An experimental validation of mathematical simulation of human thermoregulation

Comput. Blol. Med.

Pergamon

Press 1971. Vol. 7. pp. 71-82.

Prmted in Great Bntain.

AN EXPERIMENTAL VALIDATION OF MATHEMATICAL SIMULATION OF HUMAN THERMOREGULATION” S. KONZ, C. HWANG, B. DHIMAN, J. DUNCAN and A. MASUD Department of Industrial Engineering, Durland Hall, Kansas State University. Manhattan, KS 66506, U.S.A. (Received 10 November 1975;

in revised form 9 April 1976)

Abstract-An experimental validation of Stolwijk’s mathematical model of thermoregulation is presented. Although the model seems to be accepted widely, very little experimental data for validation exists in the open literature. Experimental data for transient conditions of rectal, head skin, trunk skin, arm skin, leg skin, mean skin and mean body temperature as well as cardiac output and evaporative heat loss under heat stress are presented and compared with simulation output for the model. In general, the predictions of the model are good; the difference between experimental data and the model averaged 0.2”C for mean body temperature. A version of Stolwijk’s thermoregulatory model is described briefly. The controller equations are given as well as a short discussion of the rationale for each. Tables give coefficients for the controller equations, and, for the 25 compartments, heat capacitance, thermal conductance, basal metabolic heat production, basal evaporative heat loss, and basal effective blood flow. Human model

thermoregulation Experimental Computer simulation Dynamic

verification model

Heat

stress model

Mathematical

INTRODUCTION

Over years the subject of heat stress on humans has been of great interest; Bligh [l] says over 4000 papers have been published on thermoregulation since 1940! Numerous experiments have been performed in an attempt to clarify aspects of this problem. There is no doubt that the thermoregulatory system is very complex, therefore, intuition is often not adequate as a basis for interpreting experimental data. As an alternative to using intuition, one can synthesize a mathematical model having many of the characteristics of the real system. With the help of a computer, it is anticipated that the model can serve as a useful tool for studying temperature regulation in the human. The goal is a computer program representing the model of human thermoregulation which requires input only of subject data (age, height, weight, sex, clothing), task data (walk, stand, sit, pedal, etc. as well as the taks’s metabolic rate), and environmental data (air temperature, velocity, humidity, radiation temperature). The output would be a minute-by-minute prediction of the subject’s mean body temperature, sweat rate, comfort, cardiac output, and heart rate. In addition to these “bottom line” outputs, a scientist or engineer may want intermediate output calculations such as leg skin temperature, arm skin temperature, head skin temperature, rectal temperature, etc. as these explain why the bottom lines values are what they are. The first models, such as by Richet [2], Ott [3], and Barbour [4], were descriptive of only a single component (e.g. the hypothalamus). In time, more mathematical models which described man and his environment as a system were developed in England (e.g. Burton [S]), U.S.A. (e.g. Hardy [6], and Wissler [7]), South Africa (e.g. Wyndham and Adkins [8]) and elsewhere. These models were open-loop models. For a review of these models, see Fan, Hsu, and Hwang [12]. In 1966 Stolwijk and Hardy [9] introduced a new model using feedback (i.e. a closedloop model). Perhaps even more important is that within a short time the model was written in FORTRAN for a digital computer [lo]. It is hard to overemphasize how much this has improved the development of the model since both experimenters and theoreticians can analyze the model word by word. * This study was supported by NSF Grant No. ENG-7303676.

72

S. KONZ, C. HWANG. B. DHIMAN, J. DUNCAN and A. MASUD

I I

EXERCISE

ENVIRONMENT

REFEYENCE

*

I I

I

SHIVER -

MUSCLES

S\IEAT

INTEGRATION

-I ---SWEAT

I _..._

t”nK

.._.

-

HkAT

GLANDS

I I

r\

_-_

LOSS

I

-La”’

I

BODY

HEAT CAPACITANCE

BLOOD VESSELS

VASOYOTOR

I I I I I I I

THERMAL RECEPTORS

I

’

I I I

I REGULATOR

Fig. 1. Simplified

block

;

diagram

of human

REGULATED

SYSTEM

thermoregulation.

The simplified block diagram of Stolwijk’s thermoregulatory system is shown in Fig. 1. The feedback control system is divided into a regulated system and the regulating system (regulator). The regulated system (body heat capacitance) can be subjected to a disturbance from environmental heat or cold or metabolic heat. The disturbance causes a change in the controlled variables (a body temperature or combination of temperatures). The controlled variables are measured by thermal receptors (a transducer) which generates related neural or hormonal information. This information, the feedback, is compared with reference information. The difference between the feedback and the reference, termed the error, is a measure of the effect of the disturbance on the controlled variable. The error activates a control center which provides a control action in such a way as to oppose the effect of the disturbance. In thermoregulation the control actions are means of modifying heat loss, heat production, or heat conservation by sweating, shivering or vasomotor activity. The model we evaluated in this paper is a version of Stolwijk’s model. Although Stolwijk’s model seems to be widely accepted, to our knowledge, there is no published experimental data on validation of the model yet in the open literature. In this paper, the Stolwijk model is simulated by a digital computer for a given subject in a given environment. Our computer simulation results (the prediction by the model) are compared against our experimental data on the subject in the given environment. METHOD Model

description-overview

The body is divided into 6 segments (head, trunk, arms, hands, legs and feet) each of which is subdivided into core, muscle, fat and skin for a total of 24 elements. Blood flow between the cores of the 6 segments is through a hypothetical “central blood compartment” so there are 24 + 1 = 25 elements in all. Periodically the program computes a heat balance for each of the 25 elements. The heat balance at each element is composed of heat generation (metabolism), heat input, and heat output.

An experimental

validation

of mathematical

simulation

73

Metabolism is composed of basal metabolism and activity metabolism. For the three interior layers (core, muscle and fat), heat input and output are through conduction and convection (blood flow). The outer layer (skin) has, in addition, heat exchange with the environment through evaporation, convection and radiation. As mentioned before, the key concept is the controlling system which uses temperature of each of these 25 elements as input to modify sweat rate on the skin, blood flow rate in the skin layer, and heat production rate (shivering) in the muscle layer. Model description-details

Stolwijk’s paper [lo] and Dhiman’s thesis [13] contain more detail for those who want more information than is contained in the following paragraphs. Table 1 gives the symbols used in the description of the controlled system and Table 2 gives the symbols used for the controller. Controller. In the first step for the controller, the error (or discrepancy) between temperature, T(N), and set temperature (or neutral temperature), TSET(N), is calculated for each of the 25 elements: ERROR(N) = T(N) - TSET(N) + RATE(N)*F(N). Stolwijk included the RATE(N)*F(N) term for those who feel there might be a multiplicative effect; RATE(N) is a “dynamic sensitivity factor” and F(N) is the rate of change of temperature. RATE(N) = 0 in our simulation. The second step is to check whether the sign of the error is positive or negative-that is, whether the element is warm or cold. If ERROR(N) is positive, it is redefined as WARM(N); if negative it is redefined as COLD(N).

Table

1. Symbols

used in the controlling

system Value

Symbol ERROR(N) TSET(N) RATE(N) WARM(N) COLD(N) WARMS COLDS SWEAT DILAT STRIC CHILL csw ssw PSW CDIL SDIL PDIL CCON SCON PCON CCHIL SCHIL PCHIL SKIN(I) SKINS(I) SKINV(1) SKINC(1) CHILM(1) WORKM(1) CKHLH

Total output signal from receptors in N, “C “Set point” or threshold temperature for receptors in N, “C Dynamic sensitivity of receptors in N Output from Nth receptor when it is warm Output from Nth receptor when it is cold Total integrated output from warm skin receptors Total integrated output from cold skin receptors Total efferent sweating command Total efferent vasodilation command Total efferent vasoconstriction command Total efferent shivering command Coefficient-sweating command from head core (hypothalamus) Coefficient-sweating command from skin (assume skin adds to hypothalamus) Coefficient-sweating command from skin (assume skin multiples hypothalamus) Coefficient-vasodilation command from head core (hypothalamus) Coefficient-vasodilation command from skin (assume skin adds to hypothalamus) Coefficient-vasodilation command from skin (assume skin multiples hypothalamus) Coefficient-vasoconstriction command from head core Coefficient-vasoconstriction command from skin (assume skin adds to hypothalamus) Coefficient-vasoconstriction command from skin (assume skin multiplies hypothalamus) Coefficient-shivering command from head core (hypothalamus) Coefficient-shivering command from skin (assume skin adds to hypothalamus) Coefficient-shivering command from skin (assume skin multiplies hypothalamus) Proportion of skin of each segment’s skin to total skin Proportion of sweating command to segment I Proportion of vasodilation command to segment I Proportion of vasoconstriction command to segment I Proportion of shivering command to segment I Proportion of total exercise in segment I Conversion of heat to blood flow in muscle

Table 0

3

312 33.1 0 136.0 17.0 0 10.8 10.8 0 13.0 0.4 0 Table 9 Table 9 Table 9 Table 9 Table 9 Table 9 1.0

_

S. KONZ, C. HWANG, B. DHIMAN, J. DUNCAN and A. MASUD Table Vector length

Symbol Input values C(N) TC(N)

QB(N) EB(N) BFB(N) S(1) HC(1) HR(1) H(J) V TAIR PAIR P(1) WORK INT DTR Calculated T(N) F(N) HF(N) TD(N)

2. Symbols

used in the controlled

system

Value

Definition

25 24 24 24 24 6 6 6 6

Heat capacitance of compartment N Thermal conductance between N and N+l Basal metabolic heat production in N Basal evaporative heat loss from N Basal effective blood flow to N Surface area of segment (sq m) Convective & conductive heat transfer coefficient (W/sq m-C) Radiation heat transfer coefficient (W/sq m-C) Total environmental heat transfer coefficient (W/sq m-OC) Air velocity (misec) Air temperature, dry bulb ( ‘C) Vapor pressure in environment (mm Hg) Vapor pressure table from 5 to 50°C (mm Hg) Total metabolic rate required by exercise (W) Interval between outputs (min) Integration step (h)

25 25 25 24 24 24 24 24

Temperature of N (‘C) Rate of change of temperature in N (C/h) Rate of heat flow into or from N (watts) Conductive heat transfer between N and N + 1 (W) Total metabolic heat production in N (W) Total evaporative heat loss from N (W) Total effective blood flow to N (I./h) Convective heat transfer between central blood and N (W) Relative humidity (“,) Elapsed time (h) Iteration elapsed time (h) Maximum rate of evaporation from skin (W) Saturated water vapor pressure at skin temperature (mm Hg) Cardiac output (l./min) Skin blood flow (Urnin) Heat production (metabolism + shivering) (W) Total evaporative heat loss (xE(N) + .08*WORK), (W) Mean skin temperature (‘C) Mean body temperature (“C)

Table Table Table Table Table Table Table Table Table

4 5 6 1 8 9 9 9 9

values

Q(N) E(N) BF(N) BC(N) RH TIME ITIME EMAX(1) PSKlN(1) CO SBF HP EV TS TB

6 6

The third step calculates the controller commands skin layer (SWEAT), modify skin blood flow (DILAT muscle layer (CHILL).

to the body to: sweat on the or STRIC), or to shiver in the

SWEAT = CSW*ERROR(l) + SSW*(WARMS-COLDS) + PSW*ERROR(l)* (WARMS-COLDS) DILAT = CDIL*ERROR(l) + SDIL*(WARMS-COLDS) + PDIL*WARMS(l)* WARMS STRIC = -CCON*ERROR(l) SCON*(WARMS-COLDS) + PCON* COLD( 1)*COLDS CHILL

=

-CCHIL*ERROR(l)

-

SCHIL*(WARMS-COLDS)

+

PCHIL*

ERROR(I)*(WARMS-COLDS).

Each command is the result of a signal from the hypothalamus, ERROR(l), and the skin (WARMS-COLDS). If you believe the two signals add, then set PSW, PDIL, PCON and PCHIL = 0. If you believe the two signals multiply, then set SSW, DSIL, SCON and SCHIL = 0 and CSW, CDIL, CCON, and CCHIL = 0. The fourth step is to translate the command into action. Evaporation for the core (respiratory loss) is not modified. Evaporation for the skin (the third layer), E(N+ 3), is basal (diffusion), EB(N + 3) plus sweat for cooling. UN + 3) = EB(N + 3) + SKINS(I)*2.**((T(N

+ 3) - TSET(N

+ 3))/4.)

An experimental

validation

of mathematical

75

simulation

The SKINS(I) term considers the varying amount of sweat glands on different parts of the body. The 2-raised-to-a-power term attempts to let the local skin temperature modify the “brain’s” sweat command. A final precaution is to calculate the maximum rate of evaporation possible (EMAX). EMAX is a function of environmental vapor pressure (PAIR) and the evaporative heat transfer coefficient (2.14*HC(I)). Actual sweat and thus evaporation in any skin element is limited to EMAX. EMAX(1) = (PSKIN - PAIR)*2.14*(HC(I))*S(I)) Basal skin blood flow, BFB(N+3), is modified by DILAT or STRIC. BF(N + 3) = BFB(N + 3) + SKINV(I)*DILAT/(l. + SKINC(I)*STRIC). Since some regions such as the hand and feet are more responsive than other regions such as the trunk, each of the 6 segments has its own coefficient for dilation (SKINV) and for constriction (SKINC). Maximal blood flow in the skin is limited to 7*BFB(N + 3) in our model. The third controller command, affecting only the muscle layer, is shivering (CHILL). Metabolic rate, Q(N + l), is the sum of basal metabolism, (QB(N + l)), activity metabolism, (WORK), and shivering (CHILL). Q(N+ 1) = (QB(N+ 1) + WORKM(I)*WORK

+ CHILM(I)*CHILL

Metabolic rate also affects blood flow in the muscles, BF(N + 1). BF(N+ 1) = BFB(N+ 1) + CKHLH*(Q(N+

1) - QB(N+ 1)).

CKHLH converts heat in watts to blood flow in l./hr. Maximum blood flow in the muscle is 18*BFB(N+ 1) in our model. Controlled system. Table 2 gives the symbols used for the controlled system-the body. Values of heat capacitance, thermal conductance, basal metabolic heat production, basal evaporative heat loss, and basal blood flow are given in Tables 5-9; Table 9 also gives the values of surface area and heat transfer coefficients for a 70 kg man pedalling a bicycle. These values in the tables are Stolwijk’s updated values [l l] and many values are different from those in [lo]. These tables demonstrate one of the virtues of having a mathematical model-the model forces explicit statements for the values of the coefficients. It is hoped that readers will challenge the values shown in the tables and thus aid development of a better model. Experimental

data

Konz et al. [14] conducted an experiment on dry-ice cooling; three of the control sessions did not use dry-ice cooling and are used here to check the accuracy of the computer model predictions. The experimental variables used as computer inputs are subject (21 yr, 177 cm tall, 76.5 kg male with 0.1 clo (shorts) on the torso), task (sitting at a metabolic rate of 130 W), and environmental (air temperature of 43.3”C, velocity of 0.1 m/s, 45% relative humidity, and radiation temperature of 42.8”C). The following measurements could be compared vs the computer prediction. Temperatures were measured every 10 min with YSI thermistors at head skin (1 location), trunk skin (6 locations), arm skin (2 locations), leg skin (2 locations), and rectal. From these

Table

Head Trunk Arms Hands Legs Feet Central

3. TSET(N),

set point

temperatures,

C. for the 25 elements

Segment

Core

Muscle

Fat

Skin

35.07 36.28 34.12 35.38 35.50 35.13

34.8 1 34.53 33.59 35.30 35.31 35.11

34.58 33.62 33.25 35.22 34.10 35.04

blood

36.96 36.89 35.53 35.41 35.81 35.14 36.71

S. KONZ, C. HWANG, B. DHIMAN, J. DUNCAN and A. MASUD

Table 4. C(N), heat capacitance,

W-H/C,

for the 25 elements

Segment

Core

Muscle

Fat

Skin

Head Trunk Arms Hands Legs Feet Central

0.39 18.80 3.54 0.70 10.67 0.07

0.26 4.94 0.67 0.10 1.66 0.15

0.28 1.41 0.50 0.20 1.25 0.26

blood

2.57 11.44 1.64 0.16 4.93 0.27 2.60

Table

5. TC(N),

thermal

conductance

Segment Head Trunk Arms Hands Legs Feet

Table

Table

Skin

1.61 1.59 1.40 6.40 10.50 16.30

13.25 5.53 8.90 11.20 14.40 20.60

16.10 23.08 30.50 Il.50 14.50 16.40

0.00 0.00 0.00 0.00 0.00 0.00

metabolic

14.95 52.60 0.82 0.09 2.59 0.15

0.12 5.81 1.11 0.23 3.32 0.02

0.13 2.49 0.20 0.03 0.50 0.05

0.09 0.47 0.15 0.06 0.37 0.08

0.210 0.08 1 0.132 0.010 0.020 0.000 0.1731 3.0 4.8 1.350

evaporative

heat loss from N, W

Core

Muscle

Fat

Skin

0.00 10.45 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

0.81 3.78 1.40 0.52 3.32 0.72

basal

effective blood

flow to N. 1./h

Core

Muscle

Fat

Skin

45.000 210.000 0.840 0.100 2.690 0.160

2.475 58.410 11.154 0.264 33.924 0.264

0.765 14.535 1.989 0.306 4.896 0.459

3.633 5.298 1.263 5.046 7.191 7.569

Table 9. Values Head

in N. W Skin

8. BFB(N),

Head Trunk Arms Hands Legs Feet

heat production Fat

Segment

SKINR(I) SKINS(I) SKINV(1) SKINC(1) CHILM(1) WORKM(1) S(I) HC(I) HR(I) H(I)

Fat

Muscle

Segment

Symbol

Muscle

7. EB(N), basal

Head Trunk Arms Hands Legs Feet

N + I. W/~C

Core

Segment

Table

N and

Core

6. QB(1). basal

Head Trunk Arms Hands Legs Feet

between

for various Trunk 0.420 0.48 1 0.322 0.050 0.850 0.300 0.7638 2.1 4.8 5.269

symbols Arms

0.100 0.154 0.095 0.190 0.050 0.080 0.2684 * 2.1 4.2 1.691

by element Hands 0.040 0.031 0.121 0.200 0.000 0.010 0.1002 4.0 3.6 0.761

Legs

Feet

0.200 0.218 0.230 0.200 0.070 0.600 0.6012 2. I 4.2 3.787

0.030 0.035 0.100 0.350 0.000 0.010 0.1299 4.0 4.0 I.039

An experimental

validation

of mathematical

simulation

77

we could calculate mean skin and mean body temperature. Heart rate and blood pressure were measured every 20 min. Evaporative sweat loss was measured by having the subject’s chair rest in a tub of mineral oil resting on a scale (the oil trapped sweat which dripped off rather than evaporate); weight was taken every 20min. RESULTS Figure 2 shows the rectal temperatures for the three experimental days as well as the simulation from the computer model. The skin and rectal temperature of the subject in the pretest room were averaged for the three control days; these values then were used to estimate initial temperatures of the 25 elements. As can be seen, there is a reasonably good fit between the model and the experimental data. To quantify the fit, the mean was calculated for the three experimental days at each 10 min interval. The deviation of the model value from this experimental mean was then calculated. The mean of the absolute values of the deviations, 2, was then calculated. For rectal temperature, d = O.l”C. Figure 3 shows head skin temperature for experimental vs model. The initial hump in the model ouput greatly concerned us until we saw that the experimental output had the same “hump”. For skin temperature of the head, 2 = 0.4”C.

36

,o

34-

ii! p

33.

q

JULY

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JULY

24

o

JULY

31

x

MODEL

90

lb0

32-

31 i IO

io

30

40

50

$0

TIME

Fig. 2. Rectal

temperature

from

70

tio

(MINUTES)

Ii0

IhO

0

the model deviates an average the experimental values.

of O.l”C from

0

JULY

5

A

JULY

24

o

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31

x

MODEL

90

100

the mean

of

I

IO

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30

I

1

I

40

50

60

I

I

70

MINUTE

80

I

110

120

0

Fig. 3. For head skin temperature, mean deviation of the model from the experimental is 0.4”C. The model may have insufficient sweat command on the head.

values

78

S. KONZ, C. HWANG,B. DHIMAN,J. DUNCANand A. MASUD

I

,

IO

20

30

I

*

,

*

I

40

50

60

70

80

TIME

q

JULY

A

JULY

5 24

o

JULY

31

x

MODEL

I

I

90

100

110

120

0

(MINUTES)

Fig. 4. For trunk skin, the average deviation between model and experiment is 0.6”C. The model adjustment at 30min was too large.

Figure 4 shows trunk skin temperature for experimental vs model. It seems that the model predicts temperatures consistently too low; d = 0.6”C. Figure 5 shows arm skin temperature for experimental vs model. The model predicts temperatures cu. 2°C too low for the first 30min and then gradually closes the gap to 0.6”C too low by 120 min of exposure. For the entire 120 min, d = 0.9”C. Figure 6 shows leg skin temperature for experimental vs model. The model is close to the average of the three experimental outputs; d = 0.4”C. Note that experimental data does not always replicate itself. The point to be made here is that a model differing from the data does not necessarily mean that the model is wrong-it may be that the experimental data is wrong (e.g. poor calibration on that day. placement of sensors might be different, etc.). Modelers tend to believe the experimental data is correct since they know how crude the model is; experimenters tend to believe the model is correct since they know how crude the data is. Figure 7 shows mean skin temperature for experimental vs model. After a fairly good fit during the first hour, the model seems a little low for the second hour; overall, ;i = 0.4”C. Figure 8 shows mean body temperature for experimental vs model. Skin temperature is given a weight of 0.33 and rectal temperature a weight of 0.67. Mean body temperature 2 = 0.2”C due to the 0.1 error for rectal and the 0.4 error for skin.

IO

I 20

30

I 40

50

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I 60

70

(MINUTES)

I 80

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x

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90

I 100

’ 110

I 120

e

Fig, 5. Arm skin temperature is consistently too low; the mean deviation is 0.9”C

An experimental

IO

20

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30

40

of mathematical

50

60

TIME

70

simulation

60

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0

JULY 31

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90

(MINUTES)

79

100

II0

I20

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Fig. 6. Leg skin temperature experimental data demonstrates variability of a single individual in a standard situation. Mean deviation of the model from the experimental mean was 0.4”C.

/ IO

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*

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I

20

30

40

50

60

70

80

TIME Fig. 7. Mean

(MINUTES)

0

JULY 5

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JULY 31

x

MODEL

c

90

I

100

I

110

,

120

0

skin temperature has a mean deviation of 0.4’C as the deviations body segments tend to cancel each other.

on various

36

36

35 P %

34

P

33

32

q

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Q

JULY 31

x

MODEL

31

IO

20

30

40

50

TIME Fig. 8. Mean

body

temperature

60

70

80

(MINUTES) had a deviation

90

100

of 0.2”C

110

I20

80

S. KONZ, C. HWANG, B. DHIMAN, J. DUNCAN and A. MASUD

x

so 80

MODEL

i 10

I

20

1

30

,

1

I

40

50

60

TIME

r 70

(MINUTES)

I

3

80

so

c 110

I

100

, I20

0

Fig. 9. Cardiac output estimation for the experiment was crude as it was estimated to be proportional to the product of systolic blood pressure times heart rate. Output at 0 time was defined as lo& The mean deviation was 13%.

Figure 9 compares an index of cardiac output for experimental vs model. To estimate the subject’s cardiac output, his heart rate and systolic blood pressure were multiplied together and the resulting term plotted as a percentage; that is, the value of this term at time 0 was defined as loo’%. The model’s output in liters/min was also plotted as a percentage with the value at time 0 defined as 100%. At the end of 90 minutes the model cardiac output had risen 19% while the average of the three experimental values rose 32”/,. Again, note the experimental variability. Overall 2 = 13%. Figure 10 shows EV, the evaporative heat loss predicted by the model vs required sweat loss from the heat balance equation for the experimental data &EVAPR). EV = C(E(N)) + O.O8*WORK. The O.OS*WORK adjusts for the increased respiration with activity metabolism. The fit seems reasonably good after 40 min; overall 2 = 31 W for the 5 comparisons as the deviation of 100 W at 30 min increased the average.

F

100

50

TIME Fig. 10. Evaporative The mean deviation

(MINUTES)

JULY

5

A

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24

o

JULY

31

x

MODEL

0

loss is predicted reasonably well once the model “turned the sweat on”. of 31 W is distorted by the poor prediction at one of the five comparison points-30 min.

An experimental

DISCUSSION

validation

AND

of mathematical

CONCLUDING

simulation

81

REMARKS

We [15, 161 previously modeled, simulated, and optimized a water-cooled garment in steady-state conditions as contrasted to the present modeling and simulation of a nude man in transient (dynamic) conditions. Stolwijk’s model seems to be reasonably effective in predicting temperatures, sweating and cardiac output for a sedentary semi-nude man in a heat stress environment. The validation of Ais model by experimental data from a different laboratory lends credence to the model as well as the fact that it worked for a different subject and environment than Stolwijk used. We are presently evaluating the model vs experimental data for the same subject wearing a dry ice cooling jacket and for different subjects exercising with and without dry ice jackets. We have included the detailed coefficients for the controller equations and values for heat capacitance, thermal conductance, basal metabolic heat production, basal evaporative heat loss and basal effective blood flow for others who may wish to use the model. We would like to encourage others to improve the model by modifying the controller equations and challenging the equation coefficients and table values.

REFERENCES (1973). 1. J. Bligh, Temperature Regulation in Mammals and other Vertebrates, North Holland, Amsterdam und sum Fieber, Pjugers Arch. ges. Physiol. 2. C. Richet, Die Beziehung des Gehirns zur Korperwarme 37. 624 (1885). 3 T. Ott, Heat center in the brain, J. neru. ment. Dis. 14. 152 (1887). Erwarmung und Abkuhlung der Warmezentren auf die Korper4. H. G. Barbour. Die Wirkuna unmittelbarer temperatur, Nnunyn-Schmiedeubergs Arch. exp. Path. Pharmak. 70, 1 (i912). of the theory of heat flow to the study of energy metabohsm, J. Nutrifion 5. A. C. Burton, The application 7, 497 (1934). of heat loss and heat production in physiologic temperature regulation, Harvey 6. J. D. Hardy, Control Lecture Series 49, 242 (19534). destribution in man, J. uppi. Physiol. 734-740 (1961). 7. E. H. Wissler, Steady state temperature and A. R. Atkins, An approach to the solution of the human biothermal problem 8. C. H. Wyndham with the aid of an analog computer, (paper 27), Proc. 3rd Znt. Conf: Medical Electronics. London (1960). regulation in man-a theoretical study. Pfhgers Archic. 291, 9. J. Stolwijk and J. D. Hardy, Temperature 129-162 (1966). models of thermoregulation (Ch. 48) in Physiological and Behacioral Temperuttrre 10. J. Stolwijk, Mathematical Regulation, Springfield, IL (1970). (1974). 11. J. Stolwijk. private communication 12. L. T. Fan. F. T. Hsu and C. L. Hwang, A review on mathematical models of the human thermal system, IEEE Trans. Biomed. Engng. 18, 21X-234 (1971). Simulation of a human thermoregulatory system with dry ice cooling, 1974. MS Thesis, 13. B. Dhiman. Kansas State Univ.. Manhattan, Kansas. cooling with dry ice, Am. Ind. Hygiene Assoc. 14. S. Konz, C. Hwang, R. Perkins and S. Borell, Personal J. 35, 137-147 (1974). 15. F. T. Hsu. L. T. Fan and C. L. Hwang, Simulation of a steady-state integrated human thermal system, Comput. Biol. Med. 2, 59-79 (1972). optimization of integrated human thermal system, 16 F. T. Hsu. C. L. Hwang and L. T. Fan, Steady-state Comput. Biol. Med. 3, 407425 (1973).

About the Author-STEPHAN KONZ received a B.S. in Industrial Engineering and a M.B.A. in Business Administration from the University of Michigan in 1956, a MS. in I.E. from the State University of Iowa and a Ph.D. in I.E. from the University of Illinois in 1964. He taught at the University of Illinois and at Kansas State University where he now is a Professor of Industrial Engineering. He has had industrial experience at Collins Radio, Lockheed, Western Electric and General Motors and spent his sabbatical in 1971 at the Human Sciences Laboratory in Johannesburg working on heat stress problems. His research interests are heat stress, lifting, and work physiology. About the Author-C. L. HWANG is a professor of Industrial Engineering at Kansas State University. He earned a B.S. at National Taiwan University in 1953 and received both a MS. and a Ph.D. in Mechanical Engineering from Kansas State University in 1960 and 1962 respectively. His research interests include optimization techniques, systems engineering, the human thermoregulatory system, and environmental pollution control.

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S. KONZ, C. HWANG,B. DHIMAN,I. DUNCANand A. MASUD DUNCAN received a B.S. and M.S. in Industrial Engineering from Kansas State in 1967 and 1969. After three years in the U.S. Air Force as a management engineer, he returned to Kansas State for a Ph.D. in Industrial Engineering in 1975. After a year as Assistant Professor of Industrial Engineering at the University of Tennessee, he began work in the Department of Industrial Engineering at Texas A & M in the field of ergonomics and occupational safety. His research interests are heat stress and occupational safety. Ahout the Author-JERRY

About the Author-BALI)!%

DHIMANreceived a B.S. in Aeronautical Engineering from Punjab University in 1969. He worked as a development engineer for Sul Engineering and for Sisi before coming to Kansas State where he received a M.S. in Industrial Engineering in 1975. MASUDis a graduate student in Industrial Engineering at Kansas State University. He did his B.S. in Mechanical Engineering in 1969 from Bangladesh University of Engineering and Technology, a Diploma in Business Administration in 1973 from the University of Dacca and a MS. in Industrial Engineering in 1975 from Kansas State University. He currently is working for a Ph.D. with the major area being operations research. Ahout the Author-Am