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Respiratory mechanics: fundamentals and measurement principles
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J. Ass vet Anaesth. Vol. 16 (1989)
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Respiratory mechanics: fundamentals and measurement principles S. Young Animal Health Trust, I? 0.Box 5, Newmarket, Suffolk. INTRODUCTION
Gas flow in and out of the respiratory system is largely governed by simple physical phenomena. These phenomena are fundamental to the understanding of normal respiratory physiology and the alterations in respiratory function that occur in certain pathological conditions. Because of this, measurement of the mechanical properties of the respiratory system is often required for clinical o r research purposes. To someone starting work on respiratory mechanics the subject can, however, be very confusing. Ideas such as parameter estimation may seem far removed from the physical laws upon which the theory is based. One of the reasons for this is the desirability that any measurement technique is non-invasive, so that it can be used in clinical work. This often results in a rather obscure method of measuring a simple parameter. Another reason is that the behaviour of the respiratory system is not completely explained by simple laws and a more general theory is required to explain such observed phenomena as the frequency dependence of resistance. The concept of impedance has proved very useful in this respect. The mechanical properties of the whole respiratory system are made up from the contributions of its various components: the mouth and nasal passages, pharynx, larynx, central airways, peripheral airways, lung tissue and chest wall (which includes the diaphragm and a contribution from the abdominal contents). It is often the case that one is only interested in a part of the respiratory system a n d many techniques allow respiratory mechanics to be partitioned into certain components. In addition, some techniques only measure the mechanical properties of part of the respiratory system. The nomenclature associated with partitioning of respiratory mechanics varies somewhat and the Appendix gives the meaning of some terms as used here. This article is designed to help those who are new to the study of respiratory mechanics, and is divided into two main sections. The first part describes the basic mechanical properties of the respiratory system and how they are combined to relate the pressure gradient across the respiratory system to the gas flow in and out of it. The second part reviews practical techniques for measuring respiratory mechanics and is concerned with measurement principles rather an exhaustive list of all modifications of a basic technique. Human studies are included for completeness and because in some cases the same techniques can be used on anaesthetised but not
conscious animals. Attention is, however, drawn to those methods which have proved most suitable for animal work in both small a n d large species.
FUNDAMENTAL M E C H A N I C A L
P R O P E R T I E S OF
THE
RESPIRATORY SYSTEM
There are three fundamental mechanical quantities that relate the flow of gas in and out of the respiratory system to the pressure d r o p across it: resistance, compliance and inertance. These parameters are due to the physical properties of the respiratory system as described below. In some circumstances it is easier to understand the parameters from a consideration of the fate of the energy put into the respiratory system by the respiratory muscles. Energy is dissipated instantaneously (as heat) by the resistance of the system but is stored by the compliance and inertance. A compliance stores energy as elastic potential energy, whilst an inertance stores energy as kinetic energy.
Resistance Friction between the moving gas molecules and the stationary airway walls produces a pressure drop along the airway and causes the gas to lose energy. This effect can be described in general terms by the equation: P=RV' where P is the pressure drop across the airway, V' the gas flow rate along the airway and R is defined as the resistance of the tube. For laminar flow R is independent of flow rate, but if turbulence is present R varies with flow. Lung and chest wall tissue also has a resistance. This can be imagined as arising from instantaneous energy loss caused by viscous shearing forces within the tissue.
Compliance The elastic lung tissue and chest wall are stretched as air is inspired. The tension generated in these tissues opposes the expansion of the thorax and the elastic properties of the tissues are such that the pressure required to balance the elastic forces is proportional to the inspired volume. The effect is thus described by the equation: V P= where P is the pressure required to maintain an inspired volume V and C is defined as the compliance of the thorax. 35
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A small component of the total respiratory compliance squared gives -1. In engineering this number is denoted is due to compression or rarefaction of the air within the by j, so that j2 = -1 (in the pure mathematical world the respiratory system. This is conventionally included with symbol i is usually used). All imaginary numbers are the tissue compliance. expressed as multiples of j, so that for example (592 = -25 Compliance is conventionally divided into static and and so on. dynamic compliance. Static compliance is measured Complex numbers are expressed in two during a period of apnoea when the chest volume is interchangeable formats. The Cartesian format is of the constant whilst dynamic compliance is measured with a form: Z=3+4j varying chest volume. Dynamic compliance differs from static compliance and the real and imaginary parts of the impedance are due to inhomogeneities within the lung (Otis et nl 1956), clear. The equivalent polar form of this number is: Z = 5exp(0.927j) central airway compliance (Mead 1969) and the effects of inertance (Dosman et a1 1975). Dynamic compliance where 0.927 is an angle in radians. There are conventions varies with the frequency at which it is measured and the for manipulating complex numbers (addition, measurement frequency should therefore be stated. If it is multiplication etc.) which can be found in standard not it is often assumed to be measured at the normal mathematical texts. The impedance of the respiratory system can be respiratory frequency of the subject. determined quite simply from its resistance, compliance and inertance: lizertance (a) Resistance (R) is left alone and becomes the real During respiration air moves in and out of the chest. It part of the impedance. (b) Compliance ( C ) is replaced by where j2 = -1 thus undergoes a change in velocity, i.e. an acceleration, oc and in accordance with Newton's second law of motion a and o = 2n times frequency. force must be provided to produce this acceleration. This (c) Inertance (I) is replaced by joI. (d)All the imaginary terms are added together to form force is the driving pressure, which is related to the the reactance, which is defined as the imaginary part of acceleration by the equation: the impedance. The reactance (XI of the respiratory P = I V" where V" is the acceleration of the gas and I is defined as system (with compliance C and inertance I) is therefore the inertance. 1 given by: X = j(w1) The inertance of the respiratory system has received wc (el The impedance ( Z ) is simply the sum of the much less attention than the resistance or compliance because at normal respiratory frequencies its effects are resistance and reactance, i.e Z=R+j(oI-K negligible. It becomes very important, however, at higher frequencies or if measurements are made upon intubated There are some important points that arise from this equation: subjects (Sullivan et a1 1976, Dixsaut et n1 1980). (a) The impedance a n d the reactance vary with frequency because of the presence of w in the equation. Impednnce (b) At one particular frequency the reactance wiIl be In recent years increasing attention has been paid to zero because the reactances of the compliance and another mechanical property of the respiratory system, inertance are of opposite sign (ie they are 180" out of its impedance (denoted by Z ) . This is partly because it phase) and at a certain frequency they will be of equal can accommodate such phenomena as the variation of amplitude and cancel each other out. This frequency is compliance and inertance with frequency. Another given by: 1 WI reason is that there is much knowledge in electrical engineering of how to measure and analyse impedance 1 1 or f = 2 n f i ie o = which can be applied to mechanical systems as well. The impedance of the respiratory system is a complex This frequency is the resonant frequency of the number that represents the final relationship between respiratory system. pressure and flow due to the combined effects of the Complex numbers can be represented in either polar resistance, compliance and inertance of the respiratory or Cartesian form. The Cartesian form, in which the system. It is best described intuitively as 'the total impedance is represented by its resistance and reactance, opposition to flow' (Long et al 1962). The full derivation has been used above. The polar form represents the of impedance from the equations above is given in impedance by its magnitude ( I Z I ) and phase angle ( [ Z ) . Appendix B. The two forms are completely interchangeable and are Any complex number is made up from two parts, a related by the equations: real and an imaginary part. All 'ordinary' numbers are IZI = G Z F real, and thus the real part of impedance is handled in LZ = tan-' X the same way as any other number. The imaginary part R The two forms are shown on an Argand diagram in contains a component with the property that, when squared, a negative real number results. To simplify figure 1. matters only one imaginary number is used, which when Both the Cartesian and polar forms of impedance are
3
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=s
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J. Ass. vet. Anaesth. Vol. 16 (1989) ~
w
Real axis Fig 1 : Argand diagrnwi showing the relationship between the Cartesian and polar forms of iinpedance I
Fig 3: Otis model of the lower aimmy. R l n l , Rln2, = lazcier airiiwy resistances. C l n I ,CIn2,=louwr airway coinpliaiices
of resistance' is explained by considering theoretical models of the respiratory system in which the mechanical useful; the Cartesian form has already been explained. parameters are replaced by exactly analogous electrical The magnitude of the impedance is given by the ratio of equivalents (Cutillo and Renzetti 1983). the pressure amplitude to the flow amplitude, and the Figure 2 shows a simple electrical representation of the phase angle between them is the phase angle of the respiratory system using a single resistance, capacitance impedance. At the resonant frequency the phase angle is and inductance. These correspond to total respiratory zero and thus the pressure and flow are in phase, an resistance, compliance and inertance respectively. In important result in some methods of measuring order to produce frequency dependence of resistance respiratory resistance. more complex models are used which break down the Although the impedance of the respiratory system has respiratory system into upper airway, lower airway, lung been derived above in terms of its resistance, compliance parenchyma, chest wall etc. and which have electrical and inertance the concept is in fact far more general than elements representing the mechanical properties of each this. One of the reasons for using impedance is that of these physical structures. An almost infinite number of measurement principles developed for electrical systems such models can be constructed in this fashion but two in can be applied to the respiratory system. An example of particular are frequently used. The Otis model (Fig 3 ) this is the forced random noise system developed by uses two peripheral compartments with different time Michaelson et a1 (1975) which uses power spectra to constants (the time constant is the product of resistance derive impedance rapidly over a wide frequency range. and compliance). This model was developed because it The concept of impedance in respiratory mechanics may was noticed that frequency dependence of resistance was at first seem to complicate matters unnecessarily but in much more marked in people suffering from diseases many cases the simple idea of resistance, compliance and that produced narrowed peripheral airways. Narrow inertance (or even just resistance and compliance) is quite airways have a high resistance and thus compartments inadequate. For example, if the respiratory system is that include them have a longer time constant than represented by a single resistance, compliance and normal (assuming the compliance is the same). It was inertance there is no way of explaining the marked thought, therefore, that people with narrowed airways decrease in total respiratory resistance with frequency might have a greater variation in the time constants of that is seen in patients with small airway disease their peripheral lung units than normal people. This (Grimby et a1 1968: Kjeldgaard et a1 1976: Hayes et al 1979: variation was simplified to just two lung units with Clement et a/ 1983). This 'negative frequency dependence different time constants. When analysed, the Otis model
I
R
2
C
--
Fig 2: Electrical representation of a series resistance-inertancecompliance model of the respiratory system. R = resistance, 1 = inductance, C = capacitance, 1 = airway opening, 2 = atmosphere (equivalent to electrical ground)
I v I
Fig 4: Mead model of the lower airway. C, = central compliance, R, = peripheral resistance, C, = peripheral compliance 37
J. Ass. vet. Anaesth. Vol. 16 (1989)
does indeed show frequency dependence of resistance has been improved by using more complex and complete with a suitable choice of values for the parameters. descriptions of gas flow in tubes to predict the changes in The Mead model (figure 4) has one peripheral respiratory impedance with frequency (Fredberg and compartment but includes the compliance of the central Mead 1979). The result Rohrer obtained was different to airways. The model was devised when it was shown that that obtained (by other methods) in living patients the range of frequencies over which the Otis model because of the post mortem changes in airway exhibited frequency dependence of resistance was lower dimensions. than that observed in patients with narrowed airways. Mead showed that the compliance of the central airways 2. Volume-time curves was more important than had previously been thought and produced a model which showed frequency Static deflation curves can be used to measure total dependence of resistance over a more realistic frequency respiratory resistance (Bodman 1963; Purchase 1966a and range. 196613; Mapleson and Weaver 1969; Robinson et a1 1972). The behaviour of these models at different frequencies The method assumes that compliance and resistance are is always determined via their impedance because it independent of lung volume which is not true but rough simplifies the task enormously. Not only can the values can still be calculated. Total respiratory static properties of a model be calculated but the value of each compliance (C) is measured first by inflating the lungs to element in a given model can be adjusted so that it a known volume, sealing the airway, relaxing the resembles the real respiratory system as closely as respiratory muscles and measuring the airway pressure. possible, a process known as 'parameter estimation'. Expiratory volume-time curves are then measured by When any measurement of respiratory mechanics is inflating the lungs and allowing passive expiration into a made it is very important to consider an appropriate spirometer. model of the respiratory system and determine exactly If resistance (R) and compliance (C) are constant then what is being measured. For example, all methods of the shape of the volume-time curve will be exponential measuring dynamic compliance in fact measure total and given by the equation: -t respiratory reactance. The model in figure 2 shows why V = V, exp (____ ) RC this is so: a true compliance will be obtained only if the where V, is the initial lung volume and V the volume inertance is zero. The error caused by ignoring the at time t. inertance may be small at low frequencies but will be From a plot of log(V) against time RC can be important at frequencies higher than a few Hz or if an determined and since C is known R can be calculated. additional inertance (such as an endotracheal tube) is The method can be used in trained conscious humans introduced. For this reason the measurement of the way but measurements in animals require general in which dynamic compliance varies with frequency, the anaesthesia. 'frequency dependence of compliance', is almost meaningless because what is being measured is the 3 . Flow and transpulmonary pressure measurement variation of the reactance with frequency. This latter parameter is no less useful in detecting small airway The pressure gradient across the respiratory system obstruction in man (Clement et a1 1983) and has a much less the chest wall can be found by measuring the more sound theoretical basis than frequency dependence difference between atmospheric and intrathoracic of compliance. pressure. If flow is also measured the respiratory resistance and dynamic compliance can be determined. METHODS OF MEASURING RESPIRATORY MECHANICS An oesophageal balloon will record changes in intrathoracic pressure quite well provided that care is A large number of methods for measuring respiratory taken with the positioning of the balloon and the amount mechanics in man and animals has been reported but of air inside it (Mead et al 1955; Milic-Emili et a1 1964; many of these are variations o n a common basic Derksen and Robinson 1980). The intrapleural pressure principle. This article aims to describe the principles can also be measured by direct pleural puncture. rather than every different technique. Usually the pressure a n d flow are recorded simultaneously with the subject spontaneously 1. Anatomical measurements breathing. The volume is recorded either by direct spirometry or more usually by integration of the flow Rohrer (1915) made the first study of respiratory signal. Points of equal chest volume but opposite flow resistance in humans. He measured the length and are identified and the pressure and flow differences at diameter of the airways in cadavers and calculated the these points are measured. Because the chest volume is resistance to flow using standard equations of fluid the same the intrathoracic pressure component from the dynamics. His result included a significant non-linear compliance is the same and the pressure difference is due term due to non-laminar flow and he expressed this as a to the resistance, which can then be calculated. The power series: dynamic compliance is calculated from the pressure and pressure = aV' + bV'2 volume difference at points of zero flow, i.e. peak where V' is the flow. inspiration and expiration (Mead and Whittenberger This method is cumbersome and of no clinical use but 1953). As explained above, this technique in fact 38
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determines the value of compliance which has the same reactance' as the respiratory system at the particular measurement frequency used and ignores the effects of inertance. The method has been used for so long that this error is accepted. A continuous, breath-by-breath recording of resistance and compliance may be obtained (Dennis et al 1969) by using analogue or digital circuitry to identify the points of equal volume and equal flow. The effects of lung volume on resistance and compliance can also be investigated, either by training a volunteer to breath at different lung volumes or by applying a static pressure to the airway. The method has been widely used in both man and animals and is readily applicable to studies of respiratory mechanics in conscious and anaesthetised animals. It has been used on dogs (Gillespie and Hyatt 1974; Dain and Gold 19751, guinea-pigs (Amdur and Mead 1958), calves (Kiorpes e f a1 1978) a n d horses (Willoughby a n d McDonell 1979; Derksen ef a l 1982). If the pressure difference between the pleural space and another point in the respiratory system is used rather than the pressure between the pleural space and the atmosphere, then respiratory mechanics can be partitioned (Art et al 1988). The effects of frequency on respiratory mechanics can be studied in man by making measurements at different respiratory rates, and in anaesthetised animals by using a mechanical ventilator.
alveolar gas pressure is estimated from the airflow in and out of the box. Body plethysmography has become a standard clinical method of measuring airway resistance in humans. It is quick and non-invasive but many people find the box claustrophobic. Errors can be introduced by gas in the intestinal tract (DuBois et al 1956a) but usually this is not important, and if required the degree of error can be estimated by performing special manoeuvres. In order to reduce other errors caused by variations in gas composition within the pneumotachograph, the subject is required to pant through the flowmeter and this limits the usefulness of the device in animals. Panting also reduces the variability of the laryngeal resistance by keeping the glottis open. Good results can be obtained from anaesthetised small animals but the mere size of a box that will accommodate large animals restricts its use in these species.
5. Flow interruption
If the airway is occluded then there is no air flow in or out of the chest and the pressure at any point within the airway must be the same. This is the basis of the flow interrupter method of measuring airway resistance (Mead and Whittenberger 1954). The patient breathes through a valve which is normally open to the atmosphere a n d airflow is recorded with a pneumotachograph. The valve is then rapidly closed and the pressure on t h e patient's side of the valve is 4. Whole body plethysrnography measured. After a short period the transient oscillations The whole body plethysmograph enables alveolar induced by the valve closure die away and the pressure pressure to be estimated and, if one knows the airflow as settles to a new value, which is assumed to be equal to well, the airways resistance can be determined (DuBois the alveolar pressure just before occlusion. The airways et al 195613). There are several types of plethysmograph resistance is obtained by dividing the flow immediately and many variations on the original DuBois design. In prior to interruption by the change in airway pressure the constant volume variable pressure plethysmograph caused by the valve closure. Because the pressure is the subject is enclosed in an airtight box of about 600 measured soon after interruption it is assumed that there litres volume (for human work). In a few minutes is not enough time for inspiratory force to have changed thermal equilibrium is reached and the drift in the box significantly. The method is inaccurate in cases of obstructive pressure falls to a negligible amount. The subject breathes the air in the box through a flowmeter and both pulmonary disease where there can be substantial rethe flow and box pressure are recorded. If the pressure distribution of gas within the lung after occlusion. This within the chest were the same as that within the box no can be recognised by the changing occlusion pressure, change in box pressure would be recorded; however, the and has been used to demonstrate the increase in alveolar pressure is higher than the box pressure on peripheral time constants in patients with obstructive expiration and lower on inspiration. The changing pulmonary disease (Otis et a1 1956). A theoretical analysis alveolar gas pressure causes the alveolar gas volume to of the interrupter technique has been recently published vary and this variations is detected by measuring the box (Bates et al 1988) which examines closely the results pressure. The subject's airway is now occluded and the obtained by this method a n d their physiological airway pressure and box pressure are recorded as the significance. The finite closure time of the valve induces subject makes respiratory efforts. As there is no air an error in the measured resistance, which can largely be movement within the respiratory system the airway corrected (Bates et a1 1987). Mead and Whittenberger pressure equals the alveolar pressure, and changes in box (1954) recognised that the technique might measure pressure can be related to alveolar pressure. By respiratory resistance rather than airway resistance. It is combining this with the results from the first also thought that respiratory muscle tone may produce a measurements (with the airway unobstructed) the airway result that is different from the airway resistance. The resistance is readily calculated. The constant pressure technique is simple, non-invasive and can be used in variable volume plethysmograph is very similar but the conscious and non-cooperative subjects but there are box is vented to the atmosphere through a flowmeter and serious reservations about its accuracy in measuring the subject breaths directly the air within the box. The airway resistance. 39
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acceleration and has been used to measure resistance at different frequencies (Grimby et a1 1968). (c) The resistance alone can be calculated by Instead of using the patient’s own respiratory muscles to produce air flow it can be induced by changing the measuring the changes in pressure and flow at points of pressure at the mouth or the chest wall. Usually it is zero volume acceleration (i.e. the extremes of flow) more convenient to alter the pressure at the mouth, but (Goldman ef a / 1970; Hyatt et a1 1970). At these points extra information can be obtained if both methods are both inertial and compliant effects are zero and the ratio used (Peslin e f a1 1985; Gilroy e f a1 1987). Although total of pressure to flow yields the resistance. The advantages of the forced oscillation technique are respiratory resistance could be obtained by measuring mouth pressure and airflow during a single forced that n o patient co-operation is needed, normal inspiration or expiration (assuming the compliance is respiration continues unimpeded, no pleural or already known) the patient must be apnoeic a n d oesophageal catheter is used and respiratory mechanics frequency dependent mechanical parameters will affect can be determined over a wide frequency range. By the result in a manner that is difficult to analyse. A much measuring pressure differences between various parts of more satisfactory technique is to oscillate a small Jolume the respiratory system the total respiratory impedance of air in and out of the chest at a frequency sufficiently can be subdivided, as with the oesophageal balloon above the patient’s own respiratory frequency that the techniques. The method has been used in a wide variety two superimposed waveforms can be separated of species ranging in size from rats to horses, and works electronically (DuBois et a1 1956~).The mouth pressure well in both conscious and anaesthetised animals. The higher measurement frequencies possible with the and flow are recorded and according to the method of forced oscillation technique mean that it is the only analysis used different parameters can be determined: (a) The impedance of the respiratory system can be method of estimating total respiratory inertance with any found by measuring the amplitudes of the pressure and degree of accuracy, simply because the reactive effects of flow signals and the phase angle between them. The ratio inertance are very small at normal respiratory of the pressure to flow amplitude is the magnitude of the frequencies. A variation of the forced oscillation method is the impedance, and the angle between them is the phase angle (figure 5). The resistance and reactance can then be forced random noise technique (Michaelson cf a1 1975). calculated by converting the impedance to the Cartesian Instead of using a single oscillation frequency a wide range of frequencies is applied and the pressure and flow form. (b) If the oscillation frequency is set to the resonant recorded. The subsequent signal processing is necessarily frequency of the respiratory system the pressure and more complex than when a single frequency is used and flow will be in phase and the resistance and magnitude is performed digitally using a computer. The average of the impedance will be equal. This technique was used power in the pressure and flow signals is determined at in early systems (Fisher e f a1 1968) to make the signal each of the frequencies present and the impedance is analysis easier but it is difficult to compare results from determined from the ratio of these power spectra. The patients with different resonant frequencies if there is any advantage of this complex measurement system is that frequency dependence of resistance. An ‘electronic’ the impedance is measured over a wide frequency range resonance can be induced by adding or subtracting to the much more rapidly than is possible by repeated forced flow signal a voltage proportional to volume or flow oscillation measurements. It has been used in many human studies and also in anaesthetised rats (Hantos ef a1 1987) and conscious ponies (Young 1987; Young and Hall, in press).
6. Forced oscillation
Measurement of total respiratory inertance
At
t
Fig 5: Dprivation of impedance from forced oscillation data. P = pressure,V =flow. Magnitude of impedance = Z = %/J .j}?}I “t Phase angle = LZ = i x 360 ~
The inertance of the respiratory system has received much less attention than the resistance and compliance. The main reason for this is that at normal respiratory frequencies inertive reactance is almost negligible compared to that of the compliance (Mead 1956), and inertance is therefore of minor clinical importance. Measurement of inertance uses the same basic techniques a s those employed for measuring resistance and compliance. Mead (1956) measured respiratory flow and transpulmonary pressure (with an oesophageal balloon) in h u m a n volunteers w h o breathed a t 180-300 breaths/min. to maximize inertive effects. Inertance was estimated by determining the portion of the change in transpulmonary pressure at the beginning and end of inspiration that was due to inertia, and relating this to the flow acceleration. The inertance was partitioned into 40
I. Ass. vet. Anaesth. Vol. 16 (1989) -. .
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Physiopnfh. resp. 16,545-554,1980. gas and tissue components by making measurements at increased ambient pressure which caused the gas Dosman, J., Bode, F., Urbanetti, J., Antic, R., Martin, R. and Macklem, P.T. (1975) /. Appl. Pkysiol. 38(1),64-69. component to increase but did not affect the tissue component. DuBois, A. B., Botelho, S. Y., Bedell, G. N., Marshall, R. M. and The development of forced oscillation techniques Comroe, J. H.(Jr). (1956a) I. Clin.h o e s t . 35,322-326. allows much measurements of inertance to be made DuBois, A. B., Botelho, S. Y. and Comroe, J. H.(Jr). (1956b) because of the higher measurement frequencies that can Clin. I I Z U E S ~35,327-335. . be used (Ostrander ef al 1973). Sharp ef a l (1964) DuBois, A. B., Brody, A. W., Lewis, D. H. and Burgess, B. F.(Jr). determined static compliance and then found the (1956~)/. Appl. Pkysiol. 8,587-594. resonant frequency (fres) of the respiratory system. The Fisher, A. B., DuBois, A. B., and Hyde, R. W. (1968) J. Cliii. inertance (I) was then found by solving the equation: Invest. 47,2045-2057. 1 Fredberg, J. J. and Mead, J. (1979) J. Appl. Pkysiol. 47(2), 347-351. fres =
Gas and tissue inertance were separated by repeating measurements whilst breathing gas mixtures of differing densities. This method of measuring inertance assumes a simple three-compartment model of the respiratory system. When more complex models are used the inertance is found using parameter estimation techniques.
CONCLUSION The mechanical properties of the respiratory system can be described reasonably well by its resistance, compliance and inertance. This description is however inadequate in many cases and the more general concept of impedance has proved to be very useful, not only for describing the properties of the respiratory system but also for analysing theoretical models and relating these to the real respiratory system Many techniques .have been devised for measuring respiratory mechanics. Some require patient cooperation and thus are restricted to use on humans but others can be used on conscious or anaesthetised animals, for both research and clinical purposes.
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Amdur, M. 0.and Mead, J. (1958) Am. J . Pkysiol. 192(2),364-368. Art, T., Sertyn, D. and Lekeux, P. (1988) Equine vet. J . 20(4), 268273. Bates, J. H. T., Hunter, I. W., Sly, P. D., Okubo, S., Filiatrault, S. and Milic-Emili, J. (1987) Med. I!? Biol. Eng. t3 Comput. 25,136140. Bates, J. H. T., Baconnier, P. and Milic-Emili, J. (1988) J. Appl. Pkysiol. 64(5) 2204-2214. Bodman, R. I. (1963) Anues. 18(3), 355-362. Clement, J., Landser, F. J. and Van d e Woestijne, K. P (1983). Chest 83(2), 215-220. Cutillo, A . G. and Renzetti, A. D.(Jr.). (1983) Bull. E u r o p . Pkysiopath. resp. 19,293-326. Dain, D. and Gold, W. M. (1975) J.Appl. Physiol. 38(1), 96-100, Dennis, M. W., Douglas, J. S., Casby, J. U., Stolwijk, J. A. J. and Bouhuys, A. (1969) J. Appl. Physiol. 26(2), 248-252.
Mead, J. (1956) J. Appl. Physiol. 9,208-212. Mead, J. (1969) J. Appl. Physiol. 26(5), 670-673. Michaelson, E. D., Grassman, E. D. and Peters, W. R. (1975) J . Clin. Invest. 56,1210-1230. Milic-Emili, J., Mead, J., Turner, J. M. and Glauser, E. M. (1964) J. Appl. Physiol. 19(2), 207-211. Ostrander, L. E., Chester, E. H. and Franck, J-B. (1973) J. Appl. Pkysiol. 35(4), 526-537. Otis, A. B., McKerrow, C. B., Bartlett, R. A., Mead, J., McIlroy, M.B., Selverstone, N.J. and Radford, E.P. (1956) J. A p p l . Physiol. 8,427-443. Peslin, R., Duvivier, C. and Gallina, C. (1985) J. Appl. Physiol. 59(2), 492-501.
Derksen, F. J. and Robinson, N. E. (1980) Am. /. Vet. Res. 41(11), 1756-1761. Derksen, F. J., Robinson, N. E., Slocombe, R. F., Riebold, T. W. and Bmnson, D. B. (1982)Am. 1. Vet. Res. 43(4), 598-602. Dixsaut, G., Delavault, E. and Saumon, G. (1980) Bull. € i m p
Purchase, I. F. H. (1966a) Vet. Rec. 78(18), 613-616. Purchase, I. F. H. (1966b) Vet. Rec. 79(16),467-468. Ramo, S., Whinnery, J. R. and Van Duzer, T. (1965) Fields arid Waves in Communicatiori Electronics. John Wiley & Sons Inc., New York. 41
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Robinson, N. E., Gillespie, J. R., Berry, J. D. and Simpson, A. (1972) 1. Appl. Pkysiol. 33(6), 808-812. Rohrer, F. (1915) Pfltiger's Arckiv 162,225-299. Sharp, J. T., Henry, J. I?, Sweany, S. K., Meadows, W. R. and Pietras, R. J. (1964) 1. Clin. Invest. 43(3), 503-509. Sullivan, M, Paliotta, J. and Saklad, M. (1976) J . Appl. Physiol. 41(4), 590-592. Willoughby, R. A. and McDonell, W. N. (1979) Large animal practice. 1(1),171-198. Young, S. S. (1987) J. Ass. vet. Anaesth. 14,177-178, (abstract). Young, S. S and Hall, L. W. Equine vet. I., in press.
from the airway opening to the middle of the cervical trachea V
V' V"
Volume dV ,ie flow dt ~
dt*
,ie volume acceleration
APPENDIXB The three equations defining resistance, compliance and inertance can be combined to produce a relationship between pressure and flow:
APPENDIXA
I' = RV' +
Definifions of ferms used
dV' c1 1V'dt + I .dt
By substituting voltage (V) for pressure and current (I) for flow the electrical equivalent is obtained: 1 dI V = RI + - JIdt + L C dt where R, C a n d L are respectively resistance, capacitance and inductance The full solution to this equation describes the relationship between voltage and current at all times, whereas in nearly all cases only the steady-state solution is required. If the variation of voltage (V) with time is a sinusoid of the form: v = v, cos wt where V, is the amplitude, t time and o the angular frequency then it can be shown (Ramo, Whinnery and Van Duzer p.14) that: I = Aejwt + Be-P is a steady state solution to the equation. When this solution is substituted back into the equation coefficients of eiwt and e W can be equated to give the relationships: A(R + j(wL - 0~ 1 )) = vln 2 B(R - j(oL - w c 1 )) = vln 2 The impedance ( Z )is defined as the complex number:
The meaning of terms such as respiratory resistance sometimes varies between publications. The definitions of terms as used in this article are given below. The term (***) denotes impedance, resistance, reactance, compliance or inertance as appropriate.
~
Airway opening The point at which air enters the respiratory system. Unless otherwise stated it is taken as the external nares in animals and the lips in man. Airway (***) The (***I of the respiratory system measured from the airway opening to the alveoli. The lung tissue and chest wall are not included. Lower airway (***) The (***) of the respiratory system measured from the middle of the cervical trachea to the alveoli. The lung tissue and chest wall are not included. Lower respiratory (***I The (***) of the respiratory system measured from the middle of the cervical trachea to the pleural space. The chest wall is not included.
Z = R + j (wL -
1 oc )
and can also be expressed in its polar form: Z = I Z I el0
Respiratory (***) The (***I of the respiratory system measured from the airway opening to the pleural space. The chest wall is not included. Total lower respiratory (***) The (***I of the respiratory system measured from the middle of the cervical trachea to the atmosphere. The chest wall is included.
A and B now become:
Total respiratory (***) The (***) of the respiratory system measured from the airway opening to the atmosphere. The chest wall is included. By substitution and using the identity Upper respiratory (***) The (***) of the respiratory system measured
cos x =
ex + e-x 2
42
l
1. Ass. vet. Anaesth. Vol. 16 (1989)
_-
-.
~~
The coefficients for A and B must be conjugate pairs if the current I is to be real and thus only one need be calculated because the other provides no further information. This simplification can be enacted by replacing the original voltage V = V,cos o t by V = V,ePt. The solution now becomes:
1 = vln ej (wt-9) IZI Although this cannot be a true expression for I because it is a complex quantity, it contains the required magnitude and phase. By convention the multiplier eW is understood and the result reduces to: I = V, e-je IZI ~
~
:.
I=
-
-
Vm
In an exactly analogous fashion mechanical impedance can be defined by the equation:
where P is the pressure, V ' the flow and Z the mechanical impedance. This result shows how Ohm's law can be applied to linear circuits containing reactive elements if each element is replaced by its complex impedance and only the steady state solution is required.
Atmospheric pollution by inhalational anaesthetic agents R. S. Jones University Department of Anaesthesia, Royal Liverpool Hospital, Prescot Street, Liverpool, PO Box 147, Liverpool. BACKGROUND
POTENTIAL HAZARDS
In 1967 a paper by Vaisman (1967) first drew our attention to the matter of atmospheric pollution and suggested that there may be a health hazard associated with anaesthetic practice. The subject was reviewed in 1977 for the Association of Veterinary Anaesthetists (Jones 1977). A number of studies have been published since that time but the problem is far from solved. A recent review has attempted to put the matter into a clear perspective (Spence 1987). The waste gases which pass into the atmosphere are present in expired gas and in breast milk (Corbett and Ball 1973; Cote, Kenepp, Reed and Strobe1 1976). There is still considerable debate over terminology, ie whether these exhaled agents should be referred to as either pollutants o r contaminants. By definition, pollutants are substances which are present in sufficient concentration to damage the health or the environment of man. If, however, they are present in harmless concentrations they are called contaminants. There is often considerable difficulty in differentiating between harmful pollution and harmless contamination. Whilst much of the evidence which has accumulated is from medical operating theatre studies it is probably applicable to the veterinary situation. The majority of information is, however, based upon retrospective epidemiological studies. Such studies are, by necessity, subject to errors related to poor response, methodological bias and selection of controls. Hence prospective trials may be expected to yield more confident conclusions. It is, however, possible to summarise the present position and highlight some of the problems.
The risk of spontaneous abortion is probably increased in women which are exposed to inhalational anaesthetic agents (Cohen 1980).There is also some evidence that the incidence of spontaneous abortion in the wives of exposed males may also be increased (Cohen ef a1 1980). There is n o substantial evidence to suggest any association with stillbirth, infertility or effects on live offspring such as malignancy, malformation, altered sex ratio or low birth weight (Vessey 1978). There is a significantly raised incidence of reported liver and renal disease in exposed staff. Liver disease in all forms is increased 1.7 times (Spence and Knill-Jones 1978), and renal disease (lithiasis in males and genitourinary infections in females) by 1.2 - 1.7 times (Cohen 1980). Non-specific neurological symptoms are reported more commonly in exposed staff (Cohen et al 1980). A syndrome resembling subacute combined degeneration of the cord has been described in 15 subjects chronically exposed to high concentrations of nitrous oxide (Layzer 1978). Mental performance is not affected by exposure to trace concentrations of anaesthetic gases. An early report by Bruce, Bach and Arbit (1974) has not been confirmed by other investigators. It is probable that the threshold for an effect or performance lies within the range of 0.05 to 0.1 MAC (Smith and Shirley 1978). Occupationally related mortality is no higher among anaesthetists than a n y other g r o u p of medical practitioners (Doll and Peto 1977).There is no evidence of a direct causal relationship between chronic exposure to 43
J. Ass vet Anaesth. Vol. 16 (1989)
.~
.-
Respiratory mechanics: fundamentals and measurement principles S. Young Animal Health Trust, I? 0.Box 5, Newmarket, Suffolk. INTRODUCTION
Gas flow in and out of the respiratory system is largely governed by simple physical phenomena. These phenomena are fundamental to the understanding of normal respiratory physiology and the alterations in respiratory function that occur in certain pathological conditions. Because of this, measurement of the mechanical properties of the respiratory system is often required for clinical o r research purposes. To someone starting work on respiratory mechanics the subject can, however, be very confusing. Ideas such as parameter estimation may seem far removed from the physical laws upon which the theory is based. One of the reasons for this is the desirability that any measurement technique is non-invasive, so that it can be used in clinical work. This often results in a rather obscure method of measuring a simple parameter. Another reason is that the behaviour of the respiratory system is not completely explained by simple laws and a more general theory is required to explain such observed phenomena as the frequency dependence of resistance. The concept of impedance has proved very useful in this respect. The mechanical properties of the whole respiratory system are made up from the contributions of its various components: the mouth and nasal passages, pharynx, larynx, central airways, peripheral airways, lung tissue and chest wall (which includes the diaphragm and a contribution from the abdominal contents). It is often the case that one is only interested in a part of the respiratory system a n d many techniques allow respiratory mechanics to be partitioned into certain components. In addition, some techniques only measure the mechanical properties of part of the respiratory system. The nomenclature associated with partitioning of respiratory mechanics varies somewhat and the Appendix gives the meaning of some terms as used here. This article is designed to help those who are new to the study of respiratory mechanics, and is divided into two main sections. The first part describes the basic mechanical properties of the respiratory system and how they are combined to relate the pressure gradient across the respiratory system to the gas flow in and out of it. The second part reviews practical techniques for measuring respiratory mechanics and is concerned with measurement principles rather an exhaustive list of all modifications of a basic technique. Human studies are included for completeness and because in some cases the same techniques can be used on anaesthetised but not
conscious animals. Attention is, however, drawn to those methods which have proved most suitable for animal work in both small a n d large species.
FUNDAMENTAL M E C H A N I C A L
P R O P E R T I E S OF
THE
RESPIRATORY SYSTEM
There are three fundamental mechanical quantities that relate the flow of gas in and out of the respiratory system to the pressure d r o p across it: resistance, compliance and inertance. These parameters are due to the physical properties of the respiratory system as described below. In some circumstances it is easier to understand the parameters from a consideration of the fate of the energy put into the respiratory system by the respiratory muscles. Energy is dissipated instantaneously (as heat) by the resistance of the system but is stored by the compliance and inertance. A compliance stores energy as elastic potential energy, whilst an inertance stores energy as kinetic energy.
Resistance Friction between the moving gas molecules and the stationary airway walls produces a pressure drop along the airway and causes the gas to lose energy. This effect can be described in general terms by the equation: P=RV' where P is the pressure drop across the airway, V' the gas flow rate along the airway and R is defined as the resistance of the tube. For laminar flow R is independent of flow rate, but if turbulence is present R varies with flow. Lung and chest wall tissue also has a resistance. This can be imagined as arising from instantaneous energy loss caused by viscous shearing forces within the tissue.
Compliance The elastic lung tissue and chest wall are stretched as air is inspired. The tension generated in these tissues opposes the expansion of the thorax and the elastic properties of the tissues are such that the pressure required to balance the elastic forces is proportional to the inspired volume. The effect is thus described by the equation: V P= where P is the pressure required to maintain an inspired volume V and C is defined as the compliance of the thorax. 35
J. Ass. vet. Anaesth. Vol. 16 (1989) ~
A small component of the total respiratory compliance squared gives -1. In engineering this number is denoted is due to compression or rarefaction of the air within the by j, so that j2 = -1 (in the pure mathematical world the respiratory system. This is conventionally included with symbol i is usually used). All imaginary numbers are the tissue compliance. expressed as multiples of j, so that for example (592 = -25 Compliance is conventionally divided into static and and so on. dynamic compliance. Static compliance is measured Complex numbers are expressed in two during a period of apnoea when the chest volume is interchangeable formats. The Cartesian format is of the constant whilst dynamic compliance is measured with a form: Z=3+4j varying chest volume. Dynamic compliance differs from static compliance and the real and imaginary parts of the impedance are due to inhomogeneities within the lung (Otis et nl 1956), clear. The equivalent polar form of this number is: Z = 5exp(0.927j) central airway compliance (Mead 1969) and the effects of inertance (Dosman et a1 1975). Dynamic compliance where 0.927 is an angle in radians. There are conventions varies with the frequency at which it is measured and the for manipulating complex numbers (addition, measurement frequency should therefore be stated. If it is multiplication etc.) which can be found in standard not it is often assumed to be measured at the normal mathematical texts. The impedance of the respiratory system can be respiratory frequency of the subject. determined quite simply from its resistance, compliance and inertance: lizertance (a) Resistance (R) is left alone and becomes the real During respiration air moves in and out of the chest. It part of the impedance. (b) Compliance ( C ) is replaced by where j2 = -1 thus undergoes a change in velocity, i.e. an acceleration, oc and in accordance with Newton's second law of motion a and o = 2n times frequency. force must be provided to produce this acceleration. This (c) Inertance (I) is replaced by joI. (d)All the imaginary terms are added together to form force is the driving pressure, which is related to the the reactance, which is defined as the imaginary part of acceleration by the equation: the impedance. The reactance (XI of the respiratory P = I V" where V" is the acceleration of the gas and I is defined as system (with compliance C and inertance I) is therefore the inertance. 1 given by: X = j(w1) The inertance of the respiratory system has received wc (el The impedance ( Z ) is simply the sum of the much less attention than the resistance or compliance because at normal respiratory frequencies its effects are resistance and reactance, i.e Z=R+j(oI-K negligible. It becomes very important, however, at higher frequencies or if measurements are made upon intubated There are some important points that arise from this equation: subjects (Sullivan et a1 1976, Dixsaut et n1 1980). (a) The impedance a n d the reactance vary with frequency because of the presence of w in the equation. Impednnce (b) At one particular frequency the reactance wiIl be In recent years increasing attention has been paid to zero because the reactances of the compliance and another mechanical property of the respiratory system, inertance are of opposite sign (ie they are 180" out of its impedance (denoted by Z ) . This is partly because it phase) and at a certain frequency they will be of equal can accommodate such phenomena as the variation of amplitude and cancel each other out. This frequency is compliance and inertance with frequency. Another given by: 1 WI reason is that there is much knowledge in electrical engineering of how to measure and analyse impedance 1 1 or f = 2 n f i ie o = which can be applied to mechanical systems as well. The impedance of the respiratory system is a complex This frequency is the resonant frequency of the number that represents the final relationship between respiratory system. pressure and flow due to the combined effects of the Complex numbers can be represented in either polar resistance, compliance and inertance of the respiratory or Cartesian form. The Cartesian form, in which the system. It is best described intuitively as 'the total impedance is represented by its resistance and reactance, opposition to flow' (Long et al 1962). The full derivation has been used above. The polar form represents the of impedance from the equations above is given in impedance by its magnitude ( I Z I ) and phase angle ( [ Z ) . Appendix B. The two forms are completely interchangeable and are Any complex number is made up from two parts, a related by the equations: real and an imaginary part. All 'ordinary' numbers are IZI = G Z F real, and thus the real part of impedance is handled in LZ = tan-' X the same way as any other number. The imaginary part R The two forms are shown on an Argand diagram in contains a component with the property that, when squared, a negative real number results. To simplify figure 1. matters only one imaginary number is used, which when Both the Cartesian and polar forms of impedance are
3
~
=s
36
J. Ass. vet. Anaesth. Vol. 16 (1989) ~
w
Real axis Fig 1 : Argand diagrnwi showing the relationship between the Cartesian and polar forms of iinpedance I
Fig 3: Otis model of the lower aimmy. R l n l , Rln2, = lazcier airiiwy resistances. C l n I ,CIn2,=louwr airway coinpliaiices
of resistance' is explained by considering theoretical models of the respiratory system in which the mechanical useful; the Cartesian form has already been explained. parameters are replaced by exactly analogous electrical The magnitude of the impedance is given by the ratio of equivalents (Cutillo and Renzetti 1983). the pressure amplitude to the flow amplitude, and the Figure 2 shows a simple electrical representation of the phase angle between them is the phase angle of the respiratory system using a single resistance, capacitance impedance. At the resonant frequency the phase angle is and inductance. These correspond to total respiratory zero and thus the pressure and flow are in phase, an resistance, compliance and inertance respectively. In important result in some methods of measuring order to produce frequency dependence of resistance respiratory resistance. more complex models are used which break down the Although the impedance of the respiratory system has respiratory system into upper airway, lower airway, lung been derived above in terms of its resistance, compliance parenchyma, chest wall etc. and which have electrical and inertance the concept is in fact far more general than elements representing the mechanical properties of each this. One of the reasons for using impedance is that of these physical structures. An almost infinite number of measurement principles developed for electrical systems such models can be constructed in this fashion but two in can be applied to the respiratory system. An example of particular are frequently used. The Otis model (Fig 3 ) this is the forced random noise system developed by uses two peripheral compartments with different time Michaelson et a1 (1975) which uses power spectra to constants (the time constant is the product of resistance derive impedance rapidly over a wide frequency range. and compliance). This model was developed because it The concept of impedance in respiratory mechanics may was noticed that frequency dependence of resistance was at first seem to complicate matters unnecessarily but in much more marked in people suffering from diseases many cases the simple idea of resistance, compliance and that produced narrowed peripheral airways. Narrow inertance (or even just resistance and compliance) is quite airways have a high resistance and thus compartments inadequate. For example, if the respiratory system is that include them have a longer time constant than represented by a single resistance, compliance and normal (assuming the compliance is the same). It was inertance there is no way of explaining the marked thought, therefore, that people with narrowed airways decrease in total respiratory resistance with frequency might have a greater variation in the time constants of that is seen in patients with small airway disease their peripheral lung units than normal people. This (Grimby et a1 1968: Kjeldgaard et a1 1976: Hayes et al 1979: variation was simplified to just two lung units with Clement et a/ 1983). This 'negative frequency dependence different time constants. When analysed, the Otis model
I
R
2
C
--
Fig 2: Electrical representation of a series resistance-inertancecompliance model of the respiratory system. R = resistance, 1 = inductance, C = capacitance, 1 = airway opening, 2 = atmosphere (equivalent to electrical ground)
I v I
Fig 4: Mead model of the lower airway. C, = central compliance, R, = peripheral resistance, C, = peripheral compliance 37
J. Ass. vet. Anaesth. Vol. 16 (1989)
does indeed show frequency dependence of resistance has been improved by using more complex and complete with a suitable choice of values for the parameters. descriptions of gas flow in tubes to predict the changes in The Mead model (figure 4) has one peripheral respiratory impedance with frequency (Fredberg and compartment but includes the compliance of the central Mead 1979). The result Rohrer obtained was different to airways. The model was devised when it was shown that that obtained (by other methods) in living patients the range of frequencies over which the Otis model because of the post mortem changes in airway exhibited frequency dependence of resistance was lower dimensions. than that observed in patients with narrowed airways. Mead showed that the compliance of the central airways 2. Volume-time curves was more important than had previously been thought and produced a model which showed frequency Static deflation curves can be used to measure total dependence of resistance over a more realistic frequency respiratory resistance (Bodman 1963; Purchase 1966a and range. 196613; Mapleson and Weaver 1969; Robinson et a1 1972). The behaviour of these models at different frequencies The method assumes that compliance and resistance are is always determined via their impedance because it independent of lung volume which is not true but rough simplifies the task enormously. Not only can the values can still be calculated. Total respiratory static properties of a model be calculated but the value of each compliance (C) is measured first by inflating the lungs to element in a given model can be adjusted so that it a known volume, sealing the airway, relaxing the resembles the real respiratory system as closely as respiratory muscles and measuring the airway pressure. possible, a process known as 'parameter estimation'. Expiratory volume-time curves are then measured by When any measurement of respiratory mechanics is inflating the lungs and allowing passive expiration into a made it is very important to consider an appropriate spirometer. model of the respiratory system and determine exactly If resistance (R) and compliance (C) are constant then what is being measured. For example, all methods of the shape of the volume-time curve will be exponential measuring dynamic compliance in fact measure total and given by the equation: -t respiratory reactance. The model in figure 2 shows why V = V, exp (____ ) RC this is so: a true compliance will be obtained only if the where V, is the initial lung volume and V the volume inertance is zero. The error caused by ignoring the at time t. inertance may be small at low frequencies but will be From a plot of log(V) against time RC can be important at frequencies higher than a few Hz or if an determined and since C is known R can be calculated. additional inertance (such as an endotracheal tube) is The method can be used in trained conscious humans introduced. For this reason the measurement of the way but measurements in animals require general in which dynamic compliance varies with frequency, the anaesthesia. 'frequency dependence of compliance', is almost meaningless because what is being measured is the 3 . Flow and transpulmonary pressure measurement variation of the reactance with frequency. This latter parameter is no less useful in detecting small airway The pressure gradient across the respiratory system obstruction in man (Clement et a1 1983) and has a much less the chest wall can be found by measuring the more sound theoretical basis than frequency dependence difference between atmospheric and intrathoracic of compliance. pressure. If flow is also measured the respiratory resistance and dynamic compliance can be determined. METHODS OF MEASURING RESPIRATORY MECHANICS An oesophageal balloon will record changes in intrathoracic pressure quite well provided that care is A large number of methods for measuring respiratory taken with the positioning of the balloon and the amount mechanics in man and animals has been reported but of air inside it (Mead et al 1955; Milic-Emili et a1 1964; many of these are variations o n a common basic Derksen and Robinson 1980). The intrapleural pressure principle. This article aims to describe the principles can also be measured by direct pleural puncture. rather than every different technique. Usually the pressure a n d flow are recorded simultaneously with the subject spontaneously 1. Anatomical measurements breathing. The volume is recorded either by direct spirometry or more usually by integration of the flow Rohrer (1915) made the first study of respiratory signal. Points of equal chest volume but opposite flow resistance in humans. He measured the length and are identified and the pressure and flow differences at diameter of the airways in cadavers and calculated the these points are measured. Because the chest volume is resistance to flow using standard equations of fluid the same the intrathoracic pressure component from the dynamics. His result included a significant non-linear compliance is the same and the pressure difference is due term due to non-laminar flow and he expressed this as a to the resistance, which can then be calculated. The power series: dynamic compliance is calculated from the pressure and pressure = aV' + bV'2 volume difference at points of zero flow, i.e. peak where V' is the flow. inspiration and expiration (Mead and Whittenberger This method is cumbersome and of no clinical use but 1953). As explained above, this technique in fact 38
1. Ass. vet. Anaesth. Vol. 16 (1989) ~
determines the value of compliance which has the same reactance' as the respiratory system at the particular measurement frequency used and ignores the effects of inertance. The method has been used for so long that this error is accepted. A continuous, breath-by-breath recording of resistance and compliance may be obtained (Dennis et al 1969) by using analogue or digital circuitry to identify the points of equal volume and equal flow. The effects of lung volume on resistance and compliance can also be investigated, either by training a volunteer to breath at different lung volumes or by applying a static pressure to the airway. The method has been widely used in both man and animals and is readily applicable to studies of respiratory mechanics in conscious and anaesthetised animals. It has been used on dogs (Gillespie and Hyatt 1974; Dain and Gold 19751, guinea-pigs (Amdur and Mead 1958), calves (Kiorpes e f a1 1978) a n d horses (Willoughby a n d McDonell 1979; Derksen ef a l 1982). If the pressure difference between the pleural space and another point in the respiratory system is used rather than the pressure between the pleural space and the atmosphere, then respiratory mechanics can be partitioned (Art et al 1988). The effects of frequency on respiratory mechanics can be studied in man by making measurements at different respiratory rates, and in anaesthetised animals by using a mechanical ventilator.
alveolar gas pressure is estimated from the airflow in and out of the box. Body plethysmography has become a standard clinical method of measuring airway resistance in humans. It is quick and non-invasive but many people find the box claustrophobic. Errors can be introduced by gas in the intestinal tract (DuBois et al 1956a) but usually this is not important, and if required the degree of error can be estimated by performing special manoeuvres. In order to reduce other errors caused by variations in gas composition within the pneumotachograph, the subject is required to pant through the flowmeter and this limits the usefulness of the device in animals. Panting also reduces the variability of the laryngeal resistance by keeping the glottis open. Good results can be obtained from anaesthetised small animals but the mere size of a box that will accommodate large animals restricts its use in these species.
5. Flow interruption
If the airway is occluded then there is no air flow in or out of the chest and the pressure at any point within the airway must be the same. This is the basis of the flow interrupter method of measuring airway resistance (Mead and Whittenberger 1954). The patient breathes through a valve which is normally open to the atmosphere a n d airflow is recorded with a pneumotachograph. The valve is then rapidly closed and the pressure on t h e patient's side of the valve is 4. Whole body plethysrnography measured. After a short period the transient oscillations The whole body plethysmograph enables alveolar induced by the valve closure die away and the pressure pressure to be estimated and, if one knows the airflow as settles to a new value, which is assumed to be equal to well, the airways resistance can be determined (DuBois the alveolar pressure just before occlusion. The airways et al 195613). There are several types of plethysmograph resistance is obtained by dividing the flow immediately and many variations on the original DuBois design. In prior to interruption by the change in airway pressure the constant volume variable pressure plethysmograph caused by the valve closure. Because the pressure is the subject is enclosed in an airtight box of about 600 measured soon after interruption it is assumed that there litres volume (for human work). In a few minutes is not enough time for inspiratory force to have changed thermal equilibrium is reached and the drift in the box significantly. The method is inaccurate in cases of obstructive pressure falls to a negligible amount. The subject breathes the air in the box through a flowmeter and both pulmonary disease where there can be substantial rethe flow and box pressure are recorded. If the pressure distribution of gas within the lung after occlusion. This within the chest were the same as that within the box no can be recognised by the changing occlusion pressure, change in box pressure would be recorded; however, the and has been used to demonstrate the increase in alveolar pressure is higher than the box pressure on peripheral time constants in patients with obstructive expiration and lower on inspiration. The changing pulmonary disease (Otis et a1 1956). A theoretical analysis alveolar gas pressure causes the alveolar gas volume to of the interrupter technique has been recently published vary and this variations is detected by measuring the box (Bates et al 1988) which examines closely the results pressure. The subject's airway is now occluded and the obtained by this method a n d their physiological airway pressure and box pressure are recorded as the significance. The finite closure time of the valve induces subject makes respiratory efforts. As there is no air an error in the measured resistance, which can largely be movement within the respiratory system the airway corrected (Bates et a1 1987). Mead and Whittenberger pressure equals the alveolar pressure, and changes in box (1954) recognised that the technique might measure pressure can be related to alveolar pressure. By respiratory resistance rather than airway resistance. It is combining this with the results from the first also thought that respiratory muscle tone may produce a measurements (with the airway unobstructed) the airway result that is different from the airway resistance. The resistance is readily calculated. The constant pressure technique is simple, non-invasive and can be used in variable volume plethysmograph is very similar but the conscious and non-cooperative subjects but there are box is vented to the atmosphere through a flowmeter and serious reservations about its accuracy in measuring the subject breaths directly the air within the box. The airway resistance. 39
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J. Ass. vet. Anaesth. Vol. 16 (1989) ~
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.~
.
acceleration and has been used to measure resistance at different frequencies (Grimby et a1 1968). (c) The resistance alone can be calculated by Instead of using the patient’s own respiratory muscles to produce air flow it can be induced by changing the measuring the changes in pressure and flow at points of pressure at the mouth or the chest wall. Usually it is zero volume acceleration (i.e. the extremes of flow) more convenient to alter the pressure at the mouth, but (Goldman ef a / 1970; Hyatt et a1 1970). At these points extra information can be obtained if both methods are both inertial and compliant effects are zero and the ratio used (Peslin e f a1 1985; Gilroy e f a1 1987). Although total of pressure to flow yields the resistance. The advantages of the forced oscillation technique are respiratory resistance could be obtained by measuring mouth pressure and airflow during a single forced that n o patient co-operation is needed, normal inspiration or expiration (assuming the compliance is respiration continues unimpeded, no pleural or already known) the patient must be apnoeic a n d oesophageal catheter is used and respiratory mechanics frequency dependent mechanical parameters will affect can be determined over a wide frequency range. By the result in a manner that is difficult to analyse. A much measuring pressure differences between various parts of more satisfactory technique is to oscillate a small Jolume the respiratory system the total respiratory impedance of air in and out of the chest at a frequency sufficiently can be subdivided, as with the oesophageal balloon above the patient’s own respiratory frequency that the techniques. The method has been used in a wide variety two superimposed waveforms can be separated of species ranging in size from rats to horses, and works electronically (DuBois et a1 1956~).The mouth pressure well in both conscious and anaesthetised animals. The higher measurement frequencies possible with the and flow are recorded and according to the method of forced oscillation technique mean that it is the only analysis used different parameters can be determined: (a) The impedance of the respiratory system can be method of estimating total respiratory inertance with any found by measuring the amplitudes of the pressure and degree of accuracy, simply because the reactive effects of flow signals and the phase angle between them. The ratio inertance are very small at normal respiratory of the pressure to flow amplitude is the magnitude of the frequencies. A variation of the forced oscillation method is the impedance, and the angle between them is the phase angle (figure 5). The resistance and reactance can then be forced random noise technique (Michaelson cf a1 1975). calculated by converting the impedance to the Cartesian Instead of using a single oscillation frequency a wide range of frequencies is applied and the pressure and flow form. (b) If the oscillation frequency is set to the resonant recorded. The subsequent signal processing is necessarily frequency of the respiratory system the pressure and more complex than when a single frequency is used and flow will be in phase and the resistance and magnitude is performed digitally using a computer. The average of the impedance will be equal. This technique was used power in the pressure and flow signals is determined at in early systems (Fisher e f a1 1968) to make the signal each of the frequencies present and the impedance is analysis easier but it is difficult to compare results from determined from the ratio of these power spectra. The patients with different resonant frequencies if there is any advantage of this complex measurement system is that frequency dependence of resistance. An ‘electronic’ the impedance is measured over a wide frequency range resonance can be induced by adding or subtracting to the much more rapidly than is possible by repeated forced flow signal a voltage proportional to volume or flow oscillation measurements. It has been used in many human studies and also in anaesthetised rats (Hantos ef a1 1987) and conscious ponies (Young 1987; Young and Hall, in press).
6. Forced oscillation
Measurement of total respiratory inertance
At
t
Fig 5: Dprivation of impedance from forced oscillation data. P = pressure,V =flow. Magnitude of impedance = Z = %/J .j}?}I “t Phase angle = LZ = i x 360 ~
The inertance of the respiratory system has received much less attention than the resistance and compliance. The main reason for this is that at normal respiratory frequencies inertive reactance is almost negligible compared to that of the compliance (Mead 1956), and inertance is therefore of minor clinical importance. Measurement of inertance uses the same basic techniques a s those employed for measuring resistance and compliance. Mead (1956) measured respiratory flow and transpulmonary pressure (with an oesophageal balloon) in h u m a n volunteers w h o breathed a t 180-300 breaths/min. to maximize inertive effects. Inertance was estimated by determining the portion of the change in transpulmonary pressure at the beginning and end of inspiration that was due to inertia, and relating this to the flow acceleration. The inertance was partitioned into 40
I. Ass. vet. Anaesth. Vol. 16 (1989) -. .
~~~
~
~
Physiopnfh. resp. 16,545-554,1980. gas and tissue components by making measurements at increased ambient pressure which caused the gas Dosman, J., Bode, F., Urbanetti, J., Antic, R., Martin, R. and Macklem, P.T. (1975) /. Appl. Pkysiol. 38(1),64-69. component to increase but did not affect the tissue component. DuBois, A. B., Botelho, S. Y., Bedell, G. N., Marshall, R. M. and The development of forced oscillation techniques Comroe, J. H.(Jr). (1956a) I. Clin.h o e s t . 35,322-326. allows much measurements of inertance to be made DuBois, A. B., Botelho, S. Y. and Comroe, J. H.(Jr). (1956b) because of the higher measurement frequencies that can Clin. I I Z U E S ~35,327-335. . be used (Ostrander ef al 1973). Sharp ef a l (1964) DuBois, A. B., Brody, A. W., Lewis, D. H. and Burgess, B. F.(Jr). determined static compliance and then found the (1956~)/. Appl. Pkysiol. 8,587-594. resonant frequency (fres) of the respiratory system. The Fisher, A. B., DuBois, A. B., and Hyde, R. W. (1968) J. Cliii. inertance (I) was then found by solving the equation: Invest. 47,2045-2057. 1 Fredberg, J. J. and Mead, J. (1979) J. Appl. Pkysiol. 47(2), 347-351. fres =
Gas and tissue inertance were separated by repeating measurements whilst breathing gas mixtures of differing densities. This method of measuring inertance assumes a simple three-compartment model of the respiratory system. When more complex models are used the inertance is found using parameter estimation techniques.
CONCLUSION The mechanical properties of the respiratory system can be described reasonably well by its resistance, compliance and inertance. This description is however inadequate in many cases and the more general concept of impedance has proved to be very useful, not only for describing the properties of the respiratory system but also for analysing theoretical models and relating these to the real respiratory system Many techniques .have been devised for measuring respiratory mechanics. Some require patient cooperation and thus are restricted to use on humans but others can be used on conscious or anaesthetised animals, for both research and clinical purposes.
Gillespie, D. J. and Hyatt, R. E. (1974) J. A~7pl.Physiol. 36(1), 98102. Gilroy, R. J., Peslin, R., Duvivier, C., Blum, F. and Butler, J. P. (1987) J. Appl. Pkysiol. 63(1), 121-129. Goldman, M., Knudson, R.J., Mead, J., Peterson, N., Schwaber, J.R. and Wohl, M.A. (1970) J. Appl. Pkysiol. 28(1), 113-116. Grimby, G., Takishima, T., Graham, W., Macklem, P. and Mead, J. (1968) 1.Clin. Invest. 47,1455-1465. Hantos, Z., Daroczy, B., Suki, B. and Nagy, S. (1987) J. Appl. Physiol. 63(1): 36-43. Hayes, D. A., Pimmel, R. L., Fullton, J. M. and Bromberg, P. A. (1979) Am. Rev. Resp. Diseuse 120,1095-1100. Hyatt, R. E., Zimmerman, I. R., Peters, G. M. and Sullivan, W. J. (1970) J. Appl. Pkysiol. 28(5), 675-678. Kiorpes, A. L., Bisgard, G. E. and Manohar, M. (1978) Arti. J . Vet. Res. 39(5), 773-777. Kjeldgaard, J. M., Hyde, R. W., Speers, D. M. and Reichert, W. W. (1976) Am. Rev. R q . Disease 114,501-508. Long, E. C., Hull, W. E. and Gebel, E. L. (1962) J. Alqd. Pk!ysiol. 17(4), 609-612. Mapleson, W. W. and Weaver, B. M. Q. (1969) Resp Pk!ysiu/. 6, 257-270. Mead, J. and Whittenberger, J. L. (1953) J. Appl. Pkysiol. 5, 779796.
REFERENCES
Mead, J. and Whittenberger, J. L. (1954) /. Appl. Pk!ysiu/. 6, 408416. Mead, J., McIlroy, M. B., Selverstone, N. J. and Kriete, B. C. (1955) J. Appl. Pkysiol. 7,491-495.
Amdur, M. 0.and Mead, J. (1958) Am. J . Pkysiol. 192(2),364-368. Art, T., Sertyn, D. and Lekeux, P. (1988) Equine vet. J . 20(4), 268273. Bates, J. H. T., Hunter, I. W., Sly, P. D., Okubo, S., Filiatrault, S. and Milic-Emili, J. (1987) Med. I!? Biol. Eng. t3 Comput. 25,136140. Bates, J. H. T., Baconnier, P. and Milic-Emili, J. (1988) J. Appl. Pkysiol. 64(5) 2204-2214. Bodman, R. I. (1963) Anues. 18(3), 355-362. Clement, J., Landser, F. J. and Van d e Woestijne, K. P (1983). Chest 83(2), 215-220. Cutillo, A . G. and Renzetti, A. D.(Jr.). (1983) Bull. E u r o p . Pkysiopath. resp. 19,293-326. Dain, D. and Gold, W. M. (1975) J.Appl. Physiol. 38(1), 96-100, Dennis, M. W., Douglas, J. S., Casby, J. U., Stolwijk, J. A. J. and Bouhuys, A. (1969) J. Appl. Physiol. 26(2), 248-252.
Mead, J. (1956) J. Appl. Physiol. 9,208-212. Mead, J. (1969) J. Appl. Physiol. 26(5), 670-673. Michaelson, E. D., Grassman, E. D. and Peters, W. R. (1975) J . Clin. Invest. 56,1210-1230. Milic-Emili, J., Mead, J., Turner, J. M. and Glauser, E. M. (1964) J. Appl. Physiol. 19(2), 207-211. Ostrander, L. E., Chester, E. H. and Franck, J-B. (1973) J. Appl. Pkysiol. 35(4), 526-537. Otis, A. B., McKerrow, C. B., Bartlett, R. A., Mead, J., McIlroy, M.B., Selverstone, N.J. and Radford, E.P. (1956) J. A p p l . Physiol. 8,427-443. Peslin, R., Duvivier, C. and Gallina, C. (1985) J. Appl. Physiol. 59(2), 492-501.
Derksen, F. J. and Robinson, N. E. (1980) Am. /. Vet. Res. 41(11), 1756-1761. Derksen, F. J., Robinson, N. E., Slocombe, R. F., Riebold, T. W. and Bmnson, D. B. (1982)Am. 1. Vet. Res. 43(4), 598-602. Dixsaut, G., Delavault, E. and Saumon, G. (1980) Bull. € i m p
Purchase, I. F. H. (1966a) Vet. Rec. 78(18), 613-616. Purchase, I. F. H. (1966b) Vet. Rec. 79(16),467-468. Ramo, S., Whinnery, J. R. and Van Duzer, T. (1965) Fields arid Waves in Communicatiori Electronics. John Wiley & Sons Inc., New York. 41
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Robinson, N. E., Gillespie, J. R., Berry, J. D. and Simpson, A. (1972) 1. Appl. Pkysiol. 33(6), 808-812. Rohrer, F. (1915) Pfltiger's Arckiv 162,225-299. Sharp, J. T., Henry, J. I?, Sweany, S. K., Meadows, W. R. and Pietras, R. J. (1964) 1. Clin. Invest. 43(3), 503-509. Sullivan, M, Paliotta, J. and Saklad, M. (1976) J . Appl. Physiol. 41(4), 590-592. Willoughby, R. A. and McDonell, W. N. (1979) Large animal practice. 1(1),171-198. Young, S. S. (1987) J. Ass. vet. Anaesth. 14,177-178, (abstract). Young, S. S and Hall, L. W. Equine vet. I., in press.
from the airway opening to the middle of the cervical trachea V
V' V"
Volume dV ,ie flow dt ~
dt*
,ie volume acceleration
APPENDIXB The three equations defining resistance, compliance and inertance can be combined to produce a relationship between pressure and flow:
APPENDIXA
I' = RV' +
Definifions of ferms used
dV' c1 1V'dt + I .dt
By substituting voltage (V) for pressure and current (I) for flow the electrical equivalent is obtained: 1 dI V = RI + - JIdt + L C dt where R, C a n d L are respectively resistance, capacitance and inductance The full solution to this equation describes the relationship between voltage and current at all times, whereas in nearly all cases only the steady-state solution is required. If the variation of voltage (V) with time is a sinusoid of the form: v = v, cos wt where V, is the amplitude, t time and o the angular frequency then it can be shown (Ramo, Whinnery and Van Duzer p.14) that: I = Aejwt + Be-P is a steady state solution to the equation. When this solution is substituted back into the equation coefficients of eiwt and e W can be equated to give the relationships: A(R + j(wL - 0~ 1 )) = vln 2 B(R - j(oL - w c 1 )) = vln 2 The impedance ( Z )is defined as the complex number:
The meaning of terms such as respiratory resistance sometimes varies between publications. The definitions of terms as used in this article are given below. The term (***) denotes impedance, resistance, reactance, compliance or inertance as appropriate.
~
Airway opening The point at which air enters the respiratory system. Unless otherwise stated it is taken as the external nares in animals and the lips in man. Airway (***) The (***I of the respiratory system measured from the airway opening to the alveoli. The lung tissue and chest wall are not included. Lower airway (***) The (***) of the respiratory system measured from the middle of the cervical trachea to the alveoli. The lung tissue and chest wall are not included. Lower respiratory (***I The (***) of the respiratory system measured from the middle of the cervical trachea to the pleural space. The chest wall is not included.
Z = R + j (wL -
1 oc )
and can also be expressed in its polar form: Z = I Z I el0
Respiratory (***) The (***I of the respiratory system measured from the airway opening to the pleural space. The chest wall is not included. Total lower respiratory (***) The (***I of the respiratory system measured from the middle of the cervical trachea to the atmosphere. The chest wall is included.
A and B now become:
Total respiratory (***) The (***) of the respiratory system measured from the airway opening to the atmosphere. The chest wall is included. By substitution and using the identity Upper respiratory (***) The (***) of the respiratory system measured
cos x =
ex + e-x 2
42
l
1. Ass. vet. Anaesth. Vol. 16 (1989)
_-
-.
~~
The coefficients for A and B must be conjugate pairs if the current I is to be real and thus only one need be calculated because the other provides no further information. This simplification can be enacted by replacing the original voltage V = V,cos o t by V = V,ePt. The solution now becomes:
1 = vln ej (wt-9) IZI Although this cannot be a true expression for I because it is a complex quantity, it contains the required magnitude and phase. By convention the multiplier eW is understood and the result reduces to: I = V, e-je IZI ~
~
:.
I=
-
-
Vm
In an exactly analogous fashion mechanical impedance can be defined by the equation:
where P is the pressure, V ' the flow and Z the mechanical impedance. This result shows how Ohm's law can be applied to linear circuits containing reactive elements if each element is replaced by its complex impedance and only the steady state solution is required.
Atmospheric pollution by inhalational anaesthetic agents R. S. Jones University Department of Anaesthesia, Royal Liverpool Hospital, Prescot Street, Liverpool, PO Box 147, Liverpool. BACKGROUND
POTENTIAL HAZARDS
In 1967 a paper by Vaisman (1967) first drew our attention to the matter of atmospheric pollution and suggested that there may be a health hazard associated with anaesthetic practice. The subject was reviewed in 1977 for the Association of Veterinary Anaesthetists (Jones 1977). A number of studies have been published since that time but the problem is far from solved. A recent review has attempted to put the matter into a clear perspective (Spence 1987). The waste gases which pass into the atmosphere are present in expired gas and in breast milk (Corbett and Ball 1973; Cote, Kenepp, Reed and Strobe1 1976). There is still considerable debate over terminology, ie whether these exhaled agents should be referred to as either pollutants o r contaminants. By definition, pollutants are substances which are present in sufficient concentration to damage the health or the environment of man. If, however, they are present in harmless concentrations they are called contaminants. There is often considerable difficulty in differentiating between harmful pollution and harmless contamination. Whilst much of the evidence which has accumulated is from medical operating theatre studies it is probably applicable to the veterinary situation. The majority of information is, however, based upon retrospective epidemiological studies. Such studies are, by necessity, subject to errors related to poor response, methodological bias and selection of controls. Hence prospective trials may be expected to yield more confident conclusions. It is, however, possible to summarise the present position and highlight some of the problems.
The risk of spontaneous abortion is probably increased in women which are exposed to inhalational anaesthetic agents (Cohen 1980).There is also some evidence that the incidence of spontaneous abortion in the wives of exposed males may also be increased (Cohen ef a1 1980). There is n o substantial evidence to suggest any association with stillbirth, infertility or effects on live offspring such as malignancy, malformation, altered sex ratio or low birth weight (Vessey 1978). There is a significantly raised incidence of reported liver and renal disease in exposed staff. Liver disease in all forms is increased 1.7 times (Spence and Knill-Jones 1978), and renal disease (lithiasis in males and genitourinary infections in females) by 1.2 - 1.7 times (Cohen 1980). Non-specific neurological symptoms are reported more commonly in exposed staff (Cohen et al 1980). A syndrome resembling subacute combined degeneration of the cord has been described in 15 subjects chronically exposed to high concentrations of nitrous oxide (Layzer 1978). Mental performance is not affected by exposure to trace concentrations of anaesthetic gases. An early report by Bruce, Bach and Arbit (1974) has not been confirmed by other investigators. It is probable that the threshold for an effect or performance lies within the range of 0.05 to 0.1 MAC (Smith and Shirley 1978). Occupationally related mortality is no higher among anaesthetists than a n y other g r o u p of medical practitioners (Doll and Peto 1977).There is no evidence of a direct causal relationship between chronic exposure to 43