39

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

Chapter 2

MODELING THE PHYSIOLOGICAL AND 

MEDICAL EFFECTS OF EXPOSURE TO 

ENVIRONMENTAL EXTREMES

WILLIAM R. SANTEE, PhD*; MATTHEW J. REARDON, MD, MPH, MS, MSEE†; and KENT B. PANDOLF, PhD, MPH‡

INTRODUCTION

LINKING MODELS TO USERS 

AN INTRODUCTION TO MODELING

STRATEGIES FOR FORMULATING BIOMEDICAL MODELS

A HISTORICAL OVERVIEW OF THERMAL MODELS AND INDICES 

US ARMY RESEARCH INSTITUTE OF ENVIRONMENTAL MEDICINE MODELS 

FOR PREDICTING CONSEQUENCES OF EXPOSURE TO ENVIRONMENTAL 

STRESSORS

SUMMARY 

ATTACHMENT A: FINGER-COOLING METHOD

ATTACHMENT B: WATER IMMERSION MODEL

*Research Physical Scientist, Biophysics & Biomedical Modeling Division, US Army Research Institute of Environmental Medicine, Building 42, Kansas 

Street (Office MCMR-EMB), Natick, Massachusetts 01760-5007

†Senior Consultant, Occupational & Environmental Medicine Consulting Services, LLC, 6 Office Park Circle, Suite 100, Birmingham, Alabama 35223-

2512; Colonel, US Army Reserve, Deputy Medical Director, Anniston Chemical Agent Disposal Facility, US Army Chemical Materials Agency, 7 

Frankford Avenue, Anniston, Alabama 36201; and Command Surgeon, 87th US Army Reserve Support Command, 1400 Golden Acorn Drive, Birmingham, Alabama 35244

‡Senior Research Scientist, US Army Research Institute of Environmental Medicine, Building 42, Kansas Street, Natick, Massachusetts 

01760-5007; currently, retired
40

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

INTRODUCTION

along with the requisite weather information, accessed 

via Web sites, or installed onto personal computers and 

PDAs (personal digital assistants) or other handheld 

electronic devices. Physiologically sound models can 

also be used in simulations that help to develop video 

games used as training tools for company-grade officers, junior noncommissioned officers, and medical 

personnel. This chapter focuses on thermoregulatory 

models currently in use by the US Army Research Institute of Environmental Medicine (USARIEM) as both 

a historical record of model development and as an 

indication of the promise of all biomedical modeling. 

Despite a significant investment in scientific research, 

an age-old military problem—thermal injuries—continues to plague military operations. Scientific research can 

contribute to the resolution of this problem by providing 

military leadership, at all levels, with scientifically sound 

information and pragmatic guidance. The challenge is 

how to make scientific information gained from research 

accessible to the soldier in the field. One solution is to develop biomedical models. Dr James H Stuhmiller (author 

of Chapter 10 in this volume) believes that models are 

the force multiplier of research. Once developed, these 

models can be incorporated into information networks 

LINKING MODELS TO USERS 

Biomedical models can be used to provide guidance for the deployment of forces on the battlefield. 

Understanding these models allows planners to better utilize scarce resources and preserve the fighting 

power on the battlefield, both of which can be seen as 

force multipliers. 

The relationship between environmental parameters 

and the thermal status of an individual is a product of 

the interaction of environmental conditions, individual 

physical parameters (posture, body surface area, and 

clothing), and individual physiology (initial state, 

metabolic heat production, and thermoregulation). 

Virtually all the parameters are dynamic; hence, the 

universe of potential interactions is large. Despite the 

range of possible interactions, our perception of the 

thermal environment (ie, the weather) is translated 

into the relatively simple expectations of warmth, 

cold, or comfort, and some anticipation that “the 

weather” will have some degree of influence on our 

activities, ranging from essentially none (comfortable 

state) to severe (survival is threatened). An action 

plan developed in response to the anticipated conditions typically consists of a combination of clothing 

and thermoregulatory behavior. For example, when 

dangerously hot conditions exist, the unit response 

can be a combination of modifying uniform wear and 

limiting strenuous outdoor activities. 

At one time, experience and common sense guided 

our response to potentially stressful environments. In 

a population that is closely linked to its environment, 

such as Inuit hunters, there is a shared knowledge of 

weather and survival. Military schools, such as jungle 

and mountain warfare training centers, are communicating a similar form of cultural heritage. 

Today, in a more urban, mobile society, we are no 

longer so closely linked to our local environment, or 

we may be forced to operate in unfamiliar environments, so we can no longer rely on the common sense 

developed from experience and cultural practices for 

guidance. The media weather forecasts, with their 

emphasis on commuter weather and recommendations 

for proper clothing and behavior, are responding to a 

public need. Because military leaders may no longer 

have the opportunity to develop operational skills 

tailored for all possible environmental extremes, the 

military might also need the guidance equivalent to a 

media weather forecast. One option, originally developed primarily for military and industrial organizations, is to use thermal indices or models.

As the complexity of science and technology has 

increased, few individuals are able to develop full 

competency in areas outside their specific realm of 

expertise. Environmental physiology and meteorology are scientific specialties that, like any special area 

of study, require a good general background, plus a 

concentration in the area of specialization. Although 

it is desirable to acquire the underlying knowledge 

to better use and understand the limitations of their 

potential, models and computer systems literally 

bring the expertise of an environmental physiologist/biomedical modeler to the fingertips of the field 

medical officer.

AN INTRODUCTION TO MODELING

Biomedical models are ubiquitous. They have been 

developed in almost every field of medicine and science. In 2006, for example, a MEDLINE search for human models or simulations restricted to heat or cold had 11,086 hits. The number of publications in these 

areas indicates the interest and persistent government 
41

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

and commercial support for biomedical modeling and 

simulation. Products and software applications that 

incorporate biomedical models and algorithms are 

useful and cost effective. Modeling and simulationbased applications are numerous and include tools for 

planning and decision making, forecasting, and prediction. Additional applications include education and 

training, design and virtual prototyping, and process 

visualization. In scientific research, models are used for 

concept exploration and verification, analysis and discovery, and identification of gaps in knowledge within 

specific domains. Model development and use are 

often effective ways of gaining an improved and more 

detailed understanding of complex biomedical processes that cannot otherwise be obtained. In general, 

modeling and simulation have become a military core 

technology that is becoming progressively more complex as individual models are integrated into highly 

complex, large-scale, distributed interactive systems.1,2

Biomedical models use a variety of different, but 

often complementary, representations. They can be 

descriptive, graphical, analog (eg, mechanical or electronic), biological (eg, animal or cell culture models), 

or digital (involving use of computers and software). 

Models can be formulated using mathematical equations, logical symbolism, software algorithms and 

code, or a combination of these methods. Mathematical models are particularly useful because they are 

concise, and they can be solved exactly or approximated to close tolerances using iterative numerical 

algorithms.3 Also, it is often possible to obtain exact 

equations for the sensitivity of predicted variables to 

perturbations in a model’s coefficients and independent variables. Mathematics and formal logic provide 

reliable frameworks of proven rules for manipulating 

and evaluating modeling equations and algorithms. 

Consequently, analytic models can be used to verify if 

inferences regarding biomedical processes are logically 

plausible or used to derive new results that were not 

otherwise apparent.4

Complex models can be created when outputs from 

equations representing basic processes serve as inputs 

into other equations implementing feedback control 

mechanisms. Then, various software development 

tools can be used to create intricate, computer-driven 

realizations of the mathematical models or algorithms. 

Graphic user interfaces provide convenient methods for 

visualizing modeling results in a variety of formats, such 

as multidimensional charts, graphs, and tables. Modelbased data can also serve as inputs to logical constructs 

that either discredit or help validate results and link 

them to computer-generated events, or to databases of 

advisory or cautionary messages.

There is a spectrum of model development methods.5

 At one end of the spectrum are parametric models derived using formal analytical techniques from 

well-defined biophysical principles. This includes 

mechanistic models that take advantage of concisely 

formulated a priori mathematical knowledge about 

interrelated processes. This type of model is often 

known as a “first principles” or “rational model.” At 

the other end of the spectrum are essentially nonparametric models, wherein few or no a priori assumptions 

are or can be made regarding the most appropriate 

form for a system’s governing equations or structure. 

Models based predominantly on the analysis of data 

sets are often referred to as empirical models. These 

are exemplified by models obtained by trial-and-error 

curve fitting. Models based on correlations and data 

lookup tables (coupled with simple linear interpolation between data points) are other examples of nonparametric models. Because a priori knowledge about 

the theory underlying a modeled process is usually 

not complete, models are often partly parametric or 

mechanistic and partly nonparametric. However, in 

all cases, experimental data are required for validation 

and to calculate the most appropriate (for the intended 

use) values for the coefficients. 

STRATEGIES FOR FORMULATING BIOMEDICAL MODELS

The most suitable general form for the equations 

and logical structure of a biomedical model can often 

be obtained from well-established theory in the specific 

topic area.6 For example, forms of equations describing the diffusion of heat in solids are derived from the 

basic principles and analytic expressions that describe 

conductive heat flow. Derivation of a model from such 

governing principles results in constituent equations 

that encapsulate the general characteristics of the heat 

transfer process. Experimental data, however, are 

required to transform the nonspecific derived equations into practical models. Obtaining specific equations from the general analytical equations requires 

parameter, or coefficient, estimation or identification 

processes. Parametric multiple regression techniques 

are often used to determine optimal (eg, with respect 

to minimum mean-squared error or maximum likelihood) values for the coefficients of a model’s equations 

for the available data. Additional complexity and flexibility can also be built into these models by assigning 

parameters to the coefficients for the various levels of 

co-factors (eg, demographic or morphologic characteristics) that are known to be significantly associated 

with the response or dependent variables. 
42

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

Models derived from analyses using basic biophysical principles are often at least partially represented by systems of ordinary differential equations 

or partial differential equations with their associated 

initial and boundary conditions. These techniques 

are invariably associated with compartmental 

models that describe the dynamic flux of energy 

between adjacent and distant volumes having different material properties.7

 Such models describe 

the amount of a conserved, but dynamic, substance 

in each compartment as functions of time. Typically, the solution of partial differential expressions 

is facilitated by transforming them into equivalent 

systems of ordinary differential equations and initial 

conditions. Linearization can be used to approximate 

the behavior of nonlinear differential systems about 

specified points. Such linear models can be concisely 

expressed using vector and matrix notation, thereby 

making the model’s high-level structure more apparent and facilitating attempts to obtain analytic 

solutions.8 Nonhomogeneous partial differential 

equations, however, can be difficult to solve. Often 

various transformations are required. Because the 

nature of the necessary transformations may not be 

apparent to those without substantial experience 

or training in solving nonhomogeneous partial differential equations, some expertise in mathematical modeling may be required. Time constants for 

outputs of a compartment model can be determined 

from the roots of the characteristic equation of the 

systems. Also, outputs will have exponential components to create predictable behavior (eg, increasing 

to an asymptotic or steady-state value, oscillatory, 

or unstable) and will extend out in time in a manner 

that remains valid, unlike polynomial models whose 

outputs are typically valid for relatively well-defined 

time intervals. 

Alternative approaches for model development 

are more dependent on the evaluation of experimental data than on developing a priori mathematical 

constructs that represent well-established facts or 

assumptions regarding causative processes. Developing models directly from analysis of experimental 

data is the empirical, or “black box,” approach. For 

this type of model, multiple regression techniques, 

including minimizing variance and statistical hypothesis testing, are typically used to select the best 

equations for the model, including specific values 

for the coefficients. The equations that result from 

applying this approach might have no or only fortuitous relationships to the underlying physical 

processes; their primary merit is that they best fit 

the data according to predefined criteria. Often, experienced subject matter experts will use a hybrid, 

or intermediate, method of model development. 

These modelers will usually specify from experience 

and descriptive theory, without formal derivations, 

forms (eg, sigmoidal, simple exponential, harmonic, 

and polynomial) for regression equations that comply with at least a high-level abstraction of underlying mechanisms and that will also result in a good fit 

to experimental data. Graphical visualization of the 

data being used for model development can assist in 

selecting the best form for a model’s regression equation when using this intermediate model development approach. Hybrid empirical quasi-parametric 

model development methods used by experienced 

modelers and subject matter experts often result in 

surprisingly accurate and robust models (eg, the heat 

strain model developed by USARIEM) that perform 

as well as models derived from formal mathematical 

descriptions of basic biophysical and physiological 

processes. The present version of the USARIEM heat 

strain model is labeled the heat strain decision aid 

(HSDA).9,10

The black box (or purely empirical) as well as intermediate (or hybrid) model development methods 

result in equations that usually have a narrower range 

of validity than those derived from basic principles. 

The black box method results in equations that can be 

trusted to reliably predict responses for only a limited 

range of the independent variables, usually the approximate limits of the original data set. 

Thus, an application of an empirical or hybrid 

model beyond the scope of the original conditions is 

of uncertain validity. For example, data from a study 

evaluating a process known to cause asymptotic 

responses can be seemingly well-modeled, along limited intervals of the independent variables, by linear 

or polynomial functions. However, extrapolating 

significantly beyond the range of the independent 

variable used in the studies from which the data were 

obtained would soon result in large errors, as the 

response predicted by the polynomial functions and 

actual asymptotic data increasingly diverged. Because 

equations in an empirical model typically do not represent actual processes, their selected forms primarily 

illustrate convenient mathematical representations 

that approximate experimental or observational data 

to specified tolerances. In contrast, the equations and 

terms in analytically derived models usually can be 

expanded to cover a broader range of phenomena, 

provided those conditions represent a series of similar 

mechanistic relationships. The coefficients and intermediate output values from such algorithms allow 

for state-space representation, with state variables 

that might be fully observable and measurable in the 

corresponding real system. 
43

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

A HISTORICAL OVERVIEW OF THERMAL MODELS AND INDICES

are milder than normal or standard conditions, the 

equivalent temperature is also milder than the measured temperature. These phenomena result from 

assumptions inherent in the equations, such as assuming that an individual is walking at a fixed rate, 

and hence a “calm” state includes some convective 

transfer. Weather forecasters might not have much 

trouble convincing people that, because of a strong 

wind, the temperature at –20°C is actually “colder” 

than the –20°C value the thermometer reads. However, 

people are less likely to believe that, if wind speed is 

less than normal, the temperature is less than –20°C.

In indoor office studies, where air velocity is usually a low, constant value, humidity is low because of 

central heating or air conditioning; the mean radiant 

temperature is near air temperature, thus using only 

air temperature to represent environmental variability 

is often accurate. To adjust the comfort level, the temperature setting of the thermostat should be adjusted. 

That action can, in fact, alter all four parameters, but 

the most noticeable change is in air temperature. In a 

room with an indoor swimming pool, the large water 

surface area of the pool virtually ensures a saturated 

relative humidity of 100%. In that environment, an air 

temperature that differs from the office temperature 

would have the same effect on comfort or thermal 

state. If the office environment is identified as the 

standard environment, the equivalent temperature in 

the pool room would be the air temperature required 

to achieve the same standard of comfort or thermal 

state. It is important also to identify the standard for 

equivalency, because thermal balance and comfort are 

not always achieved in the same thermal environment. 

It should be noted that thermal balance is dependent 

on an individual’s activity and clothing. Equivalent 

temperatures generally assume equivalent clothing 

and metabolic rates. A principal shortcoming of all of 

these instruments (ie, WBGT, the Oxford index, and 

WCI) is that metabolic rate and clothing are ignored. 

Those indices, as originally presented, are environmental rather than physiological indices, because they are 

not scaled for differences in metabolism and clothing. 

General Environmental Indices

An example of a general environmental index is 

operative temperature.16–18 The original concept of 

operative temperature was to calculate a single value, 

expressed as a temperature, that would account for 

heat exchange by convection and radiation, if all 

temperatures were at the same operative temperature. Operative temperatures and the derivative new 

Indices vs Models 

When the mathematical model results are expressed 

as a single value, and interpreted or indexed with a 

reference scale rather than used directly, the model 

is referred to as an index. For example, the original 

windchill index (WCI) values11 had to be interpreted 

according to a range provided by the authors. As 

computers have become more accessible, there is a 

diminished appeal for expressing modeling results 

as indices. Users are beginning to realize that more 

sophisticated predictions and guidance are just as 

accessible as simple indices. For example, versions of 

the USARIEM heat strain model12,13 directly predict 

tolerance times, water needs, and/or changes in rectal 

temperature or heart rate. At present, a transition from 

indices to more detailed models is occurring despite 

the persistence of older indices such as wet bulb globe 

temperature (WBGT)14 and new indices such as the 

environmental stress index.15

Equivalent Temperatures 

The use of a single environmental parameter to categorize the overall thermal environment is a convention 

followed by most individuals. Actual environmental 

conditions can be a combination of temperature, wind, 

radiation, and humidity, but it is more convenient 

just to say it will be “in the 70s” (°F). We can refer to 

the effects of high and low temperatures on human 

physiology when in fact we are referring to thermal 

environments that represent a strong potential for 

either heat gain (hot environments) or heat loss (cold 

environments) between the environment and the body. 

As noted previously, the thermal environment is the 

product of four parameters. To visualize the interaction 

of those parameters would require a four-dimensional 

space. In any discussion of the thermal environment, 

it would be much easier if we could use only one parameter instead of four, and temperature is the most 

easily measured and conceptualized environmental 

parameter.

Characterizing the net effect of the thermal environment on heat exchange in the units of temperature is 

the basic premise behind equivalent temperatures. A 

given combination of all four parameters is equivalent 

to an air temperature that is higher, lower, or equal to 

the measured air temperature. Thus, a windchill temperature is usually lower than air temperature; and, 

on a warm, humid day, the equivalent temperature 

is higher than the measured air temperature. One 

problem has been that, when the actual conditions 
44

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

effective temperature (ET*) and standard effective 

temperature models are discussed in detail in Chapter 

8 to illustrate the integration of weather and biophysics 

into a biomedical model.

Indices for Heat Exposure 

Not surprisingly, there are many different indices 

for calculating heat exposure. These include the following: 

	 •	 ET,

	 •	 WBGT,

	 •	 weather service indices based on temperature

humidity, 

	 •	 the Oxford (wet-dry) index (WDI),

	 •	 the predicted 4-hour sweat rate (P4SR),

	 •	 the required sweat rate (Sreq), and 

	 •	 ET*.

Effective Temperature

ET is an index based on wet bulb (Twb) and dry bulb 

(Ta) air temperatures and air velocity (u), which associates actual conditions to equivalent still air, saturated 

(100% relative humidity) conditions. It originated as a 

comfort index,19 but was modified to index physiological 

strain.20 ET is often represented as a nomogram (Figure 

2-1), which is similar to a psychrometric chart. Corrected 

ET (CET)21 substituted globe temperature (Tbg) for Ta. 

The basic criticisms of ET and CET are that the indices 

are based on light or sedentary activity, and they cannot 

be adjusted for metabolic activity. Only two levels of 

clothing—(1) nude and (2) light, indoor clothing—were 

included in the original scales. In common with other 

indices, later research has provided some guidance for 

adjusting ET and CET for different metabolic rates. For 

example, Lind22 has calculated that CET upper limits 

ranging from 30.2°C to 26.9°C for different work levels 

correspond to metabolic rates of 209 to 488 W. An additional criticism is that the original derivation of ET was 

based on initial or transitory sensations; therefore, it is 

not as useful for predicting responses during a prolonged 

exposure. ET and CET are also considered appropriate 

for only moderately warm climates, rather than extreme 

environments. The basic concept of ET has been modified several times to eliminate these criticisms. ET and 

CET have gradually been replaced by newer measures 

of heat stress, such as ET* and standard ET, which are 

discussed in Chapter 8.

Wet-Bulb Thermometer ( C)

Globe Thermometer or Dry-Bulb Thermometer ( C) 2025303540

4550556065

0510

15

202530354045

20

20

15

15

10

10

25

25

30

30

35

35

40

!

0

5

0.10

0.50

1.00

1.50

2.00

2.50 2.00

4.00

6.00 5.00 7.50

3.50

0

5

5

10

15

!

!

Corrected Effective (or Effective) Temperature ( C)

Fig. 2-1. Nomogram for corrected effective temperature for light, indoor clothing. 

Illustration: Adapted with permission from Ellis FP, Smith FE, Walters JD. Measurement of environmental warmth in SI 

units. Br J Ind Med. 1972;29:361–377. 
45

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

Wet Bulb Global Temperature Index 

The WBGT index has been described23 as an effort 

to simplify an earlier climatic index (ET). To establish 

the WBGT, three temperature sensors—(1) a shielded 

dry bulb thermometer to measure Ta; (2) a “naturally 

aspirated” wet bulb thermometer to measure primarily 

humidity (Tnwb); and (3) a 15-cm (6-in.) Vernon black 

globe thermometer (Tbg) to measure the combined effect of wind speed, air temperature, and radiation—are 

used to calculate indoor and outdoor WBGT values. 

These values are interpreted according to guidance 

provided by Yaglou and Minard24 and later researchers. 

The equations for indoor and outdoor WBGTs are:

(1) 0.7Tnwb + 0.2Tbg + 0.1Ta [outdoors, °C or °F]

(2) 0.7Tnwb+ 0.3Tbg [indoors, °C or °F].

Indoors, without significant drafts or radiation 

sources, the assumption is sometimes made that the 

black globe temperature is the same as the ambient 

temperature.25 Botsford26 discusses other equations 

for WBGT. The original empirical scale was developed 

to provide guidance for the training of acclimatized 

and unacclimatized military personnel. Application 

of the original equation is limited by the original database; fit, young US Marines in a summer military 

uniform engaged in moderately intensive exercise. 

WBGT is a simple index that uses simple sensors and 

minimal calculations. WBGT is not recommended for 

conditions with high humidity.27 It has been widely 

used by the military, particularly in the United States. 

Adjustments to WBGT have been made for different 

work rates and clothing. Sources for guidance include 

the US Army’s Technical Bulletin 507 on the prevention, 

treatment, and control of heat injury,14 the National 

Institute for Occupational Safety and Health recommended standards for exposure to hot environments,28

the American Conference of Government Industrial 

Hygiene handbook,29 and the International Standards 

Organisation guideline 7243.30

Weather Service Indices Based on Temperature 

Humidity 

The US National Weather Service (NWS) uses a 

temperature-humidity index (HI) derived from Steadman’s heat index. The NWS approach was to generate a 

fourth-order polynomial using only air temperature (TF

in °F) and percent relative humidity from Steadman’s 

model31,32 for apparent temperature.33 The rationale for 

developing the derived equation for HI was to save 

computation time and computer resources. The lowest 

thresholds for HI are possible fatigue, with prolonged 

activity beginning at HI = 80°F, and an increasing potential for heat injury—defined as “sunstroke,” heat 

cramps, or heat exhaustion—at 90°F to 105°F. Those 

injuries become likely between 105°F and 130°F, with 

a potential for heatstroke; when HI ≥ 130°F, heatstroke

is highly likely. 

A similar temperature-HI (Humidex [HD])34,35 is 

used by Meteorological Services Canada. The input 

variables are Ta (°C) and a different variable for humidity, Tdp (°C). Critical values for HD are ≤ 29°C and are

comfortable; discomfort begins at 30°C, and a majority of individuals should be uncomfortable when HD 

reaches 40°C. At HD ≥ 46°C, some activity restrictions

are merited. 

In 2001, the US and Canadian weather services 

worked together to adopt a new way of calculating 

windchill temperature. The working group was also 

tasked with considering a common HI rather than HI 

in °F and HD in °C, and different scales for interpretation. To make a comparison between the two indices, a 

USARIEM mathematical model was run with constant 

values for all parameters except Ta and humidity to 

calculate core temperature (Tc). By setting most of the 

inputs as constants, the model was essentially converted into a temperature-HI. The model Tc values were 

plotted against the respective HI or HD index values 

calculated for different combinations of temperature 

and humidity. The results indicated a linear relationship between HI and predicted Tc

, and an exponential 

relationship for HD and Tc.

35

Oxford Index 

Lind et al36 developed the Oxford index (also known 

as the WDI) from data on mine rescue workers.23,37

Weighted values of Ta and Twb are used to calculate 

WDI. There are no specific corrections for radiation, 

wind speed, clothing, or metabolic rate in the equation. 

WDI is most appropriate for environments similar to 

mines. McIntyre37 cites later work to calculate safe 

tolerance times for different metabolic rates. Eissing38

classifies WDI as a climatic index based on algebraic 

combinations of climatic parameters and cites several 

additional examples. Of Eissing’s listed indices, the 

Belgian ET39 was virtually identical to the WDI. A 

similar index for military chemical protective clothing, the heat-HI40 (HHI) uses an equal weighting of Ta

and Twb (HHI = 0.5 Ta + 0.5 Twb) to derive a value that 

is interpreted using the WBGT index scale. Bell and 

colleagues41 proposed a basic equation of 

T = p • Twb + (1 – p) • Ta

and presented different p values for sitting (0.12), 

standing (0.05), and working (0.10). Gagge and Nishi42

used 0.7 Twb + 0.3 Ta for indoor WBGT.
46

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

Predicted Four-Hour Sweat Rate 

The P4SR43 is also based on the assumption that 

sweat can be equated to the level of physiological 

strain. The P4SR is based on an empirical derivation 

of the relationship between the observed responses 

(sweat rate) of subjects and environmental stress. The 

authors assumed a maximum sweat rate of 5 liters in 

a 4-hour period. If the P4SR is less than 4.5 liters, it is 

assumed that a healthy young population would not 

experience heat-related injuries. To use the equation, 

values for Ta, Twb, Tbg, wind, and metabolism are used 

to derive a basic 4-hour sweat rate from a nomogram 

(Figure 2-2) similar to a psychrometric chart. A second 

equation is then used to calculate the P4SR based on 

clothing and metabolic rate. The original P4SR was 

based on only two clothing conditions. McIntyre37

indicated that, whereas the P4SR value increases when 

clothing insulation (and clothing amount) increases, 

in reality, actual sweat loss would decrease. Another 

criticism is that the index applies only to acclimatized 

subjects. 

Required Sweat Rate 

Required sweat rate (Sreq), ISO 7933 (1989),44 is a 

rationally derived index based on a calculation of the 

sweat required to maintain thermal equilibrium. Vogt 

and colleagues45 cite Givoni’s index of thermal stress 

as the theoretical basis for Sreq. However, to determine 

Sreq, in place of Givoni’s empirically derived estimates, 

heat exchange coefficients are used to calculate terms 

in the heat balance equations. Consequently, Sreq is 

more of a modernization of Belding and Hatch’s 

heat stress index. Required environmental inputs 

are values for Ta, Tr, v, and Pa (ambient water vapor 

Fig. 2-2. Nomogram for the predicted 4-hour sweat rate. 

WB: wet bulb.

Illustration: Adapted with permission from Ellis FP, Smith FE, Walters JD. Measurement of environmental warmth in SI 

units. Br J Ind Med. 1972;29:361–377. 

Wet Bulb Temperature ( C) !

Metabolic Rate

kcal/

m2

h

100 150

3.02.05.0

4.0

200

0.01.0

Air Velocity (m/s)

Basic 4 h Sweat Rate (L)

! Add to Wet Bulb Temperature ( C)

Air Velocity

(m/s)

28

28

30

30

31

31

32

32

33

33

34

34

35

35

37

37

82

0.25 m/s = WB4

0.35 m/s = WB3

2.50 m/s = WB1

0.37 m/s = WB2

0.05 m/s = WB6

0.15 m/s = WB5

25

2830

31

32

3333.5

34

34.5

35

35.5

36

2.50

0.37

0.35

0.25

0.15

15

0.05

21

816.0

1.0

0.5

0

1.0

5.0

6.0

4.0

3.0

2.0

-0.25

0.5

0

-0.5

2.0

3.0

4.0

5.0

35

40

45

50

30

2.50

1.50

1.00

0.05-0.37 0.37

50 100 150 200

DB
47

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

pressure). Clothing factors are represented by Re (a 

term for clothing vapor permeability resistance) and 

Icl. ISO 992046 presents methods for estimating Icl and 

Re. Methods are presented for deriving or estimating 

other clothing parameters, mean skin temperature 

(

–

Tsk), and M (or metabolic heat production). A term for 

sweating efficiency was adopted because not all sweat 

produced contributes to evaporative cooling. Sreq is the 

basis for ISO 7933.44 Parsons47 presents the equations 

and regression relationships for calculating Sreq as it is 

presented in ISO 7933.44 Allowable exposure times, or 

duration-limited exposures (DLEs), are based on either 

heat storage (DLE1) or water depletion (DLE2) for a 

maximum 8-hour shift.

Indices for Cold Exposure 

Windchill is a concept that has been used by both 

the military and civilian sectors for a considerable period of time. This section will discuss the evolution of 

the concept, as well as ways to prevent cold injury by 

identifying adequate levels of clothing insulation. 

Windchill Index and Windchill Temperature 

By far, the most widely recognized index for cold 

weather exposure is the WCI.11 It is based on the intuitive relationship between heat loss or chilling and 

increasing wind speeds. The WCI was an effort to 

calculate an index number for the cooling rate of wind 

and air temperature on bare skin. The authors of the 

index recognized that solar effects were neglected, 

and the index does not relate to clothing or a high 

activity level. 

The idea of a windchill equivalent temperature 

(WCET) is based on the same assumptions as other 

equivalent or standard temperatures.48 WCET is the 

same combination of wind speed and air temperature 

that results in the same WCI as still air. However, 

equivalent temperatures are based on the assumption 

of a minimal wind speed of 4 mph (1.8 m • s–1).

Shortly after the introduction of WCI, criticisms 

began.49 The flaws in WCI, especially the derivative WCET, were known for more than 50 years. As 

noted previously, even the authors11 identified some 

limitations of their index in the original publication. 

In 2000, a US and Canadian Joint Action Group for 

Thermal Indices, sponsored by the Office of the 

Federal Coordinator for Meteorological Services 

and Supporting Research,50 undertook an effort to 

develop a new windchill model.50–52 The principal 

modelers were Osczevski53 and Bluestein and Zecher.54 A team of researchers at Defence Research and 

Development Canada (in Toronto [DRDC Toronto]) 

conducted human testing that supported the modeling effort.55 In a situation parallel to the derivation 

of the NWS predictive equation for HI, the original 

iterative program required too great an allocation of 

computing resources. Thus, simplified equations in 

metric and English units were developed to predict 

the new windchill temperature (WCT). Figure 2-3

illustrates the relationship between Ta and WCT.

Figure 2-4 presents the revised WCT values for different combinations of Ta and wind speed. The metric 

WCT equation is:

(3) WCT = 13.12 + 0.6215Ta – 11.37V0.16 + 

0.3965TaV0.16 [°C]

V is the wind velocity in kilometers per hour (kph) 

measured at 10 m. To use the chart for a ground-level 

wind speed, multiply the ground wind velocity by 1.5. 

In addition, an equation to predict the time for freezing 

of the exposed skin on the face was developed. The 

shading on Figure 2-4 represents various calculated 

time intervals to facial frostbite. The equation that calculates time to facial frostbite is based on assumptions 

concerning the insulation of human skin that, in turn, 

varied with the age of the subjects. A revised equation for predicting time to frostbite for exposed faces 

was developed by Tikuisis and Osczevski.56,57 Thus, 

the values in the WCT table—especially the values 

for time to frostbite—should be considered advisory 

rather than absolute. 

Fig. 2-3. Comparison of air temperature and windchill 

equivalent temperatures at the US Marine Corps Mountain 

Warfare Training Center, January 27, 1988. Frostbite from 

wind exposure cannot occur above 0°C. 

PST: Pacific Standard Time

Wind Chill Temperature

Air Temperature

15

10

0 2 4 6 8 10

5

0

5

-10

12 14 16 18 20 22 24

Time (PST)

Temperature (°C)
48

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

As presently used, WCT is related to the danger 

of frostbite on bare skin. Among the most direct criticisms of windchill is the fact that a simple wind barrier (clothing or shelter) rapidly negates the effect of 

high wind speeds, but the “equivalent” combination 

of extreme low temperatures and low wind speed 

cannot be readily alleviated by clothing or a simple 

shelter. A calm day with an air temperature of –40°C 

is always dangerous, whereas an equivalent WCT of 

–40oC for a combination of –25oC (–13oF) Ta and 35 

kph at 10 m (6.5 m • s–1 at ground level) wind speed 

does not pose a great danger to an experienced or 

well-informed individual with adequate clothing or 

shelter. The difference is best demonstrated by using the example of an individual stranded inside an 

automobile. Eventually, the interior of the car may 

cool to the outdoor air temperature, but no matter 

how strong the wind blows, the interior of the car 

will never become colder than air temperature. The 

only direct effect wind speed will have on the interior 

temperature will be on the rate or time that it takes to 

cool it down to the outside air temperature.

Most windchill tables suggest that there will be little 

danger of frostbite above an air temperature of –10°C, 

regardless of the wind speed. For the face, which has 

enhanced circulation, this might be true. However, 

the situation is more complex. Military epidemiology 

from World War II58 indicates that frostbite injuries 

appear when the air temperature goes below 0°C. The 

incidence of frostbite on other parts of the body, especially from contact with cold surfaces, probably starts 

to occur when the air temperature is approximately 

0°C, and the freezing point for human tissue is about 

–0.6°C.59–61

A reason for confusion is that frostbite might not 

occur until the skin surface temperature drops well 

below –1°C. This phenomena was first reported as 

supercooling at approximately –10°C by Wilson and 

Goldman.62 Danielsson59,60 subsequently explained 

that their values were 3°C to 4°C too low because of 

an instrument error. Danielsson has estimated that the 

skin surface temperature when frostbite first occurs 

would be between –4.6°C and –8°C. 

Even though WCT overcomes some of the problems 

of Siple and Passel’s11 original work, some of the inherent limitations of indices remain because selection of 

the standard conditions for any index requires compromise. For example, the activity level is walking at 1.34 

Fig. 2-4. National Weather Service windchill calculation chart. 

Illustration: Reproduced with permission from the National Oceanic and Atmospheric Administration (NOAA). http://

www.nws.noaa.gov/om/windchill/index.shtml. Accessed May 24, 2007.
49

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

m • s–1, so the “calm” condition still involves a forced 

convection equivalent to a 1.34 m • s–1 wind. There is 

no adjustment for higher or lower activity levels. Although WCT is based on human data, the resistance or 

insulation of the facial skin layer varies.51,52,55 Selected 

skin resistance is most representative of middle-aged 

or older individuals. WCT has been presented in terms 

of the time to facial frostbite, but subsequent work by 

Tikuisis and Osczevski56,57 has raised questions regarding the efficacy of those predictions. In addition, WCT 

has no established relationship to the potential hazard 

for hypothermia. An effort was made to adjust for 

solar radiation by adding a few degrees to WCT, but 

the basis for this adjustment is limited.60

Required Clothing Insulation 

The presentation of WCI/WCT has become focused 

on the prevention of frostbite rather than hypothermia. 

In its original form, WCI is a climatic index.38 Like ET 

and WBGT, no adjustment is made for clothing or 

physiological factors. Burton and Edholm63 brought 

clothing and metabolism into their calculation of 

the insulation required to maintain a safe core body 

temperature. 

Holmér64 calculated the required insulation using 

equations from Burton and Edholm,63 Umbach,65 and 

Holmér’s66 own equations for required clothing insulation. Holmér concluded that the results for predicting 

required insulation were essentially equivalent, except 

that his equations allowed an adjustment for changes 

in –Tsk and sweating rates. 

Burton and Edholm63 recognized that adjustments 

were required for wind speed and radiation by proposing the calculation of still air-shade temperature and 

equivalent shade temperature.23 Holmér67 incorporated 

adjustments for different wind speeds, radiant load, 

humidity, and the effect of wind and motion on clothing insulation into his required clothing insulation 

index (IREQ). The IREQ index is presented in ISO-TR 

11079.68 Two levels of insulation can be calculated.

IREQmin is based on a sustainable nonhypothermic 

state with a –Tsk of 30°C, whereas IREQneutral refers to 

maintaining thermoneutrality under specified conditions. For IREQ, neutral condition is actually a state of 

comfort, whereas the minimal condition is probably at 

the lower limit of an unimpaired functional state. It is 

a guideline based on average individuals, assumes an 

even distribution of insulation, and does not address 

the problems of local cooling.

23,69

US ARMY RESEARCH INSTITUTE OF ENVIRONMENTAL MEDICINE MODELS FOR PREDICTING 

CONSEQUENCES OF EXPOSURE TO ENVIRONMENTAL STRESSORS

Various types of physiological stress-strain models 

have been developed that have proven useful for 

generating prevention guidance, assessing environmental health hazards, and predicting environmental 

stress casualty rates and performance decrements 

for work-related tasks. Of the suite of environmental 

models developed at USARIEM, model-based applications have been developed for evaluating the 

physiological strain associated with exposure to heat 

stress, cold stress, and altitude-related hypoxia. Modeling in these areas, however, has not proceeded at 

an equal pace.70 Heat strain models are currently the 

most mature and extensively validated. Considerable 

additional effort will need to be expended to produce 

equally valid, operationally capable models for other 

environmental stressors. Eventually, it might be possible to integrate separate models for evaluating different types of environmental stressors into unified 

applications.71,72 This would facilitate evaluation of 

a spectrum of environmental threats to health and 

mission effectiveness when planning operations that 

span seasons and environmentally disparate terrain. 

Likewise, mathematical modeling applications can be 

embellished to include links to medical handbooks or 

to evaluate environmental health hazards.73 Another 

potential placement for thermal models is on a portable 

device such as the PDA-based Battlefield Medical Information System–Tactical, which features electronic 

medical record keeping; electronic medical references, 

such as the Special Operations Forces Medical Handbook; 

and a telemedicine linkage.74

USARIEM Heat Strain Models

The history of the development of heat strain models at USARIEM includes multiple models with differing origins. The first USARIEM thermal model—the 

USARIEM heat strain model—is labeled the HSDA to 

differentiate this first, exclusively USARIEM model 

from the later USARIEM models of heat strain that 

include elements originating from other sources. The 

basic structure of the heat strain hybrid model was 

empirically derived over the course of approximately 

30 years, starting in the early 1970s, using data from 

numerous laboratory and field heat stress studies.12,75,76

One strength of the HSDA model, and the USARIEM 

modeling program, is the strong empirical element derived from the physiological studies conducted at the 

laboratory. The model has been continuously refined 

and updated. The major strength of this algorithm has 
50

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

been its careful, methodical development and extensive validation.77 It is a well-accepted model used for 

many purposes.78,79 It requires user input for initial 

environmental conditions (eg, temperature, humidity, 

wind speed, and radiation), personnel characteristics 

(eg, height, weight, heat acclimatization status, initial 

dehydration, and initial core temperature), type of uniform, and metabolic rate or type of activity.80 Outputs 

from the model can include the following: maximum 

recommended work–rest cycle times, maximum 

single-shot work time, water intake per hour, and core 

temperature and heart rate as functions of time. Limitations of this model include the validation envelope for 

core temperature and sweating rates, which, although 

broad, does not yet include every possible heat stress 

scenario; heart rate prediction, which has not been as 

well validated as core temperature and is therefore not 

used in decision aid applications; predicted heat stress 

casualty rates, which have not been well validated; and 

estimates of prediction errors, which are limited and 

not provided for any of the outputs.

The generic USARIEM heat strain model has been 

implemented using various computer programming 

languages and incorporated into progressively more 

capable and robust decision aids. For example, a prototype, customized, handheld calculator was developed 

in the mid-1980s that had an executable version of the 

model embedded in a read-only memory microchip.13

User estimates of environmental conditions and work 

rates were entered via the calculator’s keyboard. Some 

inputs, such as type of uniform and activity, required 

selection of the desired item from a scrolling list. After all necessary inputs were entered, the calculator 

displayed work–rest cycle and hourly water intake 

recommendations. It was intended that the heat stress 

calculator be used by small unit leaders as a heat stress 

management tool. However, its development did not 

progress beyond concept demonstration and a prototype. Software for the pocket calculator was adapted 

for use on personal computers by contractors.9 This 

version of the USARIEM heat model, including menus 

for uniforms and activities, became the basis for the 

various versions of the HSDA. At present, the process 

has gone full circle; and, in cooperation with the Army 

Research Laboratory–White Sands Missile Range, a 

simplified version of the HSDA has been developed 

for use with PDAs or similar handheld electronic devices, initially named the mobile heat stress monitor 

(MoHSM) (Exhibit 2-1).

An obvious drawback of the USARIEM heat stress 

calculator was that it was not equipped with environmental sensors. A follow-on portable, digital heat 

stress monitor prototype, however, did incorporate 

miniature sensors. The HSDA model was embedded 

in the heat stress monitor. Using the sensor readings, 

the model generated accurate, location-specific, recommended work–rest cycle times and hourly water 

intake.25,81 The sensors included a miniature black 

globe thermometer and a dry bulb thermometer, but 

substituted a humidity sensor for the natural wet bulb 

thermometer. The sensors permitted calculation of the 

WBGT using an iterative equation to calculate natural 

wet bulb temperature. This information is displayed 

on a small screen on the face of the device. The sensors 

can be stowed to form a compact, hardened package. 

Despite limited use by US Marine Corps biohazard 

and chemical clean-up teams and other units, the 

heat stress monitor did not become a general issue 

field item. It is currently manufactured in Australia, 

but only some elements of HSDA are available in the 

output of the current version. Some of the benefits of 

the heat stress monitor are available in the MoHSM 

format installed on a PDA. The concept of incorporating an HSDA model into a device that directly 

measures weather inputs continues to be pursued in 

various configurations, including handheld weather 

instruments. 

An example of an effort to implement the USARIEM 

HSDA and other thermal models has been to incorporate thermal models into integrated meteorological 

software/hardware systems for acquiring, analyzing, 

and extrapolating meteorological data in real time. This 

approach was initially demonstrated as the prototype 

MERCURY/OMEGA82,83 system. MERCURY, which 

produced digital terrain overlay images from gridded 

weather data, was originally developed by the Army 

Research Laboratory–White Sands Missile Range in 

New Mexico. However, the US Army Medical Research 

and Materiel Command (MRMC) at Fort Detrick, 

Maryland, assumed oversight for the further development of MERCURY. Under MRMC, MERCURY, which 

evolved into OMEGA, merged the gridded weather 

overlay with output from HSDA. It was successfully 

demonstrated during a pilot project (Figure 2-5) at 

Eglin Air Force Base. However, MERCURY/OMEGA 

is a stand-alone product and was therefore difficult to 

support. Capabilities similar to MERCURY/OMEGA 

were incorporated into the Integrated Meteorological 

System (IMETS), which is now a component of the Distributed Common Ground System–Army (DCGS-A).84

DCGS-A allows mobile combat planning staff to 

continuously evaluate and predict the effects of terrain 

and weather on sensor systems, weapons, and mission. 

It also uses three-dimensional digital terrain and meteorological databases with near real-time weather data 

from satellites and scattered ground sensors. DCGS-A 

software provides a variety of weather products (including models for meteorological forecasting), and the 
51

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

prediction of weapons and sensor system performance 

as a function of environmental conditions. A number 

of these weather-related decision aids are incorporated into a virtual toolbox—the Integrated Weather 

Effects Decision Aid (IWEDA).84 DCGS-A can generate contour overlays depicting isopleths or contours 

for temperature, humidity, wind, visibility, and other 

meteorological properties. 

HSDA has been incorporated into DCGS-A and 

IWEDA. Map overlays depicting the risk of heat injury 

can be generated by IWEDA. DCGS-A—using userselected values for uniform ensemble, acclimatization, 

and work rate—will estimate maximum work time, 

recommended work–rest cycles, and hourly water 

requirements. Thus, many of the OMEGA capabilities 

are provided as part of DCGS-A and IWEDA. Figure 

2-6 shows a gridded color-coded HSDA output from 

IWEDA. Access to IWEDA is available only at higher 

echelons, but a more accessible version for personal 

computers (PCs) or laptops—My Weather Impacts 

Decision Aid (MyWIDA)—is being developed that 

utilizes weather data from DCGS-A or other weather 

resources.85 Additional models for both terrestrial 

cold exposure and water immersion may be added to 

the decision aid toolbox. These cold models are based 

on another USARIEM model, the Six-Cylinder Thermoregulatory Model (SCTM),86 which is described in 

Attachment B.

USARIEM also developed a six-node analytic 

heat strain model called SCENARIO.87,88 This model 

has a similar function to that of the empirical model 

described previously, except that the module that 

simulates the thermal dynamics of the body is a system 

of ordinary differential equations derived from basic 

principles of heat exchange. This model can generate 

temperature profiles for each body compartment, 

sweating rate, heart rate, and changes in cardiac output. The model was named SCENARIO to indicate 

the capability to input a file or stream of inputs, thus 

recreating an operational “scenario.” There is some 

potential for confusion when SCENARIO is used to 

evaluate operational scenarios, and as SCENARIO 

evolves, it will be renamed to avoid this confusion. 

Core temperature, sweating rate, and heart rate 

predictions generated by this model have been extensively validated. The ability to predict accurately 

other compartment temperature profiles or changes 

in cardiac output, however, has not yet been extensively validated. This model currently predicts heat 

stress casualty rates using the same mechanism as the 

empirical model.

A novel derivative of SCENARIO and work by 

Gagge et al89 and Moran et al90 is the initial capability

decision aid (ICDA).91,92 As described in Exhibit 2-2, 

ICDA uses noninvasive surface measurements collected with the Warfighter Physiological Status Monitor 

to predict core temperature, mean skin temperature, 

and sweat rate in near real time. This provides unit 

leadership with a snapshot of the thermal status of 

each individual soldier as a physiological strain index 

based on core temperature and heart rate,90,93 and provides a basis for projecting water requirements and 

the potential for near-term heat injury with continued 

heat exposure.

Cold Strain Models

Operations and training in cold areas expose individuals to risks of cold weather injuries and hypothermia. Very cold weather can dramatically reduce 

individual and unit operational capabilities. Preventing cold injuries keeps experienced soldiers on the line 

so that missions can be completed as efficiently and 

quickly as possible with minimum casualties. Personnel evacuated for cold injuries can be replaced by less 

experienced personnel who will be at higher risk for 

becoming combat casualties and for succumbing to 

cold injuries. 

Because most individuals cannot reliably estimate 

safe durations of cold exposure, model-based decision 

aids can be useful for quantifying cold stress injury risk 

and generating exposure limit recommendations to 

reduce the risk of cold injuries to as low a level as possible. A specific use for cold strain models is to generate 

cold exposure tables based on minimum allowable extremity or core temperatures. Such guidance can then 

be incorporated into safety and casualty prevention 

standard operating procedures (SOPs) and doctrine. 

The WCT is an example of how a simple cold model 

has been incorporated into military doctrine.92

Lumped- and distributed-parameter compartmental 

models for the entire body and extremities or representative digits have been developed for predicting 

generalized hypothermia and peripheral cold injuries. 

Because the transition of physiological responses to 

heat and cold stress is not linear, a compartmental heat 

strain model cannot be used directly for also predicting 

hypothermia. Separate models for heat and cold strain, 

however, can be linked within a software implementation of a generalized temperature response model so 

that the appropriate set of coefficients and parameters 

are used for the desired range of environmental conditions. If only one compartment model is used to span 

the physiological responses to both heat and cold, the 

single set of coefficients must be calculated using appropriate data from both heat and cold exposure studies. 

This would also require that validation spans both cold 

and hot conditions, whereas using separate, previously 
52

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

EXHIBIT 2-1 

MOBILE HEAT STRESS MONITOR GUIDE*,†

The US Army Research Institute of Environmental Medicine has spent years developing and improving models to 

predict human thermal responses. Through an ongoing Memorandum of Agreement with the US Army Research 

Laboratory, one of these decision tools is deployed for use on handheld Personal Digital Assistants (PDAs). It is still 

considered developmental and is not available for purchase. The latest modifications of the biophysical algorithms 

are used (heat strain decision aid [HSDA] 2004C model), and current system specifications follow, although the model 

can be installed on various platforms. The PDA with the HSDA model installed was initially named the mobile heat 

stress monitor (Exhibit Figures E1-1 and E1-2).

Other applications of HSDA use real-time weather information 

via network connection. This version of the model requires 

user input of weather, work rate, and clothing prior to calculations. Unlike the PC version that requires numerical inputs 

for weather parameters, work rate, and clothing heat transfer 

properties, the mobile handheld version uses more limited 

data input. Default standard values are used in calculations 

instead of soldier-specific data, such as height, weight, acclimation, and dehydration status. These simplifications allow 

the user to make general predictions for a group of soldiers 

with minimal data entry. Finally, many standard outputs of 

the PC version of HSDA are suppressed in the PDA version 

for simplicity and visual clarity.

PDA Inputs

	 •	 Geolocation (latitude and longitude; current default is

Natick, Mass)

	 •	 Month, day, and time of day

	 •	 Temperature (°C or °F)

	 •	 Weather: clear or partly cloudy or cloudy or precipitation

	 •	 Wind: calm or light or moderate or strong

	 •	 Humidity: dry or normal or moist

	 •	 Work rate: resting or very light or light or moderate or

heavy

	 •	 Clothing: BDU (battle dress uniform) or MOPP-1/-2 or

MOPP-3/-4 (with other uniform configurations to be 

added). The term “Mission-Oriented Protective Posture” (MOPP) refers to the level of chemical protective 

clothing worn.

PDA Outputs

	 •	 Probability of heat stress injury (%)

	 •	 Optimum work–rest cycle time (≤60 minutes/hour)

	 •	 Maximum endurance time (up to 300 minutes)

	 •	 Water Requirements (canteens/hour, 1 canteen = 0.9

liters)

	 •	 WBGT (°F)

How to Use the PDA

	 •	 Turn on PDA power by pressing the on/off button.

	 •	 Next, use the stylus to tap “Start” at the top left of the

screen display to show menu choices. 

(Exhibit 2-1 continues)

Fig. E1-1. The PDA used for the mobile heat stress 

monitor is the Microsoft Pocket PC (Microsoft 

Corporation, Redmond, Washington). Model ID: 

Hewlett-Packard iPAQ h545 (Hewlett-Packard 

Company, Palo Alto, Calif) with the HSDA2004C 

model installed using the PDA version of decision 

support tool files. HSDA: heat strain decision aid; 

PDA: personal digital assistant.
53

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

validated models would require verifying the transition 

points at which the algorithm switched from one model 

to the other and did not cause factitious transients. 

As indicated previously, cold model development 

has proceeded in two directions. Most cold models 

can be categorized as either whole-body or extremity/

digital models. Whole-body models usually address 

hypothermia, whereas frostbite or loss of function 

tends to be the more immediate concern for the extremities. This reflects the circulatory response to cold 

	 •	 Tap “LocalHeatStress” or its icon shortcut to launch the decision support tool. To change numeric inputs, first

use stylus to highlight item to be changed. 

	 •	 Then, use stylus taps on keyboard to change inputs as desired.

	 •	 Tap stylus on list boxes to choose from options. All environmental inputs, except air temperature, are selected

from short menus of conditions. For example, the choices for humidity are dry, normal, or humid, which correspond to 20%, 50%, and 80% relative humidity, respectively.

	 •	 The solar load is computed using the location in latitude/longitude, date, local time, and the menu input for

sky condition. If the PDA has a Global Positioning System capability, the location can be accessed automatically, 

and the fault date/time can be automatically retrieved from the system. 

	 •	 To obtain the output information, tap the COMPUTE button for calculations and EXIT button to stop simulations.

Exhibit 2-1 continued

Fig. E1-2. Mobile heat stress monitor input and predicted heat strain at Fort Benning, Georgia, on July 4. (Left) Selected 

inputs, including a high air temperature (100°F), moderate humidity, full sunlight, the battle dress uniform (BDU), and 

a light work rate. (Right) Outputs indicate a relatively high probability of heat injury if the maximum work time of 85 

is exceeded or hydration is not maintained, and no work–rest cycles are sustainable for this exposure and activity level.

Max: maximum; Prob: probability; WBGT: wet-bulb globe temperature.

Photograph: Courtesy of the US Army Research Laboratory, White Sands Missile Range, New Mexico.

*Laurie A. Blanchard, Biomedical Engineer, US Army Research Institute of Environmental Medicine, Natick, Massachusetts. 

†David P. Sauter, Meteorologist, US Army Research Laboratory, White Sands Missile Range, New Mexico. 
54

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

MERCURY

Camp Rudder

AF Base Station

46th Weather Flight

MERCURY

USARIEM

Internet

RF Modem

Planned RF Modem

AF Station B-70

AF Station B-71

AF Station B-72

AF Station B-75

AF Station C-52A

AF Station C-52N

AF Station Destin

Mason Landing

Boiling Creek

Weaver River

Fig. 2-5. Schematic diagram of the MERCURY/Ranger Test 

Bed at Eglin Air Force Base in Florida. AF: Air Force; RF: 

radiofrequency; USARIEM: US Army Research Institute of 

Environmental Medicine.

exposure, which essentially sacrifices the extremities 

by vasoconstriction to preserve the core body temperature and function. 

Frostbite of the fingers, toes, and face tends to be 

the primary risk for active soldiers. In addition to the 

initial pain and loss of digital function, the appearance 

of frostbite, with the discoloration and the fear of or actual occurrence of gangrene and amputation, can have 

a psychological effect disproportionate to the immediate danger. The loss of manpower, strain on medical 

facilities, and long-term disability caused by frostbite 

are, however, very real. In addition to the WCIs, other 

models have been developed to predict probability of 

frostbite for a given set of exposure conditions.

Cold digit compartment models require that users 

input digit dimensions, blood flow, initial compartment tissue temperatures, the biophysical properties 

of gloves or boots, plus air and ground temperatures. 

The typical operational output of interest is the time 

for the tip of the digit to reach a threshold temperature 

(eg, 5°C or 41°F), below which there is increased risk 

of peripheral cold injury. 

Some peripheral hypothermia models mathematically incorporate the effects of cold-induced 

vasodilation (CIVD).93 This phenomenon effectively 

balances competing requirements for heat-conserving 

vasoconstriction and nutritive vasodilation. Unfortunately, readily identifiable individual factors that can 

predict CIVD have not been adequately established 

to include this in these models. Furthermore, without 

being able to reliably predict which personnel will respond to declining digit temperatures with CIVD, the 

longer exposure times predicted with a CIVD model 

would put those without CIVD at risk for peripheral 

cold injuries. 

A numerical model of a generic distal extremity 

(eg, finger) exhibiting simulated countercurrent arteriovenous heat exchange for predicting temperature 

response of digits to cold stress has also been developed by Shitzer and colleagues94 at USARIEM. The 

model (Attachment A) is based on the geometry of a 

multilayered cylinder and sophisticated control theory.

At the time of its development, the computational requirements for a complex, multinode model exceeded 

the computational resources that would be available 

in an operational setting. Obtaining the requisite, detailed data to expand the validation of the model has 

also been difficult. The focus at USARIEM is to link 

a simpler extremity model to the whole-body model. 

A limitation of WCT and other windchill models 

presently incorporated into military doctrine92 is that 

these models predict only local frostbite of the extremities and/or comfort. Although frostbite tends to be the 

primary risk for well-dressed soldiers who engage in 

activities that result in significant levels of metabolic 

heat production, when soldiers are forced into a sedentary state or exposed to extreme cold without adequate 

clothing, hypothermia is a significant risk. Present 

windchill models do not address hypothermia. In addition, partial immersion is a confounding condition. 

Tikuisis and colleagues,95 working at USARIEM 

and DRDC Toronto, developed several versions 

of whole-body cold models for both dry and immersed individuals. Through access to the cumulative USARIEM database, Tikuisis et al were able 

to quantitatively identify the importance of body 

fat during immersion. More recently, Xu and colleagues86 developed an improved model, the SCTM, 

that incorporated both heat and cold effects for both 

terrestrial and immersion states. Additional applications using SCTM are discussed in Attachment B.

Models of the more extreme immersion state are 

easier to validate because of both greater availability 

of data and the less complex biophysics of immersion 

in a liquid when, in the nude state, virtually the entire 

body surface is exposed to the same convective stress. 

Whole-body cold models become more complex with 

clothing, partial immersion, wet clothing, or the greater 

complexity of conductance through foot and hand 

contact, convection to air at varying velocities, evaporation, and radiant exchange in different directions. 

Because terrestrial cooling is sensitive to variations in 

clothing, wind speed, and activity over a wide range 

of air temperatures above and below freezing, it is 

particularly difficult to develop an adequate database 

for model development. 
55

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

Moran and colleagues96 proposed a cold strain index 

(CSI). They improved the version of CSI97 for dry or 

terrestrial cold exposure, suggesting that cold strain is 

a product of both core and extremity surface cooling. 

It is unlikely that an individual with severely frostbitten hands will be able to function as a soldier during 

operations, nor survive for an extended period of time 

without assistance. A successful cold model must therefore account for both extremity and whole-body cooling. 

Thus, recent efforts at USARIEM, such as SCTM, have 

attempted to link whole-body and extremity cooling.

High-Altitude Models

There is currently no operationally useful, validated 

model for accurately predicting soldier responses to 

acute, subacute, or chronic exposure to the hypobaric 

hypoxia of high altitudes.70 One fairly comprehensive 

physiological response model exists, but it does not 

link predicted physiological responses with altitude 

illness rates and has not been validated for use in military operational settings.98 Adding to the complexity 

of developing a comprehensive casualty prediction 

altitude exposure model is that ascent to high mountain altitudes is typically associated with simultaneous 

exposure to cold, harsh, and labile weather, causing 

significant risk for hypothermia and peripheral cold 

injuries, increased intensity of direct and reflected ultraviolet radiation (which predisposes one to skin and 

ocular injuries), and exposure to rugged terrain (which 

predisposes one to traumatic injuries). Also, an operationally useful high-altitude casualty prediction model 

should include the effects of prophylactic medications 

that have been found effective in reducing the risk and 

severity of high-altitude illnesses. A comprehensive 

high-altitude exposure model ideally would integrate 

these disparate but related factors to accurately predict the physiological strain, injury, and illness rates 

for proposed high-altitude missions or, conversely, 

generate recommended ascent profiles to limit altitude illness rates below a specified maximum level.

Independent or predictor variables for constructing 

high-altitude physiological and medical outcome models would necessarily include environmental, mission, 

and personal factors. Mission-related factors would be 

extremely important for predicting physiological strain 

and medical consequences of ascent to high altitude. 

Absolute altitudes and proposed rates of ascent determined by command-imposed time lines for reaching 

mission objectives would be major environmental and 

mission determinants of altitude illness rates. 

Estimated compliance rates with prescribed prophylactic medication regimens against altitude illness 

before and during ascent would be another important 

factor. Predicted environmental temperatures and 

biophysical properties of uniforms; solar intensity; 

number of hours of day versus night operations; percentage of personnel who will not have or will lose 

their sunglasses; estimates of amounts of potable water 

available per person per day; and an index of terrain 

ruggedness could all qualify as predictor variables for 

altitude, solar, cold, and traumatic injuries and illnesses 

that would be of operational importance for missions 

in high mountain areas. A comprehensive predictive 

altitude model, therefore, could be useful to commanders and their staff, and for advising medical officers to 

develop reasonably accurate quantitative estimates of 

the injury and illness rates associated with alternative 

approaches to achieving combat, peacekeeping, civil 

action, or disaster relief objectives in high mountain 

areas. 

Without a trusted prediction model to quantify these 

types of potentially preventable health risks, operational and tactical planning staff might not adequately 

consider the relative importance of these problems 

when selecting among alternative mission strategies. 

Medical planners could also use a comprehensive 

predictive altitude model to develop balanced medical 

support requirement plans. This would include better 

specification of evacuation and treatment resources. 

For example, evacuating ill or injured personnel in 

high, rugged, stormy, mountainous environments will 

often be resource intensive. 

Assumptions and Biomedical Models

Assumptions are an inescapable aspect of model 

development (including notional models). It is recommended, though, that they be explicitly identified, 

categorized, and their existence and information disseminated to users of related models. Users of modelbased analysis and decision tools should understand a 

model’s operationally important explicit and inherent 

assumptions and determine to what extent they might 

affect the accuracy and validity of its predictions for 

specific applications. For example, the USARIEM 

heat strain model has been used to develop recommended work–rest cycles and water intake tables 

for various deployment handbooks.27 Such tables are 

accompanied by a list of the important assumptions 

that the user must check before utilizing the tables. 

The assumptions include the following: that the troops 

for which the recommendations will be applied are 

basically healthy and adequately nourished (because 

the data used to develop the model were obtained 

from healthy nourished soldier volunteers), and that 

everyone starts out adequately hydrated (because the 

tables were created using an initial condition of no 
56

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

EXHIBIT 2-2

INITIAL CAPABILITY DECISION AID THERMAL PREDICTION MODEL*,†

The initial capability decision aid (ICDA) model is a heat stress prediction model developed for monitoring the physiological status of soldiers. It is a basic and abridged model derived from elements of the US Army Research Institute 

of Environmental Medicine (USARIEM) human thermal physiological simulation computer model, SCENARIO,(1) and 

the Gagge model.(2) The model can be loaded with anthropological characteristics of an individual (ie, height, weight, 

and clothing), group means, or default population values. Real-time inputs of measured heat rate and local weather 

(eg, temperatures, wind, relative humidity, and estimates of radiant load) are used by the computer model to make 

real-time predictions and estimates of the subjects’ physiological status or other physiological parameters.

A main purpose for constructing this model was to predict time estimates of the internal body temperature (Tcr), 

sweat rates (SR), and hydration status of soldiers in a battlefield situation. For instance, Tcr is the traditional and 

common physiological parameter for heat strain assessment, as it reliably indicates impeding injury.(3,4) However, 

measuring Tcr is invasive and can be impractical for real-time monitoring of soldiers dispersed over a large area 

and exposed to heat stress while engaged in long hours of varied and unpredictable tasks. Although obtaining 

“true” values of many parameters from environmental, physiological, and operational conditions is desirable 

(Exhibit 2-2 continues)

Evaporation from skin

Respiratory heat loss

Skin blood flow

Convection to air

Conduction through clothing

Radiation to

surrounding surfaces

= core

= skin compartment

= clothing property

Fig. E2-1. Schematic of core, skin, and clothing 

compartments.

Mean ICDA

Mean lab

+ 1 SD

Minutes

Core Temperature (°C)

0 20 40 60 80 100 120 140 160 180

36.5

37.0

37.5

38.0

38.5

39.0

39.5

40.0

Fig. E2-2. Summary comparisons between mean measured and predicted core temperatures from different 

heat studies. Heat study 1 (27°C, 75%; hot weather Battle 

Dress Uniform; n = 9). 

ICDA: initial capability decision aid 

Illustration: Adapted with permission from Santee WR, 

Berglund LG, Cardello A, Winterhalter CA, Endrusick 

TL. Physiological Assessment of Volunteers Wearing Battle 

Dress Uniforms (BDUs) During Intermittent Exercise. Natick, 

Mass: US Army Research Institute of Environmental 

Medicine; 2006. Technical Report T06-06, unpublished 

data, June 2006.

and increases the model’s accuracy to assess soldiers’ 

status, alternatives for the worst-case scenario (eg, 

losing signals from sensor devices, wrong calibration, 

or conflicts between sensors) still need to be considered. For these reasons, ICDA was developed to 

predict physiological responses to battlefield situations from a minimum number of noninvasive inputs. 
57

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

The thermal physiology of the ICDA model is represented 

schematically in Exhibit Figure E2-1, where the human is 

modeled as two physiological compartments (core and 

skin) surrounded by a passive clothing compartment. 

Within a compartment, the properties are uniform (ie, 

everywhere within the core at time t, Tcr has the same value). All metabolic heat production (M) occurs in the core. 

Some heat is lost directly from the core to the environment by respiration; all of the other heat from the core is 

transferred to the skin by conduction or convection with 

skin blood flow. The primary method used to regulate 

Tcr is achieved by controlling blood flow. Exhibit Figures 

E2-2 and E2-3 present the results for Tcr predictions from 

two of three heat studies used to validate the model. 

More complete information, including data from all three 

studies, are presented in other reports and publications.(5)

Recent reports from wars in Iraq and Afghanistan indicate that faster access to medical/surgical care and 

identifying evacuation situations would save more soldiers’ lives.(6,7) The current strategy to shorten the time 

lag between injury and treatment is to position a small 

surgical care unit near the battlefield.(7) The model can 

contribute this effort by forecasting both real-time and 

future probabilities of soldiers’ health status by notifying 

unit medical personnel and command elements on the 

battlefields. The ICDA will also provide a longitudinal 

Exhibit 2-2 continued

0

Mean ICDA

Mean lab

+ 1 SD

36.5

37.0

37.5

38.0

38.5

39.0

39.5

40.0

Minutes

Core Temperature (°C)

5 10 15 20 25 30 35 40

Fig. E2-3. Summary comparisons between mean measured 

and predicted core temperatures from different heat studies. Heat study 3 (35°C, 45%; protective garment; n ≤ 8).

ICDA: initial capability decision aid

Illustration: Adapted with permission from Latzka WA, 

Sawka MN, Montain SJ, et al. Hyperhydration: tolerance and cardiovascular effects during uncompensable 

exercise-heat stress. J Appl Physiol. 1998;84:1858–1864.

projection of SR, which can be used to predict soldiers’ dehydration status and water requirements. Thus, logistics 

personnel can plan for water delivery to meet the projected demand and the associated cost, and soldiers can sustain 

their physical and cognitive performances by preventing dehydration.

Predictions of soldiers’ thermal status during heat stress are promising, particularly for Tcr, using this simplified model. 

To improve predictions of skin temperature (–Tsk), the existing databases should be evaluated to determine which –Tsk

measurement site best represents the combined impact of individual variability, clothing, environment, and operations 

on –Tsk, and is, therefore, the best site to use for model development and validation of –Tsk predictions. Similarly, for SR 

predictions, the trends of individual SR patterns need to be carefully evaluated to further refine this model. Lastly, it 

is recommended that ICDA be applied to real-time situations in both laboratory and field training exercises for future 

Tcr sensitivity analysis and further model development. 

*Miyo Yokota, Research Scientist, US Army Research Institute of Environmental Medicine, Natick, Massachusetts.

†Larry G. Berglund, Biomedical Engineer, US Army Research Institute of Environmental Medicine, Natick, Massachusetts.

Data sources: (1) Kraning KK, Gonzalez RR. A mechanistic computer simulation of human work in heat that accounts for physical 

and physiological effects of clothing, aerobic fitness, and progressive dehydration. J Therm Biol. 1997;22:331–342. (2) Gagge AP, Fobelets AP, Berglund LG. A standard predictive index of human response to the thermal environment. ASHRAE Trans. 1986;92:709–731. 

(3) Amos D, Hansen R, Lau WM, Michalski JT. Physiological and cognitive performance of soldiers conducting routine patrol and 

reconnaissance operations in the tropics. Mil Med. 2000;165:961–966. (4) Pandolf KB, Goldman RF. Convergence of skin and rectal 

temperatures as a criterion for heat tolerance. Aviat Space Environ Med. 1978;49:1095–1101. (5) Yokota M, Berglund LG. Initial Capability Decision Aid (ICDA) Thermal Prediction Model and Its Validation. Natick, Mass: US Army Research Institute of Environmental 

Medicine; 2006. Technical Report T06-9. (6) Bilski TR, Baker BC, Grove JR, Hinks RP. Battlefield casualties treated at Camp Rhino, 

Afghanistan: lessons learned. J Trauma. 2003;54;814–822. (7) Gawande A. Casualties of war—military care for the wounded from Iraq 

and Afghanistan. N Engl J Med. 2004;351:2471–2475.

more than 1% dehydration). Other assumptions are 

that it would be impractical to create separate tables 

for every possible combination of the situationally less 

important independent variables. Therefore, representative values are used. The extent to which actual 

conditions deviate from these assumptions, as well as 

how the recommended or assumed values should be 

adjusted, needs to be assessed by the users if direct 

consultation with the modeling group that created the 

tables is not feasible.

Numerous legitimate assumptions are frequently 

invoked during model derivation and development. 
58

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

They might be necessary to simplify complex processes, to make the modeling effort tractable, or to 

permit spanning knowledge gaps that would otherwise prevent model completion. Assumptions might 

be necessary when users want a practical, easy-to-use 

model in lieu of a cumbersome, full-featured, highresolution version. Assumptions can also be necessary to account for the effects of uncertainty and the 

seemingly random variations. In addition, they might 

Fig. 2-6. Graphic representation of the risk of heat injury 

generated by the Integrated Weather Effects Decision Aid 

(IWEDA). Color-coded output for the risk of heat injury, 

based on the USARIEM Heat Strain Decision Aid (HSDA), 

which is incorporated into the IWEDA component of the 

Distributed Common Ground System–Army (DCGS-A) 

weather “toolbox.” The map represents, for each colored 

pixel, the highest risk of thermal injury projected for an area 

in Afghanistan for a 24-hour period (0700 on May 10, 2011 

to 0800 on May 11, 2011) for warfighters wearing the Army 

Combat Uniform with body armor while engaged in moderate activity, and assumes partial (5 days) heat acclimatization. 

Red represents a greater than 50% risk of heat injury, amber 

indicates a risk between 25% and 50%, and no color (usually 

represented as green) indicates the risk is below 25%. The 

color coding may be adjusted to reflect different risk levels. 

For the whole area, each colored pixel represents a 15-km 

area, and the temporal resolution is 3 hours. For the smaller 

area outlined in blue, a more detailed weather forecast, a 

Weather Running Estimate (WRE)—based on interpolation, surface observations, and upper air soundings—is 

available. For the WRE, the resolution is 1.5-km pixels for 

30-min intervals. Information for this area, with an associated projection of risk from IWEDA, is presented in a colored 

chart that presents the threat level for an expanded 48-hour 

timeline. Additional information regarding maximum work 

times, work–rest cycles, and water requirements is available 

from DCGS-A. 

Photograph: Courtesy of US Army Project Manager, Distributed Common Ground Station–Army.

be necessary during, or an inevitable consequence of, 

the model implementation process. For example, the 

form of derived or empirically selected equations, 

the numerical methods used to generate output, and 

the inherent logic in a software realization can affect 

the accuracy and stability of the model. Furthermore, 

although the many equations in a complex model 

might be stable and well-behaved when evaluated 

individually, often there remains the unproven assumption that the overall model will also be stable and 

well-behaved within the variable space over which 

each equation individually was determined to be valid.

Most users of model-based products will not have 

the technical background, interest, or time to verify 

model correctness or validation. Therefore, they must 

usually assume that the model was developed properly, that algorithms are correct, that the forms of the associated regression equations are appropriate, that the 

implementation is debugged, and that the model and 

implementation have been validated. As referenced 

in chapter 1, there is a formal process for validation, 

verification, and accreditation (VV&A) of models. 

Model developers must systematically establish the 

credibility of their products. This can be accomplished 

by organizing a model development process with documented control mechanisms that will ensure (to the 

greatest extent feasible) and certify model correctness 

and validation prior to product release. Incomplete, 

operationally invalidated models, however, are useful for proof-of-concept demonstrations and to elicit 

feedback from prospective users during the concept 

development and exploratory development phases of 

a modeling project.73

Physiological heat strain models, for example, are 

often associated with a number of important assumptions. Algorithms that generate predictive core temperature profiles versus time do not explicitly model 

the effects of skin temperature. However, skin temperature is clearly a relevant factor in thermoregulation. It 

determines the core-to-skin and skin-to-ambient temperature gradients that influence rates of conductive 

heat flow from core to skin and skin to environment. 

Also, the vapor pressure and rate of evaporation of 

the layer of sweat adhering to the skin’s surface are 

functions of skin temperature.

A certain amount of inaccuracy in some types of 

predictive heat strain algorithms might be related to 

not explicitly including terms for skin temperature. 

However, skin temperature effects will be implicitly 

included in heat strain models whose coefficients 

were obtained using data from heat stress studies. 

The experimental data in such situations implicitly 

reflect all the thermoregulatory processes affecting 

changes in core temperature. For example, actual core 
59

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

temperature measurements include the effects of skin 

temperature, sweating, and changes in skin blood flow. 

Therefore, an empirical regression model can predict 

core temperature quite reliably, even though skin temperatures are not explicitly delineated in the model. In 

such circumstances, the effects of skin temperature are 

in the model, but distributed among its coefficients in 

a manner that is not separable or directly discernable. 

These types of predictive thermal strain models will 

be algorithmically less complex than if skin temperature effects were explicitly included. Initial skin temperatures during use of such a model are necessarily 

assumed to be those from the data from which the 

model was developed. If skin temperature is modeled 

explicitly, users may then have a mechanism for entering situation-specific initial skin temperatures that can 

result in more accurate core temperature predictions.

A serious mistake of modeling the effects of skin 

temperature could occur, however, if an analytically 

derived model with empirically determined coefficients, but not modeling skin temperature, was “enhanced” or upgraded with additional skin temperature 

equations or terms having coefficients calculated from 

separate data. This could result in an incorrect model, 

because skin temperature effects would be duplicated, 

to some extent, using such an approach. A similar, 

but incorrect, alternative that is sometimes used in 

practice is the inclusion of terms to explicitly model 

a new process variable, such as skin temperature (or 

any other factor not in the initial model), and then 

“tweaking” miscellaneous parameters in the new and 

original terms until the predictions from the enhanced 

model match experimental data. With this approach, 

the modeler, in effect, arbitrarily reallocates the unmodeled thermoregulatory effects between new and 

previously defined coefficients. 

The preferred method for expanding a model requires that parameter identification and model validation be completely redone. This can be facilitated 

by the availability of a robust statististical analysis 

application for performing complex multiple regressions conveniently linked to large data sets from an 

extensive database of heat stress study results.99

The body tissue compartment is a common abstraction used in the formulation of biomedical and pharmacological models. It involves important simplifying 

assumptions. In compartment models, portions of the 

body (eg, the digits in models for predicting maximum 

cold exposure times) are neatly partitioned into a small 

number of discrete stereotypical geometric volumes 

(eg, concentric cylinders) having homogeneous tissue 

and biophysical properties. A typical compartment 

structure depicted graphically has a central blood 

compartment and a solid cylindrical core compartment representing viscera, intrathoracic, and cranial 

tissues surrounded by successive concentric hollow 

cylinders representing muscle, fat, vascular skin, 

and nonvascular skin. Each compartment can also be 

represented as a single point having the temperature 

and biophysical properties of all other points in the 

compartment. This is one reason why a compartment 

model is also referred to as a lumped-parameter model. 

Except for the outer skin surface, the surface areas of 

the intercompartmental interfaces are not actually 

measurable. They are calculated in accordance with 

the geometric model using best obtainable estimates 

of average compartment volumes and densities. This 

type of model implicitly assumes that properties and 

values of the predicted variables are time-dependent, 

but not functions of location along the interface. 

Heat and cold strain models for predicting tissue 

compartment temperature profiles intrinsically assume that all points in a compartment are always at 

the same temperature and change simultaneously by 

identical amounts. Therefore, this results in a lowresolution model that admits transcompartmental, but 

not intracompartmental, temperature gradients. This 

restriction necessarily implies that heat flows infinitely 

fast within compartment boundaries. This would be an 

untenable assumption if it were not for the extensive 

and fairly uniform plexus of blood vessels that traverse most tissues. This allows rapid convective heat 

transfer between compartments, thereby creating the 

tendency for temperature equalization within tissue 

compartments. The compartment assumption is, in a 

sense, an abstraction of the details of this convective 

blood flow process. For most practical applications, 

this assumption results in a sufficiently accurate and 

reliable heat or cold strain prediction model. 

Greater predictive accuracy and spatial resolution can theoretically be obtained with distributedparameter models; however, their solutions are often 

more difficult to derive. This class of mathematical 

model also uses compartments, but the biophysical 

properties of tissue within each compartment are 

specified with greater resolution as functions of specific 

location. Likewise, values for predicted variables are 

functions of exact intracompartmental location and 

time. Distributed-parameter models determine timedependent heat conduction from point to point within 

each compartment. There is not just one temperature 

per compartment; rather, there are as many separate 

temperatures as permitted by the spatial resolution of 

the solution method. As advantageous as that might 

be, this type of model is not as commonly used as the 

lower resolution, lumped-parameter type, because it is 

much more difficult to identify the functions or specific 

values describing spatially varying tissue properties 
60

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

and initial conditions. Also, a distributed-parameter 

model is generally more difficult, expensive, and timeconsuming to validate, if it can be done at all. This is 

because validation requires that initial values for the 

predicted variables be obtained for points throughout 

the volumes being modeled. For many variables, the 

technology might not exist to make this possible. Also, 

even if a distributed-parameter model can be validated 

in carefully controlled experimental settings, it can be 

impractical during operational use to fully and accurately determine or specify the functional form of a 

large number of initial and boundary conditions.

Other modeling assumptions that do not involve 

simplification of morphological characteristics and the 

natural distribution of tissues and biophysical property 

gradients can be illustrated by examining the link in 

the USARIEM heat strain model between predicted 

core temperature response and likelihood of heat stress 

casualties. The more mathematically complex portion 

of the model is the empirically derived algorithm that 

predicts core temperature as a function of numerous, 

situation-specific personnel and environmental factors. 

The other component predicts heat stress casualty rates 

as a single function of the calculated core temperature. 

A 50% rate of heat stress casualties is predicted when 

core temperature reaches a mean of 39.5°C (103.1°F). 

The casualty rate function has an effective standard 

error of approximately 0.3°C (0.54°F), so that a 95% 

heat stress casualty rate is associated with a core temperature of 40.1°C (104.2°F). 

The predicted casualty rate refers to heat stressrelated illnesses that require evacuation to a medical 

treatment facility. Unfortunately, the model, as it currently exists, cannot partition the predicted total heat 

stress casualty rate into diagnostic categories, such as 

dehydration, dermatological conditions, heat exhaustion (mild, moderate, recurrent), or heatstroke (moderate, severe, lethal). This limitation restricts the ability of 

extending the model in ways that would be useful for 

medical planners. For example, diagnostic resolution 

is required for estimating the medical resources necessary to transport, treat, and rehabilitate different types 

of heat stress casualties. The heat strain model would 

need to be expanded to be able to predict different 

types of heat illness. It is unlikely that such an extended 

heat illness prediction module would be accurate if 

the output were a function of core temperature only. 

Additional variables—including skin temperature, 

dehydration, and rate of core temperature increase, as 

well as direct dependency on mission (eg, work rates) 

and environmental input factors—would be necessary 

considerations. To link casualty and required medical 

logistics support would require adding a third component to the current model. 

Development of a component for predicting the 

logistic requirements for a potentially complex and 

dynamic mix of the types of heat illness would need 

to be derived by obtaining data retrospectively from 

treatment records, or preferably by conducting prospective studies that would collect, in an unbiased 

and as complete a manner as necessary, representative 

medical logistical data on heat stress illness. In Chapter 

12, an example of a database of medical records—the 

Total Army Injury and Health Outcomes Database—is 

described. Logistical support requirements for the 

evacuation, treatment, and disposition of heat stress 

casualties could be modeled as a function of available 

medical evacuation and treatment personnel and technology, type of operational scenario, terrain, tempo, 

and other complex variables.71 To develop a predictive 

logistics component for the overall model, observational or experimental data regarding requirements 

for evaluation, treatment, and evacuation resources 

required for each type of environmental stress casualty 

would need to be obtained.100

Validation of Biomedical Models

All models used for training or decision-making 

should be validated.101 Although, as noted previously 

and referenced in Chapter 1, there is a formal process 

for VV&A (MIL-STD 3022), the application of the process to physiological models presents a challenge. This 

is a process that verifies that there is no statistically 

significant difference between measured and predicted 

outcomes. From a practical standpoint, however, the 

deployment of model-based products usually cannot 

await complete validation. The number of inputs for 

the mathematical algorithms of the models and the 

alternative branching in the traversal of many logical 

structures in the software implementations can be so 

complex and numerous, or span such a wide range 

of plausible values, that it is not feasible to validate 

predicted effects of every possible combination of 

values for the independent variables. Validation of 

models and simulation algorithms can be performed 

for only points or small areas or volumes at a time in 

a hyperdimensional space defined by the plausible 

range of values for the independent variables. Because 

the envelope for the validated region can usually be 

expanded only by a limited amount through any 

particular validation study, extensive validation of a 

model can become very costly and extend over many 

years or even decades. The envelope of the independent variable regions for which a model has been 

validated expands as successive validation studies 

are performed. 

Statistical evaluation is required during validation 
61

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

because, although models are often deterministic, 

measured data contain noise or variability for a wide 

variety of reasons, including the changing influences 

of variables and factors that are not measured or controlled. Compared with the output from deterministic 

models, which always generate the same output values 

for the same initial conditions, real-world data always 

include noise; that is, model-based predictions will 

not usually precisely match actual results. Because 

model-based predictions are not always exactly correct, some individuals categorically reject their use. 

However, well-constructed and validated models, even 

if not always precisely correct in their predictions, are 

often more accurate, consistent, and able to evaluate 

more factors simultaneously than unaided subjective 

estimation processes. 

The “failure” of models is sometimes the result of 

inflated expectations. Physiological responses to equivalent stress, even for the same individual, demonstrate 

a degree of variability. In addition, measurement methodology allows some error. Under field conditions, any 

claim of a precise replication of conditions should be 

suspect. Thus, a categorical rejection of a model when it 

does not exactly match field data is naive. In addition, 

no event can be completely physiologically isolated. 

Wallace et al,102 for example, in an epidemiology study, 

determined that heat injury was strongly correlated to 

a history of cumulative exposure to heat stress over 

at least the previous day. A practical demonstration is 

that the NWS issues a heat wave warning based on the 

persistence of high air temperatures over a 3-day period, rather than exposure to high temperature, per se. 

In a similar manner, as an operation progresses, most 

individuals are unable to maintain peak physiological 

conditioning as progressive sleep deprivation, muscle 

fatigue, nutritional short falls, and mental fatigue take 

a toll. At present, no model compensates for all aspects 

of a sustained operation.

Pielke and Conant103 used weather forecasts to illustrate how a better understanding of models could 

establish their utility despite some inherent error. As 

they indicate, weather forecasts are model predictions, 

and practical experience indicates that those predictions are not wholly accurate. However, most people 

do not completely reject or dismiss the forecasts due 

to that inaccuracy. Certainly, no one rejects weather 

reports based on a one-time over- or underprediction. 

Rather, we learn to work with the limitations of the 

predictions and, as we become more familiar with the 

inherent error, we learn to take the possibility of error 

into our decision-making process. Familiarity with 

predictions from a specific model promotes better use 

of the model. By incorporating models into training 

doctrine, units will be prepared to use the guidance 

during actual operations.

Most models are deterministic abstractions of natural processes that exhibit considerable variance when 

repeatedly measured at each value of the independent 

variables. Mathematical models can be constructed to 

incorporate such variation if error terms, obtainable 

from regression analysis results for the parameters of 

interest, are incorporated into the model rather than 

discarded, as is often the case in practice. The parameters or coefficients in modeling equations would then 

be statistically parameterized with corresponding 

means and standard deviations (for determining variance of predicted results for individuals) or standard 

errors (for determining variance of predicted results 

for a group). Although the estimates of true (often 

unknowable) model parameter values are usually 

assumed to be normally distributed, the distribution 

of the predictions might not be. When simple mathematical algorithms incorporate parameter variances, 

it might be possible to analytically determine distribution (eg, normal, chi square) of the predicted output. 

This is usually not possible for a complex mathematical 

algorithm; Monte Carlo simulation and hypothesis 

testing methods are required to characterize the statistical distribution of the output. 

Differences between predicted variables and measured values will always occur because a model cannot 

fully account for all the complexities (manifesting as 

apparent randomness) of personal, environmental, and 

mission-related processes. Another source of disparity 

between predicted and actual responses is measurement error for user inputs. Primarily, this refers to the 

uncertainty or error in ascertaining the true values 

for the initial conditions. For example, a heat strain 

model might require the user to input a value for the 

ambient WBGT, and/or the three weather variables 

used to compute WBGT. However, WBGT values, as 

a function of dynamic weather patterns and terrain, 

often are a relatively rapidly changing set of inputs. For 

example, WBGT values obtained 5 km, 1 km, 100 m, 

or 1 m away from a group of working individuals can 

result in significantly different model-generated recommended work–rest cycles. WBGT values obtained 

in the immediate work area are the most appropriate (assuming a properly functioning and calibrated 

WBGT instrument), because they will most accurately 

reflect actual conditions and result in more accurately 

predicted physiological responses. When personnel 

are wearing thick or impermeable uniforms, however, 

ambient WBGT values will usually not be a good 

predictor of the rapid onset of heat strain, because the 

ambient WBGT values in such circumstances will not 

accurately reflect conditions within the microclimate in 

the layer between the skin and inner layer of clothing. It 
62

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

is the microclimate in this layer that is most influential 

in characterizing the heat strain response rather than 

the ambient WBGT values. Ambient and skin–clothing 

microclimate values can differ substantially, because 

air movement in the skin–clothing microclimate layer 

is limited to air pumping from body movements. Occlusive clothing restricts the venting of microclimate 

air into the ambient air, thereby seriously reducing convective heat loss potential. In addition, the increased 

humidity in the microclimate skin–clothing layer has a 

positive feedback effect on increasing heat strain from 

reduced sweat evaporation rates. 

The correlations between distant to local WBGT 

might be weak and nonstationary. They might be 

time-shifted, as the effect of clouds, wind, and other 

meteorological phenomena on spatial-temporal 

variations of WBGT traverse from one location to 

the other. However, variations in terrain features 

can be independently associated with substantial 

differences in WBGT readings. If only dry bulb temperatures are available, a model might require the 

user to measure or estimate ambient humidity, wind 

speed, and solar load. Such estimates will always be 

fraught with error. However, similar estimations are 

routinely made when exercising unguided judgment 

to decide how long to work when the weather is hot. 

In this respect, the model is no more susceptible to 

measurement inaccuracy than comparable unaided 

decision-making processes. Of course, ad hoc mental 

modeling is analogous to fuzzy logic algorithms, 

which are generally better suited than mathematical 

algorithms for processing imprecise inputs.104 Fuzzy 

logic typically generates imprecise, but easy-tocomprehend useful recommendations or predictions. 

With fuzzy logic, precise measurements for the input 

variables are not necessary. If they are available, they 

must be “fuzzified” (ie, the precise input data must 

be appropriately categorized with respect to defined 

levels). In some instances, this “fuzzification” process 

can negate the effects of incorrectly specified initial 

values. Even though certain input variables must be 

estimated, model-generated predictions can still be 

more accurate than subjective opinions. 

Some methodologies—such as Monte Carlo techniques to develop statistical probability boundaries, 

or the use of individual training sets with neural 

TABLE 2-1

FAMILY OF THERMAL STRESS MONITORING SYSTEMS PROPOSED BY USARIEM

Model-based Guidance 

Direct Model Applications Documents

System MoHSM for Heat Stress Tactical

Name: PSM PDA/BMIS-T Monitor Decision Aid IWEDA Area Guides Heat Doctrine

Models: ICDA HSDA SCTM HSDA SCENARIO HSDA SCTM HSDA All Models

Users Soldier information Medic/small Independent Company or Battalion or Individual Corp/division

available through unit leader small unit battalion other field soldier, command, 

medical and staff grade staff small unit and medical 

command use and leadership and logistics

networks disseminate planners

 information

Status PSM under Testing and Tested as Not deployed Weather Available for TB MED 507

development development prototype product — all soldiers doctrine

 (see text) upgrade in via PHC based on 

 progress WBGT—

 new

models 

needed to

improve

guidance

BMIS-T: Battlefield Medical Information System–Tactical; HSDA: heat strain decision aid; ICDA: initial capability decision aid; IWEDA: Integrated Weather Effects Decision Aid; MoHSM: mobile heat stress monitor; PDA: personal digital assistant; PHC: US Army Public Health Command (formerly CHPPM [US Army Center for Health Promotion and Preventive Medicine]); PSM: (Warfighter) Physiological Status Monitor; 

TB MED: technical bulletin medical; USARIEM: US Army Research Institute of Environmental Medicine; WBGT: wet bulb globe temperature.
63

Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

network models—can help address the issue of individual variability. Generally, however, models cannot 

predict precise responses for any specific individual. 

The predicted responses are mean responses for a 

group having the specified characteristics. Hence, 

models usually are not designed to handle the effects 

of natural variations within a group of individual 

characteristics or differences in clothing and workloads. A number of factors influence how this affects 

prediction accuracy. 

The operational use of model-based decision aids 

should be incorporated into staff and medical services 

processes, as delineated in SOPs or guidance. Modelbased products can then become ingrained into normal 

workflow and their use sanctioned in organizational 

publications. This helps ensure that decision aids will 

be used appropriately. Such references can also provide guidance for the proper use of model-based tools, 

including acceptable assumptions for nonmeasurable 

input variables.

There are two aspects to the USARIEM thermal 

modeling effort. The first, more scientific endeavor 

has been to develop a suite of thermal models, such 

as HSDA, SCENARIO, and SCTM. The second effort 

has been an attempt to transition the scientific knowledge to field applications. To that end, USARIEM has 

proposed a family of environmental health monitoring systems, as depicted in Table 2-1. This family of 

systems could help prevent heat injury or illness at 

the individual war fighter, small unit, and corps or 

division level. The plan, as conceptualized in Table 

2-1, has not been achieved, but IWEDA incorporates 

the USARIEM thermal models as weather products 

on the system. SCENARIO has been developed as a 

PC-based analytical tool; and the simplified MoHSM 

does provide access to thermal models at the small 

unit or individual level. The heat stress monitor—because of a lack of a formal requirement, weight, cost, 

and bulk—was not accepted by the military, but the 

basic concept of the heat stress monitor continues to 

be pursued using other platforms, such as handheld 

weather instruments. These or similar modeling products should help provide the war fighter with a vital 

link to prevent thermal injury or illness. 

SUMMARY

Models and simulations allow exploration of the 

likely consequences of high-risk situations or alternatives that are too dangerous, expensive, numerous, or 

time-consuming to actually test and evaluate. There 

are, however, some potential disadvantages in the 

use of models and simulations. The fidelity of models 

and simulations will always be limited to some extent. 

Transfer of training from model-based simulation to 

actual situations will never be perfect and, in some 

cases, there might be negative training transfer. The 

range of valid outputs will always be constrained to 

varying degrees by inherent assumptions. Modelbased algorithms will become outdated as new information becomes available through experience or 

research. Also, the use of model-based products needs 

to be integrated into organizational practices, doctrine, 

and guidance. Models can be plagued by technical 

problems that are not readily apparent. For example, 

models that generate plausible outputs for certain 

ranges of input variables can have an algorithm that 

is partially or entirely incorrectly formulated. Thus, 

models should be verified as correct by subject matter 

experts. The structure and logic of a model might be 

correct, but biased because of the coefficients obtained 

from data in which test subjects or study conditions 

were not representative of the more general conditions 

for which model outputs are more commonly applied. 

The model results should be validated for the range 

of conditions and characteristics of populations for 

which the model will be considered applicable. Also, 

models almost always include simplifying assumptions. Therefore, results will be accurate insofar as 

the assumptions used in developing the model apply 

to the specific situation under consideration. A unit 

responsibility is that model assumptions or limits 

need to be disseminated. These qualifiers should be 

used as part of a checklist or other method to ensure 

that model limitations are understood and any restrictions are followed. This important step to ensure the 

appropriate use of models is often neglected or poorly 

done. Lastly, model development is often a lengthy 

and expensive process that frequently necessitates 

conducting research studies. A project management 

plan should be implemented in the early stages in the 

development of modeling applications that includes 

provisions for life-cycle product support.

Neglecting how the characteristics of prospective 

users and their corporate or military environments 

will affect model-based product acceptance and compliance with usage guidelines are common oversights 

in attempting to institutionalize the use of models 

and simulation-based applications. A comprehensive 

life-cycle project management approach for modeling and simulation products should be delineated, 

documented, and initiated during the early design 

phase. This type of long-term management approach 

for the development of biomedical models should 

also address and guide processes for identifying the 
64

Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

technical competencies required for their effective use 

in operational settings. Provisions should also be made 

for product marketing and testing, document development and distribution, and product introduction 

and training. To maximize acceptance and integration of model-based applications into organizational 

processes, their use should be formally endorsed by 

leadership, starting with a formal, peer-reviewed 

requirements certification process based on MIL-STD 

3022. Authority to modify doctrine and SOPs should 

be obtained from the organization’s leadership and 

appropriate committees so that they support use of the 

new modeling or simulation product, because it adds 

capabilities or efficiencies useful to the organization or 

decreases operational risks and costs. If these administrative actions are not planned and accomplished, 

distributed model-based products that are fielded will 

largely be ignored and classified by intended users 

as the latest curiosity among a seemingly unending 

parade of unendorsed technological toys. The needs 

and potential usefulness of proposed model-based 

applications should be clearly and honestly identified 

and promulgated long before the product is ready 

for distribution. One practical reason for this is that 

individuals do not have the free time to learn new 

software or modify well-developed work processes to 

accommodate new, model-based applications that do 

not seem to offer significant or profitable new function, 

the use of which has not been explicitly mandated by 

leadership.

During military operations, the human costs of bad 

decisions can be serious. For example, miscalculation 

of the limitations of heat stress tolerance or water 

intake requirements in hot desert conditions, the difficulties and dangers to life and health of cold weather, 

or the susceptibility of personnel to incapacitating or 

lethal altitude illnesses can result in operational debacles, with the loss of not just a few personnel, but 

entire units. All military personnel should know the 

following facts without having to rely on elaborate 

mathematical models: 

	 •	 that heat stress can kill;

	 •	 that running out of water, especially in hot

desert areas, in hot desert areas can mean 

death from dehydration; 

	 •	 that excessive lengthy immersion in coolto-cold water, or exposure to cold, windy 

weather without adequate protective clothing 

and shelter can result in frostbite or eventual 

death from hypothermia; and 

	 •	 that ascending to high altitudes too quickly

can result in high rates of acute mountain 

sickness and death from rapidly progressive 

high-altitude pulmonary edema and highaltitude cerebral edema. 

Common sense, foresight, analysis of observations 

and individual experiences, attention to practical 

details, and effective leadership have been and will 

continue to be of paramount importance in preventive medicine efforts during field operations. When 

environmental stress casualties occur, lapses in basic 

leadership and supervision, and failure to adequately 

consider and protect against the many potential adverse effects of conducting physically and psychologically demanding missions will almost always be at the 

root of the problem.

Models for predicting the effects of environmental 

strain are a modern refinement that can assist planners 

and preventive medicine personnel in detecting those 

circumstances in which apparent common sense or 

superficial qualitative evaluations might be fooled by 

effects that are more serious than expected. They can 

also be useful in identifying nonlinear effects that we 

cannot accurately sense, such as nearness to threshold of sudden performance decrements, or a sudden 

increase in heat stress casualty potential caused by 

seemingly slight changes in mission or environmental conditions. Model-based decision aids have been 

shown to be effective in refining plans for minimizing rates of environmental stress casualties that are 

already low, and even more so when attempting to 

maximize less visible—but operationally important—

personnel effects, such as physiological reserve and 

performance potential. Environmental strain models 

broaden the capacity of planners to rapidly and accurately evaluate the effects of many combinations 

of environmental, mission, and personnel variables 

on the risks of environmental stress casualties. 

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Modeling the Physiological and Medical Effects of Exposure to Environmental Extremes

ATTACHMENT A: FINGER-COOLING MODEL

A generic, numerical finger-cooling model exhibiting simulated countercurrent arteriovenous heat exchange for predicting 

temperature response of digits to cold stress has also been developed at the US Army Research Institute of Environmental 

Medicine (USARIEM).1 This type of model is of considerable interest because the fingers and toes are among the most 

vulnerable parts of the body to cold stress. Also, a whole-body thermoregulatory model can be formed by linking sets of 

cylindrical models for the extremities to a central body cylinder. At USARIEM, Shitzer and colleagues2,3 developed a series 

of sophisticated models to predict the cooling and risk of frostbite in a single finger. The finger models included the effects of 

	 •	 heat conduction,

	 •	 metabolic heat generation,

	 •	 convective heat transfer by blood perfusion,

	 •	 heat exchange between tissues and large blood vessels, and

	 •	 arteriovenous heat transfer.

The effects of handwear on heat transfer to the environment were also simulated using biophysical data from handwear 

insulation testing.4

The generic digit was modeled with four concentric compartments, from the center to the outer surface, consisting of 

core, muscle, fat, and skin, with heat flow along both the radial and axial directions. A system of distributed-parameter differential equations mathematically described the dynamics of heat balance within and between compartments and to the 

environment, metabolic heat generation, as well as countercurrent arteriovenous heat flow. Solutions for the time-dependent 

distribution of digit temperatures were obtained via use of the Thomas alternating direction method, which was extensively 

tested for convergence, accuracy, and stability. Interrelated parameters describing geometric tissue density, specific heat, 

basal metabolic rates and blood flow, and minimum nutritional blood flow were required for each compartment to complete 

the model description. Heat transfer coefficients, defining rates of heat transfer from skin to ambient air, were also identified 

for still air and moderate breeze for both bare and gloved fingers. 

Shitzer and colleagues2,3 provided an excellent example of how benchmark testing can be used in verifying stability and 

convergence of the software implementation of a complex thermoregulatory model. Through such testing, for example, they 

determined that, when the numerical algorithm used less than 20 nodes, results were a function of the number of nodes or 

temperature points within compartments. The complexity of the model has thus far limited its utility, but the countercurrent 

model serves as an excellent tool for illustrating the relative effects of countercurrent arteriovenous heat transfer on finger 

temperature patterns for various levels of ambient cold temperatures. 

REFERENCES

1. Shitzer A, Stroschein LA, Vital P, Gonzalez RR, Pandolf KB. Numerical Model of the Thermal Behavior of an Extremity in a 

Cold Environment Including Counter-Current Heat Exchange Between the Blood Vessels. Natick, Mass: US Army Research 

Institute of Environmental Medicine; 1994. Technical Report T94-10. 

2. Shitzer A, Stroschein LA, Gonzalez AA, Pandolf KB. Lumped parameter finger tip model exhibiting cold induced 

vasodilatation. In: Roemer RB, ed. Advances in Bioheat and Mass Transfer Microscale Analysis of Thermal Injury Processes 

Instrumentation Modeling: Clinical Applications. New York, NY: The American Society of Mechanical Engineers; 1993.

3. Shitzer A, Bellomo S, Stroschein LA, Gonzalez RR, Pandolf KB. Simulation of a cold-stressed finger including the effects of wind, gloves, and cold-induced vasodilatation. J Biomech Eng. 1998;120:389–394.

4. Santee WR, Blanchard LA, Chang SKW, Gonzalez RR. Biophysical Model for Handwear Insulation Testing. Natick, Mass: 

US Army Research Institute of Environmental Medicine; 1993. Technical Report T7-93.
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Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine

ATTACHMENT B: WATER IMMERSION MODEL

Examples of immersion models are the lumped-parameter compartmental models developed for predicting body temperature responses to cold water immersion. For example, the US Army Research Institute of Environmental Medicine (USARIEM) developed SCTM, a six-segment (head, trunk, arm, hand, leg, and foot), whole-body cold immersion subprogram 

that included countercurrent arteriovenous heat transfer in the extremities.1 The trunk and extremity segments were each 

modeled as solid cylinders containing four concentric compartments—(1) core, (2) muscle, (3) fat, and (4) skin—and associated blood flows. The head was modeled as a sphere having spherically concentric compartments. The passive intercompartmental heat transfer process was represented as a system of first-order, lumped-parameter differential equations. The 

lumped parameters represented compartment-specific values for thermal conductance, heat capacitance, blood flow, and 

metabolic rate. Simulation of the active vascular and thermogenic (shivering) processes added the necessary thermoregulatory feedback components to the cold water immersion model to make it dynamic and consistent with known cold stressinduced compensatory processes. The immersion model was validated against measured core temperature data for military 

test subjects immersed in 20°C and 24°C water. The model closely predicted core temperature changes in those conditions. 

This model will be an excellent candidate for predicting safe cold water immersion times and will therefore be suitable 

for inclusion in various environmental stress analysis applications and decision aids. For example, this type of model could 

be incorporated into MyWIDA (My Weather Impacts Decision Aid), a PDA (personal digital assistant), or other handheld 

electronic device. The system or device would be capable of providing unit-level, site-specific, time-limit guidance for immersion in cool to cold water (eg, units that must consider routes that require wading across ravines or marches to achieve 

their objectives), as well as for heat stress evaluation and prevention in other settings. 

If incorporated into MyWIDA,2 this type of cold immersion model could provide contour overlays of recommended safe 

immersion times (based on reaching a selected core temperature limit) for training or operational areas where water immersion is a significant risk. This could then be used to direct units to avoid areas that pose an excessively high risk of immersion hypothermia or to recommend maximum exposure times that would be disseminated to the potentially affected units. 

Another possible application of this type of tool is to assist in the planning of search-and-rescue operations. An example 

is the Probability of Survival Decision Aid (PSDA), based primarily on SCTM, that was developed for the US Coast Guard

as a supplemental tool for search-and-rescue decision support.3,4

REFERENCES

	 1. 	 Xu X, Giesbrecht G, Gonzalez R. Real Time Thermoregulatory Model for Extreme Cold Stress: Applicable to Objective Force 

Warrior (OFW). Natick, Mass: US Army Research Institute of Environmental Medicine; 2003. Technical Report T03/5.

2. Knapp D, Zeng S, Szymber J, et al. MyWIDA: a personalized Weather Impacts Decision Aid. In: Battlespace Atmospherics 

and Cloud Impacts on Military Operations Conference, April 13–15, 2010. Omaha, Neb: Director of Defense Research and 

Engineering, and Creighton University. Available at: http://ats.creighton.edu/BACIMO/media/WIDA/10KNAPP_

BACIMO2010_WIDA.pdf. Accessed April 14, 2011.

	 3. 	 Xu X, Amin A, Santee W. Probability of Survival Decision Aid (PSDA). Natick, Mass: US Army Research Institute of 

Environmental Medicine; 2008. Technical Report T08-05.

4. Allen A. CG move to a new survival model. In: Rawles E III, ed. On Scene: The Journal of the U.S. Coast Guard Search 

and Rescue. Washington, DC: US Coast Guard; 2011: p. 24. COMDTPUB P16100.