THE ELECTRICAL ANALOGUE OF LUNG

Brit. J. Anaesth. (1963), 35, 684 THE ELECTRICAL ANALOGUE OF LUNG BY DONALD CAMPBELL AND JAMES BROWN University Department of Anaesthetics, Royal Infirmary, and Royal College of Science and Technology, Glasgow, Scotland SUMMARY An electrical analogue of the human lung is described. The purpose of this communication is to show the advantages to be gained by the use of a simple nonsophisticated analogue in the elucidation of problems in lung mechanics. An attempt has been made to use the analogue to predict the optimum ventilatory pattern for patients with respiratory disease who may require intermittent positive ventilation. The results of two simple experiments on five analogue patients are discussed. It is possible, given the appropriate data, to arrive at these results by calculation. This, however, involves the solution of a second-order non-linear differential equation. Intuitive solution by ad hoc means is often wildly wrong and, when non-linearity is considerable, recourse must be made to digital or analogue computers. The analogue can also be used to demonstrate some of the effects of intermittent positive ventilation to trainee anaesthetists. An analogue is a specialized form of computer in which the constants of one system are transformed into the equivalent constants of another, e.g. a pneumatic system can be directly described by an equivalent electrical system. An electrical analogue is particularly convenient for the following reasons: (1) Measurements within the system are easily made. (2) These measurements may be displayed by a pen-recorder or oscilloscope for visual assessment. (3) The constants of the system can be altered at will. (4) Measurements can be taken from the analogue which may distort "normal" conditions if attempted on the original system. (5) The relevant techniques are already well developed and the components required are cheap and readily available. Nunn (1957) drew attention to the analogy between the pneumatic system of the human lungs and an electrical network comprising resistance and capacitance (fig. 1). The common mathematical relationships for pneumatic and electrical networks are: Voltage (volts) = Pressure (cm H 3 O) Current flow (amps) = Gas flow (l./sec) Electrical resistance = Airway and tissue resist- (ohms) ance (cm H 2 O sec/1.) Quantity (coulombs) = Volume (1.) Capacitance (farads) = Compliance (l./cm H 2 O). Mushin, Mapleson and Lunn (1962), using a model lung-airway system, emphasized the importance of the patient's pneumatic time-constant (airway resistance x total compliance or r). The electrical technique to be described here not only makes use of time-constants, but employs an extremely useful concept in the "time scale multiplier", that is to say the time during which an event takes place on the analogue need not be the same as in the actual pneumatic system but can be arranged to facilitate measurement. 684 METHODS In constructing an analogue it is often difficult or impossible to maintain exact equivalence but, examining the equations of flow for any system, it can be seen that the product R x C (resistance x capacitance or resistance x compliance) is import-

THE ELECTRICAL ANALOGUE OF LUNG 685 ENOO-TRACHEAL TUBE RESISTANCE TRACWEO - BRONCHIAL RESISTANCE LUNG COMPLIANCE CHEST WALL COMPLIANCE PHOTO- ELECTRIC WAVEFORM GENERATOR LUNS ANALOGUE ] Ri R.2 / c V INPUT -VENTILATOR 1 SHORT - SELF SUSTAINED CIRCUIT A ALVEOLAR INTRATHORACIC yy PRESSURE PRESSURE VENTILATOR - SHORT CIRCUIT DIFFERENCE AMPLIFIER SELF SUSTAINED - I N P U T FIG. 1 Electrical analogy. When the voltage is applied at R, and the other end of the network is short-circuited, the diagram represents the effect of IPPR with a generator ventilator. The addition of a high resistance before R, duplicates the performance of a ventilator of the flow generator type. With the voltage applied at C 2 and a short-circuit at the junction of Rj and R 2 the diagram represents the conditions pertaining when the patient breathes spontaneously. 2- CHANNEL OSCILLOSCOPE FIG. 2 Simple block diagram of the waveform generator and analogue apparatus. Changes in gas flow in the circuit are represented by the voltage drop across a known resistance measured by the difference amplifier. ant. For example, when a capacitance is discharging through a resistance the equation governing the flow is, v 2 t l0g ~ = CR where v x =initial voltage. v 2 = final voltage. t =time of discharge or current flow, and, in the pneumatic system, when a vessel empties through a resistance the equation governing the flow is. P, t l0g P7= CR where P t = initial. P 2 = final. t =time of gas flow. For equivalence CR would be the same in both systems but the equations are unaltered if t and CR are multiplied by a constant n (the time scale multiplier referred to above), so that if we multiply the CR of our electrical system by 100 then the time over which events are measured must also be multiplied by 100,,, v 2 t x 100 hence log T = CRTTOO- ' When the time-constant of one section is determined and constant n is chosen, all other values are automatically fixed. The electrical analogue used in this study is developed from a system designed to compute the heat flow in a refrigerator compressor (Clark, 1962). This apparatus was designed to function at a frequency between 12 and 100 cycles/sec. However, a suitable time scale multiplier enables the apparatus to simulate automatic ventilators which normally operate at a frequency between 12 and 40 cycles/min. Figure 2 shows the block diagram of the analogue. The waveform generator passes a signal into the analogue and then from the analogue the various voltages or current measurements are taken to the difference amplifier. This amplifier passes to the oscilloscope a signal which can be either the voltage at any point in the analogue or the current flow through the network. The voltage represents the at the various points and the current represents the flow of air into and out of the patient's lungs. The pattern for the waveform generator can be chosen to suit any known or hypothetical ventilator. This is simply done by cutting out the appropriate shape of the time curve on a strip of opaque paper and inserting

686 BRITISH JOURNAL OF ANAESTHESIA this on a rotating drum. The method of generation is that described by Sunstein (1949). A twochannel oscilloscope is used so that the difference in the slope, amplitude and time intervals between the various waveforms may be recognized and measured. The appropriate electrical values are chosen to match the pneumatic values required for endotracheal tubes, pulmonary resistance, lung compliance and chest wall compliance. Pressures are measured at upper airway, alveolar and intrathoracic levels. The airflow is measured at an arbitrary level between mouth and alveolus. Tidal volume can be measured by integration of the volume flow rate. It should be noted that, since this present analogue is linear, measurements are pro rata, thus if the at the generator is doubled then the at any given point will also be doubled. The development of the analogue to include nonlinear components is being pursued. Determination of values for C and R. In order to set up the analogue for any problem it is necessary to know the appropriate constants for the patient concerned. These constants can be determined by the technique of pneumotachography (Hill, 1959). The diagram shown in figure 3 outlines the method used for this investigation. An oesophageal tube with a 10-cm balloon attached is placed at the level of the left atrium under topical analgesia. The patient is then connected to the pneumotachograph flow-head by a rubber mouthpiece. Pressure leads are taken from the oesophageal tube and from the mouthpiece and led to a differential manometer. Changes in volume flow rate are measured by the pneumotachograph flow head and, by integration, corresponding changes in tidal volume are derived from this. All patients in this investigation were examined in the sitting posture but any posture may be adopted, provided it is borne in mind that the oesophageal may be artificially TP&NS PU VOL riow RA.TC 1 TPANS PuLMtwiW PRESS AP TIOM VOLUMC Vl IIMt CONSTANT or LUN6 11MOSPHIQE AIRWAY DirrtBtMiiAv nrrcaei I AIBWAY PRtStURC ~ ^ MJ**4Olt MAxoMCita [~~ patmuai "ssasfrh fly FIG. 3 In order to measure the total compliance and derive the time-constant for the lung-thorax system the oesophageal lead is closed at tap A (see diagram detail). The arm is now open to atmosphere and the airway only recorded with tidal volume.

THE ELECTRICAL ANALOGUE OF LUNG 687 TABLE I The constants for the patient's airway derived from pneumotachography as used to set up the analogue for the two experiments described. The values for the neonate and the endotracheal tube resistances were derived from tables. Due to the use of linear elements in the analogue the observed patient values have been matched to the accuracy of the analogue. Adult Normal High resistance Low compliance High resistance + low compliance Resistance (cm.h 2 O sec/1.) Endotrach. tube 8 8 8 8 50 Pulmonary (airway + pulmonary tissue) 0 0 300 Total 10 28 10 28 80 Compliance (I./cm H 2 O) Lungs 0100 0100 0 0 0 0 0005 Chest wall 015 015 015 015 001 Total 0 060 0 060 0018 0018 0003 Time constant (7) sec 0-600 1680 0180 0-505 0-240 raised above the intrathoracic in the supine position. In this way values for the patient's pulmonary resistance (i.e. the sum of airway + pulmonary tissue resistance), lung or total compliance and the time-constant of the patient's airway system are measured. The values for compliance shown in table I were not derived from static differences, measured at no-flow rates, but from the mean slope of the dynamic /volume loops. The pneumotachograph used for this investigation was constructed with the aid of the Regional Physics Department of the Western Regional Hospital Board and is essentially of the same design as that produced by Godart Mijnhardt. For the analogue experiments about to be described, the necessary compliance and resistance measurements were made on a normal adult, an adult with high airway resistance (advanced obstructive lung disease), an adult with low lung compliance (asbestosis and pulmonary fibrosis), an adult with high airway resistance and low compliance (pulmonary fibrosis and obstructive lung disease), and a normal neonate. The values for pulmonary resistance, compliance and time-constants for the four adults were derived from actual patients under treatment in this hospital, but the values for the normal neonate were taken from tables (Cook et al., 1955, 1957). The appropriate endotracheal tube resistances which were required for the experiments were also derived from tables (Macintosh, Mushin and Epstein, 1958). These various figures are detailed in table I. It can be seen that, in the adult with high airway resistance, as a result of obstructive lung disease, the time-constant is nearly three times longer than that of the normal adult under the same conditions. The patient with low compliance has a time-constant three times shorter in duration than the normal adult. In the patient with both high resistance and low compliance the timeconstant is nearly of the same duration as in the normal adult. In the case of the neonate the timeconstant is of the same order of duration as that of the adult patient with low lung compliance. "VENTILATOR" CHARACTERISTICS Two series of experiments were carried out on the five "analogue" patients. In the first series of experiments two different "ventilators" were used. The first was a constant generator and the maximum used was + cm H^O at the ventilator. The ratio of duration of inspiration to duration of expiration was 1:2 and the frequency of ventilation was /min in the adults and 40/min in the neonates. The second ventilator used was a hypothetical variable generator, again with a maximum of + cm H O at the ventilator. The frequency of ventilation was again cycles/min in the adults and 50 cycles/min in the neonate. In the adults, the at the ventilator rose uniformly (i.e. linearly) during each cycle from zero to its maximum value in 0.86 sec, returning to zero in 1.54 sec, and was followed by a pause of 0.6 sec: these time intervals were halved for

Upp airw press 0 Alveo press Flow 0 uppe airwa 0 Intratho pressu Normal High resistance Low compliance High resistance + low compliance FIG. 4A Comparison of waveforms and flow patterns in the five analogue patients in Experiment 1, using a constant generator. The upper trace in each case is the ventilator pattern, the lower trace the patient's airway or flow pattern.

m o s 00 cm H2O Upper airway cm H.2O Alveolar O - cm HaO Intrathoraeic, I- cm H2O Flow in upper airway Normal High resistance AA,,lr Low compliance High resistance + low compliance FIG. 4B Comparison of waveforms and flow patterns in the five analogue patients in Experiment 1, using a hypothetical variable generator. The upper trace in each case is the ventilator pattern, the lower is the patient's airway or flow pattern.

690 BRITISH JOURNAL OF ANAESTHESIA the neonate. This unusual wave was selected rather than a standard ventilator pattern, partly to illustrate the versatility of the analogue and partly to determine if any advantage was to be gained from its use. As before, measurements were made of the upper airway, alveolar and intrathoracic s and the volume flow rate of gas during the respiratory cycle in each patient. The comparison of airway s, and gas flow patterns, and the analysis of effects of varying the ventilator frequency, discussed below, were obtained using the second and more unusual ventilator pattern, but it should be noted that the general conclusions arrived at also apply when the orthodox constant generator is used. In the second series of experiments the variable generator was again used but the frequency of ventilation was varied. The alveolar at the end of the inspiratory phase and the volume flow rate of gas in the airway were then recorded. In order to allow for the increase in resistance due to airway turbulence at higher rates of ventilation, the electrical resistance values were increased. Ideally, of course, non-linear components would be incorporated in the analogue. However, the degree and range of nonlinearity have yet to be determined with sufficient accuracy and until this has been done the aforementioned alterations in the network resistances were considered to be a reasonable compromise in this preliminary investigation. RESULTS Comparison of airway s and gasflowrates. Figures 4A and 4B demonstrate, in the five patients, the patterns from different points in the airway and also the pattern of gas flow on the two "ventilators". As previously mentioned, all the values discussed in this experiment and in the second experiment were calculated for the conditions illustrated in figure 4B. In the normal adult the maximum volume flow rate was 24.4 l./min during the inspiratory phase. This flow was reduced by half in the patient with high airway resistance (10.46 l./min), but there was a rise in the upper airway (6.5 to 7.3 cm H,O). As expected, the s at the alveolar and intrapleural levels are reduced in the patient with high airway resistance compared to the normal adult, approximately in the same ratio as the reduction in flow. In the patient with low lung compliance there is a similar reduction in maximum volume flow rate (8.03 l./min) but here the at alveolar level at the end of the inspiratory phase is extremely high (almost equal to the at the mouth), while the intrapleural, outside the "stiff" lungs, is very low. It is possible in the patient with high airway resistance to compensate to some extent for the reduction in flow if the ventilator is raised, but such a manoeuvre, in the patient with low compliance, would result in an intolerable increase in the alveolar with undesirable effects on the cardiovascular system. It is apparent that the correct way to compensate for the low volume flow rate in the non-compliant patient is to increase the frequency of ventilation and not to increase the at the ventilator. In the patient with the combined defect of high airway resistance and low lung compliance there is a dilemma. One cannot easily improve upon the low gas flow (7.50 l./min) either by raising the ventilator or by increasing the frequency of the cycling. It is interesting at this point to reconsider the significance of the time-constant values. It would appear from these results that the time-constant may be associated with the ventilator frequency. The product of the time-constant and the ventilator frequency (r x f) is a "dimensionless parameter". Such dimensionless quantities have been found to be useful in the study of fluid flow, for example, Reynolds' number, Mach number, etc. The rf values for the five patients are given in table III. It will be seen that the dimensionless constant values for the normal adult, the adult with high resistance and low compliance, and the neonate, are almost identical. In table II it can be seen that the alveolar s in these three patients are also almost identical. The similarity of the shapes of the airflow and alveolar diagrams can also be seen in figure 4. If we assume that we have obtained the best possible pattern of ventilation for the three patients whose dimensionless constants are similar, then by adjusting the frequency of ventilation in the other two patients until the values for ri are of the same magnitude we should also get the best pattern of ventilation for these patients, i.e. decrease the frequency in the patient with high airway

THE ELECTRICAL ANALOGUE OF LUNG 691 TABLE II The calculated s and flow rates for the five analogue patients during experiment one are shown. The generator ventilator was set at + cm H 2 O operating and a frequency of /min and 40/min in the adults and neonate respectively. Upper airway (cm H 2 O) Alveolar (cm H 2 O) Intrathoracic (cm H 2 O) Maximum instantaneous volume flow rate (l./min) Adult Normal High resistance Low compliance High resistance + low compliance 6-5 7-3 91 8-2 7-1 6-2 2-8 90 6-2 6-7 2-9 1-2 1-3 0-94 24-4 10-46 8 03 7-50 2-54 TABLE III Table of dimensionless constants for the five analogue patients. Since the time constant is in seconds and the ventilator frequency in cycles/minute, the product rf must be divided by 60 to derive the dimensionless constant. The ventilator frequencies were chosen since they are those commonly used clinically. Patient Adult (1) Normal (2) High airway resistance (3) Low compliance (4) High airway resistance + low compliance Patient's time constant (r)/sec Ventilator frequency (f) cycles/min Dimensionless constant (-f/60) 0-600 1-680 0180 0-505 0-240 40 0-0 O-560 0 060 0-168 0 160 resistance and increase the frequency in the patient with low compliance. It should be possible with the help of an electrical analogue to construct a nomogram from which, if a patient's time-constant is known, the ideal ventilator frequency for intermittent positive ventilation can be derived. This would, of course, be used in conjunction with a ventilation nomogram of the Radford type. Analysis of the effects of varying ventilator frequencies. The five "analogue" patients were ventilated, therefore, over a wide range of frequencies but the waveform and ventilator were kept the same as in the first experiment. The adult patients were ventilated at frequencies of 10, and 40 strokes/min and the neonate at frequencies of, 40 and 80/min. Figure 5 shows the effect of varying the frequency of ventilation on the maximum instantaneous volume flow rate of gas in the airway during the inspiratory phase of the cycle. A ventilator frequency of about per minute gives the maximum flow rate in the normal adult, but in the patient with high pulmonary resistance the flow falls progressively as the rate of ventilation rises. For this patient the maximum volume flow rate of gas occurs at a ventilator frequency of about 10/min. When low compliance is a major factor, the volume flow rate increases with a rise in ventilator rate and at 40/min has only fallen slightly below the level at /min. In the adult with both high resistance and low compliance there is an initial rise in the gas flow rate as the ventilation rate increases to /min, but the flow falls fairly rapidly with any further increase in rate due to the resistance effect predominating. The graph of maximum volume flow against rate of ventilation for the neonate resembles in outline that of the normal adult. An increase in frequency up to about 40/min improves the flow in the neonate. From 40 to 80/min there is a steady fall in flow. However, before deciding upon the optimum frequency of ventilation for each of these patients it is necessary to consider the effect of ventilator frequency on the airway at alveolar level.

692 BRITISH JOURNAL OF ANAESTHESIA 10 3O 4O 50 60 Ventilator frequency (f/min) FIG. 5 This graph shows the effect on the peak flow rate, in the upper airway of the five patients, of varying the frequency of ventilation alone during IPPR. For convenience the flow axis for the neonate is drawn to 10 times the actual scale. O O Normal adult. x : X Adult, high airway resistance. # # Adult, low compliance. D Adult, high airway resistance + low compliance. Normal neonate. 7O 3O 4O 50 60 Ventilator frequency (f/min) FIG. 6 This graph shows the effect on alveolar of varying the frequency of ventilation alone during IPPR. For comparison, the arbitrary level of + 5 cm H 2 O has been chosen to indicate the ideal frequency of ventilation in each patient. O O Normal adult. X x Adult, high airway resistance. 0 9 Adult, low compliance. D Adult, high airway resistance + low compliance. Normal neonate. A high flow of gas attained at the cost of high alveolar and intrathoracic s is undesirable. In achieving adequate ventilation the aim is to obtain the highest flows at the lowest possible airway and intrathoracic s. Figure 6 demonstrates the relationship between ventilator frequency and maximum (end-inspiratory) alveolar in the analogue patients. Although it is convenient to refer to the maximum alveolar as end-inspiratory, this is not strictly correct since it implies that this event always takes place precisely at the end of inspiration. Due to phase shift in any pneumatic or electrical system, this is not always the case and, therefore, the time correlation of any such event cannot be assumed. Similar graphs could be drawn to show the relationship between the frequency of ventilation and the maximum at other points in the airway including the intrathoracic. In all cases the alveolar falls with the increase in rate. For a maximum alveolar of +5 cm H 2 O, the frequencies of ventilation for each patient are: normal adult 25/min; adult with high pulmonary resistance 16/min; adult with low compliance 33/min; adult with low compliance and high airway resistance 22/min; normal neonate 47/min. It is interesting to note how closely these frequencies agree with those already obtained for maximum volume flow rate in the upper airway shown in figure 5. These results underline the importance of Fenn's concept of the optimum frequency of ventilation for the minimum build-up of intrathoracic during intermittent positive ventilation (Otis, Fenn and Rahn, 1950; Fenn, 1951). REFERENCES Clark, D. M. (1962). Heat transfer analogue. Associateship Thesis, Royal College of Science and Technology, Glasgow. Cook, C. D., Cherry, R. B., O'Brien, D., Karlberg, P., and Smith, C. A. (1955). Studies of respiratory physiology in the newborn infant. I: Observations on normal, premature and full-term infants. /. din. Invest., 34, 975. Sutherland, J.M., Segal, S., Cherry, R. B., Mead, J, Mcllroy, M. B., and Smith, C. A. (1957). Studies of respiratory physiology in the newborn infant. Ill: Measurements of the mechanics of respiration. /. din. Invest., 36, 440. Fenn, W. O. (1951). Mechanics of respiration. Amer. J. Med., 10, 77. Hill, D. W. (1959). The rapid measurement of respiratory s and volumes. Brit. J. Anaesth., 31, 352.