THORAX

100

2
°

0.22 MPH wind

a: )
s
T

»
so
T

40 MPH wind

WATER-LAYER MASS (g)

8

0 10 20 30 40 50 60

TIME AFTER SPRAYING (min)

Figure 10. Model-predicted changes in the mass of water on the
thorax after the subject was sprayed and then subjected to cold and
windy environmental conditions.

THORAX
S
e 7
uw 20
& 0.22 MPH wind
e
3
Ww 18+
a
ii
ul 40 MPH wind
Git
>
=<
ond
:
fia
fo oi4t
<
= 1 Led 1 L s
0 10 20 30 40 60 60

TIME AFTER SPRAYING (min)

Figure 11. Temperature changes of the water layer for the conditions
shown in Fig. 10.


150 >
O°C WATER IMMERSION

o z)
£ S,
=
3 100
ra y s.4
w
<
a 7
Q
6 Ss,
< f
ti
=
° :
9 10 RO 30

TIME AFTER IMMERSION (min)

Figure 2. Predicted increases in metabolic rate induced by
the 3 components of the shivering controller for a 0°C water
immersion. The time intervals between the arrows are the
times for which the components had reached the maximum
value allowed.

°

CHANGE IN SKIN TEMPERATURE (°C)

C) 10 20 30 40 50 60

TIME AFTER IMMERSION (min)

Figure 3. Experimental data (7,8) and model predictions of
mean skin temperature changes after immersion.

8


9. Holman, J.P. Heat transfer, New York:McGraw-
Hill, 1968. Ed. 2.

10. Kuznetz, L.H. A model for the transient metabolic
thermal response of man in space. NASA Manned
Spacecraft Center internal note MSC-Ec-R-68-
4:1966.

11. Montgomery, L.D. A model of heat transfer in
immersed man. Ann. Biomed. Eng. 2:19-46, 1974.

12. Nadel, E.R. and S.M. Horvath. Peripheral in-
volvement in thermoregulatory response to an
imposed heat debt in man. /.Appl. Physiol.
27:484-8, 1969.

13. Nadel, E.R., S.M. Horvath, C.A. Dawson, and A.
Tucker. Sensitivity to central and peripheral

thermal stimulation in man. /.Appl. Physiol.
29:603-9, 1970.

14, Raven, P.R, and S.M. Horvath. Variability of
physiological parameters of unacclimatized
males during a two-hour cold stress, 5°C.
Int.].Biometeorol. 14:309-20, 1970.

15. Stolwijk, J.A.J. and J.D. Hardy. Temperature
regulation in man - A theoretical study. Pflugers
Arch. 291:129-62, 1966.

16. Stolwijk, J.A.J. and J.D. Hardy. Control of body
temperature. In: Handbook of physiology. Reaction
to environmental agents, edited by Lee, D.H.K.
Bethesda: Am. Physiol. Soc., 1977, p. 45-67.

18

17. Tikuisis, P., R.R. Gonzales and K.B. Pandolf.
Thermoregulatory model for immersion of hu-
mans in cold water. /.Appl Physiol. 64:719-27,
1988.

18. Tikuisis, P., R.R. Gonzales and K.P. Pandolf.
Human thermoregulatory model for whole body
immersion in water at 20 and 28°C. US Army
Res.Inst.Env.Med. T23-87:1-46, 1987.

19. Timbal, J., C. Boutelier, M. Loncle and L. Bogues.
Comparison of shivering in man exposed to cold

in water and air. Pflugers Arch. 365:243-8, 1976.

20. Wissler, E.H. A mathematical model of the human
thermal system. Bull. Math.Biophys. 26:147-66,
1964,

21. Wissler, EH. Comparison of computed results
obtained from two mathematical models — A
simple 14-node model and a complex 250-node
model. /. Physiol. Paris 63:455-8, 1971.

22. Wissler, E.H. An Evaluation of Human Thermal
Models. Part A. US Air Force. (Sci. Res. Rep.
AFOSR-82-0214) 1984.

23. Wissler, E.H. Mathematical simulation of human
thermal behavior using whole body models. In:
Heat transfer in medicine and biology, edited by
Shitzer, A. and Eberhart, R.C. New York: Ple-
num, 1985, p. 325-73.

‘YU. GOVERNMENT PRINTING OFFICE: 1998 -660-088/60057


ACKNOWLEDGMENTS

We thank the Federal Aviation Administration’s William J. Hughes

Technical Center for their support of this project.

iii


TABLE 4
Thermal response to CWSS

TEMPERATURE CHANGE (°C)
WIND AIR CORE SKIN METABOLIC
VELOCITY RATE
MPH x BASAL
UNSPRAYED

0.22 0 0 0 1.00

0.22 -24.1 -0.69 TA 2.05
40 0 -0.61 5.7 1.70
40 -24.1 2.15 211 4.53

SPRAYED

0.22 0 -0.60 -3.9 1.50

0.22 -24.1 0.98 -8.8 2.61
40 0 -0.65 5.7 1.73
40 -24.1 -2.17 -21.1 4.53

We used the classic 25-node model of Stolwijk and
Hardy (16) with parameters modified anatomically by
Tikuisis et al. (18) with the general 3-component
approach of Wissler (23) for the shivering controller.
This model could predict with reasonable accuracy
transient data for metabolic rate, rectal and skin
temperature after cold-water immersion (see Figures 1
and 3-6). Therefore, it is highly likely that it can
predict with sufficient accuracy the response to skin
wetting by the CWSS. The major finding was that,
compared with the effects of cold-air and high-wind
exposure, the effect of the CWSS was relatively small
(see Table 4). The greatest stress to the human thermal
system was seen under normal environmental condi-
tions, but even here, the effect was not large.

There is still considerable argument over both the
anatomical description (i.e., number of nodes) and the
form of the controller equations to describe human
thermal responses to cold conditions. Whereas these
arguments are unlikely to influence our conclusion
that the CWSS would have insignificant effects on
airline passengers, it is important for other applica-
tions that they be resolved.

The question of the number of nodes required has
been directly addressed only in one situation. Wissler
(21) compared responses of head-core and trunk-skin
temperatures in his 250-node model and the 14-node
model of Kuznetz (10) to a combination of air cooling

and light exercise. The important finding was that the
14-node model significantly overestimated the de-
crease in skin temperature. Wissler suggested that any
time thermal gradients between core and skin are
significant, these errors would occur. There are no
similar studies to evaluate the decrease in this error of
expanding the model to 25-nodes, or even larger, as
did Gordon et al. (4) and Montgomery (11). In the
case of water immersion, the overestimation in the skin
temperature would probably be decreased because of
the rapid equilibration between skin and water tem-
peratures, but the resulting large gradient between
skin and core might produce similarly large errors in
the core temperatures.

The form of the controller equations for shivering is
still not settled. The original model of Stolwijk and
Hardy (15) postulated that the increase in MR was
dependent on the product of changes in average skin
temperature and the head-core temperature. This
assumption was not altered in their subsequent model
(16) or in the changes made by Montgomery (11) to
adapt the model for water immersion predictions.
Gordon et al. (4) made the first substantial change.
They assumed that the MR increase was sensitive to a
sum of three terms, each proportional to either 1) skin
temperature, 2) head-core temperature, or 3) heat
flux. They found controller parameter values, which
produced close prediction of transient MR, rectal


An unusual feature in the present model was a limit
on the S, component, which varied with time (see
Figure 2). This kind of limit was necessary for the
model prediction to approximate the slower rise in
MR after the initial peak. This limit became a factor
only in the lower-temperature water immersion cases.
Wissler (23) suggested that the S, component in his
model be modified by a time-varying factor to account
for MR increases during prolonged exposure to cold.
He suggested that this effect could account for the
influence of thermoreceptors besides those in the
hypothalamus and skin. Our variable limit accom-
plishes the same purpose and may represent the same
phenomena. Alternatively, the time-varying limit may
represent an increase in thermoreceptor sensitivity
after prolonged intense stimulation.

This study has demonstrated for the first time that
the thermal behavior of immersed humans can be
predicted for a wide range of temperatures. However,
it would be desirable if the model could also be
applicable to cold-air exposure conditions, since no
available models have been able to predict thermal
behavior for both kinds of conditions. Besides the
application of the model of Gordon et al. (4), which
was limited to a comparison with one data set, Haslam
and Parsons (6) recently compared rectal and skin
temperature predictions of two different models under
cold-air exposure conditions. The models were a 2-
node model of Gagge et al. (2) and the 25-node
Stolwijk and Hardy (16) model. They found that
neither of these models could describe the data with
sufficient accuracy over the entire range of cold tem-
peratures considered. The results of the present study
have shown that the model can predict changes in MR
and skin temperatures for the one case of cold-air
exposure considered (see Figures 7-9), but the rectal
(core) temperature predictions are in the opposite
direction to experimental findings (4). The reasons for
this discrepancy have not been reconciled. Timbal et
al. (19) found that the changes in MR after the initial
peak occurring during water immersion of tempera-
tures down to 24°C could be described as a function
of the sum of two factors, one proportional to the
change in skin temperature and the second propor-
tional to rectal temperature. However, in their study,
rectal temperature increased during the immersion,
which is opposite to the findings of Tikuisis et al. (17)
and Hayward et al. (7,8). Timbal et al. proposed that

a decrease in skin temperature and an increase in rectal

17

temperature both acted to increase MR. However, this
relationship did not hold for cold-air exposure, so they
were forced to assume a different relationship here,
which did not contain the influence of core tempera-
ture. Timbal et al. (19) were bothered by this conclu-
sion that the body responds differently to the type of
thermal stress, but they were left with no alternative.
The single set of controller equations developed in the
present study is a step forward in that one does not
have to postulate different equations for different
conditions, but the direction of core temperature
changes is still unresolved.

REFERENCES

1. Daniel, W.W. Biostatistics: A Foundation for Analysis
in the Health Sciences, New York:Wiley, 1987.
Ed. 4.

2. Gagge, A.P., A.P. Fobelets, and L.G. Berglund. A
standard predictive index of human response to
the thermal environment. ASHRAE Trans.
92:709-31, 1986.

3. Gagge, A.P. and Y. Nishi. Heat exchange between
human skin surface and thermal environment.
In: Handbook of Physiology. Adaptation to the
environment, edited by Lee, D.H.K. Bethesda:
Am. Physiol. Soc., 1964, p. 69-92.

4. Gordon, R.G., R.B. Roemer, and $.M. Horvath. A
mathematical model of the human temperature
regulatory system - Transient cold exposure
response. JEEE Trans. Biomed.Eng. BME-23:434-
44, 1976.

. Hardy, J.D. Models of temperature regulation - a
review. In: Essays on temperature regulation,

Amsterdam: North-Holland, 1972, p. 163-86.

6. Haslam, R.A. and K.C. Parsons. Using computer-
based models for predicting human thermal
responses to hot and cold environments. Ergo-

nomics 37:399-416, 1994.

. Hayward, J.S. and J.D. Eckerson. Physiological
Responses and survival time prediction for hu-
mans in ice-water. Aviat.Space Environ.Med.

55:206-12, 1984.

. Hayward, J.S., J.D. Eckerson and M.L. Collis.
Thermoregulatory heat production in man: Pre-
diction equation based on skin and core tempera-
tures. Appl Physiol. 42:377-84, 1977.

w

N

oo


CHANGE IN SKIN TEMPERATURE (°C)

0 20 40 60 80 100 120

TIME AFTER EXPOSURE TO 4.7°C AIR (min)

Figure 8. Comparison between experimental data (4) and model
predictions for various skin temperatures during cold-air exposure.

CHANGE IN SKIN TEMPERATURE (°C)

n n 4. n rl 2 a

oO 20 40 60 80 100 120

TIME AFTER EXPOSURE TO 4.7°C AIR (min)

Figure 9. Comparison between experimental data (4) and model
predictions for various skin temperatures during cold-air exposure.

12


TABLE 1
Determination of steady-state component of Ss,

rs ae T(r, 34) AMR
°C °C/min (°C/miny®C Kcal/hr/m?
Experimental Predicted*
26.7" -0.098 0.715 114 117
28.9 -0.086 0.439 70 721
30.7 -0.091 0.300 62 49.3
33.4 -0.0104 0.062 5.5 10.1

T,, skin temperature; T., core temperature; AMR, change in metabolic rate from baseline.
“Experimental data in Tables 1 and 2 are derived from the data of Nadel and Horvath (12).
The following equation was assumed to predict' the MR data with the constant of 164 found
to provide the best fit using linear, least-squares regression analysis (1). This constant was
taken as A,, in Eq. 3, T, is assumed to be equivalent to 7, in that Eq., and the change in 7,
from 34°C is equivalent to the integrated COLDS signal.

ame = 164 Te, 34)

TABLE 2
Determination of exponential decay rate of s,
TIME MR
Hrs Fraction of maximum value Mean + SE Predicted’
0.083 0,380 0.640 0.742 0.59 + 0.11 0.57
0.208 0.200 0.029 0,338 0.19 + 0.09 0.24
0.542 0.070 0.114 0.226 0.14 + 0.05 0.02
+Predicted from the equation
MRy= e'*""

where MR, is the fraction of the maximum MR and the value, K,, = 6.87/hr, was found to give the
best fit to the mean data.


EFFECT OF AN AIRPLANE CABIN WATER SPRAY SYSTEM
ON HuMAN THERMAL Benavior: A THEORETICAL STUDY
UsinG A 25-NoDE MODEL OF THERMOREGULATION

INTRODUCTION

The advent of manned space flight in the 1960s
spurred the development of mathematical models of
human temperature regulation aimed at understand-
ing the response to the thermal challenge of strenuous
exercise in harsh environments. In the early 1960s,
Wissler (20) developed an extremely complex model
in which the body was subdivided into 250 tissue
regions (each region lumped and considered as a
node). In 1966, Stolwijk and Hardy (15) developed a
much simpler 8 node model which was expanded to
14 nodes by Kuznetz (10) in 1968 and to 25 nodes in
1971 by Stolwijk and Hardy (16). The 25-node
model has become the standard anatomical approach
to modeling human temperature regulation. Adop-
tion of the Stolwijk and Hardy approach by the
National Aeronautics and Space Administration
(NASA) has probably contributed to the relatively
widespread acceptance of the Stowijk and Hardy
model.

The approach of the present study was to use the
25-node model (16) to study the effect of a cabin water
spray system (CWSS) on thermoregulatory responses
of passengers after being wetted by the spray system.
The aim was to see if an individual, after being sprayed
with water in an airplane, might be subjected to
injurious thermal stresses after exiting into a cold
environment. Examination of the literature revealed
experimental and theoretical studies where minimally
clothed humans were immersed in cold water or
exposed to cold air (8,14), but no studies were found
pertinent to the clothed individual being wetted and
then exposed to a cold environment. Theoretically, if
the 25-node model could predict human thermal
changes during cold-water immersion, then it could
be modified for use under water-spray conditions.

In 1972, Hardy (5) found that the controller
equations of the 25-node temperature regulation model
could not accurately predict the effects of cold environ-
ments on human thermal responses. As a result, in

1976, Gordon et al. (4) developed a new model
increasing the number of nodes to 42 and substan-
tially changing the form of the controller equations.
This model was able to closely predict transient skin
and rectal temperature changes and the increases in
metabolic rate (MR) due to cold-air exposure. How-
ever, more recently, Wissler (22) found that this
model was unsuitable for predicting cold-water im-
mersion data.

The latest model of human thermoregulation was
by Tikuisis et al. (17). The model was designed
specifically to predict transient rectal temperature and
MR data measured in that study under cold-immer-
sion at 20 and 28°C water temperatures. They used
the 25-node model, but updated the anatomical
parameter values for the body composition of their
experimental subjects according to the formulas given
in Montgomery (11). Montgomery had expanded the
25-node model to 61 nodes to study the thermal
behavior of divers in wet suits exposed to cold water,
but he had kept the original cold controller equations.
Tikuisis et al. (17) showed that these controller equa-
tions were inadequate to predict their data. Therefore,
they modified these equations so that the shivering-
induced MR increase was sensitive to the change in
skin temperature in addition to the sensitivity to the
product of changes in skin and core temperature as in
the original Stolwijk and Hardy models (15,16).
However, Tikuisis et al. never compared their model
predictions to available data from Hayward et al. (7,8)
for lower water temperatures. These data show an
initial rapid rise in MR that the Tikuisis et al. model
can not reproduce. This finding led us to investigate
other possible controller formulations.

In 1985, Wissler (23) proposed a major modifica-
tion of the temperature controller for the induced MR
increase due to shivering. He suggested that the MR
controller be composed of three components, the first
sensitive to the rate of skin cooling, the second sensi-
tive to some function of changes in skin and core
temperatures and the third sensitive to the rate of core




the leg data are predicted quite closely. The finger and
toe data show a somewhat more rapid approach to
steady-state than the model predictions for the hand
and foot, but considering the anatomical difference for
experimental and predicted results, the comparison is
satisfactory. It is likely that altering the partitioning of
blood flow and shivering metabolism to these sections
would improve the fit. However, since the bodily
compositions of the experimental subjects in the
various studies were significantly different, we decided
not to make changes to the model to make it fit any one
data set.

One significant discrepancy observed for the air-
cooling data was that the experimentally measured
rectal temperature (4) increased by about 1°C during
the 2 hrs of exposure. In contrast, the model prediction
was a 1°C decrease. At present, we can not explain this
discrepancy. Timbal et al. (19) also found that rectal
temperature increased when subjects were exposed to
cool air, but they also found that immersion in water
down to 24°C produced initial increases in rectal
temperature, which contrasts to the data of Tikuisis et
al. (17). These differences in experimental data cannot
presently be explained.

Cabin water spray system.

The next objective was to use the model to predict
thermoregulatory responses after an individual had
been wetted by a cabin water spray system and exposed
to a cool environment. The basic model had to be
modified by adding the effects of clothing and a water
layer next to the skin, which evaporates and draws heat
from the skin.

The effects of the CWSS were evaluated by deter-
mining the spray induced changes in MR, trunk-core
temperatures, and various skin temperatures during
exposure up to 1 hr to ambient air conditions of
temperatures down to 0°C, with wind velocities up to
40 MPH. Figure 10 shows the decrease in the mass of
the sprayed water layer on the thorax as the layer
evaporates. The conditions imposed are 25% body
wetting, which is the maximum considered and 0°C
ambient air. The upper line shows that under normal
wind conditions the mass of the layer decreases about
40% over the 60-min period after spraying. The rate
of decrease is almost constant because it depends only
on the vapor pressure of the water layer, which in turn
depends upon the water-layer temperature, which
changes very little over this period (see Figure 11).

When the ambient air temperature was 24°C, the
decrease in mass was almost identical. With a 40 MPH
wind velocity, the evaporation of the layer is much
more rapid because of the increase in the convective
heat-transfer coefficient. As seen, the layer completely
disappears in <15 min after exposure to the wind.

The temperature of the water layer on the thorax
under the various wind conditions is shown in Figure
11. The temperature rises slightly even when the
ambient temperature is 0°C because the high conduc-
tivity from the skin produces heat transfer to the layer
sufficient to overcome the loss to the environment.
However, when the wind velocity increases to 40
MPH, the combination of the low ambient tempera-
ture and the increased convective heat loss produces a
rapid decrease in water-layer temperature, which cools
the skin. Data from the water layers on the head and
arms are similar in their transient behavior.

Table 4 shows changes in selected variables for 60
min of exposure to changes in ambient conditions
both for the unsprayed (top section) and sprayed
individual. It is clear that the CWSS produces the
largest changes under the normal ambient conditions.
Core (rectal) and skin temperatures dropped by 0.6
and 3.9°C, respectively, whereas MR increased by
50%. When air temperature was reduced to 0°C
(24.1°C decrease), the changes in core and skin tem-
peratures relative to the unsprayed condition were
only -0.29 and -1.7°C, respectively. The MR in-
creased from 2.05 times basal to 2.61 times after
spraying. For the high wind velocity condition, spray-
ing produced very little further decreases in tempera-
tures or increase in MR over the effect of the high
velocity itself. Therefore, the CWSS would not appear
to significantly increase the risk of exposure to a harsh
environment.

DISCUSSION

The purpose of this study was to develop a math-
ematical model of human temperature regulation
under cold conditions that could be used to predict
the thermal response to a cabin water spray system
activated during a fire. Since the individual would be
wet on parts of the body and then could be exposed to
very cold and windy conditions upon exiting the
airplane, it was necessary for the model to accurately
simulate conditions similar to cold-water immersion
over a range of water temperatures.


S2= Asx COLDS x AT, (2)

where S, is the second MR component of shivering,
AT, is the change in hypothalamic temperature from
the set point and A,, is a constant.

Bex Kal Aax Dt xCOLDS $4) (3)
where S, is the third MR component of shivering, dT,
/ dt is the time rate-of-change of hypothalamic
temperature, KX’, is a time constant and A, is a constant.
The constants for the S, and S, components were
determined as described in the RESULTS section.
The constants for the S, component were determined
from the data shown in Tables 1 and 2, which were
derived from the data of Nadel and Horvath (12).

This formulation has five significant differences
from that of Wissler (23). 1) Wissler proposed that all
3 components were time varying since he wrote each
one as a differential equation. However, he did not
offer any experimental evidence for this assumption
with regards to the S, and S, components. In the
absence of such data, we chose the simpler formulation
shown above. 2) Wissler suggested that the steady-
state S, component has the form suggested by Hay-
ward et al. (8). However, the data used by Hayward et
al. to derive their relationship did not take into
account the effect of changes in core temperature on
metabolic rate as expressed in the S, component. As a
consequence, we incorporated only the product rela-
tionship of central and peripheral effects as in the
Hayward et al. relationship. 3) Wissler proposed that
the S, term be proportional to 47, / dt, but did not
include the modifying effect of changes in skin tem-
perature as in our formulation. This latter effect was
suggested by the experimental data of Nadel and
Horvath (12), who found that the magnitude of the
metabolic response to a centrally imposed heat debt
depended upon the skin temperature. 4) We found it
necessary to limit each of these components to some
maximum value (see RESULTS). 5) Wissler multi-
plied the S, component by a time-varying factor,
which accounted for the finding that metabolic rate
continued to increase during prolonged exposure to
cold even though rectal and skin temperatures were
relatively stable. As described below, we found it
necessary to impose a limit on the S, term that varied
with time. Therefore, our approach may produce a
similar effect as the factor used by Wissler.

The total shivering MR, CHILL, was then
CHILL = §;+ S2+S3 (4)
and this sum was also limited.

Simulation of head-out, cold-water immersion.

When the model was to be used to describe thermal
regulation during water immersion, except for the
head-skin compartment, all other skin compartments
no longer transferred heat to the ambient air. Instead,
they now communicated with a water layer of constant
temperature. The experimental data of Hayward et al.
(7,8) showed that skin temperature rapidly decreased
after the immersion. We found that the same transient
decreases in skin temperature could be achieved (see
Fig. 3) by multiplying the skin-air heat transfer
coefficients by a factor of 14 to convert them to skin-
water coefficients. This procedure avoided the much
more complicated approach of Tikuisis et al. (17),
which required estimation of actual heat transfer
coefficients.

The water temperatures considered were 28°C and
20°C to compare with the data of Tikuisis et al. (17)
and 10°C and 0°C to compare to the data of Hayward
etal. (7,8). Our general approach was to determine the
value of the CHILL controller constants that gave the
best overall fit to the metabolic rate and rectal tem-
perature data from these sources.

Simulation of cabin water-spray system responses.

Our approach to simulating the effect of the CWSS
on human thermoregulation was to assume that the
spray produces a film of water on the unclothed skin
(head) of a uniform thickness. The spray, which
contacts the clothing on other parts of the body, wets
this clothing and causes it to “stick” to the skin, also
producing a uniform water layer, but thicker than for
the unclothed surface. When the individual exits the
airplane and is exposed to the ambient air, water
evaporates from the layer on the head and from that in
the clothing, and the thickness of these layers de-
creases. When the layer on any skin surface is fully
evaporated, heat transfer from the skin reverts to the
normal condition. In the model, heat loss (Keal/hr)
from the water layer due to evaporation is proportional
to the difference between the vapor pressures of the water
layer and ambient air multiplied by the convective


DOT/FAA/AM-98/4

Office of Aviation Medicine
Washington, D.C. 20591

Effect of an Airplane Cabin
Water Spray System on Human
Thermal Behavior: A Theoretical
Study Using a 25-Node Model

of Thermoregulation

Matthew B. Wolf

Department of Physiology
University of South Carolina School of Medicine
Columbia, SC 29208

Robert P. Garner

Civil Aeromedical Institute
Federal Aviation Administration
Oklahoma City, OK 73125

February 1998

Final Report

This document is available to the public
through the National Technical Information
Service, Springfield, Virginia 22161.

@

U.S. Department
of Transportation

Federal Aviation
Administration


model was run on a Intel microprocessor-based digital
computer. The integration algorithm was an adjust-
able step size modified Euler method. Such an adjust-
able step size method was required because of the large
gradients imposed when the model was subjected to
rapid changes in ambient conditions.

The thermoneutral temperature for each node was
determined by solving the steady-state equations.
This was done with the matrix inversion approach
using a commercially available computer spreadsheet
program.

RESULTS

Water immersion.

Figure 1 shows the experimental MR data (solid
squares and circles) from Hayward et al. (7,8) as
compared to the predictions of the model (solid and
dashed lines) for water immersion in 0°C and 10°C
water, respectively. The data are expressed as multiples
of the pre-immersion (basal) MR. As seen, a promi-
nent feature of the experimental data is an initial rapid
increase in MR, which is presumed to be due to the

45

4.0

3.5

3.0,

METABOLIC RATE ( x Basal)

H t 1 n 1 4 J

0 10 20

1.0 ! 1 1 1 rl n

30 40 50 60

TIME AFTER IMMERSION (min)

Figure 1. Change in metabolic rate relative to basal level after immersion in cold water.
The filled squares and circles are experimental data from Hayward et al. (7,8) at 0 and
10°C, respectively, whereas the solid and dashed lines represent the corresponding

model predictions.



heat-transfer coefficient between water and air (16).
The rate of evaporation of the layer is this rate of heat
loss divided by 0.586 cal/g (3).

Heat transfer between the skin and the water layer
is by conduction. The thermal conductivity (TC,,)
between the skin and the water layer of varying
thickness is determined at each instant in time using
the approach of Tikuisis et al. (18) derived from
elementary heat-transfer theory (9) as follows:

3
wert
r= Ur tnt )

where r, and r, are the outer radii of the water layer and
skin, respectively and V, is the volume of
the water layer. 4n
ry ee
24444
Ks rsen Ts Kw Fs Twem
where K, and K, are the specific thermal conductivities
of skin and water, respectively, and r,, andr, _,, are the
radii to the centers of mass of skin and water,
respectively.

Trunk and arms (cylinders)
rE lr +

where L is the length of the section.
2aL

Head (sphere)

(5)

6)
1)

(7)

TCsw= T (8)

inte 4 win( 2 )
Ks sem Ksub rs

Because the water layer is relatively thin, r,_, was
determined as (r, + r,)/2.

When only part of a skin segment was initially in
contact with a water layer, then the skin compartment
was subdivided into two parts: wet and dry. The wet-
skin compartment was in contact with its water layer
and heat transfer occurred between them. The dry-
skin compartment continued to communicate with
the ambient air. Each compartment communicated
separately with that portion of the fat layer beneath it.
Similarly, the metabolism, insensible heat loss and
blood flow were partitioned between these skin com-
partments on the basis of the initial fraction of skin
wetted. There was no heat transfer between the wet-
and dry-skin compartments. The skin temperature for
a partially wet segment was the average of the wet and
dry temperatures, as weighted by the fraction of
thermoreceptors in each section.

The thermal effects of clothing were accounted for
in the model by multiplying the heat transfer coeffi-
cient between skin and air by a constant (F,,) for each
body segment other than the head. F.,, takes on values
from 0 (perfect insulation) to 1 (no insulation), as
described by Gagge and Nishi (3). For the present
study, F_, was assumed to be 0.52, which represents a
lightly clothed individual. With this clothing fac-
tor, the thermoneutral ambient temperature be-
came 24,1°C.

The effect of wind velocity was included in the
model by modifying the convective heat-transfer coef-
ficient for each anatomical segment. The values given
by Tikuisis et al. are for a standard velocity of 0.1 m/
sec (0.223 MPH). It was assumed that the coefficient
changes as the square root of the ratio between the
ambient velocity and the standard value (16).

The initial thickness of the water layer on the thorax
and arms was taken as 0.06 cm. This value gave a
water-layer mass of 344 g on the thorax and 196 g on
the arms if both of these areas were fully wetted. The
total water mass of 540 g was equivalent to the water
content of a thoroughly wet, long sleeve, cotton shirt.
The initial water layer on the head was assumed to be
only one-half as thick (0.03 cm) because it was not
covered by a layer of clothing, which would hold water
and increase the effective thickness.

From design considerations of the CWSS, it was
decided that a maximum of 25% of the body surface
could be wetted. The first 7% wetted would be the
head and between 7% and 25%, equal surface areas
would be wetted on both the thorax and arms. There-
fore, for example, if 5% were wetted, then 5/7 of the
head area would be wetted and nothing on the trunk
and arms. If 25% were wetted, the head would be
100% wet, whereas only 30% and 53% of the trunk
and arm surface areas, respectively, would be wetted
because of the larger surface area of the trunk. Under
the 25% wetted condition, the initial masses of water
on the head, trunk and arms were 40 g, 104 g, and 104
g, respectively.

Simulation methods

The model equations were simulated using the
SCoP computer program developed at Duke Univer-
sity under grant number RR1693 from the National
Institutes of Health, Division of Research Resources.
SCoP includes a language for expressing the model in
familiar equation form, as well asa library of solvers and
an interactive simulation environment. The compiled


cooling. There have been proponents of these indi-
vidual factors in the control of shivering, but no one
had proposed that all three were important.

In the present study, our approach was to use the
25-node model and see if a set of controller equations
similar to those proposed by Wissler (23) for shivering
would be sufficient to predict temperature and MR
data for cold-water immersion. Our finding was that,
in general, the shivering controller equations sug-
gested by Wissler had the ability to fulfill this task.
Therefore, this paper will describe 1) the details of the
basic model, 2) the comparison of model prediction
with literature data and 3) the modification of the
model for application to the water-spray problem and
the model predictions for this situation.

METHODS

The anatomical model used is essentially the 25-
node model of Tikuisis et al. (18), which is derived
from the original Stolwijk and Hardy model (16).
Tikuisis et al (18) derived new parameter values to fit
the body composition of their experimental group.
Briefly, the body is subdivided into six parts: head,
trunk, arms, legs, feet, and hands. Each of these
sections is further subdivided radially from the center
into the concentric annular sections, core, muscle, fat,
and skin. Including the blood volume, there are 25
individual anatomical units, which are assumed ho-
mogeneous and are therefore called compartments.
There is a characteristic compartmental (nodal) tem-
perature.

Heat flows radially via conduction between adja-
cent compartments and heat is convected between
each compartment and the central blood pool. This
latter process can be modulated by vasodilatation for
both muscle and skin blood flows and by vasoconstric-
tion for skin blood flows. Countercurrent heat ex-
change in the skin was not included. Heat transfer
between the skin and the environment occurs by
evaporation (insensible and sweating), conduction,
convection and radiation. Heat is produced metaboli-
cally in each compartment, except the blood. Heat
production can be increased in the cold by shivering.
Heat is also lost by respiration. The passive heat
transfer equations for this system are those given by
Stolwijk and Hardy (15).

The model anatomical parameters were for a mod-
erate-fat content male as described by Tikuisis et al.
(18). These parameters are weight = 79.2 kg, body fat
= 17.62 kg and surface area = 1.94 m?. The parameters
used for thermal conductances, capacitances, etc. are
given in Tikuisis et al. (18).

Thermoregulatory control is via a central integra-
tor, which receives information on skin and hypotha-
lamic (head core) temperatures. This information is in
the form of error signals, which indicate differences
between the individual temperatures and their set-
point values. Set-point values are determined from the
solution of the steady-state heat transfer equations for
the unclothed mathematical model under ther-
moneutral conditions (ambient air temperature of
28.5°C). These values are unchanged throughout the
simulation process. Cold error signals from each skin
section are weighted by the fraction of total skin
thermoreceptors in that section (16) and summed to
produce the integrated peripheral COLDS' signal.

Efferent outputs from the central controller in
response to the cold stress produce skin vasoconstric-
tion and muscle vasodilatation and metabolic heat
generation through shivering. The skin vasoconstric-
tion is driven by a linear combination of the COLDS
signal and the hypothalamic temperature error as used
previously (16). Muscle vasodilatation is proportional
to the metabolic heat generation. What is new and
different in the present model is the treatment of the
shivering phenomena. In 1985, Wissler (23) proposed
that metabolic heat generation due to shivering could
be described as the sum of three components, as
described below. Wissler presented the general equa-
tions for these components, but did not give parameter
values, even though he apparently came up with these
values to compare his model predictions to experimen-
tal data.

In the present model, the shivering phenomena was
modeled as follows: dT;

si

= AyD
Si= As dt

where S, is the first MR component of shivering, 47,
/ dt is the time rate-of-change of the ith skin
temperature, SKINR[i] is the fraction of skin
thermoreceptors in the ith skin section and A, is a
constant.

x SKINR[i] (1)

‘COLDS is the variable used in the computer program that represents a thermoreceptor weighted skin temperature during cold exposure.

2


temperature, and various skin temperatures during
exposure to ~5°C air. However, Wissler (21) found
that this model was unable to predict the thermal
response to cold-water immersion.

In 1985, Wissler (23) suggested a different three-
component shivering MR controller. The MR was a
sum of terms proportional to 1) the time-rate of
change of mean skin temperature (dT, / dt), 2) the
product of the changes in mean skin temperature and
central (core) temperature as formulated by Hayward
et al. (8), and 3) the time-rate of change of central
temperature. Wissler formulated the first component
(S,) as a set of differential equations, each governing
the change in MR at different magnitudes of dT, / dt.
However, he gave little justification for his assump-
tions, nor did he list most of the parameter values
required to use this formulation. There is substantial
evidence that there is a rapid transient increase in MR
coincident with a drop in skin temperature. This
response is very evident in the data of Hayward et al.
(7,8) during cold-water immersion, in the data of
Raven and Horvath (14) during cold-air exposure, and
in the results of Timbal et al. (19) for both cold-water
immersion and cold-air exposure. Consequently, we
incorporated this effect in the present model, but we
found that to fit the available MR data it was not
necessary to describe it by a set of differential equa-
tions. Instead, as given by Eq. 1, the S, component was
simply proportional to the sum of the weighted rates
of change of the individual skin temperatures. The
time lags introduced by the differential equations
would have slowed the MR increase upon cooling,
which was not indicated by the experimental data (see
Figure 1). In contrast, Tikuisis et al. (17) did not
incorporate this effect in their model. Instead, they
had a term proportional to skin temperature, which
they included to produce a rapid increase in MR with
skin cooling because their experimental MR data (see
Figure 5) did not show the subsequent rapid fall in
MR as in the data for colder water temperatures (see
Figure 1). Perhaps it takes a certain minimum rate of
skin temperature decrease to initiate the transient
effect, or the effect was not seen in the Tikuisis et al.
data because data sampling was not sufficiently rapid.

The second component (S,) proposed by Wissler
(23) was taken from the findings of Hayward et al. (8)
during water immersion at 10°C. They proposed that
the steady-state MR increase observed could be de-
scribed by a product relationship of changes in skin

16

and core temperatures. However, the changes were not
relative to normal values of these variables, but to
reference values of 41-42°C, presumably the values at
which neural firing from the receptors ceases. It is
possible that this relationship is incorrect because
Hayward et al. ignored the involvement of time-
varying core temperature changes during their mea-
surements. In 1969, Nadel and Horvath (12) showed
that a centrally imposed heat debt resulting in a
sustained decrease in core temperature of ~0.1°C/min
induced a rapid increase in MR peaking at a value
dependent upon mean skin temperature, which was
held constant at different values during the MR
measurements. At the normal skin temperature, the
heat debt had no significant effect on the MR. In a
subsequent paper, Nadel et al. (13) discussed the
presence of a rate component in MR increases, but
they did not formalize this component as they tried to
predict only steady-state changes. Wissler (23) recog-
nized that this rate effect could be important and
proposed that the third component of shivering (S,)
was proportional to dT, / dt, but he ignored the
modulating effect of skin temperature in this formula-
tion. Assuming the existence of this effect, then the
MR data of Hayward et al. (7,8) must have been
affected because core temperature was decreasing
throughout the measurement period. As a conse-
quence, their expression derived for MR changes is
not valid.

In the present study, the product effect of changes
in skin and core temperatures was incorporated as the
S, component (see Eq. 2), but the changes were
derived from the thermoneutral setpoint established
prior to immersion. The effect of a time lag for this
component, as produced by the differential equation
formulation of Wissler (23), was not included because
of a lack of experimental evidence for its necessity. The
S, component was described (see Eq. 3) as a product
of skin temperature change and the rate of change of
core temperature. This component was described by a
differential equation because Nadel and Horvath (12)
found that after the peak MR was reached, the MR
subsequently declined with time back to the steady-
state values. The peak values and the steady-state
values were used (see Tables 1 and 2) to derive the
parameter values for this relationship. The parameter
values for the other constants (see Table 3) were
derived to fit the model to experimental data, as
described in the RESULTS section.




The A, and K, parameters were determined from
the experimental data of Nadel and Horvath (12)
given in Tables 1 and 2. The resulting magnitude of
the S, component is shown in Figure 2. As seen, it
plays the most dominant role in determining longer
term MR increases for the 0°C immersion case because
the largest changes in the rate of decrease of core
temperature and of the decrease in skin temperature
occur for this lowest temperature. For the 10°C im-
mersion and higher temperatures, the S, term plays a
less dominant role than the S, term in determining
increases in MR. Also seen in Figure 2 is that it was
necessary to limit S, to ensure that the total MR did
not increase beyond the maximum limits shown in
Figure 1. From a modeling approach, this effect also
could have been achieved from the limit on total MR.

Hypothalamic (head-core) temperature decrease is
a primary stimulus for shivering. However, this tem-
perature is not generally measurable, but the related
rectal (trunk-core) temperature is usually measured.
Figure 4 shows experimental data (solid squares and

circles) of Hayward et al. (7,8) for water immersion at
0°C and 10°C temperatures, respectively. As seen,
after the initial 5-min period where the temperature
change was small, the rectal temperature began to fall
rapidly, and the rate of decline increased with time for
both immersion temperatures. This rapid rate of
decline helps to produce the steep increase in the S,
component seen in Figure 2 and the absolute decrease
in temperature also drives the increase in the S,
component. The model predictions (solid and dashed
lines) for these temperature changes were quite good,
in general, although the predicted results did not fall
as rapidly as the experimental data in the later stages
of the immersions.

MR data from the study of Tikuisis et al. (17) is
shown in Figure 5 for immersion at 20°C and 28°C
temperatures. As seen, these data do not show the
initial MR peak, which is very prominent in the
Hayward et al. (7) study (see Figure 1). The absence
of this feature may be due to the wide spacing of the
data points (6 min apart). However, the Tikuisis et al.

0.0

1.0

RECTAL TEMPERATURE CHANGE (°C)

n n L

ni 1 L 1 5

0 10 20

TIME AFTER IMMERSION (min)

30 40

Figure 4. Experimental data (7,8) and model predictions (trunk-core
temperature) of rectal temperature changes after immersion.

9


0.0

0.5

1.0

RECTAL TEMPERATURE CHANGE (°C)

4 n 4 4 L 1 . 3

0 10 20 30 40 50 60

TIME AFTER IMMERSION (min)

Figure 6. Experimental data (17) and model predictions (trunk-core temperature) of
rectal temperature changes after immersion.

METABOLIC RATE ( x Basal)
had .

1 A rn L 1 L L 4 L

° 20 40 60 80 100 120

TIME AFTER EXPOSURE TO 4.7°C AiR (min)

Figure 7. Comparison between experimental data from Gordon et al. (4) and model
predictions of increases in metabolic rate due to exposure to cold air. The shivering-
controller parameter values were unchanged from the water-immersion conditions.

ll


Technical Report Documentation Page

1. Report No.
DOT/FAA/AM-98/4

2. Govemment Accession No.

3. Recipient's Catalog No.

4, Title and Subtitle

Effect of an airplane cabin water spray system on human thermal behavior:

A theoretical study using a 25-node model of thermoregulation

5. Report Date
February 1998

6. Performing Organization Code

7. Authors)
Wolf, M.B.', and Garner, R.P.”

8. Performing Organization Report No.

9. Performing Organization Name and Address
"University of South Carolina
Department of Physiology
Columbia, SC 29208

*FAA Civil Aeromedical Institute

10. Work Unit No. (TRAIS)

P. O. Box 25082

Oklahoma City, OK 73125

11. Contract or Grant No.

12, Sponsoring Agency name and Address
Office of Aviation Medicine
Federal Aviation Administration
800 Independence Avenue, S.W.
Washington, DC 20591

13. Type of Report and Period Covered

“14. Sponsoring Agency Code

15. Supplemental Notes

16. Abstract

This study was conducted to assess the effect of an aircraft cabin water spray system on thermoregulatory responses of
passengers after being wetted by the spray system. A mathematical model was developed that could adequately describe
experimentally determined transient changes in metabolic rate (MR), and core and skin temperatures of human beings
exposed to water-immersion conditions (0 to 28°C). The model was the basic 25-node description of Stolwijk and
Hardy as modified to apply to a male with medium fat content. The MR increase induced by shivering was described by
3 components sensitive to 1) time-rate of change of skin temperature, 2) the product of changes in skin and head-core
temperatures and 3) the product of skin temperature change and the time-rate of change of head-core temperature. The
model was also able to closely predict the changes in MR and skin temperatures induced by exposure to cold air.
However, the predictions of rectal temperature changes were in the opposite direction to the experimental data for this
case. The model was modified to describe the effects of spraying individuals with water on their heads, arms and torsos
to simulate the action of a cabin water spray system activated by a fire in an airplane. The model predicted that an
individual, after being sprayed and exiting into a cold and windy environment, would encounter only a minor increase
in thermal stress compared to the dry state. We conclude that mathematical simulation is an effective method of
predicting thermal behavior of humans under a variety of cold conditions.

17. Key Words

Aviation safety, aircraft, passengers, mathematical model,
human thermoregulation, water immersion

18. Distribution Statement

Document is available to the public through the
National Technical Information Service

Springfield, Virginia 22161

19. Security Classit (ofthis repor)
Unclassified

20, Security Cassi. (of his page)
Unclassified

21. No.of Pages
22

22. Price

Form DOT F 1700.7 (8-72)

Reproduction of completed page authorized



NOTICE

This document is disseminated under the sponsorship of
the U.S. Department of Transportation in the interest of
information exchange. The United States Government
assumes no liability for the contents or use thereof.


rapid decrease in skin temperature upon cold water
immersion (see Fig. 3). However, this feature is tran-
sient, as the MR falls back to much lower levels over
the next few min. At 3-5 min after immersion, the MR
begins to rise again and reaches near maximum values
at 10 min for the 0°C water immersion. In contrast, for
the 10°C immersion, the MR plateaus at an interme-
diate value (3 times basal) until ~30 min and then rises
to near maximum values by 45 min. The model-
predicted curves generally mimic the shape of the data;
however, the very rapid fall in MR for the 0°C data
(squares) after the initial peak occurs a few minutes
later in time for the model predictions (solid line) and
the plateau in the 10°C data (circles) is only roughly
approximated by the model (dashed line). In our
attempts to predict these experimental data and the
data for higher temperatures presented below, it was
clear that inconsistencies in the data must exist;
features existed in one data set not present in others.
Therefore, model predictions did not exactly dupli-
cate any one set, but the overall predictions were good.

To produce the fits shown in Fig. 1, controller
parameter values had to be determined. These values
are shown in Table 3. The value of the A,, parameter,
coupled with the rate of decrease of skin temperature,
determined the initial MR peak. However, for the 0°C
data, the peak was further limited by the value for
Sima: Figure 2 shows the three components of the
metabolic response to the 0°C immersion. As seen, the
S, component rises rapidly to a maximum determined
by Suge and the limit is sustained for another min, as
shown by the arrows. Then the contribution of this
component decreases rapidly, and by 10 min it no

longer has a significant role. The magnitude of S, is
closely coupled to the rate of decrease in skin tempera-
ture as seen in Figure 3. The time-lag term suggested
by Wissler (23) was not incorporated in this response
because it would have further delayed the reduction of
the MR after the initial peak. The very close compari-
son between experimental skin temperature data and
model predictions was produced by increasing by a
factor of 14 each of the skin-air heat transfer coeffi-
cients upon water immersion. As seen in Figure 3, the
first data point for the 0°C immersion case was 5 min
after immersion. Therefore, it is possible that the
experimental skin cooling rate before 5 min approached
steady state faster than the simulation result. If so, this
factor could account for the apparent delay in the
predicted MR response in Figure 1.

The A., parameter partially determines the steady-
state MR during the immersion, but is also a factor in
the transient changes. In Figure 1, this parameter was
partially responsible for the steep rise in MR predicted
by the model at 5 - 10 min, but thereafter the limits
on S, and S, had more important effects. At higher
water temperatures, these limits did not come into
play; therefore, the A,, value was determined primarily
to match near steady-state MR data during immersion
at these higher water temperatures (see Figure 5). The
variable limit on S, was determined to modulate the
rapid rise in MR after the initial peak, especially for the
10°C data. As seen by the arrows in Figure 2, S, is
limited for all times >8 min after immersion for the
0°C data and it was limited for all times >12 min for
the 10°C data (not shown).

TABLE 3
Shivering-controller parameter values
PARAMETER VALUE UNITS
Aa 0.62 Kealhr'(m’)"
Ag 5.67 Kealhr'(m’)"
As 2.74 KeathrTM(m’)"
Ks 6.87 hr?
Sima Kealhr"(m?)"
Somax Variable (25.8 - 124)" KealhrTM(m’)"
Ssmax 82.5 Kealhr'(m’)
Snax Keal hrm’)

‘This limit varied exponentially with time with a time constant of 0.8 hrs.


(17) data also look different because they reach values
of near steady-state by the first sample, in contrast to
the responses shown in Figure 1. The model predic-
tions are quite close to the experimental data after >20
min of immersion, but they do not show the sustained
high values of MR shown early in the experimental
data. These differences in MR patterns for the differ-
ent data sets make it very difficult to accurately predict
the data over the whole time range with a single set of
constant controller parameters.

Rectal temperature changes measured by Tikuisis
etal. (17) are shown in Figure 6. The 28°C immersion
data (solid circles) are predicted quite well by the
model, but the model grossly overestimates the de-
crease in rectal temperature for the 20°C immersion
case. It appears that the experimental data for both
temperatures are very close, even though the MR
patterns shown in Figure 5 are distinct. At present, we

can not reconcile this inconsistency; however, it un-
derscores the necessity of comparing model predic-
tions with a number of experimental data sets.

Exposure to cooled air.

To see how well the model predicts thermal behav-
ior in response to a different stress, a comparison was
made to the data of Raven and Horvath (14) for
exposure to 4.7°C air as presented by Gordon et al. (4).
This data set includes both MR data, as well as
extensive skin temperature data, which provide a
comprehensive test of the model. Figure 7 shows the
MR experimental data (solid circles) and the model
prediction (solid line). It is clear that the prediction is
generally acceptable, considering no controller param-
eter adjustments were made. Skin temperature data
are shown in Figures 8 and 9. As shown, our model
underestimates the arm-skin data significantly, whereas

3.0

2.0

1.5

METABOLIC RATE ( x Basal)

ate I

e

Figure 5. Change in metabolic rate relative to basal level after
immersion in cool water. The filled squares and circles are
experimental data from Tikuisis et al. (17) at 20 and 28°C,
respectively, whereas the solid and dashed lines represent the

corresponding model predictions

10