Vol. 90, Issue 5, 1943-1954, May 2001
Individualized model of human thermoregulation for the
simulation of heat stress response
George
Havenith1,2
1 TNO Human Factors, Soesterberg 3769ZG, The Netherlands;
and 2 Human Thermal Environments Laboratory, Loughborough
University, Loughborough LE11 3TU, United Kingdom
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ABSTRACT |
A population-based dynamic model
of human thermoregulation was expanded with control equations
incorporating the individual person's characteristics (body surface
area, mass, fat%, maximal O2 uptake, acclimation). These
affect both the passive (heat capacity, insulation) and active systems
(sweating and skin blood flow function). Model parameters were
estimated from literature data. Other data, collected for the study of
individual differences {working at relative or absolute workloads in
hot-dry [45°C, 20% relative humidity (rh)], warm-humid [35°C,
80% rh], and cool [21°C, 50% rh] environments}, were used for
validation. The individualized model provides an improved prediction
[mean core temperature error, 
0.21 
0.07°C (P < 0.001); mean squared error, 0.40 0.16°C, (P < 0.001)]. The magnitude of improvement varies substantially with the
climate and work type. Relative to an empirical multiple-regression model derived from these specific data sets, the analytical simulation model has between 54 and 89% of its predictive power, except for the
cool climate, in which this ratio is zero. In conclusion, individualization of the model allows improved prediction of heat strain, although a substantial error remains.
heat strain; body temperature; exercise; body fat; fitness
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INTRODUCTION |
NUMERICAL
MODELS of human responses to heat and cold exposure are widely
used to predict the risk of exposures or to evaluate preventive
measures (changes to the climate, protective clothing). Some of these
models are empirical (1, 6), others are restricted to heat
balance calculations (22) or include a thermoregulatory system with sweating and blood flow regulation (4, 41,
45), and some include detailed physics of clothing (27,
44). The validity of the predictions by these models is
dependent on the combination of the climate, clothing, and workload for
which they were designed. Most calculate the body core temperature
(Tco) for the given conditions and exposure time and use
this as an indicator for the risk of the exposure. All models are
population based. Hence, they calculate the predicted average response
of the population. In the actual use of these models, an important problem became apparent; e.g., when actual work places were evaluated, it was shown that, according to the heat stress assessment model ISO
7933, many conditions in the mining industry were well above the
model's safety limits (25, 24). However, at these
workplaces few problems were encountered. One of the possible
explanations is that workers at these locations are fitter than average
and also acclimated, resulting in a lower strain (i.e.,
Tco) for the same climatic stress compared to the average
population. For a proper assessment of the risks in such a case, an
individualized model would be needed. Most models do not have an option
to individualize the inputs (5, 22, 27), and in those that
have, the possibilities are limited or have received limited validation
(41).
The intention of the present paper is to review individual
aspects of thermoregulatory response, to incorporate these in an analytical simulation model, and to determine whether this actually improves the prediction of heat stress responses in various conditions. These conditions were chosen to represent the typical experimental paradigms used in thermal physiology, both for climates (cool, hot-dry,
warm-humid), which challenge different parts of the thermoregulatory system, and for work (heat production) conditions [workloads relative to maximal O2 consumption
(
O2 max) vs. fixed loads]. Model
parameters will be estimated based on data from the literature. For
validation, data sets not used for the derivation of model parameters
will be used.
The value of this model development should be twofold: it allows for a
test of the theories developed over the years regarding relevance of
individual characteristics and, if successful, should provide an
improved prediction tool.
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SELECTION OF A MODEL |
It was decided to select an existing analytical model as the
starting point for this study. Because the properties of the model
itself (number of compartments, solution method) were not the focus of
study, but rather the possibility to individualize it, and because the
study was limited to heat stress, the choice was made for a readily
available two-node model of temperature regulation (5)
that had been expanded with a detailed clothing section
(27). However, the principles discussed in this paper can
be applied to other, more complex, models as well, and the observed
effects should be similar.
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THE ORIGINAL MODEL |
The model used as a starting point was described by Lotens
(27). It comprises a physiological part based on the Gagge
(for detailed description see Ref. 5)
two-node1 model and a
physical model describing the heat transfer characteristics of clothing
(27). The physiological model contains a number of control
functions for physiological processes as well as the heat transfer
properties of the human body. The principle is represented in
Fig. 1. Core, skin, and mean body
temperatures are used as input for several setpoint-defined feedback
loops controlling effector responses (skin vasoconstriction/dilation,
sweat production, shivering). The effector responses together with
metabolic heat production (basal + work) result in a certain heat
loss or gain, which then affects the "passive" system (the body),
resulting in a new body temperature (i.e., the feedback). The relation
between effectors and resulting body temperature is affected by
environmental parameters (heat transfer properties) and heat production
levels (activity). The passive system itself is defined in terms of
heat capacity, mass, and surface area, which are constants in the
original model (27).
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Fig. 1.
Schematic representation of the physiological
control system in the original model, the inputs (climate, clothing,
and activity), and heat exchanges between body core and environment.
The countercurrent heat exchange was not present in the original Gagge
model but was introduced by Lotens (27). Ta,
temperature; Pa, humidity or vapor pressure; rad,
additional radiation between environment and skin; wind, wind speed;
Tsk, skin temperature; Tbody; body temperature;
Tcore, core temperature; Metab, metabolism; Hcap, heat
capacity; sk, skin; BF, blood flow; SKBF, skin blood flow; Ref,
reference temperature (setpoint); shiver, shivering metabolic rate;
RESP, respiratory heat loss; Dry, dry (convective + radiative)
heat loss; EVAP, evaporative heat loss;  , relative size of skin
compartment.
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In performing simulations, the original model expects as inputs a time
sequence of the climatic parameters (temperature, humidity or vapor
pressure, wind speed, and additional radiation between environment and
skin, e.g., fire or sun), the clothing parameters (heat and vapor
resistance, ventilation, and radiation properties), and the person's
activity level (expressed as the external workload and the metabolic
rate, excluding the additional effect due to shivering, which is
generated by the model itself). The main model output is the
resultant body temperature (Tco and skin temperature). Any
other variables (skin blood flow, sweat rate, etc.) can also be
requested as output. The standard iteration interval used is 1 min.
Considering the above-mentioned input parameters, it is obvious that
the model does not discriminate between different individuals when
performing a simulation. It will produce the same output, based on
parameter estimations on a population level, whether the subject is
small or big, fit or unfit, acclimated or not. Individual differences
may affect the control system as well as the passive system. Thus, to
improve the model's performance for individuals, changes and additions
to the model were made.
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THE NEW MODEL |
General Description
Starting with the inventory of interindividual differences in heat
stress response by Havenith (9) and a survey of more recent literature on this subject, the model makes several additions and changes to the governing equations of both the passive (mass, heat
capacity, etc.) and active (effector responses as sweating) components
to "individualize" its response. The new model is
schematically represented in Fig. 2.
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Fig. 2.
Schematic representation of the physiological control
system in the new model, the inputs [climate, clothing, activity,
mass, fat content, acclimation (Acclim), maximal O2
consumption (O2 max), and body
surface area (AD)] and the heat exchanges
between body core and environment.
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The main change, compared with the original model, is the increased
number of input parameters. Apart from the input of climate, clothing,
and activity, the following variables (fixed or absent in the old
model) were added: body mass (m), body fat layer thickness, body
surface area (AD),
O2 max, and acclimation state.
These can either be entered directly, or the model will help to deduce
them from other, often more readily available parameters (AD from mass and height; fat layer thickness
from fat percentage, gender, and age; acclimation state from number of
acclimation days).
Apart from adding more input parameters and introducing their effects
in the governing equations of the model, some changes to the model's
structure were also made. These concern changes in the calculation of
the (variable) size of the core and skin compartments, and elimination
of mean body temperature as separate parameter from the control
functions. These changes are discussed elsewhere (10).
The changes related to the individualization, or the reason for not
changing an item, will be discussed in detail in the following paragraphs.
Anthropometric Characteristics and Adiposity
The original model mimics a standard man (1.83 m, 75 kg, 15%
fat). To enable the user to adjust the simulation to individual anthropometrics, an input option for the values for mass, height, and
adiposity of the subject was added. The effects of these variables among subjects on body surface area, body heat capacity, and
core-to-skin heat conductance were incorporated in the manner explained below.
Body surface area.
With increasing AD, the area for sweat
production will increase. For this reason, the amount of sweat produced
by the body is made linearly dependent on AD by
using the standard subject (75 kg, 1.83 m) with an
AD of 1.97 m2 as a reference. The
same approach has been chosen for skin blood flow (more skin area = more flow) and for maximal sweat production and maximal skin blood
flow. The proposed equations are
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(1)
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(2)
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For skin blood flow and maximal skin blood flow, identical
equations apply.
Body heat capacity.
Body heat capacity, relevant for determination of the magnitude of the
body temperature change at a certain heat storage rate, is determined
by body mass and the specific heat of body tissue. The specific heat of
body fat amounts to 2.51 J/g, whereas that of the other tissues (skin,
skeleton, muscle, etc., combined) is on average 3.65 J/g
(41). For the calculation of body temperature changes, the
following equation for the specific heat of body tissue
(cb) is used
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(3)
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Because the distribution of fat over skin and core compartment
shows a strong variation among subjects (for which no predictor is
available) and over thermal conditions (depending on the change in
relative size of the core vs. the skin compartment), this specific heat
value is taken as equal for both segments.
Core-to-skin heat conductance.
The resistance to heat transport from the body core to the skin is
formed by the body shell. This consists of muscle, fat, and skin. The
muscles are enclosed in the core segment once they become well perfused
as in exercise. When the shell is vasoconstricted, the heat flow from
core to skin is mainly by conductance. When blood flow through these
tissues increases, a convective component is added to the heat flow. In
the original model, core-to-skin heat conductance is independent of
adiposity and only dependent on thermally regulated skin blood flow.
This was deemed to be an oversimplification in respect to the goal of
this study. By combining data from different sources (31, 36, 37,
42, 43), a general model for tissue conductance or resistance
can be developed.
FAT LAYER.
Individuals' shell insulation shows a good correlation with the
subcutaneous fat thickness, giving an insulation of 0.0048 m2 · °C · W
1 per millimeter
of fat thickness (43) in addition to an insulation of
0.0022 m2 · °C · W1 per
millimeter of skin (31, 37, 43). Toner et al.
(42) also observed a relation between total body mass and
shell conductance, with large, heavy subjects having a lower
conductance. Their groups, though having equal fat percentages,
differed in mass and total skinfold thickness. The latter parameter,
and not the actual mass, may be the cause of the observed effect.
MUSCLE LAYER.
When vasoconstricted, the muscle layer forms a substantial part of the
core-to-skin insulation (60-80%, measured in relatively lean
subjects; Ref. 37). When a person becomes active, the
perfusion of the working muscle increases strongly, and the muscle
contribution to the shell insulation is extremely reduced. Increases in
work rates in respective experiments correlated well with reductions in
shell insulation (31, 37, 43). At high activity levels (>10 times basal metabolic rate), the shell insulation is between one-fifth and one-tenth of the maximal (0.05 m2 · °C · W1)
insulation value (37).
In the old implementation of core-to-skin resistance in the model, as
mentioned earlier, no relation with body composition was present. Also,
metabolic rate had no direct effect on core-to-skin resistance. In the
cold, however, muscle and skin blood flow are not necessarily related.
From the literature described above, a different representation can be
developed with the following characteristics: 1) Increasing
work rate and metabolic rate will increase core-to-skin conductance
through the increase in muscle blood flow. Because this blood flow is
mainly axial (extremities), there is a correlation with radial heat
flow, rather than an actual radial convective heat transport.
2) Skin blood flow in itself will affect core-to-skin
conductance through its convective heat transport, which shortcuts the
tissue conductive resistances. This was already present in the model.
3) The subcutaneous fat layer thickness represents a
constant conductive heat resistance.
These points are incorporated in the new representation of core-to-skin
conductance in the model using the data from the given literature, with
an emphasis on the paper by Rennie (37). The essentials of
the new description are
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(4)
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with
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(5)
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Because muscle blood flow as such is not defined in the model but
evidently is related to metabolic rate, this factor can be represented
as a function of metabolic rate. Skin blood flow is already a
parameter in the model, incorporated as a function of body temperature.
The other parameters were deduced from the data in the mentioned papers
(31, 37, 43), with the assumption that, because of the
experimentation in water at critical water temperature, the tissue
insulation was maximal and skin blood flow, even during exercise, was
minimal. The equations for the three components of core-to-skin
resistance put into the model then read
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(6)
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where 
is countercurrent heat exchange efficiency,
cblood is blood heat capacity
(J · l1 · °C), and SKBF is skin blood
flow (l · m2 · s1).
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(7)
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with 0.05 as maximal muscle insulation and the denominator
relating muscle blood flow to energy consumption.
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(8)
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The thickness of skin and fat is readily available to model users
when they apply the common method of measuring skinfold thickness
(preferably an average of >5 sites) for adiposity assessment
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(9)
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If the skinfold thickness is not available, but instead only the
body fat percentage is known, the mean skinfold thickness can be
derived by using relations between the two (23). For the
model, using gender, age, and body fat percentage as input, the sum of
seven skinfolds (SF) was derived with these equations, and from this SF
the average superficial fat + skin layer thickness was estimated
(10).
Gender and Age
The gender and the age of the subjects will not be introduced in
the model as factors directly affecting thermoregulation. Enough
evidence is present in literature (for a discussion, see Refs.
9, 15, and 12) showing that the main
influence of age and gender in exercise heat exposure really acts
through concomitant differences in aerobic power, fat content, mass,
and AD. Optionally, the user may be given the
choice to select gender and age for an individual subject, but in the
model this would be translated in a change in aerobic power, fat
content, mass, etc. based on epidemiological data of differences in
these parameters between genders and ages.
Sweating control.
Individual differences in sweat production can be quite large but
are reduced when heat stress increases (20). For the
modeling of individual differences in sweat output, major parameters
are the training level of the subject (18, 32) as well as
the level of acclimation (2, 26, 28). Although most
textbooks follow the relations between training, acclimation, and sweat rate as presented by Nadel et al. (32), it was decided to
reevaluate the literature on this point because the data of Nadel et
al. were not as conclusive as suggested by those citing them. The "typical" graphs presented always are from single subjects, and responses from different individuals within a group were often inconsistent. Also, exposures were very short, so a possible time constant of the system would have a strong impact on the observed relation (9). An overview of those references from
which quantitative data could be obtained is presented in Table
1.
Training vs. acclimation.
Several studies have separated the actual training effect from that of
heat acclimation alone or the combination of heat and training.
Comparison of quantitative effects is difficult, because the size of
effects is strongly related to the training loads used (34,
40). Furthermore, relative loads decrease in the process of
training and need adjustment for the proper effects to be present. For
the interpretation of data for the "maximal sweat rate," a problem
is that usually heat stress tests before and after the treatment (i.e.,
acclimation) were identical, and thus the treatment may have resulted
in a reduced strain in the second test. Thus, although equal or even
lower sweat rates may be observed after treatment, actual maximal sweat
capacity may have increased.
SWEAT THRESHOLD.
Considering the results summarized in Table 1, it seems that heat,
exercise, and the combination of heat and exercise all have an effect
on the threshold for sweat appearance at the skin surface. Threshold
shifts due to exercise training alone (changes in
O2 max of 12-17%) range between
0.1 and 0.4°C, but, considering the numbers of subjects used in
different studies, a shift of 0.1°C seems the best consensus. Heat
acclimation after exercise training (32, 38) produces an
additional threshold shift of 0.12-0.2°C. The total threshold
reduction of heat + training amounts to 0.22-0.5°C.
Threshold shifts due to heat acclimation alone are only available from
Henane and Bittel (17) and amount 0.27°C. Low exercise
during heat acclimation results in a shift of ~0.25-0.5°C
(8, 14), which is not substantially less then heat + high exercise. In general, the main shift in threshold seems to be
caused by the heat exposure.
GAIN.
With respect to the change in gain of the sweat rate-Tco
relation, observations (Table 1) range from 36 to 67% increase for exercise training, from 0 to 14% for a subsequent heat with exercise regime, and from 54 to 67% for the total of heat + exercise
training acclimation. Heat alone (17) results in increased
gain in part of the subjects, but an average number could not be
obtained from the data. Heat + low exercise (8, 14)
results in 0-47% gain increase. Thus training seems the major
factor in the gain increase, but heat by itself also has an effect.
For modeling purposes, training and acclimation need an operational
definition, which will be considered below.
ACCLIMATION.
No quantitative data are available on differences of humid vs. dry heat
acclimation on thresholds and gains of the sweat system nor on the
effects of different stress levels (e.g., 30°C and 40°C wet bulb
globe temperature). The higher the acclimation load, the higher
the expected change in thermoregulatory stability is expected to be. In
absence of such data, it was chosen to operationalize acclimation in
the model as a simple parameter: the number of acclimation days
[exposures to a stressful climate (wet bulb globe temperature > 30°C), which increased body core temperature substantially]. The
equation for this relation (Eq. 10) was adapted from Givoni and Goldman (7) and Neale et al. (33).
TRAINING.
For a training effect on the regulation characteristics of sweating
(and skin blood flow) to be present, an actual increase in
O2 max has to be observed. Thus the
absolute value of O2 max by itself (a
sum of genetic and training influences) does not have to be a valid
parameter for the "acclimation-like" effects of exercise training.
However, on a population basis, a strong correlation of
O2 max with heat tolerance has been
observed (34, 35), and it seems fair to use
O2 max (expressed in
ml · kg1 · min1 for
separation from the mass effect) as an indicator for training- and
aerobic power-induced effects on the sweat rate-Tco relation.
The aerobic power level of the subjects used in the training
experiments of Table 1 ranged between 38.1 and 42.7 ml · kg1 · min1 (below
average to average; Ref. 29) before training. The level increased after training to average or above average. Over all experiments, the starting aerobic power level of all subjects ranged
from below average to good. When considering the studied effects over a
larger population, one may expect a wider distribution in aerobic power
levels, and thus the differences in associated thermoregulatory
responses are likely to be larger than observed here. Therefore, the
model will use this range as a linear scaling factor for changes
outside this range of O2 max values. The practical implementation of the effects of aerobic power and heat
acclimation on the model's sweat control function is illustrated in
Fig. 3A. The
O2 max range used for having an effect on the sweat rate-Tco relation is arbitrarily chosen to be
20-60 ml · kg1 · min1.
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Fig. 3.
Graphic representation of the influence of aerobic power
and acclimation on the control function for sweating (A) and
skin blood flow (B), assuming a constant skin temperature.
For clarity of the figure, unfit acclimated and normal acclimated
curves are omitted.
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For the threshold shift related to
O2 max, a number of 0.1°C was derived
from Table 1 for a 10 ml · kg1 · min1 range. For
the full range (40 ml · kg1 · min1), this is
extended to 0.4°C. For the gain change, the increase seen in Table 1
of 36-67% for the 10 ml · kg1 · min1 range was
extended to 200% for the full range (double from unfit to fit). Taking
the aerobic power average of 40 ml · kg1 · min1 as a
reference (18- to 45-yr average; Ref. 29), this leads to
the following training and acclimation based adjustments in the
governing equations, which modify threshold and gain
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(10)
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(11)
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(12)
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(13)
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For maximal sweat rate (MSR), a difference of 100% between unfit,
unacclimated, and fit, acclimated was arbitrarily chosen (doubling from
unfit, unacclimated to fit acclimated), mainly on the basis of data
from methacholine injection studies (21) and studies
comparing medium-fit, unacclimated subjects with fit, acclimated
subjects (Ref. 47; Table 1)
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(14)
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Skin Blood Flow
Regulation of skin blood flow was studied by using
data from plethysmography and core-to-skin conductivity. Extremity
blood flow is regarded as indicative and representative for total body skin blood flow and provides a more direct measure than core-to-skin conductivity does.
Data on the effect of training and acclimation on skin blood flow are
limited and often conflicting. Acclimation results in a reduced core
temperature threshold for forearm, hand, chest, and ear vasodilation
(8, 38). Also maximal conductance measured at the chest
increases (8). Besides increased vasodilation, venoconstrictor tone also increases in the first days of acclimation. Comparisons before and after acclimation do not show changes in skin
blood flow, however. This may be due to the same requirement of heat
transfer from core to skin, although the actual core and skin
temperatures (strain levels) are lower. Also, venous tone is strongly
affected by nonthermal influences.
Wyndham (46) studied the effect of acclimation (with
exercise) during extreme heat exposure. With this maximal stimulus, forearm blood flow increased from 14 to 26 ml · 100 ml1 · min1. Roberts et al.
(38) provided quantitative data on threshold and gain of
the forearm blood flow-Tco relation. They observed a
reduction in threshold for vasodilation of 0.2°C by exercise training
(O2 max: 42.7 47.7 ml · kg1 · min1) and
another reduction of 0.26°C by successive exercise + heat acclimation. The change in gain was less consistent. Exercise training
resulted in an average gain increase of 1.3 ml · 100 ml1 · min1 · °C1
and subsequent acclimation by heat and exercise in a reduction with 0.8 ml · 100 ml1 · min1 · °C1.
However, the validity of these gain changes for a generalized model is
questionable because different subjects showed very different reactions.
The maximal value of skin blood flow in relation to aerobic power has
received little attention in the literature. Because competition exists
during heat stress between blood flow for supply of nutrients and
oxygen to muscles and skin blood flow for core-to-skin heat transport,
it is likely that a high maximal cardiac output is a good indicator for
the ability to produce and maintain a high skin blood flow. Maximal
cardiac output is strongly related to
O2 max (3). Thus it seems
reasonable to relate maximal skin blood flow in the model to aerobic
power. Acclimation will have an effect on maximal skin blood flow
because of its stabilizing effect on circulation. However, the size of
this effect is smaller than that of aerobic power.
In absolute terms, maximal skin blood flows of ±240
l · m2 · h1 have been
observed (39), but this was for passive subjects, with
values for exercising subjects being much lower because of competition
for blood flow by the muscle. For forearm blood flows, maxima above 30 ml · 100 ml1 · min1 have
been observed in exercising supine subjects. For seated or upright
subjects, the maxima went down to below 20 ml · 100 ml1 · min1 (30). In
the original model, the basal skin blood flow rate is 6.3 l · m2 · h1 with a maximum
of 90 l · m2 · h1, the
latter seeming quite low. Skin blood flows measured with plethysmographic techniques are ~1 ml · 100 ml1 · min1 at rest and on average 15 ml · 100 ml1 · min1 at
maximum during work in the heat. These are similar ratios as in
the model. The maximal skin blood flow between subjects of different
aerobic power levels usually ranges between 10 and 20 ml · 100 ml1 · min1 (13). Thus,
translated to model units, the maximum, assuming working subjects,
should range from 60 to 120 l · m2 · h1 for different
aerobic power levels, with a mean of 90 l · m2 · h1 at an average
aerobic power.
For the model, equations graphically represented in Fig. 3B
were used. For the threshold shift, considering the limited amount of
data, an analogy with the threshold shift due to training for sweating
was chosen, resulting in a relation as described in Eq. 12.
For the gain, no effect was introduced because of the inconsistency in
the data. For maximal skin blood flow (MSKBF) the effects of aerobic
power and acclimation were formulated as follows
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(15)
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DISCUSSION |
When evaluating the present model, one should keep in mind that
most parameters were derived from population average-based studies.
Typically, studies used would compare subject groups differing only on
one parameter, while all other characteristics were matched, whereas
subjects in the validation data sets differed on many characteristics
at the same time. Also, for the description of some parameters (e.g.,
O2 max effect), inferences were made
for differences between subjects that were based on data observed when
that parameter changed within a subject (training). Given the available
data, there is no alternative available for this at the moment, and the
reasoning behind the inferences is presented with the actual data.
Sensitivity
Results for the improvement of the model will be presented for the
full model, including all aspects of individualization. To provide an
indication of the sensitivities of the model to the various individual
characteristics, simulations were performed using the 5th and 95th
percentile of each of the characteristics of the subject group used for
validation (Table 2) and are presented in
Table 3. Sensitivities for relative (Rel)
vs. absolute (Abs) workloads are, as is to be expected, identical for
all parameters except O2 max. The
anthropometric parameters (i.e., the passive system) have a low impact
in a cool climate (Co; 20°C, 50%). Mass and
AD have the highest impact overall, and fat has a high impact in the warm humid (WH; 35°C, 80%) climate only. Where
evaporative heat loss is not restricted [hot dry (HD); 45°C, 20%],
AD has the highest effect. Where heat loss is
restricted, mass and fat content play the bigger role, representing the
"size" of the heat sink. Increasing
O2 max has a high impact in lowering
body temperature when evaporation is not limited and work rates are
equal for all (HD/Abs) but has no effect in HD when the work rate is
relative to O2 max.
In WH, with a limited evaporation, a high
O2 max is still beneficial when work
rates are equal (WH/Abs) but has a strong detrimental effect when work
rates are relative (WH/Rel). In that case, because of the limited
cooling power in that climate, the higher absolute workload is not
compensated by the better heat loss capacity. Because of its
effect on sweat production, acclimation has the highest impact in HD
and a lower impact in WH, again related to sweat evaporation capacity
of the climate. All these principles, including the reversal of the
O2 max effect depending on the
condition, have been observed in the real data set as well
(11), except for the effect of
O2 max in the Co climate, which was not
significant in the real data. This may explain the low predictive power
of the model for that condition.
Validation Methods
With all the listed changes incorporated in the model, the
question needs to be answered whether the changes actually lead to an
improvement of the prediction results on an individual basis. For this
purpose, both the original and new model's predictions for individual
heat stress responses were evaluated with the use of data sets from our
laboratory. These data sets had not been used in the design of the new
model and are therefore independent. The experiments for these data
sets were specifically designed for the study of individual
characteristics and their interactions with climate and work type.
Subject groups were selected to show a wide variation in individual
characteristics (contrary to most experiments, in which subjects are
matched for all but one characteristic), and typical paradigms for the
study of thermal responses were used for both climate (Co, WH, HD;
stressing different parts of the thermoregulatory system) and work type
(Rel, Abs; Refs. 11-13, 15). An overview
of the subjects' characteristics in these data sets is presented in
Table 2.
The validation was performed by using data for body core (rectal)
temperature. The original model, without individualization, produced a
single mean response for all subjects per condition. For the new model,
for each subject and condition, a separate simulation run with the
actual data for climate, external work rate,
O2 max, body mass, height, body fat
content, and acclimation status was performed. Acclimation was set to
zero for all subjects and was thus not a part of this
validation. The approach used for heat acclimation in the
current model has been evaluated before by Neale et al.
(33) with good results, and repetition was not deemed necessary.
The validation of the new model with the data sets mentioned resulted
in 181 (3 × 24 + 80 + 29; see Table 2) simulation runs. Simulations followed the same pattern as the actual experiments, starting with a 30-min rest period and then moving on to 60 min of
exercise (Table 2). The model's performance will be discussed for the
new vs. original model, for the new model on its own (the individualization), and for the new model vs. a regression model that
was based on the data sets used for the evaluation (11). It was chosen to evaluate how the individualization resulted in discrimination between subjects' heat tolerance as defined by the
response measured at the end of the exposures, rather than analyzing
the dynamics of the response. The dynamics are considered to be more
related to the general model used than to the individualization, and
even when the subjects would not have achieved a steady state after the
90-min exposure, their ranking in terms of heat (in)tolerance is not
expected to change thereafter. It is this ranking that is considered
most relevant to test the model's individualization.
Parameters used for the quantitative validation are 1) the
mean of the difference (error) between computed and real output values
at the end of the exposure and the mean squared error; both
compared for old vs. new model (paired t-test and Wilcoxon signed rank test for related samples); 2) the correlation
(both Pearson and Spearman rank order) between the computed and the real output values; and 3) the differences in explained
variance (r2) between simulation and regression model.
Validation Results
New vs. old model.
In Table 4, the performance of the
original model (27) vs. that of the new model is
illustrated on the basis of the mean values for the prediction error in
Tco of the models (computed minus measured value) for each
condition. These numbers in Table 4 clearly show a reduction in the
mean error in Tco. Thus the average systematic
under- or overestimation (mean error) by the new model, including all
changes, is smaller. These improvements are statistically highly
significant (P < 0.001) for all data lumped, as well
as for three out of five of the different experiments. For the other
two conditions, WH/Rel and HD/Abs, no significant change was observed.
For the latter condition, the systematic error was negligible for both
old and new model. From this it can be concluded that the performance
of the new model has improved compared with the original model. Quite a
substantial error in individual predictions remains, however, as can be
seen in Table 4 and in the graphic presentation of the old and
new model's results in Fig. 4.
Individualization (new model).
Although the performance of the new model represented by the mean error
has improved compared with the old one, this improvement is not
necessarily due to individualization. The mean error may have improved
because of a lower systematic error alone, without actually improving
the prediction of an individual's deviation from the group mean. The
latter can be studied in two ways: first by looking at the correlation
between computed and measured points (Fig. 4) and second by looking at
the mean squared error of the prediction, which represents the quality
of individual predictions. The latter (Table 4) has been significantly
improved overall (P < 0.001) and in four out of five
of the conditions used (P < 0.05).
The correlations between computed and real data values are presented in
Table 4 (for the old model, when analyzed per condition, these are 0, because of the lack of variance within each condition). Correlations
were calculated as Pearson correlation coefficients for continuous data
and secondly by using the presumption that the performance of the model
can be judged on whether it ranks the individuals correctly for their
heat tolerance using a Spearman rank-order correlation test. Table 4
shows that for both criteria the individual predictive value for the
model varies strongly between conditions. Both correlations are highly
significant overall (P < 0.001) and also in three out
of five of the conditions simulated. Overall correlation has improved
drastically compared with the old model. Differences between Pearson
and Spearman correlation coefficients are small, indicating that the
rank orders closely follow the continuous data.
New model vs. empirical regression model.
In the papers in which the used data were described
(11-13, 15), the data for Tco were
analyzed for the influence of individual characteristics on the heat
stress response, separately for each condition, by multiple linear
regression analysis (for the actual constants in the equations, please
refer to Refs. 11-13, 15)
|
(16)
|
Because all other influences (climate, work) are constant within
each of the tested conditions, this regression model analyzes purely
the contribution of individual characteristics to the variation in
Tco response; i.e., all predictive power in the regression models is to be attributed to individual characteristics. It is therefore interesting to compare the analytical computer model's predictive capacity for these data with the descriptive power of the
multiple-regression models. This comparison is presented in Table
5. Column three gives the correlation
between predicted values and real values when the regression models
(Eq. 16) are used to predict core temperatures.
Because this empirical regression model was derived from these specific
data sets and from the characteristics of actual participating
subjects, the explained variance in these regression models may be
considered as the maximum achievable explained variance. In column 4 of
Table 5, the r values are given for the prediction of the
analytical computer model, which was developed independently of the
data sets. Comparison of the two model types (r2
new model/r2 regression) shows that, except
for the cool condition, the computer model predicts quite well the
variance in the data for Tco that could be attributed to
individual characteristics (last column in Table 5).
View this table:
[in this window]
[in a new window]
|
Table 5.
Correlation coefficients of the predicted Tco of the
computer simulation model and the real Tco data, and
correlation of the predicted Tco values by the empirical
multiple regression model and the real data
|
|
Overall performance.
The pattern that is visible in both Table 4 and Table 5 is that the
individualized model provides significant improvement in body core
temperature prediction. For the individual person, the predictions are
improved over the old model in all conditions except for the Co and
HD/Rel conditions (based on the r values). In
general, one may expect this for all those Rel conditions in which the
climate does not limit evaporative cooling. Here, differences in heat
strain between individuals are drastically reduced when relative
workloads (same %O2 max), compared
with absolute workloads, are used (15). The smaller the
expected differences in actual data, the lower the correlation one can
expect to obtain, given the low signal-to-noise ratio in this case. For
the WH/Rel condition, however, a good correlation between predicted and
observed values is found. In this situation, in which evaporative heat loss is limited, the passive system of thermoregulation (mass, heat
capacity, tissue heat resistances) is more important, and this seems to
be well represented by the current model. An additional factor in the
deficient prediction in the cool climate may be a too-small
effect of body fat content on insulation in the model, given that in
the multiple-regression model it was adiposity that had the strongest
influence in this condition (11). The insulative effect of adipose tissue is in the new model strongly dependent on skin
blood flow. In the model, for most subjects, this increases above 30 l · m2 · h1 for the cool
condition, which is about one-third of the maximum skin blood flow. In
the actual experimental data, the forearm blood flow is for most
subjects below 3 ml · 100 ml1 · min1, which is about
one-tenth of the maximum. Thus the insulative effect in the cool
condition may well be underestimated because of a too-high skin blood
flow, which may explain the poor predictive effect for that situation.
Apart from the possible causes mentioned above, it should be noticed
that a large amount of "noise" is always present when comparing
heat stress responses. In the present case, any test-retest difference
for an individual would have added to the overall reduction in
explained variance. Jette and coworkers (24) have given a detailed report on the day-to-day variation in a person's response in
terms of body core temperature. They found this to be so high that they
questioned the use of body temperature responses as indicator of, e.g.,
clothing insulation differences. Hence, given this noise, the observed
explained variances in the present study (except for the Co and HD/Rel
conditions) can be considered to be substantial.
In conclusion, the changes and additions to the model have
significantly improved the prediction of individual heat strain, be it
that the size of the improvement varies with the climate and work type.
However, a substantial part of the differences in individual responses
remains unexplained, suggesting that the current knowledge of causes
for individual differences is far from complete.
| |
ACKNOWLEDGEMENTS |
Dr. Wouter Lotens and Prof. Rob Binkhorst are thanked for valuable
comments on the manuscript.
| |
FOOTNOTES |
This project was funded by TNO-Human Factors, and the TNO-Division of
Defense Research, Soesterberg, The Netherlands.
Address for reprint requests and other correspondence: G. Havenith, Dept. Human Sciences, Human Thermal Environments
Laboratory, Loughborough Univ., Loughborough LE11 3TU, UK (E-mail:
g.havenith{at}lboro.ac.uk).
1
Two-node model: The nodes represent the body
core and the body shell, the core being the compartment with the
regulated and defended temperature, the shell being the buffer between
core and environment, whose temperature is determined by the heat
exchanges with the core and with the environment. Lotens
(27) converted this into a five-node model by dividing the
skin node into a clothed vs. an unclothed part and these into a
radiated area and a nonradiated area. Heat transfer may be different in
these areas, but control characteristics are identical, and in the
current study the distinction is irrelevant.
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 28 June 2000; accepted in final form 21 December 2000.
| |
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ABSTRACT
INTRODUCTION
