Abstract
Serikov, Vladimir B., E. Heidi Jerome, Neal W. Fleming, Peter G. Moore, Frederick A. Stawitcke, and Norman C. Staub.Airway thermal volume in humans and its relation to body size.J. Appl. Physiol. 83(2): 668–676, 1997.—The objective of this study was to investigate the influence of volume ventilation (V˙e) and cardiac output (Q˙) on the temperature of the expired gas at the distal end of the endotracheal tube in anesthetized humans. In 63 mechanically ventilated adults, we used a step decrease in the humidity of inspired gas to cool the lungs. After change from humid to dry gas ventilation, the temperature of the expired gas decreased. We evaluated the relationship between the inverse monoexponential time constant of the temperature fall (1/τ) and eitherV˙e orQ˙. WhenV˙e was increased from 5.67 ± 1.28 to 7.14 ± 1.60 (SD) l/min (P = 0.02), 1/τ did not change significantly [from 1.25 ± 0.38 to 1.21 ± 0.51 min^{−1},P = 0.81]. In the 11 patients in whom Q˙ changed during the study period (from 5.07 ± 1.81 to 7.38 ± 2.45 l/min,P = 0.02), 1/τ increased correspondingly from 0.89 ± 0.22 to 1.52 ± 0.44 min^{−1}(P = 0.003). We calculated the airway thermal volume (ATV) as the ratio of the measured valuesQ˙ to 1/τ and related it to the body height (BH): ATV (liters) = 0.086 BH (cm) − 9.55 (r = 0.90).
 cardiac output
 ventilation
 temperature
 lungs
 lung mass
 lung capacity
 heat exchange
 conductivity
 noninvasive measurement
despite many years of development, reported techniques for noninvasive measurements of cardiac output are not satisfactory (2). Development of a simple noninvasive method based on the indicatordilution principle remains an important physiological goal. Noninvasive indicatordilution techniques are based on assessment of the mass exchange between the respired air and the circulation (17). Energy exchange between the respired air and the pulmonary circulation can also be used for these purposes. Heat exchange in the lungs occurs naturally and efficiently as a result of the process of air conditioning (12). The temperature of the expired gas that reflects the lung heat exchange can be easily measured. Previously, we reported that indexes of nonsteadystate lung heat exchange vary with changes in lung water content and pulmonary blood flow (16).
In individuals quietly breathing through their nose, conditioning of the inspired gas occurs entirely in the upper respiratory tract (13). However, when they breathe cold air or after endotracheal intubation, the whole respiratory tract down to generations 14–16 of the bronchial tree participates in heat exchange with the environment (13, 14). The loss of heat from the lungs to the environment and subsequent cooling of the airways and blood have been demonstrated in many studies (57, 13). During hyperventilation with cold dry air, the distal airways (7), pulmonary venous blood (11), and mediastinum (4) are cooled. The temperature of the expired gas is determined by the temperature of the walls of the airways (10). When the temperature difference between two quasisteady states with normal and presumably high cardiac output was studied in humans, the role of the pulmonary circulation in lung heating was not evident (7). In accordance with the predictions of models of lung heat exchange at the steady state (3, 8, 20), changes in the difference of the absolute temperatures between steady states at normal and high blood flow are small. However, the rate of lung heating should be proportional to the pulmonary blood flow (16, 18), which determines the thermal conductivity of the lung. Blood flow, therefore, can be determined from the rate of lung cooling or heating. Depending on the coefficients of thermal conductivity, the contribution of ventilation compared with the contribution of circulation to the rate of equilibration may be important or negligible. These coefficients have not been studied in humans, but our previous data in animals (16) showed that the thermal conductivity of the circulation is ∼10fold higher than the thermal conductivity of the ventilation in the physiological range of ventilation and cardiac output. The effect of ventilation on the time constant should therefore be negligible.
If it is blood flow that primarily determines the time constant of the temperature decline, the ratio of the total blood flow to the inverse time constant gives us one lumped coefficient with the dimension of volume, i.e., airway thermal volume (16). The mass of the normal lung should also be related to the size of the lung or its volume. We hypothesized therefore that, in humans without significant pulmonary pathology, airway thermal volume should also be related to body size.
The goal of this study was to investigate the influence of cardiac output and ventilation rate on the dynamics of pulmonary heat exchange and to estimate the relationship between airway thermal volume and body size in intubated human adults. The first aim was to determine the role of cardiac output and ventilation rate on the inverse time constant of the change in temperature of the expired gas. Our second aim was to determine the airway thermal volume in a large group of intubated humans and analyze the relationship between the airway thermal volume and body height.
Glossary
 ATV
 Airway thermal volume (liters)
 BH
 Body height (cm)
 Bi
 Biot number (nondimensional); Bi = αs/h
 C
 Mean mass concentration of water vapor in expired gas (kg/m^{3})
 C_{pG}
 Heat capacity of gas (J ⋅ kg^{−1} ⋅ °C^{−1})
 C_{pW}
 Heat capacity of water (J ⋅ kg^{−1} ⋅ C^{−1})
 C_{0}
 Mean mass concentration of water vapor in inspired gas (kg/m^{3})
 h
 Thermal conductivity (J ⋅ s^{−1} ⋅ m^{−1} ⋅ °C^{−1})
 H
 Heat of water vaporization (J/kg)
 j_{B}
 Total heat flux from circulation (J/s)
 j_{V}
 Heat flux into ventilatory gas (J/s)
 K_{T}
 Effective coefficient of lung thermal conductivity (J ⋅ m^{−3} ⋅ °C^{−1})
 Nu
 Nusselt number (nondimensional); Nu = αx/h′, where x is characteristic dimension of the tube,h′ is thermal conductivity of fluid; Nu =BRe^{E}Pr^{F}, whereB, E, and F are constants
 Pr
 Prandtl number (nondimensional); Pr = vρC_{p}/h
 Q˙
 Pulmonary blood flow (cardiac output; l/min)
 Re
 Reynolds number (nondimensional); Re = wh/v, where w is linear velocity, h is characteristic dimension, and v is viscosity
 s
 Characteristic dimension of the body (m); s = V/S
 S
 Surface area (m^{2})
 T
 Mean temperature of expired gas (°C)
 T
 Mean temperature of the blood (°C)
 TG0
 Mean temperature of inspired gas (°C)
 T_{t}
 Meanintegrated temperature of volume V (°C)
 T_{t0}
 Meaninitial temperature of volume V at t = 0 (°C)
 T_{0}
 Initial temperature of expired gas at t = 0 (°C)
 t
 Time (s)
 TLC
 Total lung capacity (liters)
 V
 Airway tissue volume (liters)
 V˙e
 Minute volume of ventilation (l/min)
 ΔT
 Difference between temperatures of expired gas during humid and dry gas ventilation (°C)
 α
 Coefficient of heat transfer from the surface (J ⋅ s^{−1} ⋅ m^{−2} ⋅ °C^{−1})
 ρ_{G}
 Gas density (kg/m^{3})
 ρ_{W}
 Water density (kg/m^{3})
 τ
 Characteristic time constant of temperature fall (min)
 1/τ
 Inverse time constant (min^{−1})
METHODS
Theory
Ventilation with dry gas cools the lungs. As a result, the temperature of the expired gas decreases until a new steadystate condition is reached. Heat flux from the lungs into the environment is balanced by heat transfer from the circulation into the lung tissue. The major heat source for the lungs is the pulmonary blood flow (19). According to bioheat equations, the heat flux from the circulation into the tissue is proportional to the volume of blood flow (21, 22).
As a firstorder approximation, we can assume that the system is well equilibrated and the lumped heat capacity model may be applied for its description (9). Parameters in the heat balance equation then become the meanintegrated values over the whole volume of the lung. The rate of lung cooling is therefore directly proportional to the sum of heat fluxes associated with the volume ventilation and the pulmonary blood flow and inversely proportional to the lung heat capacity. The lung mass determines the total heat capacity. Because the geometry of the actual system determines the heat transfer coefficients and temperature profile distributions, the relative contributions of these variables (mass, ventilation, blood flow) must be determined experimentally. The difference in the temperature of the lung between two steady states is proportional to the ratio of the thermal conductivities associated with ventilation to those associated with pulmonary circulation. Inasmuch as the thermal conductivity associated with ventilation is much smaller than that associated with circulation, the direct use of this relationship for practical purposes is restricted to a narrow range of ratios of ventilation to circulation (high ventilation vs. low blood flow). Inasmuch as the heat flux with the exhaled air is small and lung heat capacity and blood flow are large, the temperature change of blood passing through the lungs is <0.1°C. Blood temperature may therefore be assumed constant, and the heat flux from the circulation can then be determined simply from the inverse time constant (1/τ) of the lung cooling or heating, as measured by the expired gas temperature. The temperature distribution in the lungs is not necessarily uniform in the actual system. However, for a fixed minute volume of ventilation (V˙e) and tidal volumes, we assume that the rate of lung cooling is adequately reflected by the changes in the peak temperature of expired gas, which can be adequately described by the lumped heat capacity model.
To determine the relative importance of ventilatory heat loss and circulatory heat gain, it is necessary to investigate the relationship betweenV˙e, cardiac output, and 1/τ. These effects may be described by a simple model (see ). In the steady state, heat flux associated with ventilation equals heat flux from the circulation. During the dynamic transition from one steady state to another, heat fluxes are different. The ventilatory heat loss can be calculated fromV˙e and the temperatures and humidities of inspired and expired gas. It is ∼2–5 W in a normal, resting subject (12). Analysis of the relative contribution of the heat fluxes due to circulation, ventilation, and metabolism (see ) shows that metabolic heat production is small and can be neglected. The 1/τ for the ventilatory heat loss of 2.5 W (assuming no circulation is present) in the lungs with a mass of 500 g will be ∼0.05 min^{−1} by usingEqs. EA1 and EA2 . In reality, the 1/τ values are on the order of 1 min^{−1}. Thus the thermal conductivity related to ventilation is small compared with the thermal conductivity related to the circulation. Because we also found no influence of theV˙e on 1/τ (see below), we estimated airway thermal volume (ATV) as simply the ratio of cardiac output to 1/τ. Inasmuch as the ATV represents the total lung heat capacity, or lung mass, it is related to the lung size (or lung mass). Lung size should be related to body size in the same manner in which lung volume is related to body size (1).
Study Protocol
Patient population.
After Human Subjects Research Committee approval of the protocol, data were obtained from 63 patients (37 men and 26 women) 16–81 yr of age (67.6 ± 13.1) and 78 ± 15 kg average body wt. Two groups of patients were studied. The first group consisted of 29 ASA class II to class IV patients undergoing elective surgical procedures that necessitated general anesthesia and placement of a SwanGanz catheter for intraoperative monitoring. This group consisted primarily of patients undergoing major vascular or abdominal surgical procedures. Patients with severe chronic obstructive pulmonary disease or thoracic surgical procedures were excluded from study. The second group (n = 34) consisted of nonsurgical patients from the intensive care unit who required mechanical ventilation and SwanGanz catheter monitoring. These were predominantly patients from the trauma service. Patients with severe chronic obstructive pulmonary disease, pulmonary edema, acute respiratory distress syndrome, pulmonary embolism, pulmonary hemorrhage, or blunt chest trauma were excluded from the study.
Measurement procedure.
The endotracheal tube was suctioned for mucus before positioning of a sterile thermocouple (type K, 0.005 in. diameter, Omega Engineering, Stamford, CT) probe 1–2 cm above the distal end of the tube. A threeway stopcock was introduced into the respiratory circuit proximal to the humidifier. The second port of the stopcock was attached to a T connector placed just proximal to the endotracheal tube (Fig.1). Patients in the operating room were ventilated with a servo ventilator (model 900C SeimensElema, Solna, Sweden) and a humidifier (model SCT 3000, Marquest Medical Products, Englewood, CO). Variables of ventilation [tidal volume, frequency, and minute ventilation (atps)] were measured by the ventilator respiratory monitor. Thermodilution cardiac outputs were calculated with a cardiac output computer (model COM2, BaxterEdwards Critical Care Division, Irvine, CA). Patients in the intensive care unit were ventilated with a volume ventilator (model 7200, PuritanBennett, Carlsbad, CA). The circuit included a heatedwire humidifier (ConchaTherm III, Hudson Respiratory Care, Temecula, CA). Cardiac output was calculated with a cardiac output computer (Explorer, BaxterEdwards Critical Care Division). In both groups, patients were first ventilated with warm (36–40°C) humid air for 5–10 min, until equilibration between the inspired and expired gas was achieved. Ventilation was then switched to cold (room temperature) dry gas for 5–6 min. Concurrent measurements of cardiac output by thermodilution were performed in triplicate by the attending anesthesiologist or intensive care unit nurse.
Specific protocols.
In study 1 we investigated the effects of changes in the frequency of ventilation at a constant tidal volume in eight patients.
In study 2 we investigated 11 patients in whom cardiac output increased (n = 8) or decreased (n = 3) during the study period. We also compared the 1/τ in all 48 subjects regardless of their body height, with cardiac output <4, 4–8, and >8 l/min.
In study 3 (all 48 patients), the retrospective study, we estimated the ATV as the ratio of cardiac output to 1/τ and compared it with body height as documented in the patient’s medical record.
In study 4 (15 patients), the prospective study, in a separate group of patients we estimated the ATV from the patient’s body height, measured 1/τ, and compared its product with the thermodilution cardiac output.
Temperature recording and data analysis.
Data from the thermocouples were conditioned by a custombuilt multichannel thermocouple amplifier board with optoisolators for patient protection. The data were captured by a dataacquisition system (model SCXI1000, National Instruments, Austin, TX) using an analogtodigital converter board (model AD1200, National Instruments). Data were then logged to disk by a laptop computer (model T1860CS, Toshiba) running National Instruments LabView software (version 3.1.1) with custom routines for realtime display of temperature.
In the analysis we used the maximum temperature of the expired gas for each exhalation. The time plot of these points represents the monoexponential fall of the lung’s temperature. We used two different methods to determine the time constant of these curves. In the first method, curves were analyzed by Origin (version 3.1, Microcal Software, Northampton, MA) software. We used a monoexponential fit to determine the time constant and the temperature drop (ΔT), defined as the difference between the temperatures of expired gas during humid and dry gas ventilation. A second approach was to determine numerically the area (integral) under the curve of the peak temperatures of expired gas and divide ΔT by this integral. For an ideal monoexponential curve, both methods give the same answer. We used the mean of these two estimates for the time constant.
Statistical analysis.
Data were compared by unpaired and, when appropriate, paired Student’sttest and by regression analysis. Values are means ± SD, with statistical significance accepted atP < 0.05. For agreement analysis we used the method of Bland and Altman (1a).
RESULTS
A typical curve of the expired gas temperature is shown in Fig.2. During ventilation with the humid, heated gas the temperature of the inspired gas reaches the temperature of the expired gas. After the switch to dry gas ventilation, there is a steady decline of the expired gas temperature. The fall of the expired gas temperature is typically close to monoexponential.
Study 1: Relationship Between Temperature of Expired Gas, the Inverse Time Constant, and Volume Ventilation
In eight patients with a stable cardiac output, we found that changes in minute ventilation did not cause changes in the time constant of the expired gas. Individual data pairs are shown in Fig.3. MeanV˙e was 5.67 ± 1.28 l/min and mean 1/τ was 1.25 ± 0.38 min^{−1} before the increase in ventilation. Cardiac output was 5.33 ± 1.89 l/min. After minute ventilation was increased to 7.14 ± 1.60 l/min (P = 0.02), the mean 1/τ was 1.21 ± 0.51 min^{−1}(P = 0.81; Fig.4) and cardiac output was 5.20 ± 2.09 l/min (P = 0.88). The correlation between V˙e and 1/τ for all 48 patients was weak (linear regression: 1/τ = 0.37 + 0.107V˙e,r = 0.64). We conclude that the time constants of the expired gas were not related to minute ventilation. The temperature difference between the two steady states was not significantly different, although there was a tendency for ΔT to be increased after higher ventilation from 1.61 ± 0.48 to 1.96 ± 0.51°C (P = 0.13).
Study 2: Relationship Between Temperature of Expired Gas, the Inverse Time Constant, and Cardiac Output
In 11 cases in which cardiac output changed during the study, we observed subsequent changes in the time constant of the temperature of expired gas. In Fig. 5 two typical curves of the maximum expired gas temperature are given to illustrate the effects of increased cardiac output in a patient during constant minute ventilation. The 1/τ rose after the increase in cardiac output. The relationship between cardiac output and 1/τ in 11 individual observations in 11 patients is illustrated in Fig.6. In eight observations, cardiac output rose, and in three observations it decreased. During constant ventilation, 1/τ was proportional to cardiac output. The mean data for the groups with lower and higher cardiac outputs in these 11 patients are illustrated in Fig. 7. In the group with lower cardiac output, its mean value was 5.07 ± 1.81 l/min, 1/τ was 0.89 ± 0.22 min^{−1}, ΔT was 1.64 ± 0.53°C, andV˙e was 6.55 ± 2.16 l/min. In the group with a mean cardiac output of 7.38 ± 2.45 l/min (P = 0.02 compared with baseline), 1/τ was 1.52 ± 0.44 min^{−1}(P = 0.003 compared with baseline), ΔT was 1.74 ± 0.44°C (P = 0.71 compared with baseline), andV˙e was 6.06 ± 1.40 l/min (P = 0.53 compared with baseline).
To estimate the power of the relationship between 1/τ and cardiac output regardless of body size, we compared three groups of patients:group 1 with cardiac outputs <4 l/min (n = 15), group 2 with cardiac outputs of 4–8 l/min (n = 23), and group 3 with cardiac outputs >8 l/min (n = 10). In group 1 the mean cardiac output was 3.10 ± 0.59 l/min, mean 1/τ was 0.67 ± 0.16 min^{−1}, mean body height was 165 ± 12 cm, and meanV˙e was 5.69 ± 1.65 l/min. In group 2 the mean cardiac output was 5.67 ± 1.04 l/min (P < 0.001), mean 1/τ was 1.26 ± 0.26 min^{−1}(P < 0.001), mean body height was 166 ± 11 cm (P > 0.05), and meanV˙e was 8.15 ± 2.49 l/min (P = 0.02 compared with group 1). Ingroup 3 the mean cardiac output was 10.38 ± 3.39 l/min (P < 0.001 compared with group 2), mean 1/τ was 1.98 ± 0.64 min^{−1}(P < 0.001 compared withgroup 2), mean body height was 177 ± 12 cm (P < 0.05 compared withgroups 1 and2), and meanV˙e was 10.66 ± 5.11 l/min (P < 0.01 compared with group 1,P = 0.07 compared withgroup 2). Cardiac output and 1/τ were significantly different among all three groups. The correlation between cardiac output and 1/τ for all 48 patients was excellent (r = 0.89, linear regression: 1/τ = 0.23 + 0.16Q˙; Fig.8). Similar analysis of the correlation between body height and cardiac output did not show significant correlation (r = 0.40). These results strongly demonstrate that cardiac output determines the time constant of the temperature decay of the expired gas.
Study 3: ATV Compared With Body Size
The relationship between body height and ATV is shown in Fig.9. There is a linear proportionality between ATV and body height (BH) of 140–185 cm (linear regression: ATV = 0.086BH − 9.55, r = 0.90). Also in Fig. 9, the relationship between body height and estimated total lung capacity (TLC) is shown. TLC was estimated from body height as follows: TLC = 5.6(BH)^{2.67} for men and TLC = 4.0(BH)^{2.73} for women (where TLC is in cm^{3} and body height is in cm) (1) [linear regression: TLC (liters) = 0.082BH − 8.82, r = 0.99]. Figure 9 clearly shows that the ATV and the TLC are closely related [ATV (liters) = 1.06TLC (liters) − 0.27,r = 0.91]. Analysis of the agreement between estimated TLC and ATV is shown in Fig.10. The bias (mean difference) between the two was −0.02 liter, and precision (SD of the difference) was 0.44 liter. It appears that ATV can be reliably predicted from the estimated TLC.
Study 4: Comparison Between Thermodilution Cardiac Output and Cardiac Output Predicted by ATV
In 15 patients, comparison between thermodilution cardiac output and the product of estimated ATV and the 1/τ shows a high correlation (r = 0.96; Fig.11). The bias (mean difference) between the two methods was −0.2 liter, and precision (SD of the difference) was 0.62 liter. Estimation of ATV from body height combined with the measurement of the 1/τ can reliably predict cardiac output.
DISCUSSION
The first important finding of this study is a clear linear relationship between 1/τ and cardiac output (Figs. 6, 7, 8). The lumped heat capacity model of the lung heat exchange (see ) predicts such a linear relationship. Thus the use of the bioheat equation in the form ofEq. EA4 is valid. A general relationship for heat transfer based on empirical correlation (Eq. EA5 ) appears to be adequate for the pulmonary vasculature. The lungs are not different from other organs in the basic principles of heat exchange (18), for which the linear relationship between blood flow and heat flux has been postulated (22). The bronchial tree serves as a cooling probe that is embedded in a network of pulmonary vessels. The main heat transfer occurs in this “core” of the lung, between the bronchi of the first 15 generations and surrounding blood vessels (1214). Bronchial blood flow is 50–100 times lower than pulmonary blood flow, and it is clear that the pulmonary vessels accompanying the bronchi ensure a much larger heat source (19). The pulmonary vascular tree mirrors the bronchial tree, and this is the anatomic basis for the heat equilibration before gas reaches the alveoli. The routing of the pulmonary veins away from airways also ensures optimal heat delivery. A considerable increase in bronchopulmonary shunting may provide additional heat supply and become a source of error in measurements. This requires further investigation, including a measurement of the amount of shunting.
We did not find any statistically significant influence of minute ventilation on the time constant of the temperature of the expired gas (study 1). As predicted by our model, the thermal conductivity related to the heat flux out of the lungs with ventilation under nonsteadystate conditions is relatively small compared with the thermal conductivity related to the circulation (1.5% at normal ventilation rates or at total ventilationtoperfusion ratios < 1.5). Ventilation, according to Eq.EA12 , cannot contribute significantly to the estimated value of 1/τ, unless the ventilationtoperfusion ratio is >5. This may happen at very low blood flows (<2 l/min) or very highV˙e. None of these cases was observed in our study, which validates the use ofEq. EA13 .V˙e was different in groups 1 and2 of study 2, as in general should be expected for different cardiac outputs. Ventilation was not statistically different ingroups 2 and3, whereas mean 1/τ values were different. Also the correlation betweenV˙e and 1/τ (r = 0.64) was much weaker than the correlation between cardiac output and 1/τ (r = 0.89). As expected, there was an effect of ventilation on ΔT, although it was not very large. We did not measure the humidity of the expired and inspired gas in this study, although humidity is an important term in Eq.EA10 , which determines the value of ΔT. We assumed that the inspired gas was dry (compressed oxygen and air) and that the expired gas was totally humidified. This assumption is based on the findings of full saturation of the expired gas from several previous studies where the water content of the collected expired gas was determined (5, 10, 12, 14). Reliable dynamic measurement of humidity inside an endotracheal tube is an unsolved technical problem, inasmuch as none of the existing methods to measure humidity can provide sufficient accuracy and response time. Although the humidity of the gas at a steady state affects ΔT, it does not affect 1/τ (Eqs. EA11 and EA12 ), which we used for analysis.
As demonstrated by Gilbert et al. (7), increased ventilation in exercising subjects produced a decrease in the expired air temperature of 5°C over 4 min. Other direct measurements (13) also show that the temperature of gas changes along the longitudinal axis of the bronchial tree. Because of the importance of local heat transfer phenomena in the determination of the expired gas temperature, changes in circulation will have a small effect on the absolute temperature of the expired gas (7). According to Eq.EA10 , cardiac output is the hyperbolic function of ΔT and, under physiological ranges of ventilation and perfusion, the slope of this function is small (∼0.05–0.1 °C/l of cardiac output). This value is close to noise from the heat exchange in upper airways. At the same time, the time constant of lung heating or cooling will depend on the circulation, regardless of the magnitude of ΔT. To observe this effect, a step function (immediate change) of humidity or temperature should be applied to the inspired gas. We found that a typical response time of the human lung is ∼40 s. Thus the input function should have the characteristic time of <10 s (1–2 breaths).
Our second important finding is the strong relationship between measured ATV and body height. What we estimate as ATV is an effective parameter that is defined as the ratio of total lung heat capacity (lung mass × specific heat capacity) to lung thermal conductivity (K _{T},Eq. EA13 ).
It is well known that lung volumes, like TLC, are strongly related to body size (1). TLC represents the size of the lungs or the mass of tissue. Thus the relationship between body height and ATV should represent the relationship between the lung mass and ATV in humans. We believe that the relationship between the TLC and body height can be used to estimate ATV in humans without lung diseases. If this estimate of ATV can be made reliably, then the absolute value of cardiac output can be estimated from the time constant of the decay of the expired gas and the body height.
The sizes of the pulmonary and vascular passages scale to patient size. This probably results in the observation that patients of the same height have similar observed values of ATV. If we can assume that the heat exchange effectiveness of each region of the lung volume is a function of the size of the respiratory and circulatory vessels and, since their linear dimensions will increase with patient height, we can reasonably expect ATV to increase with patient size.
As shown in study 4, in patients without evident lung pathology, measurement of 1/τ and estimation of ATV from body height can provide good estimates of cardiac output. Cardiac output does not simply depend on body height or ATV, inasmuch as the correlation between body height and cardiac output is poor (r = 0.4, study 3). It is the product of ATV and the response time of the lung to cooling that allows us to estimate cardiac output according to Eq. EA13 . This is an encouraging finding that allows us to recommend further development of this technique for practical purposes of measuring cardiac output. Deviations from the simple lumped heat capacity model in various pathological states should also be studied. One factor that might cause ATV to deviate from this relationship is pulmonary edema. To the extent that the edema is present near the more central lung region, which we believe dominates the heat exchange process, the increase in lung density should imply a roughly proportionate increase in ATV. Other possible factors include gross geometric changes such as onelung ventilation (with or without the other lung), gross ventilation changes from typical volume ventilation patterns, and dense lung masses. We deliberately did not include patients with any gross pulmonary pathology in this analysis, inasmuch as our aim was to determine a reference of ATV for future analysis. Studies of the effects of maldistribution of ventilation and perfusion should be done with a corresponding reference method to evaluate these factors independently. Other methods of curve analysis and more complex models should be used to determine the effects of ventilationperfusion mismatch.
In summary, the time constant of the expired gas is determined by cardiac output and does not significantly depend on minute ventilation under the physiological range of ventilations. We measured ATV as the ratio of the thermodilution cardiac output to 1/τ. There is a strong correlation between ATV and body height.
Acknowledgments
This study was supported in part by a HewlettPackard external research project grant.
Footnotes

Address for reprint requests: V. B. Serikov, Dept. of Anesthesiology, TB170, School of Medicine, University of California, Davis, CA 95616.
 Copyright © 1997 the American Physiological Society
Appendix
The details of our nonsteadystate model of lung heat exchange are given elsewhere (16). In the simplest case the rate of change of the temperature (T) in a body with volume V, surface areaS, density ρ, and heat capacityC
_{p}, where the ventilatory heat flux isj
_{V}, is determined as follows
Heat flux from the circulation, according to the general bioheat equation (21, 22), linearly depends on blood flow
To use the abovedescribed lumped capacity model, Bi should be <0.1 (9). We calculated Bi as Bi = αs/h(9), from characteristic dimension s = V/S. We assume that surface area of heat exchange does not exceed 1 m^{2}andj
_{V}= 5 W, T_{t} −
The outward heat flux,j
_{V}, can be determined from the temperature and humidity difference between inspired and expired gas and from the total amount of gas that enters the lungs. We assume that the expired gas is totally humidified at its temperature so that the humidity and corresponding evaporative heat losses can be calculated by knowing the expired gas temperature. For practical purposes, it can be given as
The expired gas temperature (T) equals the meanintegrated temperature on the gas side of the bloodgas barrier; then the heat flux from the circulation is driven by the difference between T and the mean temperature of the blood (T̅). Because the gas expired from the lungs is fully saturated with water at its temperature, we can calculate water vapor mass concentration from the temperature of this expired gas (2). Then Eq.EA1
can be given as
Equation EA7
can be solved for the two different steadystate conditions in terms of temperature difference between steady states (ΔT) and the characteristic time constant (τ). Q˙ and V are obtained as
This model allows us to make some estimates ofj _{B},j _{V}, andj _{M}.j _{V}can be easily calculated from Eq. EA6 , and for a human withV˙e = 10 l/min it ranges from 2 to 5 W, depending on inspired gas temperature and humidity. If we assume that metabolic heat production per kilogram of body weight in the lungs is close to that of the whole body, thenj _{M}is <5%j _{V}and can be neglected.