillation of respiratory frequency, appears in the Wates symposium report of Lietner and Dejours (1968). They divided each respiratory cycle up into six equal time intervals, or 'bins'. The firing was added up for each bin separately for a number of cycles (in this case 75) then divided by the number of cycles. This gave the average firing for each of the six parts of the respiratory cycle. They showed a difinite and fairly smooth oscillation. Its (full wave) amplitude was 40% of the mean firing rate. It was shown by Black and Torrance (1971), by cross perfusion, that respiratory (PCO2) oscillations in the arterial blood from a donor cat (supplying the carotid arteries of a recipient) could cause 'beats' in the ventilation of a recipient cat breathing spontaneously at a slightly different rate. These consisted of intermittent larger breaths, as expected from the difference in the two frequencies. Hence, Paco2 oscillations can have an effect reflexly via the peripheral arterial chemoreceptors. Goodman et al. (1974) published studies suggesting that the (averaged) respiratory oscillations in sinus nerve chemoreceptor discharge were a result of Paco2 oscillations. Band et al. (1978) showed that the averaged oscillations in discharge disappeared when recorded pH~ oscillations were eliminated via carotid arterial mixing chambers. Sometimes return of pH a oscillations was no longer accompanied by chemoreceptor oscillations (oscillations in chemoreceptor discharge firing rate) but this deterioration probably resulted from loss of sensitivity to the fast P~co2 changes of the arterial Pco2 oscillations, Respiratory sensitivity (with tidal volume alternation) to PaCO2 oscillations of two breaths duration in cats (Wolff, 1977) was found to disappear when intravascular pipes were used on more than one occasion. This 'fast sensitivity' could also disappear with time despite considerable care over the cleanliness of intravascular equipment. It seems that the normal 'fast' sensitivity may deteriorate as a result of some property of the experiment. This seems likely to include intra-vascular clotting or debris. The sensitivity of the carotid arterial chemoreceptor to rapid Paco2 changes has also been tested by means of small CO 2 pulses generated in the cat at the aortic root by means of an

476

C.B. Wolff 5 sec

~

[

A

ALkaLi

5o

©

~

20

it

35 jl

25

I

35

L

l

45

1

I

55

497

n 45

A

I 55

I

l 65

P~CO 2 ( m m Hg)

P~CO2 (mm Hg )

Fig. 17. Examples are given here of ventilation/Paco2 plots from sheep undergoing CO 2 infusion (Phillipson et al., 1981c). On the left the sheep was intact and on the right the carotid bodies had been resected (CBR). Symbols: • . . . . normal oxygen tension; O . . . . hyperoxia; /k . . . . hypoxia. There is isocapnia in the normal sheep breathing air (up to 3.5 times resting l)'co2) and in hypoxia but not in hyperoxia. In the CBR sheep none of the curves is isocapnic. Furthermore, hypoxia depresses the response (compared with normal oxygen) while hyperoxia is relatively stimulatory.

up to two and a half times resting I?co 2. Above this, there was some hypercapnia. In the third study (Phillipson et al., 1981b) three sheep with carotid body resection (CBR) were compared with normal sheep. Infusion led to increased P~coz in CBR sheep. In normal sheep 'v'/Paco2 response curves were near vertical at normal P~,o2 (Fig. 17), sloped backwards in hypoxia and were depressed in hyperoxia. This is opposite to the CBR sheep and shows that isocapnic responses to increased I?CO 2 require the presence of the carotid body. Phillipson's studies also involved lowering the effective Vco 2 (~'co2 lung) to zero, by withdrawing as much CO 2 from the exchanger as was being produced by the sheep. Under these circumstances ventilation also dropped to zero (Phillipson et al., 1981). Apnoea appeared to do no harm presumably because oxygen was available from the gas exchanger. This is further confirmation that oscillations in P~co: may be important as they would be absent in the apnoeic sheep. The studies of P.hillipson et al. (1981b) and Linton et al. (1977) suggest that it is possible for changes in Vco 2 to give rise to some signal which enables P~co2 to be kept constant, much as suggested by Yamamoto and that the carotid bodies are the organ detecting the signal• Furthermore the study of Linton et al. (1977) directly suggests that the l;"co~_ related signal is carried by Paco_2 oscillations. The reason for the Paco2 rise accompanying raised Vco , in the negative studies quoted (see table) is not clear. There is certainly a strong tendency for sensitivity to fast changes in P~co, (e.g. within breath pulses--Chapter 4) to disappear while experiments are being performed, especially where these are invasive. Platelet emboli have been found in studies

498

C.B. Wolff

involving cannulation of the carotid arteries and have been associated with loss of P~co: sensitivity (Band et al., 1978" Wolff, 1977). Although the insensitive series cannot be explained at present, it is possible that the raised Pco:S occurring with increases in Vco 2 represent failure of a system which normally sustains isocapnia rather than representing the normal state. The occurrence of the positive finding (homeostasis for P c o : when only g c o : has changed) cannot be ignored, especially as it seems to pose very similar questions to the real life situations where homeostasis for P c o : is sustained, as in exercise. C O 2 response curve sensitivity (steady-state sensitivity) is not the same as sensitivity to

within breath pulses, or to CO 2 transients. They are part of a spectrum. A brief enough within-breath change in P~,co2 can act on a tiny instantaneous fragment of a breath, whereas steady-state CO 2 sensitivity concerns average ventilation over 20 min or so. The effect of a pulse of CO 2 or afferent sinus nerve stimulation can act transiently within an inspiratory period (Fig. 18). This cannot be explained in terms of CO 2 response curve sensitivity.

secon 50 ml.[ I

II

No stimulus Fig. 18. Spirometric recordings of two tidal volumes are shown Eldridge (1972). A control breath is shown on the left. On the right the carotid body was stimulated briefly (by changing Pco2 in the carotid artery (see double arrow). The inspiratory tidal volume profile increased briefly as a result of the stimulus but then returned to the expected (control) profile before the end of the inspiratory period.

The drive from CO 2 oscillations, if that is what makes isocapnia possible with increased l/co 2, is a dynamic one whereas the CO2 response curve drive is a static one. Studies of simulated tube breathing (CO2 inhalation during the early part of inspiration) suggest that the static CO 2 response can be affected by the contour (a dynamic component) of the respiratory oscillation (Cunningham, 1972; Cunningham et al., 1973). Tube breathing extends the rising expiratory CO 2 ramp of the PACO2 oscillation further than normal into early inspiration. A similar effect (reverse tube breathing) can be produced by giving CO 2 enriched gas late in inspiration. This starts the expiratory ramp of the PACO2 oscillation earlier than normal, during late inspiration. When ventilation and PACO,_ are measured in tube breathing and reverse tube breathing the points lie above and below the orthodox CO 2 response curve of the subject. The tube breathing and reverse tube


499

breathing ventilations are significantly different from one another. Here, oscillation changes have altered steady state ventilation. In other words a dynamic component (Pco: oscillation) can affect a static one (mean Pco:). The hypothesis that CO z oscillations act as a drive to breathing might suggest that their phase relation to the respiratory cycle should be consistent. This could mean that the oscillations would be 'in phase' with breathing (see Fig. 19). Here the down slope of the Paco,_ oscillation would occur during inspiration (as it does in the P,-xco2 oscillation). For this to occur there would be a lung to carotid body time delay (lag) equal to a whole number of respiratory cycles. In the cat there usually appears to be a lag of about one respiratory period (Wolff, 1984). In man, various lags have been recorded but a striking illustration of a lag of two cycles being sustained in exercise is provided by Coulter et al. (1980), illustrated in Cunningham et al. (1986). The lung to carotid body circulation time falls in proportion to the respiratory period as they shorten together in exercise. It is tempting to speculate about which is cause and which effect.

Inspiratory Tidal Volume Timing

~p'.Exp

J

/I

i

Arterial PC02

~

I

A

NN~

I I

cycle

B cycles

,

~,

I

Fig. 19. This diagram shows just over three respiratory periods with, at the top, the timing of inspiratory tidal volume and below this PACO2"Paco2 at the carotid body has been generated as a delayed version of PACO2:version A has been generated from a delay of one respiratory cycle and oscillates precisely in phase with the PACO2oscillations (and breathing); for version B the alveolar to carotid body delay is 11/2 respiratory cycles and the carotid arterial Pco2 is 'out of phase' with PAco,.

In Chapter 6 we shall see that a new model for CO2, which incorporates oscillations, homes in on a phase relation of about 1.4 respiratory cycles. The Paco2 oscillation rise occurs at the simulated carotid body during most of inspiration but reaches its peak shortly before the end of the inspiratory period. Further understanding is required of the way the putative dynamic CO 2 drive may work and the new model may be of some help in this regard.

500

C.B. Wolff

Neurogenic Drive A series of studies undertaken by Kao on dogs showed that neural input from electrically' stimulated limbs would sustain appropriate ventilation in the absence of a humoral stimulus from CO. flux (Kao, 1963; Kao er al., 1963a,b)--see also Mahler (1979). All the blood from the exercising limbs of one (neural) dog went to the inferior vena cava of a second (humoral) dog, which in turn, from its aorta, supplied the neural dog's lower limbs with arterial blood. The idea was to see whether the neural stimulus from the electrically stimulated limbs would affect the neural dog's ventilation. It did, but caused lowering of PAco, and P~coe which inhibited ventilation. The experiment was then repeated having provided normal cerebral blood gases by linking the cerebral vasculature of the neural dog with that of a third (donor) dog. The donor dog's blood gases were kept at normal values, so the neural dog's cerebral arterial blood gases were normal, even during exercise with increased ventilation. The neural dog's ventilation then increased as much as would have been required to sustain isocapnia, even though there was no increase in Vco: at its lungs or change in the arterial chemical signal in the carotid arteries. This work led to the idea that there may be "metaboreceptors' in exercising muscle causing ventilation to change in proportion to 1)co _, (Mahler, 1979; Wasserman et al., 1986). The metaboreceptors concept and Yamamoto's hypothesis appear, at first sight, to be in conflict. They can both drive ventilation adequately in exercise on their own. How is it that under normal circumstances when both operate we do not have double the drive and true hyperventilation, i.e. ventilation of an inappropriately large amount, with excessive lowering of PAco, and P:,co:? One answer, given by Cunningham et al. (1986), is that there is a "redundancy' of drives. This still requires us to explain why two drives, each of which is capable of driving breathing adequately on its own, do not cause hyperventilation when they act together. Control theory offers some useful clues on this (see Chapters 6 and 9). A type of neurogenic drive to breathing which acts in parallel with the 1/co: humoral drive has been demonstrated in subjects undergoing isometric exercise (Imms and Mehta, 1989). In this study, isometric handgrip or leg extension at 20% of maximum voluntary contraction (MVC) were undertaken for 5 min. 40% MVC was also undertaken for 2 min for each type of exercise. Oxygen consumption was doubled by these manouevres (except with isometric leg extension at 20% MVC where it was tripled). Ventilation was increased to the point where, in most cases, P~tco, was lowered, usually throughout the period of isometric exercise, often remaining low for half a minute or more afterwards. On one occasion, instead of falling, Pctcoz rose, with a peak of 8 mm Hg above resting for 3/4 min. The fact that Pco2 was not normal means that alveolar ventilation and l/co . were not matched and we have to assume that these neurogenic drives over-ride whatever mechanism normally matches 12a to lPco :, whether humoral (1)'co: related) or even neurogenic. Stimulation of afferent nerve fibers from muscles increases ventilation and the effect persists for some time after the stimulus has been removed (see Wasserman et al., 1986). Persistence of the effect of excess ventilatory stimulation in the isometric exercise study of Imms and Mehta (1989) is compatible with this finding.


501

Similarly, persistence of hyperventilation (low Pco~_) occurred in the study of Sargeant et al. (1981) and that of Bradbury et al. (1993) involving metabolites trapped in muscle. Sargeant et al. (1981) exercised their subjects with occlusion of circulation (to and from) their exercising legs for the first 2 rain and for the last 2 min of an 8 min dynamic exercise period. P~co: and arterialized ear-lobe Peon_ fell similarly during each occlusion. Restoration of normal Pco-_ took about 12 sec following the first occlusion. In the study of Bradbury et al. (1993) intermittent isometric contraction of the legs was undertaken at 40% MVC. The subject alternated this with rest periods. Contraction and rest were each of 2 sec duration. The experimental run lasted 3 min, either with circulatory occlusion to the lower leg (test run) or without occlusion (control run). Control 12o~- increased by 120 ml min-~ with Petco2 remaining normal. With circulatory occlusion (test run), Vo_- increased less and yet Petco_, fell. The authors thought that this could be due either to central drive, as an overflow from the increased neural motor activity required to maintain muscular contraction, or to increased afferent neural drive from the muscle. They therefore left the circulatory occlusion in place after exercise on a number of occasions. Lowered PetcO2 then persisted for much longer than was the case without occlusion. These results support the idea that metabolites may be responsible for neurogenic drive and that this drive may act alongside the humoral drive, independently of it, or may over-ride it.

Arterial Potassium Ion Potassium ions have already been mentioned in Chapter 4, where it was pointed out that increased arterial concentrations augment oscillations in discharge frequency in carotid sinus nerve afferent chemoreceptor fibres and (temporarily) increase mean discharge. The mean discharge, after an abrupt increase due to a step (up) of [K~+], decays slowly, taking 30 sec to reach half the fall occurring by 5 min. The [K, +] increase in exercise occurs as a result of K + release from exercising muscle with circulation to the systemic arteries. [K~+] levels have been recorded continuously and shown to rise from resting levels after an approximately 20 sec lag, much as expected for the time blood will take to come from the exercising muscles to the systemic arteries, in the transition from rest to 100 W exercise (Linton et al., 1984). After an initial fast [K~ +] rise (see Fig. 20) the rise

E 4-",/

t

o

I I

I 2

Min Fig. 20. The figure shows how [K,,+] increases in exercise with a lag after the onset of exercise (A) representing the time taken for K + to circulate from muscle to systemic artery. The rapid fall after the end of exercise (B) is due to tissue uptake.

502

C.B. Wolff

continues less rapidly reaching a plateau (at moderate work rates) by about 3 min. The decay at the end of exercise starts after a shorter lag (10-15 sec in this study) reflecting higher cardiac output. The fall follows a time course with a time constant of just over 1 min. In the study of Linton et al. (1984) the initial rate of fall (from a plateau of 5.4 raM) was about 2 mm min -~. With a cardiac output of 15-20 1 min-t (Kao, 1972), this meant a tissue uptake of approximately 30--40 mM min-l initially, with a progressive reduction in uptake as recovery proceeds and [K~ +] approaches resting values. The resting values are the same as the general venous level. The sites of uptake and regulation are discussed in the review of Lindinger and Sjogaard (1991). There is evidence, as one might expect, that the K~+ concentration reflects the metabolic rate, though the relationship is non-linear, see Lindinger and Sjogaard (1991). There is also considerable individual variation even when each individual subject's {/E/K~* correlation is good (Newstead et al., 1990). Differences within individuals can also occur according to the type of exercise they undertake. In the study of Newstead et al. (1990) 17E was linearly related to [K~,+] in both cycling and rowing exercise. However, the lines were displaced, so a given 12E occurred with a different [K~,+] for the two types of exercise. There is also a tendency for [K~ +] to rise progressively with time in heavy exercise (Paterson 1992). This makes the idea of [K,, +] being a potential metabolically related drive to breathing less attractive than would be the case with a simpler and more reproducible linear relationship. However, ventilation is stimulated by increases in [K~-], as shown in cats by Sneyd et al. (1988). Increasing [K, +] by 2 mM caused an approximate doubling of ventilation and a fall in Paco2 of 2-3 mm Hg (NB odd discrepancy between ventilatory and P~coe changes). This ventilatory change occurred at all oxygen tensions. Ventilation was increased similarly in the rhesus monkey in the study of Paterson (1992). Here the response was eliminated by hyperoxia. Band et al. (1985) showed that ventilation was increased by potassium infusion in anaesthetized cats before, but not after, sinus nerve section. Transiently increased [K,, +] (as mentioned earlier in this chapter in the section on dynamic Pco2 and Po: effects on ventilation) was shown by Dejours (1963) to cause increases in single tidal volumes. This has been matched by the KCI stimulations produced by Linton and Band (1985) mentioned in Chapter 4. [K~ +] pulses each caused an increased tidal volume when the peak coincided with inspiration. It seems to be established that ventilation can be increased by increasing [K~+] and yet the expected reduction in ventilation does not occur in exercising subjects whose [K~ +] is reduced by the administration of glucose and insulin (Paterson et al., 1989). Similarly, [Ka +] rises much higher than normal in exercise in subjects taking beta blocking drugs (Linton et al., 1984; see also Cunningham et al., 1986 and Lindinger and Sjogaard, 1991) and yet P~co: is not lowered significantly. There is therefore apparently normal respiratory control despite high [K~+]. As with the neural and humoral drives, we see that reducing (or increasing) one of them may make very little difference. Again, we have the situation where expecting to add drives up, as though they each contributed to a proportion of the ventilation, could mislead us into discounting their effectiveness (for example when acting alone). The difficulty presented by beta blockade may have a simpler answer, as proposed by Cunningham et al. (1986). Paterson and Nye (1988) showed that the carotid chemoreceptor mean discharge and sensitivity to [K~+] were


503

reduced in the anaesthetized cat after beta-blockade. This would cause a reduction in the effectiveness of [Ka +] as a drive. Potassium is further reviewed by Paterson (1992).

Drives Do Not Add Up Even with metabolic rates which are increased to three times the resting values, Paco2 has been sustained at, or close to resting values with the humoral signal acting alone, the neural signal acting alone or with both signals acting together. There are also well substantiated drives from the cortex, arterial potassium and also perhaps a cardiogenic drive (Wasserman et al., 1974). These drives cannot act by simple summation. The search for some substance which acts as a 'calibrated drive', precisely the right amount of drive to run in scaled form through from receptors to brain and respiratory muscles, is no longer sensible. The precision needed would be impossibly great. Yamamoto and Edwards (1960) seem more likely to be correct, that Vco 2 information is needed and is implemented, instant by instant. Man made mechanisms with the required precision incorporate feedback and it seems likely that biological mechanisms do too. The next chapter will discuss feedback as part of control theory, respiratory models of exercise and a CO, model designed to incorporate fast (within-breath) CO 2 changes.

Chapter 6

Control Theory and Respiratory Models

Control System Characteristics The respiratory system, amongst many others in the body, seems to involve many of the elements found in man made control systems, for example 'feedback'. It therefore seems worthwhile to examine one or two of the most basic forms of control system where the elements are understood and where theoretically predicted advantages have been repeatedly confirmed in practice. The use of feedback consists of comparing the output (either as it stands or amplified) with the input signal (or reference value). This (feedback) and the other most fundamental elements are shown in Fig. 21. The input is often called the reference or command value or even 'set point'. This is the desired value for the o u t p u t - - s e e for example Randall (1962). With 100% feedback (where B in Fig. 21 is 1) a value equal to the output value is subtracted from the input

Input signal Reference Command Set point

ein ~( ~ ~. .~

Amplifier Effector XG I

eerr Error

FEEDBACK

edis -->--eout

X B .JSensor; feedback element

Fig. 2]. The system shown here consists of an input (eln) and output (eou0 linked such that eout is kept close to a desired value. A signal equal to the output is fed back, often with multiplication (B) to be compared with the input (comparator). The difference (eerr) is part of the forward path and is multiplied by a factor (G). A disturbance (edit) is shown between the amplifier (G) and the output and feedback offshoot. 504


505

value. The difference is, of course, the error, the extent to which the output differs from the desired value (the input or reference). One of the main aims of the system is to minimize the error, yet this error is next multiplied by the factor G at the amplifier to give a value close to the desired output. In this case with a disturbance as indicated (edis) , the aim is that the value of the amplifier output (eout--edis) should be as close as possible to (ein-%~). The ratio of the output to the input (eo,,tlei,.,) is known as the closed loop gain. This can be found from first obtaining an expression for the amplifier gain (G) and the ratio of its output to its input (the error). The error is e i , - f e e d b a c k = ei.,.,-Beou t. Hence:

G = (eout-edis)/(ein-Beou O.

(46)

eou, = ( G % + %s)/(1 + BG).

(47)

Rearranging:

Where there is no disturbance, the closed loop gain is:

eou]% = G/(I + BG).

(48)

The 'open loop gain' is the amplification achieved by a signal passing completely around an open loop, i.e. through the feedback element and the amplifier. Its value, BG, is an important guide to how well the system sustains constancy of the output signal, minimizes error and compensates for external disturbances. The effect of the disturbance, edis, on the output is, from Eq. (47), edi](1 + BG). Where BG (open loop gain) is large the effect of a disturbance will therefore be small. Since the error (with no disturbance) is eo,.,.t/G, from Eq. (47), error = ein/(1 + BG). The error will therefore also be small when the open loop gain is large. Riggs (1963) points out that 1/(1 + BG) is in effect the 'magnification' of change in error per unit change in input (Ae~r/Aein) produced by closing the loop. Since closing the loop is designed to make the error small he prefers the concept which he calls minification, where: minification = 1/magnification = 1 + BG. However, with zero feedback i.e. with B or G equal to zero, the minification value is unity, even though the system would then have an effectiveness of zero. He therefore proposes the term homeostatic index, defined as (minification - 1 ) . The homeostatic index is therefore BG and is the same as open loop gain. The various accounts of control theory point out that even when there is no feedback element in the formal sense shown here, there will be something which is an equivalent if, for two variables in a feedback loop, one affects the other positively and the other affects the first one negatively. If there are many elements in a feedback loop then there must be at least one negative influence to achieve negative feedback. If there are more negative influences then there must be an odd number of them if there is to be negative feedback.

506

C.B. Wolff

In the system shown in Fig. 21, the negative (or backward) relationship is eerr = e m - B e o u t. The slope of the line relating eout to eerr (input to the amplifier or effector) is - B . So the variables on either side of the amplifier are related negatively in this relationship. The positive (or forward) relationship is: eou t = G(e,,. r + edis). Here the slope of the line is G. Since the loop gain (open loop gain) or homeostatic index is B G , open loop gain is defined as the negative product of the slopes of the forward and backward relationships. In the resPiratory system, VE = S ( P c o ~ - B )

(49)

is a 'forward' type of relationship between 12E and Pco_, with a positive slope, S (Milhorn, 1966; Riggs, 1963). The corresponding 'backward' relationship, normally providing feedback) is: PACO2 = PlCO2 + ~"Co2"PB/VA '

(50)

In most situations P~co, is not appropriate and the equation here is then the same as Eq. 9 (i.e. PACO, = 12co£/~Jg.A) • Although there is no negative sign and the relationship is non-linear, increases in V A reduce PACO2' The effect is negative and hence the slope of the relationship dPAco,/dl2 A is negative. Differentiation of Eq. 50 gives the slope: dPAco2/dl~'g = --~'cozPB/VA 2. From this and the slope of the forward relationship, the open loop gain (homeostatic index) is: S. ~ZCo2"PB/VA2

(51)

Figure 22 shows the functional arrangement of the elements in this physiological feedback loop. The positive relationship (corresponding to 'drive') is now called the controlling system (rather than the amplifier). The negative relationship is provided by the physical properties of the body, with increased ventilation reducing Pco2. This corresponds to a combined feedback element and comparator. There is no specific comparison with any

Dist.

PCO 2

Fig. 22. Elements in a feedback loop for regulating carbon dioxide partial pressure, after Milhorn (1966). Dist., represents disturbance. The controlling system is a standard CO 2 response curve, the controlled system a metabolic hyperbola. The lower metabolic hyperbola represents rest, the higher one exercise. Earlier presentations in this form (Milhorn, 1966) only included the resting metabolic hyperbola.


507

reference level or input in the scheme shown in Fig. 22. The ventilation obtained depends on the simultaneous solution of the equations for the forward and backward relationships (Eqs 49 and 50). Whether the inspired CO 2 concentration or the metabolic rate are changed, this model (for that's what it is) can only give ventilation values obeying the forward relationship and hence Pco2 must increase as f," increases. The open loop gain is very high at normal P c o . (28 approximately) but drops very fast indeed with inhaled CO 2 (2 at 44 mm Hg, 5.9 l

1.8 16 1.4 1,2 1.0

-4

-3

-2

-I

0

A C S F PCO 2 (ram Hg)

Fig. 32. This linear relationship between i/ and APcsFCO 2 was obtained by linear regression through points derived from two plots of van Beek (1983). His two plots related, 1. 1)" to Pao2 in a preparation with isolated central perfusion (peripheral P~o2 and Paco2 constant) and 2. APcsFCO 2 to Pao2- The points for the present figure each corresponded to a given oxygen tension in van Beek's original figures. Hence 1;' and APcsFCO 2 were each found for a given Pao2. The ventilatory sensitivity (AV / APcsF.co2) for the present (derived) plot is similar to that found in separate hyperoxic studies. The inhibitory effect of the central PCSF.CO, change shown in the figure appears to be enough (in mild to moderate hypoxia) to neutralise the stimulatory effect of hypoxia at the peripheral arterial chemoreceptor.

Olievier et al. (1982) and van Beek (1983) also measured ventilatory sensitivity to changes in Pcsv.co,_ in hyperoxia. There was a moderately wide range of values with a mean of 0.172 1 min-X/mm Hg (1.29 1 min-1/kPa). The hypoxic value obtained above (Fig. 32, 0.208 1 rnin-I/mm H g - l . 5 6 I min-VkPa) fell well within the range for hyperoxia. Hence, sensitivity to Pcsv.co, change is much the same in acute hypoxia and hyperoxia. This was also concluded by the Berkenbosch group (Berkenbosch et al., 1984) see also Cunningham and Drysdale (1976). The comment of van Beek seems apt here: ". . . . . changes in the Pco2 at the site of central chemoreception play an important role in the ventilatory depression by central hypoxia." There are others with a similar view; to quote: " . . . depression during mild hypoxia (Sao,- > 85%, 52 mm Hg, 6.9 kPa) resulting

526

C.B. Wolff

from transient brain stem alkalosis secondary' to increased brain blood flow. . . . . '" (Neubauer et al., 1990). The fall in PcsF.co: which occurs in hypoxia must, at least partially, result from the increase in cerebral blood flow which hypoxia is known to cause. It is also possible that it will persist into the chronic phase, though this needs investigation. The other potential cause of the fall in PCSF,CO-, is the Haldane effect. It is proposed (Downes and Lambertsen, 1966) that lowering of venous Pco: results from the extra desaturation which results from hypoxia. However, the arterial Pco: is determined by Vco: and 17 at the lung and, in the mild hypoxia range, is unchanged (even though the content will be greater than at normal oxygen tension). On addition of the cerebral metabolic CO 2 the change in Pco: is probably no greater than occurs at normal P~o: unless there is a significant increase in the slope of the in vivo CO2 dissociation curve in hypoxia. It therefore seems likely that it is mainly the response of the cerebral blood flow (CBF) which is behind the lowering of PCSF.CO:. Finding a delay between the onset of hypoxia and the central depression which is greater than the lag time from lung to brain could suggest CBF involvement rather than the Haldane (chemical) effect. Decreased ventilation resulting from isolated central perfusion in cats was delayed for more than two minutes after the change to hypoxia in the study of Berkenbosch et al. (1983). However, much of the delay involved the time from gas exchanger to venous circulation. These authors also found a fall in PCSF,CO:in the intact animal exposed to isocapnic hypoxia, though the delay was then less than a minute. A review covering much of this area has been provided by Berkenbosch and de Goede (1988). Berkenbosch et al. (1991) have shown that the ventilatory depression expected from increasing cerebral blood flow can also be produced by adding papaverine (a cerebral vasodilator) to blood perfusing the brainstem of the anaesthetised cat. They concluded that their results "support the hypothesis that cerebral vasodilatation by itself contributes to the decrease in ventilation by brain stem hypoxia". The hypothesis is, in summary, that mild hypoxia causes an increased ventilatory drive from the peripheral arterial chemoreceptors, but this is initially masked by the alkaline change/low ECO: occurring at the central chemoreceptors due to increased cerebral blood flow. This suggests an experiment in which newly applied hypoxia (by inhalation) would cause an increase in ventilation between the time of arrival of the hypoxic blood at the peripheral arterial chemoreceptor (about 6 sec) and the later time at which it reached and affected (speeded up) cerebral blood flow. The longer of the two lags (onset of hypoxia to central depression) would either be equal to the lung to central chemoreceptor lag time for the circulating blood, or could be longer if the vasculature then takes time to respond and could also be prolonged if it took a significant time for cerebral tissue Pco2 to equilibrate. These points need further experimental clarification. The central negative effect on PCECF.COewould cancel out the peripheral stimulation from then on. This could be comparable in its usefulness to the 'single breath N2 test' (Dejours, 1963, Chapter 5). It might even yield both peripheral and central chemoreceptor lag times. To return to the acclimatization process in mild hypoxia, the lowered PcsF.co_, (despite unaltered ventilation or Paco2) appears to provide the required error signal, necessary before acclimatization can occur. Either the alkaline change or the fall in PCSF,CO_,or


527

both counteract the ventilatory stimulation from the peripheral arterial chemoreceptors. From the study of Schuitmaker et al. (1987) discussed in Chapter 4, it is probably both.

Further Changes in Altitude Acclimatization The first adjustment made in acclimatization to mild hypoxia involves reduced PCECF,CO: without any change in Paco,_ or ventilation. There will also be an alkaline change in PHcEcF. Paco,_ eventually falls to the chronically acclimatized value but is held back at this early stage by both alkalinity and reduced Pco: at the central chemoreceptor. Something presumably erodes the inhibition. Theoretically, since [H +] = N x Pcoz/[HCO3-] inhibition will be released either a result of a rise in PCECF.CO, or a fall in pHcEcF (rise in H+). If the CBF response to hypoxia were to become a.ttenuated, PCECF,CO2 would rise and reduce central inhibition so the hypoxic peripheral drive would reduce Paco2. This is one possibility. The other possibility is that some unknown mechanism reduces pHcEcF by lowering [HCO3- ] as was suggested by Severinghaus et al. (1963) and others, with the suggestion that PHcEcF homeostasis was achieved. The reduced inhibition would, again, allow P~co2 to fall. If the pH remained alkaline in the CSF it could, hypothetically, later be returned a moderate amount back towards normal. This does occur according to the study of Bouverot (1976) and Bureau and Bouverot (1975). Their study involved a fall in [HCO3- ] which presumably reduced central chemoreceptor inhibition from previous low [H +] allowing more ventilation and hence a fall in P~co:. The mechanisms involved in [HCO3-] and pH reduction are not clear and descriptions of such changes in CECF with time which would help a great deal are unfortunately few and far between. The study of Bouverot (1976) is one of the very few studies giving values for arterial blood and cerebrospinal fluid at reasonably short time intervals. Conscious dogs were used. Unfortunately, the initial Pao2 (just over 50 mm Hg, 6.7 kPa) fell below the mild to moderate range. Hence, on initial exposure to hypoxia there was an immediate fall in P:,co_, (from 34.5 mm Hg on air to 29.2 mm Hg in hypoxia) by 5.3 mm Hg (0.71 kPa). Instead of no P~co, change and CSF changes wholly attributable to the central effects of hypoxia (as in mild hypoxia), the fall in PcsF.co2 was partly due directly to the change in P~,co: and partly to the central effects of hypoxia. The initial central Pco: fall was 6.0 mm Hg (from 44.0 to 38.0 mm Hg--0.81 kPa). Hence, the central Pco2 fall exceeded the P~,co: fall by 0.7 mm Hg (0. I kPa). Most of the central inhibition here was therefore from the P,~co: fall (88%), the rest being a result of the excess central Pco2 fall (12%). After the initial pH change centrally (from 7.336 to 7.384) pH remained unchanged for an hour, despite a further fall in central Pco2 (to 36 mm Hg, 4.8 kPa). CSF HCO 3- fell during this time and continued to fall with no further change in PCSF.CO: over the rest of the first day. Hence pHcs v was brought down to 7.335. There was then hardly any further change over the rest of the first week. This study suggests there is an active process which, in this study at least, came near to correcting CSF pH. The problem of conflicting reports on the degree of pH correction in the environment of the central chemoreceptors is not resolved. It is discussed in the review by Forster and Dempsey (1981) and more recently by Fencl (1986).

528

C.B. Wolff

It may be some time before we know why normal man adjusts his Paco2 to 0.25 Pao: + 15 mm Hg (0.25 Pao: + 2 kPa). However, it is a useful relationship which can help doctors to decide the extent of normal hypoxic regulation in patients. Studies remain to be undertaken to unravel the mechanisms responsible for this relationship.

Chapter 8

Long Term Respiratory ControlmMetabolic Acidosis

Acute Versus Chronic Sensitivity and Other Problems Metabolic acidosis differs from hypoxia in that it only occurs in disease, it is usually difficult to generate acute exposure and it has tended to be less readily measurable in man than is the case with hypoxia. Furthermore, the site of action of the hypoxic stimulus is known to be at the peripheral arterial chemoreceptor, whereas there has been a long standing argument about the site of action of metabolic acidosis. The problem was whether metabolic acidosis acted on the central chemoreceptor, or on the peripheral arterial chemoreceptors. Published studies are quoted which support both a purely central action and a purely peripheral one. This conflict seems to have been largely resolved by the finding that metabolic acidosis affects both central and peripheral chemoreceptors, as discussed in Chapter 4 (Schuitmaker et al., 1987). Differences between acute and chronic sensitivity seem likely to involve the processes associated with reduction of central [HCO3- ] ([HCO3-]csF) to the value found in the steady state of metabolic acidosis. This reduction in [HCO3-]csFis associated with a degree of correction of central pH (pHcEcv) in the face of lowered central Pco:- The lowering of central Pco_, which is found after completion of adaptation accompanies a lowering of arterial Pco2 which is precisely related to the degree of metabolic acidosis. How this point is reached, with its near normalization of central pH and precise arterial Pco2, remains a subject for debate.

Chronic Acidosis and

CO 2

Response Curves

Chronic acidosis has been studied in normal subjects, for example, (Cunningham et al., 1961; Lloyd and Cunningham, 1963; Nielsen and Smith, I951/2) along with acute responses to CO 2 and O 2. Acidotic CO x response curves are displaced to the left of those at normal pH. In other words there is one fan of lines (CO x response curves), each line being at a different Poz, for normal pH and another fan of lines for acid pH, each line for acid pH being parallel to the one for the same Po2 in the non-acidotic subject. The usual description of this information suggests that the acid stimulus simply has an effect on ventilation which is additive to the acute stimuli, in contrast to hypoxia which, of course, acts multiplicatively with C O , (Chapter 4). This description fails to consider 529

530

C.B. Wolff

the possibility that the long and short term effects of metabolic acid may differ. In other words, sensitivity may differ if acidosis is acute rather than chronic. Acute and chronic sensitivity seem quite likely to differ, by analogy with hypoxia (Chapter 7). Hypoxia and CO 2 administration, in experiments of the type just described, can be referred to as acute whereas the acidosis is chronic (typically' requiring a preliminary' week of ammonium chloride administration).

Response to Acidosis It has been recognised for many years that Paco~_is lowered in chronic metabolic acidosis (Peters, 1917). This lowering has usually been quoted in relation to arterial [HCO3-], used as an index of metabolic acidosis. However, arterial pH is now measured directly and its use avoids considerable potential for ambiguity. It is therefore worth considering advantages of employing the relationship between the fall in Paco_. (response) to the fall in pH (stimulus). The older expression of the sensitivity to metabolic acid base change, APcoz/A[HC03-], has the disadvantage that it varies numerically according to the degree of acidosis or alkalosis (Forster and Dempsey, 1981). If the chronic response to metabolic acid is expressed in terms of P~coz and pH a, sensitivity is then APaco2/ApHa. As will be seen shortly, the relationship between P~co2 and pH a is linear so that (unlike APaCo2/A[HCO3-]) sensitivity related to pH (kP~co2/ApHa) is constant in the face of a wide range of metabolic acid-base changes. Reports in the older literature using APaco2/AHC03- have, nevertheless, been of great value in showing that acute and chronic states of metabolic acidosis do differ, displaying less of a fall in P~co2 in the early stages than is found in the steady state. The mechanisms which determine differences between acute and chronic sensitivity to metabolic acid and the transitional stages require investigation. First let's examine the steady-state (chronic) Paco2/PHa relationship.

Chronic Response in Terms of Paco2 Displacement of CO 2 response curves to the left by chronic metabolic acidosis, as mentioned above (Cunningham et al., 1961; Lloyd and Cunningham, 1963; Nielsen and Smith, 1951/2), also involves a modest increase in ventilation for the air breathing point. This is because the two points (normal and acidotic) both lie on the (resting) metabolic hyperbola (see Chapter 2). PACO2 is reduced as a response to the acidosis. This (acidotic) Pcoz is presumably a new operating point for the control system. Pco2 in chronic acidosis (breathing air) should therefore not change in the face of a wide range of metabolic rates (rest and moderate exercise). Experimental confirmation would be useful. It would also be interesting to know whether CO 2 response curves in acidotic subjects undergoing mild to moderate exercise are parallel to the ones at rest, as found in subjects with normal pH (Cunningham, 1974). The relationship between Paco2 and pH~ which has been derived from data in the literature, quoted in Table 4, is:

Paco2 = 70pHi, - 478 mm Hg

(65)

531


Table 4. P~.co:/pH,, relationship

1st author

Year

Slope (ram HNpH u)

Intercept (ram Hg)

r

p ~

Control of mitochondrial respiration in the heart in vivo.

Thorax radiography with e.c.g. and respiration control.

Activity and physiological significance of the pleopods in the respiration of Callianassa californiensis (Dana) (Crustacea: Thalassinidea).

A dual control system for assisting respiration.

Physiological and environmental control of yeast prions.

Peptides, serotonin, and breathing: the role of the raphe in the control of respiration.

Characterisation of the control of respiration in potato tuber mitochondria using the top-down approach of metabolic control analysis.

The physiological significance of postinspiration in respiratory control.

Physiological role for leptin in the control of thermal conductance.

Physiological and electrochemical effects of different electron acceptors on bacterial anode respiration in bioelectrochemical systems.

Oscillation and chaos in physiological control systems.

The physiological target for LeuRS translational quality control is norvaline.

Oxygen regulated gene expression in Escherichia coli: control of anaerobic respiration by the FNR protein.

Insights into organohalide respiration and the versatile catabolism of Sulfurospirillum multivorans gained from comparative genomics and physiological studies.

Control of functional electrical stimulation with extended physiological proprioception.

Physiological control of brain catechol synthesis by brain tyrosine concentration.

Physiological and environmental control of Gram negative bacteria on skin.

Conditional symbolic analysis detects nonlinear influences of respiration on cardiovascular control in humans.

Metabolic control analysis of mitochondrial aconitase: influence over respiration and mitochondrial superoxide and hydrogen peroxide production.

Positive FNR-like control of anaerobic arginine degradation and nitrate respiration in Pseudomonas aeruginosa.

Continence and micturition: physiological mechanisms under behavioral control.

Variable setpoint as a relaxing component in physiological control.

Competition for neuronal processing time: a physiological seizure control mechanism?

Assisted respiration.