Noninvasive measurements of cardiac output in sheep: an improved thermometry method

PII: S1350-4533(97)00021-0

Med. Eng. Phys. Vol. 19, No. 7, pp. 618–629, 1997  1997 IPEM. Published by Elsevier Science Ltd Printed in Great Britain 1350–4533/97 $17.00 + 0.00

Noninvasive measurements of cardiac output in sheep: an improved thermometry method Vladimir B. Serikov and E. Heidi Jerome Cardiovascular Research Institute and Department of Anesthesia, University of California, San Francisco, CA 94143, U.S.A. Received 30 September 1996, accepted 2 April 1997

ABSTRACT In 25 sheep and 5 goats, which were anesthetized, intubated and mechanically ventilated a sudden decrease in the inspired gas humidity was used to cool the lungs. The dynamics of the temperature of expired gas and its relationship to ventilation rate and cardiac output measured by thermodilution were investigated. In six animals minute ventilation was changed at a stable cardiac output and in 14 animals cardiac output was changed by infusion of saline or by bleeding at a constant ventilation. The difference between the blood temperature and the expired gas temperature at a steady state is proportional to minute ventilation and is inversely proportional to the cardiac output. The inverse time constant of the decay of temperature of the expired gas is proportional to the cardiac output and does not depend on ventilation. The lungs function as a natural humidifier of the respiratory gases with an inner heat source from the pulmonary circulation and an outer heat sink to the expired gas. A simple lumped heat capacity model of non-steady state heat exchange in the lungs was developed, which may be used as a basis for the non-invasive method for determining cardiac output. The coefficient of the lung thermal conductivity (KT/(␳WCpW) = 0.156 ± 0.056) was determined and applied to measure cardiac output in a separate group, designed as a prospective study. When calculations of cardiac output were done based on the lung mass, estimated from the body weight (12 g/kg), bias and precision compared with thermodilution were ⫺0.27 l/min and 0.38 l/min, respectively in 15 animals. Measurements of blood flow by the air thermometry correlated very well with thermodilution cardiac output (r = 0.92). Thermometry of the expired gas is a promising approach to measure the cardiac output non-invasively.  1997 IPEM. Published by Elsevier Science Ltd Keywords: Blood flow, expired gas, temperature, thermometry, heat exchange, ventilation, lung mass, non-invasive measurement, humidity Med. Eng. Phys., 1997, Vol. 19, 618–629, October

1. INTRODUCTION Most methods used to quantify cardiac output and pulmonary oedema are invasive1,2. Cardiac output measurements based on thermodilution or dye dilution are accurate but require the placement of a pulmonary arterial or a systemic arterial catheter. Development of airway indicator-dilution techniques is important to provide new non-invasive, reliable and simple methods to measure cardiac output and lung water. The lungs possess an extensive branching system of airways which are in contact with tissue layers and pulmonary vasculature. These layers allow equilibration of heat throughout the lung and exchange with blood flow. In intubated and mechanically ventilated subjects, heat exchange occurs entirely in the lungs rather than in the upper respiratory tract. The ability of the lungs to lose heat into the environment and to cool the airways has Correspondence to: V. Serikov.

been demonstrated in many studies3–5. During hyperventilation or cold air breathing, the airways, blood6 and even the tissue of the mediastinum7 are cooled. Cooling of the airways is reflected by a decrease of the expired air temperature. Previously we have discussed and validated a non-invasive method for determining pulmonary blood flow and lung mass by measuring lung heat exchange during hyperventilation8–10. The method uses heat as the permeant indicator, which is delivered through the airways. The difference in the expired gas temperatures at the two “steady states” was used to estimate blood flow and the rate of temperature decrease to estimate the lung heat capacity (Airway Thermal Volume). The Airway Thermal Volume has been shown to increase when pulmonary oedema was present8. Also, a good correlation between estimates of the pulmonary blood flow (cardiac output) and the perfusion rate in perfused lungs was found by differences in “steady states”. However, hyperventilation was discovered not to be the most appropri-

Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome

ate manoeuvre to change lung heat exchange, because it affects the circulation during the measurement. Instead of hyperventilation, in the current study the humidity of the inspired gas is changed in order to cool the lung. Changing humidity of the expired gas from hundred to zero percent provides a considerable heat challenge due to evaporative water loss. The dynamics of the lungs cooling and changes in expired temperature have not been studied previously under well controlled conditions. There is substantial experimental evidence that the pulmonary blood flow is the major heat source for the lungs11, although relationships between the pulmonary blood flow and lung heat exchange have not been studied. In other organs the heat flux from the circulation to tissue is proportional to the blood flow rate, which is the essence of the bioheat equation12. If the bioheat equation, validated for other tissues and organs13–15, may be applied to the pulmonary heat exchange, then the pulmonary blood flow can be determined from the rate of cooling of the lung. Previously the bioheat equation for the lungs was applied only for the local heat transfer inside the airways16. Several model investigations of a steadystate heat exchange in the airways have been published16–19, but a lumped heat capacity model of non-steady heat exchange in the lungs has not been further developed and tested experimentally. Though some data on airway temperature in humans during hyperventilation with dry and cold air are available20,21, neither the cardiac output or the lung mass were measured in these studies. The goal of the present study was to present a theoretical basis for a method of non-invasive measurement of cardiac output by analysis of dynamics of the expired gas temperature and to verify it experimentally, providing step changes in the humidity of the inspired gas in anesthetized, intubated animals. First, in section 2, we outline the principal theoretical considerations, which are essential for understanding the concept of the technique and its basic assumptions. Second, we describe the results of our experimental study, in which the first aim was to determine the relationship between the inverse time constant of the decay of temperature of the expired gas and the minute ventilation. Our second aim was to determine the relationship between the inverse time constant of the decay of temperature of the expired gas and the cardiac output. We then used the results obtained to achieve the third aim: to develop a simple lumped heat capacity model of a non-steady state heat exchange in the lungs, which describes the observed phenomena and allows us to calculate the cardiac output. Finally, a fourth aim was to apply the model to estimate the cardiac output and compare it with thermodilution cardiac outputs. Our experimental results demonstrate that the dynamics of the expired gas temperature following the switch from humid to dry gas ventilation depends on the pulmonary blood flow. Lungs are heated by the pulmonary circulation and the inverse time constant of the temperature decay is

linearly proportional to the pulmonary blood flow. Heat exchange in the lungs may be described by a simple lumped heat capacity model of heat exchanger, from which the mean integrated or effective coefficient of the lung thermal conductivity can be derived. The model allows us to estimate cardiac output non-invasively from the dynamics of the expired gas temperature.

2. METHODS 2.1. List of abbreviations

␣

is the coefficient of heat transfer at the surface (J s⫺1 m⫺2 °C−1); Bi is Biot number (non-dimensional), Bi = ␣s/h, where s is the characteristic dimension of the body; CpG is the heat capacity of gas (J kg−1 °C−1); CpW is the heat capacity of water (J kg⫺1 °C⫺1); C 0 and C are the mean mass concentration of water vapour in inspired and expired gas, respectively (kg m⫺3); jB is the total heat flux from the circulation (J s⫺1); jV is the heat flux into ventilatory gas (J s⫺1); H is the heat of water vaporisation (J kg⫺1); h is the thermal conductivity (J s ⫺ 1 m⫺1 °C⫺1); KT is the effective coefficient of lung thermal conductivity (J m⫺3 °C⫺1); Nu is Nusselt number (non-dimensional), Nu = ␣x/h⬘, where x is the characteristic dimension, h⬘ is the thermal conductivity; Re is Reynolds number (non-dimensional), Re = wh/v, where w is linear velocity, h is characteristic dimension and v is viscosity; Pr is Prandtl number (non-dimensional), Pr = v ␳Cp/h; Q is pulmonary blood flow (cardiac output) (l min⫺1); S is surface area (m2); TG0 and T are the mean temperatures of inspired and expired gas, respectively (°C); T0 is the initial temperature of expired gas at t = 0 (°C); Tt is the mean-integrated temperature of volume V (°C); TB is the temperature of the blood (°C); ␶ is the characteristic time of temperature decay (s); t is time (s); Ve is the minute ventilation (l min⫺1); V is the lung tissue volume (litres); ␳G and ␳W are the gas and water density (kg m⫺3), respectively; ⌬T is the difference between the temperatures of expired gas in the two steady states (°C).

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Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome

2.2. Theory In this section we provide general theoretical considerations and assumptions, which were used to develop the concept of the method. 2.2.1. Lumped heat capacity system. Earlier descriptions of our method and a mathematical model of the lung heat exchange have been published previously8–10. Heat loss is calculated from the ventilation, temperature and humidity differences between the inspired and the expired gas. It is assumed that the expired gas is totally humidified at its temperature, so that the humidity and corresponding evapourative heat losses can be calculated by knowing the expired gas temperature. During ventilation with the dry gas the lungs are cooled, and the temperature of the expired gas decreases22. A new steady state is achieved at which the heat transfer from the lungs into the environment is balanced by the conductive heat transfer from the circulation into the lung tissue. If there is no circulation through the lungs, it cools down to the temperature of a wet-bulb thermometer. Previously, we hypothesized that the pulmonary blood flow provides the inner heat source for the lungs8,9. Experimental observations11, as well as our own data in hyperventilated canine lungs10, were consistent with this hypothesis. The bioheat equation states that the heat flux from the circulation into the tissue is proportional to the velocity of blood flow12,13. The lungs may be thought of as a heat exchanger, which has two heat fluxes: from the pulmonary blood flow, which heats the lung tissue and increases the temperature of expired gas, and into the airways, which cools the lung tissue. For a small change in the temperature the heat flux into the lungs is linearly proportional to the pulmonary blood flow and the difference between the air temperature and the blood temperature. As a first-order approximation, we assume that the system is well equilibrated and the lumped heat capacity model may be applicable23. For the simplest case (one heat flux) the rate of the temperature Tt change in a body (lung) with thermal volume V, surface S, density ␳ and heat capacity Cp by the heat flux j is determined by the equation: j = ⫺ ␳CpV(dTt/dt) = S␣(Tt ⫺ TG0),

(1)

with the solution:

where jV is the ventilatory heat flux, which is taken out from the lungs by ventilation, jB is the circulatory heat flux, which heats the lungs due to the pulmonary blood flow, and jM is the metabolic heat production, which is negligible in lungs compared with jV and jB. Heat flux from the circulation, according to the general bioheat equation 12 depends on blood flow linearly: jB = Keff ␳CpQ "gradT ⬘ = ␣SgradT ⬘ = QKTgradT ⬘, (4) where Keff is the effective coefficient of heat transfer according to 12, Q⬙ is the local blood flow, grad T⬘ is the temperature gradient between blood and tissue, ␣ is the heat transfer coefficient, and KT is the effective thermal conductivity coefficient for the lungs. We consider that the heat exchange between the circulation and tissues in the lung is similar to the heat exchange in a fluid flow through a branching network of tubes. The coefficient of heat transfer from the flowing fluid to the walls of tubes is usually given in the form:

␣ = Nu h⬘/x = (BReEPrF) h⬘/x,

(5)

where Nu is Nusselt number, h⬘ is thermal conductivity of fluid, x is characteristic dimension, B, E, F are the empirical coefficients which are specific for the system23. As the pulmonary circulation is a very complex network of branchings tubes of different lengths and varying diameters with different local values of ␣ at each level of branching, the coefficient ␣ in Equation (4) represents the mean-integrated value for the whole pulmonary circulation. For the pulmonary circulation the mean-integrated value x may be assumed to be constant, as well as h⬘ and Pr for the blood. The empirical equations have been proposed for relationships between ␣ and Re in heat exchangers23. Following Ref. [19] we assume that for the pulmonary circulation the same empirical relationships are valid. Re number is the function of linear fluid velocity and for 100 ⬍ Re ⬍ 1000 the coefficient E is 0.7 ⬍ E ⬍ 1.0. The coefficients B and F are constants. Thus, the mean integrated values of ␣ are the linear function of cardiac output, which determines values of Re in the pulmonary circulation. 2.3. Convection boundary conditions

Here ␶ is the time constant of temperature change and ␣ is the coefficient of heat transfer from the surface, Tt0 is the initial temperature of lung and TG0 is the temperature of the gas used to ventilate the lung. In an actual lung there is a sum of heat fluxes, associated with the ventilation, circulation and tissue metabolism. The sum of the heat fluxes in the lung equals:

The above given theory would be satisfactory for a tissue or an organ with rapid thermal equilibrium. However, in the lung it is possible that the gradients of temperature exist, and other effects, such as the counter-current heat exchange in the airways22 and counter-current heat exchange between arterial and venous vessels12,14, may play important roles. For Biot numbers larger than 0.1 the surface-convective resistance is small compared with internal-conductive resistance. Boundary conditions for Equation (2) may include the convection heat transfer at the surface:

Σj = ⫺ jV + jB + jM,

S␣(Tt ⫺ TG0)兩x = 0 = ⫺ hS(dTt/dt)兩x = 0.

(Tt ⫺ TG0)/Tt0 ⫺ TG0) = exp( ⫺ t/␶),

(2)

where 1/␶ = S␣/␳CpV.

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(3)

(6)

Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome

Parameters in Equation (1) then may become the mean-integrated values over the whole lung tissue volume V. We calculated Biot number, Bi = ␣s/h from the effective characteristic dimension s = V/S. We assumed that the surface area of heat exchange in the lungs S does not exceed 1 m2, jV = 5 W, and Tt ⫺ TG0 = 2°C, and h for the lung tissue is the same as for water (h = 0.6 J s⫺1m °C⫺1). We analysed the simplest case, when there is no circulation and lungs are only cooled by ventilation, Σj = j V. The time constant of lung cooling without blood flow is approximately 800 s, and from Equation (2): 1/␶ = 0.00125 = ␣/(s␳WCpW); s = ␣/(0.00125 ␳WCpW). From Equation (1) ␣ = jV/S (Tt ⫺ TG0) = 2.5 W m⫺2 °C⫺1, then s = 0.0005 m; and Bi = 2.5*0.0005/0.6 = 0.002. The lumped sum model can be applied. 2.3.1. Model verification. The lumped heat capacity model predicts the following effects for the lung heat exchange: the temperature difference between two steady states is proportional to the ratio of thermal conductivities, associated with the outgoing and incoming heat fluxes. The inverse time constant of lung cooling should be proportional to the sum of thermal conductivities related to the blood flow and volume ventilation, and inversely proportional to the lung mass. The thermal conductivity associated with circulation is the product of the coefficient of thermal conductivity KT and blood flow (cardiac output). We used a simple linear model, with one mean ⫺ integrated coefficient of lung thermal conductivity, KT. The coefficient KT represents the mean-integrated over the whole lung complex (S␣/Q) [Equations (1)–(4)]. The importance of the ventilation and the blood flow depends on the geometry of the system (which determines heat transfer coefficients and temperature profile distribution). The mass of the lung determines the total heat capacity. A larger lung mass specifies a slower rate of lung cooling than does smaller lung tissue mass. As the thermal conductivity associated with the ventilation is much smaller than the thermal conductivity associated with the circulation, the direct use of the temperature difference between steady states for practical purposes (calculation of blood flow) is restricted to a narrow range of ratios of the ventilation to circulation (large ventilation vs low blood flow). As the ventilatory heat flux is small, while heat capacity of blood and the blood flow are large, blood changes its temperature after passing lungs by less than 0.1°C. The blood temperature may be assumed to be constant and the thermal conductivity of the circulation can be determined from the inverse time constant of lung cooling or heating. We assume that over the physiological range of cardiac outputs, the relationship between ␣ and Re [Equation (5)] of the blood flow in the lungs (cardiac output) is linear. To verify this assumption we need to determine the inverse time constant of the temperature decay (1/␶) at different cardiac outputs. As in Equation (2) there is a sum

of heat fluxes, we also need to determine the relative importance of jV, or the influence of the minute ventilation Ve on 1/␶. Depending on the coefficient of the lung thermal conductivity, relative role of ventilation compared with circulation may be different. Our previous data in animals 10 show, that the thermal conductivity of the circulation is approximately 10-fold higher than the thermal conductivity of the ventilation. The effect of ventilation on the time constant should be small. The time constant for the whole lung should be determined primarily by the thermal conductivity of circulation. A solution for the lumped heat capacity model can be obtained easily when at the initial steady state heat flux from the lungs is zero. Then the temperatures of the inspired and expired gas are equal, and they should be equal to the blood temperature. 2.4. Experimental studies 2.4.1. General experimental protocol. We studied 25 sheep and 5 goats. Experiments were conducted to a standard that is consistent with the Animal (Scientific Procedures) Act of 1986 (Britain). The animals were weighed prior to the study and anesthetized with 15 mg/kg i.e. sodium Pentothal, endotracheally intubated with a 9 mm tracheostomy tube (Portex, Keen, NH) and ventilated with a constant-volume pump (Model 607, Harvard Apparatus, Millis, MA) at a tidal volume of 15 ml/kg. Anesthesia was maintained with 1–2% halothane in air or 50% O2. Spontaneous breathing was prevented with pancuronium bromide, 1 mg i.v. every 2 h. Through a neck incision we placed catheters in the carotid artery. In closed-thorax sheep, we positioned a Swan–Ganz thermodilution catheter (Baxter, Valencia, CA) into the pulmonary artery. In open-thorax sheep we placed a thermistor probe (2F; Baxter Co, Valencia, CA) into the main pulmonary artery through a thoracotomy in the fourth left interspace. We measured cardiac output with a thermodilution cardiac output computer (Model 3500; Mansfield Scientific, Mansfield, MA) by injecting 5 ml of 4°C saline into the right atrium. In 10 studies the total lung mass, residual lung blood, extravascular lung water and the wet-to-dry weight ratio of blood-free lung were determined as described in Ref. 24. To measure air temperature we positioned an alumel-chromel thermocouple (0.01 in. in diameter (response time 100 ms, Omega Engineering, Stamford, CT) in the middle of the gas stream 2 cm from the distal end of the tracheostomy tubing. The thermocouple was connected to an amplifier and chart recorder (Model 0585, Linear Instruments, Reno, NV). Before each experiment the thermocouple and thermodilution catheter were calibrated together in a water bath against a mercury thermometer (25–40°C). We fully humidified and warmed the inspired gas to 38–39°C with a Concha Therm III humidifier (Respiratory Care, Ohio, IL) connected to the

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Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome

2.4.2. Specific protocols. In all our experiments, we measured the systemic arterial pressure, arterial blood gases and cardiac output during a stable 1–2 h baseline. 2.4.2.1. Study 1 To answer the specific aim one in six closed-thorax sheep, we measured thermodilution cardiac output and expired gas temperature. We kept the tidal volume constant and changed ventilation rate. Five of these sheep were then used in Study 2.

2.4.3. Temperature data analysis. Temperature data from the chart recorder were digitized by an operator blindly and then analyzed by software

622

3.1. Relationship between temperature of expired gas and minute ventilation To answer specifically aim 1, we investigated effects of ventilation on the expired gas temperature. A typical curve of the expired gas temperature during ventilation with the humid, heated gas and the following switch to the dry gas is shown in Figure 1. While ventilating with the humid heated gas we were able to reach a condition, in which the temperature of expired gas was equal to the temperature of inspired gas. The switch to dry gas ventilation resulted in a decay of the expired gas temperature, the decay being close to a monoexponential in most cases. An increase in ventilation rate resulted in a further decrease of the expired gas temperature (Figure 1). When ventilation was stopped, the temperature in the airways increased, owing to continued heating of the lungs by the circulation. 40

38

36

7

2.4.2.4. Study 4 To answer specific aim 4, we applied the model solution to calculate cardiac output in 13 additional anesthetized sheep and two goats, making one comparison between thermodilution (in triplicate) and air thermometry in each animal. In some experiments we followed changes in cardiac output for 2–4 h.

3. RESULTS

60

2.4.2.3. Study 3 To answer specific aim 3, we solved Equation (4) for fixed boundary conditions. We used data from study 1 and 2 to determine coefficient KT from the model solution.

2.4.4. Statistical analysis. Data were compared by unpaired and, when appropriate, paired Student’s t-test, as well by regression analysis. The data are expressed as the mean ± SD, with statistical significance accepted at p ⬍ 0.05. We used the Bland–Altman method25 to calculate agreement between thermodilution and thermometry cardiac output in Study 4.

50

2.4.2.2. Study 2 To answer specific aim 2 in nine open-chest and closed-chest sheep and three goats we compared the pulmonary arterial blood temperature, (measured using thermodilution catheter) with the airway temperature (obtained at the point of zero net heat flux). In some animals we injected into the right atrium 10–20 ml of ice cold saline and simultaneously recorded temperature in the pulmonary artery and in airways. We increased cardiac output in 14 sheep by rapid intravenous infusion of 500–1000 ml of warmed saline (39–40°C) over 5 min, then decreased it by withdrawal of 600–800 ml of blood from the carotid artery. We measured the thermodilution cardiac output, following each of these interventions. In some animals we stopped ventilation for up to 4 min and recorded temperature in the airways.

“Origin 3.1” (Microcal Software, Northampton, MA). We used a monoexponential fit to the curves to determine the time-constant and temperature difference, ⌬T.

Air temperature (°C)

inspiratory line of the respiratory circuit, until equilibrium was achieved between inspired and expired gas temperature. We then altered the humidity and temperature of the inspired gas by switching to dry gas ventilation at room temperature (26°C) for 6–8 min. Inspiratory lines for humid and dry gas were connected by a small dead space T-connector at the proximal end of the tracheostomy tube. The switch from humid to dry gas ventilation was done with a stopcock, positioned before the humidifier. We cleaned condensate and mucus from the respiratory circuit and tracheostomy tube before making each measurement, and we inspected the probe after each measurement. If it was not free of mucus, the results were discarded and the measurement was repeated.

34 0

2

4

6

8

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12

Minutes

Figure 1 Temperature record in the intubation tubing under different ventilatory conditions. At first the lungs are ventilated with warm humid gas. The temperature of inspired gas is increased until the temperature of expired gas equals the temperature of inspired, as indicated by the single arrow. Then ventilation is switched to dry gas and the temperature of expired gas declines until another steady state is reached. Frequency of the ventilation is increased two-fold (two arrows) and the expired air temperature declines until another steady state is reached. Ventilation is then stopped (three arrows). The temperature of expired gas is measured after single inspirations at 1, 2 and 3 min. Airway temperature increases during apnea, but even after 3 min of stopped ventilation the expired gas temperature is 0.7°C less than the blood temperature.

Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome

The inverse time constant, 1/ second

0.05

0.04

0.03

0.02

0.01

0 0

6

12

16

20

24

Ve, I/ min

Figure 2 Relationship between inverse time constants of the expired gas temperatures and minute ventilation in Study 1. Data from six individual experiments are shown by lines.

3.1.1. Study 1. The relationship between the inverse time constants of the expired gas temperature decay and the minute ventilation is shown in Figure 2 for cardiac outputs over the range 2.5– 4 l/min. The correlation between these variables was poor. We conclude that the time constants of the expired gas were not related to volume ventilation. The temperature difference between two steady states was related to volume ventilation in individual experiments, as shown in Figure 3. An increase in Ve at a constant cardiac output usually resulted in an increase of temperature difference between steady states. For individual experiments the intercept of the regression line with the Y-axis was 0.7–1.5°C. 3.2. Pulmonary blood flow To answer specific aim 2, we investigated effects of the pulmonary arterial blood temperature and the blood flow on the temperature of the expired gas. We compared the pulmonary arterial blood temperature (measured using the thermodilution catheter) with the airway temperature (obtained at the point of zero net heat flux). We found that at this point the temperature in the airways was 3

∆ T, C

2.5

2.0

closely correlated with the temperature in the pulmonary artery (r = 0.96), as expected. When we injected 10–20 ml of ice-cold saline into the right atrium, we observed a decrease in the expired gas temperature, which was proportional to the amount of indicator injected (Figure 4). The decrease in temperature and the following recovery were closely related to the changes in the temperature in the pulmonary artery and followed its pattern. The rapid decrease in the temperature of blood in the pulmonary artery resulted in cooling of the lung tissue, which was immediately reflected in the temperature of the expired gas. These observations prove that changes in the expired gas temperature reflect changes of the temperature of the whole lung due to heat exchange. These results also show that the rate of lung cooling and heating from the circulatory side depend on the cardiac output. In Figure 5, typical temperature curves are given from one experiment with the constant minute ventilation and the lung mass, but at high cardiac output [Figure 5(A)] and low cardiac output [Figure 5(B)]. Comparison of these records clearly shows that a decrease in cardiac output results in an increased temperature difference between steady states and slowing of the time constant of the temperature curve. An increase in cardiac output would have caused opposite changes. These results demonstrate that the pulmonary circulation provides heat to the lungs, which are cooled by ventilation. The temperature drop between two steady states is inversely proportional to the cardiac output. Two temperature curves corresponding to different ventilation rates in one experiment (curve 1, Ve = 6 l/min and curve 2, Ve = 12 l/min), are illustrated in Figure 6. The relationship between the temperature drop and cardiac output is hyperbolic. At high cardiac outputs large changes in blood flow result in small changes in the temperature drop. The relationship between the inverse time constant of the expired gas and cardiac output in individual experiments is illustrated in Figure 7 for animals with body weight 14–30 kg. In Figure 8 the same relationships are given for animals with body weight 30–50 kg. The inverse time constant of expired gas is linearly proportional to the cardiac output. In four animals we measured the temperature of expired gas for 8–10 min after the heart stopped. The mean value of the estimated time constant was 790 ± 90 s for the lungs without blood flow.

1.5

3.3. Lumped heat capacity model 1.0

0.5 4

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Ve, L/ min

Figure 3 Relationship between the temperature drop, ⌬T, and minute ventilation.

To answer specifically aim 3, we obtained the solution of the model equations for the fixed boundary conditions and used data from Studies 1 and 2 to obtain model coefficients. 3.3.1. Model solution. The outward heat flux, jV, can be determined from the temperature and

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Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome 40 10 cc 40.0

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Temperature °C

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Figure 5 Temperature records of the expired gas temperature. Typical curves of the expired gas temperature during the high cardiac output (A) (4.2 l/min) and low cardiac output (B) (1.6 l/min) in a single experiment.

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(B)

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(C) Figure 4 Temperature changes in the pulmonary artery (closed circles) and the expired gas temperature (open squares) after the infusion of cold saline into the right atrium (arrow). (A) Volume of injectate is 10 ml, cardiac output 2.75 l/min; (B) volume of injectate is 20 ml, cardiac output is 2.8 l/min; (C) volume of injectate is 20 ml, cardiac output 1.05 l/min.

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Figure 6 The temperature drop, ⌬T, at different cardiac outputs. Curve 1 was obtained at a ventilation of 6 l/min and curve 2 at a ventilation of 12 l/min. Data are from a single experiment S30.

humidity difference between inspired and expired gas and from the total amount of gas that enters the lungs. For practical purposes it can be given as the sum of finite-difference elements as:

Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome

The inverse time constant, 1/ second

0.07

state balance between heat loss to the environment and heat gain from the pulmonary blood flow is achieved, at which point jV = jB. The corresponding equation for the unsteadystate cooling of the lung tissue can be given as:

0.06 0.05 0.04

V␳WCpW(dTt/dt) = jB ⫺ jV.

0.03

We assume that the temperature of the lung is proportional to the expired gas temperature. Since the gas expired from the lungs is fully saturated with water at its temperature, we can calculate water vapour mass concentration from the temperature of this expired gas. A linear approximation of the mass concentration (absolute humidity) of saturated water vapour in air is used:

0.02 0.01 0 0

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Cardiac output, L/ min

Figure 7 Relationship between the time-constants of the expired gas and cardiac output, in seven animals weighing 14–30 kg.

C(T) = 0.0018[k gm⫺3 °C⫺1]T ⫺ 0.02[kg m⫺3], (9) where C(T) is water vapour mass concentration (kg m ⫺ 3) and T is the temperature in °C. This linear approximation is valid for temperatures over the range 20–38 °C. Then Equation (8) can be given as:

0.07 The inverse time constant, 1/ second

(8)

0.06 0.05

dT/dt + AT + B = 0,

0.04

(10)

0.03

where, for dry gas ventilation, the constants A and B are:

0.02

A = (1/V)(QKT/(␳WCpW) + Vex2), (11) B = ( ⫺ 1/V)(QT¯ KT/(␳WCpW) + Vex1TG0 + Vex3),

0.01 0 0

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Cardiac output, L/ min

Figure 8 Relationship between the time-constants of the expired gas and cardiac output, in seven animals weighing 30–50 kg.

⫺ jV = Ve[(TG0 ⫺ T) ␳GCpG (7) + (TG0CpWC0 ⫺ TCpWC) + (C0 ⫺ C)H], where Ve is the minute of ventilation, TG0 and T are the mean temperatures of inspired and expired gas, respectively, ␳G is the gas density, CpG is the heat capacity of gas, CpW is the heat capacity of water, C0 and C are the mean mass concentration of water vapour in inspired and expired air, respectively, and H is the heat of water vaporisation. If we assume that the expired gas temperature, T, equals the mean-integrated temperature on the gas side of the blood–gas barrier, then the heat flux from the circulation is driven by the difference between T and the mean temperature of the blood, TB [Equation (4)]. Heat flux from the circulation linearly depends on the blood flow. The thermal conductivity is determined by the product of blood flow Q and the coefficient of lung thermal conductivity KT. We also assume that KT, mean-integrated over the effective surface area is a constant. A change in the humidity and temperature of the inspired gas cools the lungs, so that the temperature of the expired gas, T, decreases (Figure 1). Heat loss to the expired gas also changes. jV and T are functions of time until a new steady-

where x1, x2 are dimensionless parameters: x1 = ␳GCpG/␳WCpW = 2.63 × 10⫺4, x2 = x1 + 0.0018H/␳WCpW = 1.24 × 10⫺3 and x3 = 0.02H/␳WCpW = 10.9 × 10⫺3 (dimension °C). The density and heat capacity of lung tissue are assumed to be those of water. The analytical solution of Equation (10) can be easily obtained: T(t) = T0(exp( ⫺ At))(1 + B/AT0) ⫺ B/A,

(12)

where T0 is the initial expired gas temperature and t is time. In the proposed technique T0 is the temperature of expired gas at a zero outgoing heat flux, when the temperature of expired gas equals the temperature of inspired gas (Figure 1). T0 also equals TB, the temperature of circulating blood. Equation (12) can be solved for the two different steady-state conditions in terms of temperature drop, ⌬T—the difference between the temperatures of expired gas in the two steady states, and the characteristic time of the temperature fall, ␶. Pulmonary blood flow, Q, and the lung thermal volume, V, are obtained as: Q = Ve␳WCpW(T0x2 ⫺ TG0x1 ⫺ ⌬Tx2 ⫺ x3)/(⌬TKT).

(13)

V = ␶(Q(KT/(␳WCpW)) + Vex2).

(14)

Q = (1/␶)(V␳WCpW)/KT ⫺ Vex2KT/(␳WCpW). (15) Equation (13) establishes the relationship between the cardiac output, the volume venti-

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Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome

KT/(␳WCpW) = Ve(T0x2 ⫺ TG0x1 ⫺ ⌬Tx2 ⫺ x3)/(⌬TQ),

(16)

Baseline

Volume load

8

Cardiac output, L/ min

lation and the temperature drop ⌬T. Equation (15) shows the relationship between the cardiac output, the inverse time constant of the temperature curve and the lung thermal capacity. The second term in the right part of Equation (15) is small, compared with the first term, as x2 is small. There are two ways to calculate KT: from Equation (13):

Bleeding

6

4

2

or from Equation (15): KT/(␳WCpW) = V/(Q␶) + Vex2/Q.

(17)

0 10

V = body weight × 12.1/1000. In Equation (17) for a lung with V = 0.2 l, ␶ = 0.5 min, Q = 2 l/min, and Ve = 10 l/min, the first term (V/(Q␶)) is one-to-two orders of magnitude larger than the second (Vex2/Q), as x2 = 1.24 × 10⫺3. Thus, for practical purposes we used Equation (17) as: KT/(␳WCpW) = V/(Q␶). Q was determined by thermodilution and ␶ by the air thermometry. Using these estimates we calculated KT/(␳WCpW) = 0.156 ± 0.056. This value is close to what we found previously10 from the relationship between Ve and ⌬T in hyperventilated sheep (KT/(␳WCpW) = 0.20).

11.0

11.5

12.0

12.5

13

Time, hours

Figure 9 The time-course of cardiac output in animal G11 measured by thermodilution and estimated by the air thermometry during baseline, volume load and bleeding. Open circles, the thermodilution cardiac output; closed circles, cardiac output by air thermometry. 5 Air thermometry cardiac output, L/ min

3.3.2. Determination of the lung thermal conductivity coefficient. Equation (13) shows that the relationship between Q and ⌬T is hyperbolic, which correlates well with the experimental relationship (Figure 6). The use of ⌬T to calculate Q makes the measurement unstable, as slight changes in ⌬T, caused by noise or variations in position of the temperature probe may produce a large error. In Equation (15) the relationship between Q and the inverse time constant (1/␶) is linear, which is preferable. However, the lung tissue volume (V) must be known to estimate KT. We determined the relationship between the total lung mass and body weight in these and separate measurements10 as 12.1 ± 2.4 g/kg of body wt and used it to estimate V (l) from body weight (kg) as:

10.5

4

3

2

1

0 0

1

2

3

4

5

Thermodilution cardiac output, L/ min

Figure 10 Correlation between the thermodilution cardiac output and the air thermometry cardiac output by Equation (18) in Study 4.

(18)

is high (r = 0.92) for estimates based on the calculated lung mass and the time-constant of the temperature of the expired gas. The pulmonary blood flow measurements are well reproducible at a stable cardiac output. Duplicate measurements under stable conditions were not different (p = 0.3) (data not shown). The coefficient of variation was 5.4%. Analysis of agreement between the air thermometry and the thermodilution cardiac output is shown in Figure 11. Bias (difference of the mean) was 0.27 l/min and precision (SD of difference) was 0.38 l/min.

where 60 is the constant to convert Q into l/min. We used the ratio of lung mass per kg body wt to estimate V from body weight. In Figure 9 the timecourse of cardiac output in an individual animal is illustrated. It shows a good agreement between the changes in cardiac output during volume load and bleeding. The results of correlation between estimates of cardiac output by the air thermometry and measurements by thermodilution are given in Figure 10. The correlation between the two methods

4. DISCUSSION This study shows that, according to the dynamics of the expired gas temperature, the pulmonary blood flow heats the lungs after a step change in humidity of the inspired gas. Experimental evidence supports the assumption that the thermal conductivity of the circulatory heat source is linearly proportional to the cardiac output. This observation allows us to use the dynamic changes in the temperature of expired gas as a basis of a

3.4. Estimates of cardiac output by air thermometry compared with thermodilution To answer specifically aim 4, we estimated cardiac output (l/min) using Equation (15) in a simplified form: Q = (60/␶)(V/0.156),

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Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome Difference thermodilution - thermometry cardiac output, L/ min

4

2 + 2 SD 0

– 2 SD –2

–4 0

1

2

3

4

5

Mean cardiac output, L/ min

Figure 11 Agreement between cardiac output measured by thermodilution and by the air thermometry in 15 animals by the Bland– Altman method 25. Bias = ⫺ 0.27 l/min; precision = 0.38 l/min.

new method to estimate cardiac output non-invasively. In a non-steady state, the inverse time constant of the decay of temperature of the expired gas mainly depends on the circulation, but not on ventilation (Figure 2). In a steady state there are other major determinants of the temperature of expired gas: the temperature of blood and the ventilation rate (Figure 3). The temperature of the blood determines the temperature of the lungs and expired gas, when the external heat flux is zero (Figure 1). We found an excellent correlation between the blood temperature and the airway temperature, measured when the temperature of the inspired gas was identical to the temperature of the expired gas. During dry gas breathing the ventilation primarily determines the absolute values of the expired gas temperature. We found a linear relationship between the temperature drop and minute ventilation, as is predicted by our model for constant blood flow. It was shown previously that the extent of lung cooling is proportional to the rate of ventilation and inversely proportional to the temperature of the inspired gas20–22. Gilbert et al. (1990) increased ventilation in exercising subjects and produced a decrease in the expired air temperature of 5°C over 4 min20. Other direct measurements also show that the temperature of gas changes along the longitudinal axis of the bronchial tree17,21. The temperature of expired gas reflects the heat exchange between gas and the bronchial tree. In turn, the bronchial tree is cooled by gas, but is heated by the circulating blood. Thus, the temperature of the expired gas represents the superposition of the effects of local heat transfer in the bronchial tree and non-steady-state exchange among the bronchial tree, gas and blood. The absolute values of the expired gas temperature are influenced by the local heat exchange phenomena in the conducting airways, but the dynamics of the temperature of expired gas is determined by overall heat balance. Utilizing extrapolation methods we found that the expired air at zero ventilation is about 0.7– 1.5°C cooler than the blood temperature (Figure

3). That may be due to several effects. Unheated gas mixes with heated gas to cause a decrease in the temperature of expired air, analogous to the dilution of exhaled CO2 by dead space ventilation. Temperature profiles in the lung are determined by combined convection and conduction within airways and in tissue layers surrounding the bronchial tree. If the vascular tree does not exactly match the air passages of the bronchial tree, the occurrence of non-linear effects is possible. Our major finding is that the rate of lung cooling at a constant lung mass is determined by the thermal conductivity of the circulation (Figures 5 – 7). Our results demonstrate that the inverse time constant of the lung cooling is linearly proportional to the cardiac output (Figure 8). Blood flow is the major heat source of the lung as lung tissue metabolism accounts for less than 5% of lung heat loss into the environment. Heat may be provided by either the pulmonary or the bronchial circulations, or both. Direct evidence that pulmonary blood flow provides most of the heat to the lungs comes from experiments by Solway and coworkers (1986), in which interrupted pulmonary blood flow to a lung lobe resulted in an exponential decline of expired air temperature11. Bronchial artery occlusion had no effect on expired air temperature. We observed a close relationship between the temperature in the pulmonary artery after infusion of cold saline and temperature in the airways (Figure 4). However, the temperature changes of the expired gas occur slower than do the temperature changes in the pulmonary artery, because heat is distributed from pulmonary circulation into a large lung mass. The recovery process occurs due to heating of the lung by the warm blood. The reheating process was slowed down at lower cardiac output. The temperature in the airways represented the dynamics of the temperature of the lung tissue, which was first cooled and then heated by the pulmonary circulation. In the same fashion when ventilation with the humid gas is changed to the dry gas ventilation the temperature of expired gas represents changes in lung temperature due to evaporative cooling at the gas side. Our finding that the thermal conductivity of the circulatory heat source is linearly proportional to cardiac output is consistent with current views on the heat exchange between tissues and blood flow, i.e. the bioheat equation14,15. The lungs should not be different from other organs in the basic principles of heat exchange between blood and tissue, for which the linear relationship between the blood flow and heat flux has been postulated12,13. As the major temperature gradient inside the lung exists in the first several generations of the bronchial tree, the main part of heat transfer occurs in the core of the lung, between bronchi of 0–10 generations and large blood vessels which surround them. The value of the effective coefficient, KT, which we determined (KT/(␳WCpW)) = 0.156) has physical meaning. It shows that a certain portion of cardiac output directly participates in heat exchange

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in the lungs at any moment. As heat is distributed extremely rapidly, the cooled blood exchanges with uncooled and also mixes with it. Thus, all of the pulmonary blood flow participates in heat transfer, though gradients of temperature between blood and airways are different in major and small vessels, and, respectively heat fluxes are different. The dynamics of the temperature change is determined by the flow rate in large blood vessels, rather than in the capillary bed. This makes the method more stable in terms of local variations in pulmonary blood flow distribution or ventilation-perfusion mismatches (which are zonal or local phenomena). The value of KT/(␳WCpW) shows that the pulmonary blood flow-related thermal conductivity is approximately ten-fold larger than the thermal conductivity related to jV. This is also seen from the fact that lungs without circulatory heat source have a time constant of cooling of 800 s, while in a normally functioning lung it is approximately 30 s. Change from the humid to dry gas ventilation, which is the input signal in our method, should be performed instantly. As in any other non-steady-state system tested with a step-like function, output (which is dynamics of the expired gas temperature) depends on the input. Equations (4)–(6) were solved for a step input function. In practice, if the input function is slow (change in humidity or temperature is slow) the output time constant will be slowed down considerably. If the input time constant is close to output or larger, there will be no relationship between the time constant of the decay of the temperature of the expired gas and the cardiac output. In this case the time constant of expired gas will simply repeat the time constant of the input change in humidity. For that reason slow changes in ventilation or humidity will be the most significant source of error. We tried to avoid deviations of input humidity by minimizing the dead space of a system and keeping it dry. We did not measure humidity of inspired gas, as this is not a trivial task. Measurements of the humidity of inspired and expired gas will allow us to improve the performance of the technique. Applicability of our lumped heat capacity model depends on how rapidly thermal equilibrium is achieved within the lung. We made estimates of the Biot number ⬍ 0.1, based on the rate of cooling of the lung without circulation. In the lungs with circulation, the Biot number is even less. This validates the use of the lumped model. Although the lumped model oversimplifies the real process, it permits us to determine the most important variables and make it suitable for practical use. The effective coefficient of the lung heat transfer KT/(␳WCpW) may depend on the lung size, particular lung structure, the blood flow and other parameters. To measure it precisely, it is necessary to measure precisely the airway gas input and output enthalpy function and measure accurately the cardiac output. The latter appears to be a difficult task, as thermodilution gives up to 20% error, which can be used only for rough

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estimates of cardiac output. However, within this range of accuracy of the thermodilution method, we can follow changes in cardiac output (Figure 9) and estimate the absolute values of cardiac output (Figure 10). The proposed technique may be implemented in clinical practice, as it is much less invasive than the thermodilution. For clinical implementation, the patient should be intubated and mechanically ventilated. Humidifiers are routinely used as a part of the breathing circuit. Technically, only minor modifications should be required: placement of a three-way stopcock before the humidifier and an additional respiratory line for the delivery of dry gas, bypassing the humidifier. Standard three-way connectors enable attachment of the dry gas line immediately at the proximal end of a tracheal tubing. Also, external or internal heating of the connectors and tracheal tube is desirable to prevent water condensation inside the breathing circuit. However, the presence of antibacterial filters, moisture/heat exchanges with the tracheal tubing may produce errors for the measurements and is not desirable. The procedure of dry gas ventilation in the patient lasts 5–6 min, which should not produce airway drying. Currently we are investigating the reliability and accuracy of this technique in ventilated patients. Though theoretically both the lung water and blood flow can be determined from one curve of the expired gas temperature, it is clear that the small changes in temperature of the expired gas may cause significant errors. Application of this method may also allow us to quantify pulmonary oedema, when cardiac output is measured by any other method. Most pulmonary oedema liquid is located in the loose peribronchial connective tissue26. The interstitial spaces which are close to the central airways are the primary sites of oedema liquid accumulation and therefore are readily measured by this method. At the same time, the presence of pulmonary oedema may provide an error in measurements of cardiac output, as it increases the lung tissue mass. Thus, use of the technique for the measurements of cardiac output should not be recommended in patients with clinically manifested pulmonary oedema or gross lung pathology. In summary, we investigated a modification of our non-invasive method for measuring pulmonary blood flow and extravascular lung water by measurement of the dynamics of the expired gas temperature. Experimental data show that the thermal conductivity of the circulatory heat source is substantially larger than the thermal conductivity of ventilatory heat loss. The inverse time constant of the lung cooling is linearly proportional to the cardiac output. The temperature of the expired gas can be used as an indicator of the dynamics of the pulmonary heat exchange. The dynamics of the lung heat exchange, when tested with a step-like input function of decreased humidity permits us to make estimates of cardiac output in intubated animals.

Cardiac output by airway thermometry: V. B. Serikov and E. H. Jerome

ACKNOWLEDGEMENTS We thank Oscar Osorio and Dr Masataka Fukue, M.D. for technical assistance and Dr Norman C. Staub for reviewing the manuscript. Supported by Program Project Grant HL 25816, HL 40891 and the American Society of Anesthesiologists Young Investigator Award (E. H. Jerome). REFERENCES 1. Casaburi, R., Wasserman, K. and Effros, R. M. Detection and measurement of pulmonary edema. In Lung Biology in Health and Disease. Lung Water and Solute Exchange, ed. N. Staub. Marcel Dekker, New York, 1978, pp. 323–377. 2. Lilly, C. M., Ishizaka, A. and Raffin, T. A., The measurement of lung water. J. Crit. Care, 1990, 5, 252–264. 3. Ingenito, E. P., Solway, J., McFadden, J. R., Drazen, J. M. and Cravalho, E. G., Finite difference analysis of respiratory heat transfer. J. Appl. Physiol., 1986, 61, 2252–2259. 4. Geladas, N. and Banister, E. W., Effect of cold air inhalation on core temperature in exercising subjects under heat stress. J. Appl. Physiol., 1988, 64, 2381–2387. 5. Ferrus, L., Guenard, H., Vardon, G. and Varene, P., Respiratory water loss. Respir. Physiol., 1980, 39, 367–381. 6. Mather, G. W., Nahas, G. G. and Hemingway, A., Temperature changes of pulmonary blood during exposure to cold. Am. J. Physiol., 1953, 173, 390–392. 7. Eschenbacher, W. L. and Sheppard, D., Respiratory heat loss is not the sole stimulus for bronchoconstriction induced by isocapnic hyperpnea with dry air. Am. Rev. Resp. Dis., 1985, 131, 894–901. 8. Serikov, V. B., Rumm, M. S., Pasternack, G. I. and Belyakov, N. A., Mathematical model of mass transfer role in heat exchange in respiratory tract. Phyziologichesky zyrnal USSR named after Sechenoff, 1986, 72, 1415–1418. 9. Rumm, M. S., Serikov, V. B. and Shoolga, V. P., Model of non-steady-state heat and mass exchange of air in the lung. Phyziologichesky zurnal (USSR), 1989, 35, 113–119. 10. Serikov, V. B., Rumm, M. S., Kambara, K., Bootomo, M. I., Osmack, A. R. and Staub, N. C., Application of respiratory heat exchange for the measurement of lung water. J. Appl. Physiol., 1992, 72(3), 944–953. 11. Solway, J., Leff, A. R., Dreshaj, I., Munoz, N. M., Ingenito, E. P., Michaels, D., Ingram, R. H. and Drazen, J. M., Circulatory heat sources for canine respiratory heat exchange. J. Clin. Invest., 1986, 78, 1015–1019.

12. Bowman, H. F. Estimation of tissue blood flow. In Heat Transfer in Medicine and Biology, ed. A. Shitzer and R. C. Eberhart. Plemun Press, New York, 1985, pp. 193–230. 13. Weinbaum, S. and Jiji, L. M., A new simplified bioheat equation for the effect of blood flow on local average tissue temperature. J. Biomech. Eng., 1985, 107, 131–139. 14. Zhu, L. and Weinbaum, S., A model for heat transfer from embedded blood vessels in two-dimensional tissue preparations. J. Biomech. Eng., 1995, 117, 64–73. 15. Brinck, H. and Werner, J., Efficiency function: improvement of classical bioheat approach. J. Appl. Physiol., 1994, 77(4), 1617–1622. 16. Hanna, L. M. and Scherer, W. P., A theoretical model of localized heat and water vapor transport in the human respiratory tract. J. Biomech. Eng., 1986, 108, 12–18. 17. Ray, D. W., Ingenito, E. P., Strek, M., Schumacker, P. T. and Solway, J., Longitudinal ditribution of canine respiratory heat and water exchange. J. Appl. Physiol., 1989, 66(6), 2788–2798. 18. Daviskas, E., Gonda, I. and Anderson, S. D., Mathematical modeling of heat and water transport in human respiratory tract. J. Appl. Physiol., 1990, 69(1), 362–372. 19. Tsu, M. E., Babb, A. L., Ralph, D. D. and Hlastala, M. P., Dynamics of heat, water and soluble gas exchange in the human airways:1. A model study. Ann. Biomed. Eng., 1988, 116, 547–571. 20. Gilbert, I. A., Fouke, J. M. and McFadden, E. R., The effect of repetitive exercise on airway temperatures. Am. Rev. Resp. Dis., 1990, 142, 826–831. 21. McFadden, E. R., Pichurko, B. M., Bowman, H. F., Ingenito, E., Burns, S., Dowling, N. and Solway, J., Thermal mapping of the airways in humans. J. Appl. Physiol., 1985, 58(2), 564–570. 22. McFadden, E. R., Respiratory heat and water exchange: physiological and clinical implications. J. Appl. Physiol., 1983, 54, 331–336. 23. Holman, J. P. Heat Transfer. McGraw-Hill, New York, 1968, pp. 73–161. 24. Pearce, M. L., Yamashita, B. A. and Beasel, J., Measurement of pulmonary edema. Circ. Res., 1965, 16, 485–488. 25. Bland, J. M. and Altman, D. G., Statistical methods for assessing agreement between two methods of clinical measurement. Lancet, 1986, 8, 307–310. 26. Staub, N. C., Nagano, H. and Pearce, M. L., Pulmonary edema in dogs, especially the sequence of fluid accumulation in the lungs. J. Appl. Physiol., 1986, 22, 227–240.

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