| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1 Department of Anesthesiology, 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.
cardiac output; ventilation; temperature; lungs; lung mass; lung
capacity; heat exchange; conductivity; noninvasive measurement
INTRODUCTION 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 indicator-dilution principle remains an important physiological goal.
Noninvasive indicator-dilution 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 non-steady-state 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 (5-7, 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 quasi-steady 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 ~10-fold
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
METHODS Theory
The objective of this study was to investigate the influence of
volume ventilation
(
E) and
cardiac output (
) 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/
) and either
E or . When
E was
increased from 5.67 ± 1.28 to 7.14 ± 1.60 (SD) l/min
(P = 0.02), 1/ 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 changed during the study period
(from 5.07 ± 1.81 to 7.38 ± 2.45 l/min,
P = 0.02), 1/ increased
correspondingly from 0.89 ± 0.22 to 1.52 ± 0.44 min1
(P = 0.003). We calculated the airway
thermal volume (ATV) as the ratio of the measured values
to 1/ and related it to the body height (BH):
ATV (liters) = 0.086 BH (cm) 
9.55 (r = 0.90).
ATV
Airway thermal volume (liters)
BH
Body height (cm)
Bi
Biot number (nondimensional); Bi =
s/h
C
Mean mass concentration of water vapor in expired gas
(kg/m3)
CpG
Heat capacity of gas
(J · kg
1 · °C1)
CpW
Heat capacity of water
(J · kg
1 · C1)
C0
Mean mass concentration of water vapor in inspired gas
(kg/m3)
h
Thermal conductivity
(J · s
1 · m1 · °C1)
H
Heat of water vaporization (J/kg)
jB
Total heat flux from circulation (J/s)
jV
Heat flux into ventilatory gas (J/s)
KT
Effective coefficient of lung thermal conductivity
(J · m
3 · °C1)
Nu
Nusselt number (nondimensional); Nu =
x/h
,
where x is characteristic dimension of the tube,
h is thermal conductivity of fluid; Nu = BReEPrF, where
B, E, and F are constants
Pr
Prandtl number (nondimensional); Pr = v
Cp/h
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 (m2)
T
Mean temperature of expired gas (°C)
Mean temperature of the blood (°C)
TG0
Mean temperature of inspired gas (°C)
Tt
Mean-integrated temperature of volume V (°C)
Tt0
Mean-initial temperature of volume V at t = 0 (°C)
T0
Initial temperature of expired gas at t = 0 (°C)
t
Time (s)
TLC
Total lung capacity (liters)
V
Airway tissue volume (liters)
EMinute volume of ventilation (l/min)
TDifference between temperatures of expired gas during humid and
dry gas ventilation (°C)
Coefficient of heat transfer from the surface
(J · s
1 · m2 · °C1)
GGas density (kg/m3)
WWater density (kg/m3)
Characteristic time constant of temperature fall (min)
1/
Inverse time constant (min
1)
As a first-order 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 mean-integrated 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/) 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
(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 between
E, cardiac
output, and 1/. These effects may be described by a simple model
(see APPENDIX). 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 from
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
APPENDIX) shows that metabolic heat
production is small and can be neglected. The 1/ 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
min1 by using
Eqs. A1 and A2. In reality, the 1/ values are
on the order of 1 min1.
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 the
E on 1/
(see below), we estimated airway thermal volume (ATV) as simply the
ratio of cardiac output to 1/. 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 Swan-Ganz 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 Swan-Ganz 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 three-way 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 Seimens-Elema, 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 COM-2, Baxter-Edwards Critical Care Division, Irvine, CA). Patients in the intensive care unit were ventilated with a volume ventilator (model 7200, Puritan-Bennett, Carlsbad, CA). The circuit included a heated-wire humidifier (Concha-Therm III, Hudson Respiratory Care, Temecula, CA). Cardiac output was calculated with a cardiac output computer (Explorer, Baxter-Edwards 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/
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/ 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/, and compared its
product with the thermodilution cardiac output.
Temperature recording and data analysis.
Data from the thermocouples were conditioned by a custom-built
multichannel thermocouple amplifier board with optoisolators for
patient protection. The data were captured by a data-acquisition system
(model SCXI-1000, National Instruments, Austin, TX) using an
analog-to-digital converter board (model AD-1200, 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 real-time 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 (T), 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 T 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's
t-test and by regression analysis.
Values are means ± SD, with statistical significance accepted at
P < 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. MeanE was
5.67 ± 1.28 l/min and mean 1/ was 1.25 ± 0.38 min1 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/ was 1.21 ± 0.51 min1
(P = 0.81; Fig.
4) and cardiac output was 5.20 ± 2.09 l/min (P = 0.88). The correlation
between E and
1/ for all 48 patients was weak (linear regression: 1/ = 0.37 + 0.107E,
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 T 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/ rose after the increase in cardiac output. The
relationship between cardiac output and 1/ 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/ 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/ was 0.89 ± 0.22 min1, T was 1.64 ± 0.53°C, and
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/ was 1.52 ± 0.44 min1
(P = 0.003 compared with baseline),
T was 1.74 ± 0.44°C (P = 0.71 compared with baseline), and
E was 6.06 ± 1.40 l/min (P = 0.53 compared
with baseline).
1; in
curve 2, cardiac output = 12.0 l/min
and inverse time constant = 2.22 min1.
To estimate the power of the relationship between 1/ 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/ was 0.67 ± 0.16 min1, mean body height was
165 ± 12 cm, and mean
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/ was 1.26 ± 0.26 min1
(P < 0.001), mean body height was
166 ± 11 cm (P > 0.05), and mean
E was 8.15 ± 2.49 l/min (P = 0.02 compared
with group 1). In
group 3 the mean cardiac output was
10.38 ± 3.39 l/min (P < 0.001 compared with group 2), mean 1/
was 1.98 ± 0.64 min1
(P < 0.001 compared with
group 2), mean body height was 177 ± 12 cm (P < 0.05 compared with
groups 1 and
2), and mean
E was 10.66 ± 5.11 l/min (P < 0.01 compared with group 1,
P = 0.07 compared with
group 2). Cardiac output and 1/
were significantly different among all three groups. The correlation
between cardiac output and 1/ for all 48 patients was excellent
(r = 0.89, linear regression: 1/ = 0.23 + 0.16; 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 cm3 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.
, ATV; 
, TLC.
Diagonal line, linear fit: ATV (liters) = 0.086 BH (cm) 9.55 (r = 0.9).
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/ 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/ can reliably predict cardiac output.
DISCUSSION
The first important finding of this study is a clear linear
relationship between 1/ and cardiac output (Figs. 6, 7, 8). The lumped heat capacity model of the lung heat exchange (see
APPENDIX) predicts such a linear
relationship. Thus the use of the bioheat equation in the form of
Eq. A4 is valid. A general
relationship for heat transfer based on empirical correlation
(Eq. A5) 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 (12-14).
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 non-steady-state conditions is relatively
small compared with the thermal conductivity related to the circulation
(1.5% at normal ventilation rates or at total ventilation-to-perfusion ratios < 1.5). Ventilation, according to Eq. A12, cannot contribute significantly to the estimated
value of 1/, unless the ventilationto-perfusion ratio is >5.
This may happen at very low blood flows (<2 l/min) or very high
E. None of
these cases was observed in our study, which validates the use of
Eq. A13.
E was
different in groups 1 and
2 of study
2, as in general should be expected for different cardiac outputs. Ventilation was not statistically different in groups 2 and
3, whereas mean 1/ values were
different. Also the correlation between
E and 1/
(r = 0.64) was much weaker than the
correlation between cardiac output and 1/
(r = 0.89). As expected, there was an
effect of ventilation on T, 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. A10, which determines the value of T. 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 T, it does not affect 1/
(Eqs. A11 and A12), 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. A10, cardiac output is the hyperbolic function of T
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 T. 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 (KT, Eq. A13).
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/ 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. A13. 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 one-lung
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 ventilation-perfusion 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/. There is a strong
correlation between ATV and body height.
ACKNOWLEDGEMENTS
This study was supported in part by a Hewlett-Packard external research project grant.
FOOTNOTES
Address for reprint requests: V. B. Serikov, Dept. of Anesthesiology, TB-170, School of Medicine, University of California, Davis, CA 95616.
Received 4 December 1996; accepted in final form 10 April 1997.
APPENDIX
The details of our non-steady-state 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 area
S, density , and heat capacity
Cp,
where the ventilatory heat flux is
jV,
is determined as follows
|
(A1) |
|
(A2) |
= S/CpV,
is the time constant of temperature change, is the coefficient
of heat transfer from the surface, Tt0 is the
initial temperature of the lung, and
TG0 is the
temperature of the gas (9). In an actual lung the blood flow heats
tissues and the rate of the changes in the lung temperature is
determined by a sum of heat fluxes. The sum of heat fluxes in the lung
equals
|
(A3) |
Heat flux from the circulation, according to the general bioheat equation (21, 22), linearly depends on blood flow
|
(A4) |
is local blood flow, T is the
temperature gradient between blood and tissue, is the heat
transfer coefficient, S is the surface
area, and
KT
is the thermal conductivity coefficient for lungs. The coefficient
KT
is defined as the product
S(/) for the
whole lung. We consider that heat exchange of the circulation with
tissues is similar to heat exchange in a fluid flowing 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
|
(A5) |
is
thermal conductivity of fluid, x is
characteristic dimension, and A, B,
and C are empirical coefficients (9).
In Eq. A4 is the
mean-integrated value. For the pulmonary circulation the
mean-integrated dimension x is assumed
to be constant, as well as h
and Pr for blood. The relationship between and Re is known for
complex systems (9).
To use the above-described lumped capacity model, Bi should be <0.1
(9). We calculated Bi as Bi = s/h
(9), from characteristic dimension s = V/S. We assume that surface area of
heat exchange does not exceed 1 m2 and
jV = 5 W, Tt TG0 = 2°C,
and h for the lung tissue is the same
as for water (i.e., 0.6 J · s1 · m1 · °C1).
We analyzed the simplest case, when there is no circulation and the
lungs are cooled only by ventilation,
j = jV.
The time constant of lung cooling without blood flow is ~800 s, and
from Eq. A2, 1/ = 0.00125 s1 = /(sWCpW);
s = /(0.00125WCpW).
From Eq. A1, = jV/S(Tt TG0) = 2.5 W · m2 · °C1;
then s = 0.0005 m, and Bi = 2.5 * 0.0005/0.6 = 0.002.
The outward heat flux, jV, 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
|
![+ (C<SUB>0</SUB> − C)<IT>H</IT>]](/content/vol83/issue2/fulltext/668/img007.gif)
|
(A6) |
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 (
). 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. A1 can be given as
|
(A7) |
|
(A8) |
|
(A9) |
GCpG/WCpW = 2.63 × 104,
x2 = x1 + 0.0018H/WCpW = 1.24 × 103, and
x3 = 0.02H/WCpW = 10.9 × 103
(dimension °C).
Equation A7 can be solved for the two
different steady-state conditions in terms of temperature difference
between steady states (T) and the characteristic time constant
(). and V are obtained as
|
(A10) |
![V = &tgr;[<A><AC>Q</AC><AC>˙</AC></A>(<IT>K</IT><SUB>T</SUB>/&rgr;<SUB>W</SUB><IT>C</IT><SUB>pW</SUB>) + <A><AC>V</AC><AC>˙</AC></A><SC>e</SC><IT>x</IT><SUB>2</SUB>]](/content/vol83/issue2/fulltext/668/img013.gif)
|
(A11) |
|
(A12) |
(KT/WCpW),
which represents
jB,
is one to two orders of magnitude larger than the second term
Ex2,
which represents jV,
inasmuch as
x2 = 1.24 × 103 and
KT/WCpW = 0.1-0.2 (16). For
E/ = 2, the term associated with the ventilation is only 2% of the term
associated with blood flow. It can be neglected, unless the total
E/ > 5. Thus
jV can be neglected in use of Eq. A11 for
the total
E/ < 3. For practical purposes we use Eq. A11 as
|
(A13) |
WCpW/KT)
represents ATV.
V(WCpW)
is the total thermal mass of the lung.
KT
is the coefficient of lung thermal conductivity, given by
Eqs. A4 and A5.
This model allows us to make some estimates of
jB,
jV,
and
jM.
jV
can be easily calculated from Eq. A6,
and for a human with 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, then
jM
is <5%
jV
and can be neglected.
REFERENCES
| 1. | Altman, P. L., and D. S. Dittmer (Editors). Biological Handbooks. Respiration and Circulation. Bethesda, MD: FASEB, 1971, p. 51. |
| 1a. | Bland, J. M., and D. G. Altman. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 8: 307-310, 1986. |
| 2. | Casaburi, R., K. Wasserman, and R. M. Effros. Detection and measurement of pulmonary edema. In: Lung Water and Solute Exchange, edited by N. Staub. New York: Dekker, 1978, vol. 7, p. 323-377. (Lung Biol. Health Dis. Ser.) |
| 3. |
Daviskas, E.,
I. Gonda,
and
S. D. Anderson.
Mathematical modeling of heat and water transport in human respiratory tract.
J. Appl. Physiol.
69:
362-372,
1990 |
| 4. | Eschenbacher, W. L., and D. Sheppard. Respiratory heat loss is not the sole stimulus for bronchoconstriction induced by isocapnic hyperpnea with dry air. Am. Rev. Respir. Dis. 131: 894-901, 1985[Medline]. |
| 5. | Ferrus, L., H. Guenard, G. Vardon, and P. Varene. Respiratory water loss. Respir. Physiol. 39: 367-381, 1980[Medline]. |
| 6. |
Geladas, N.,
and
E. W. Banister.
Effect of cold air inhalation on core temperature in exercising subjects under heat stress.
J. Appl. Physiol.
64:
2381-2387,
1988 |
| 7. | Gilbert, I. A., J. M. Fouke, and E. R. McFadden. The effect of repetitive exercise on airway temperatures. Am. Rev. Respir. Dis. 142: 826-831, 1990[Medline]. |
| 8. | Hanna, L. M., and W. P. Scherer. A theoretical model of localized heat and water vapor transport in the human respiratory tract. J. Biomech. Eng. 108: 19-27, 1986[Medline]. |
| 9. | Holman, J. P. Heat Transfer. New York: McGraw-Hill, 1968, p. 73-161. |
| 10. |
Ingenito, E. P.,
J. Solway,
J. R. McFadden,
J. M. Drazen,
and
E. G. Cravalho.
Finite difference analysis of respiratory heat transfer.
J. Appl. Physiol.
61:
2252-2259,
1986 |
| 11. | Mather, G. W., G. G. Nahas, and A. Hemingway. Temperature changes of pulmonary blood during exposure to cold. Am. J. Physiol. 173: 390-392, 1953. |
| 12. |
McFadden, E. R.
Respiratory heat and water exchange: physiological and clinical implications.
J. Appl. Physiol.
54:
331-336,
1983 |
| 13. |
McFadden, E. R.,
B. M. Pichurko,
H. F. Bowman,
E. Ingenito,
S. Burns,
N. Dowling,
and
J. Solway.
Thermal mapping of the airways in humans.
J. Appl. Physiol.
58:
564-570,
1985 |
| 14. |
Ray, D. W.,
E. P. Ingenito,
M. Strek,
P. T. Schumacker,
and
J. Solway.
Longitudinal distribution of canine respiratory heat and water exchange.
J. Appl. Physiol.
66:
2788-2798,
1989 |
| 16. | Serikov, V. B., M. S. Rumm, K. Kambara, M. I. Bootomo, A. R. Osmack, and N. C. Staub. Application of respiratory heat exchange for the measurement of lung water. J. Appl. Physiol. 72: 943-955, 1992. |
| 17. | Severinghaus, J. W., G. M. Ozanne, and H. Louderbough. Measurement of lung weight and cardiac output by single breath and rebreathing methods with a mass spectrometer. Acta Anaesthesiol. Scand. Suppl. 70: 161-164, 1978[Medline]. |
| 18. | Shitzer, A. (Editor). Heat Transfer in Medicine and Biology. New York: Plenum, 1985, p. 193-230. |
| 19. | Solway, J., A. R. Leff, I. Dreshaj, N. M. Munoz, E. P. Ingenito, D. Michaels, R. H. Ingram, and J. M. Drazen. Circulatory heat sources for canine respiratory heat exchange. J. Clin. Invest. 78: 1015-1019, 1986. |
| 20. | Tsu, M. E., A. L. Babb, D. D. Ralph, and M. P. Hlastala. Dynamics of heat, water and soluble gas exchange in the human airways. 1. A model study. Ann. Biomed. Eng. 16: 547-571, 1988[Medline]. |
| 21. | Weinbaum, S., and L. M. Jiji. A new simplified bioheat equation for the effect of blood flow on local average tissue temperature. J. Biomech. Eng. 107: 131-139, 1985[Medline]. |
| 22. | Zhu, L., and S. Weinbaum. A model for heat transfer from embedded blood vessels in two-dimensional tissue preparations. J. Biomech. Eng. 117: 64-73, 1995[Medline]. |
This article has been cited by other articles:
|
|
 |
|
  V. B. Serikov and N. W. Fleming Pulmonary and bronchial circulations: contributions to heat and water exchange in isolated lungs J Appl Physiol, November 1, 2001; 91(5): 1977 - 1985. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
E. R. McFadden Jr. Invited Editorial on "Airway thermal volume in humans and its relation to body size" J Appl Physiol, August 1, 1997; 83(2): 331 - 332. [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
ABSTRACT
