Prediction of performance reduction in self-paced exercise as

modulated by the rating of perceived exertion

Anthony E. Iyoho, Lisa N. MacFadden, Laurel J. Ng

L-3 Applied Technologies Inc.10770 Wateridge Circle, Suite 200

San Diego, CA, USA 92121

Corresponding AuthorAnthony E. Iyoho

Anthony.Iyoho@L-3com.comTel: 858-404-7970Fax: 858-404-7898

1

Overview

A thermoregulatory model (TRM) was developed to provide core temperature and mean-weighted skin

temperature predictions for the RPE calculation. In the TRM, the human anatomy is approximated with ten body

segments, where each segment is concentrically composed of a core, muscle, fat, and skin layer (see Figure 1 of this

supplementary document). All body segments are treated as cylinders, except for the head which is given a spherical

representation. We have modeled in detail the heat exchange due to the cardiovascular system where blood

circulates in a closed loop from the central artery. This blood is distributed to the ten regions, undergoing

countercurrent heat exchange between the arterioles and venules, and heat exchange in the tissues before collecting

in the central vein where it is pumped by the heart to the lungs, and back to the central artery.

The model allows for the input of individual characteristics like body mass, height, and percent body fat, and

material properties like clothing resistance and clothing permeability. Environmental inputs like air temperature,

radiant temperature, relative humidity, and wind speed are specifiable. Additionally, parameters related to activity

like work level, net mechanical efficiency, walking speed, and cycling pedal frequency can also be specified. The

walking speed and cycling pedal frequency are used to calculate an effective air velocity for convective heat

transfer.

The model equations are simultaneously solved using Matlab v7.13 with Simulink toolbox v7.8 (MathWorks,

Inc.). A variable time step with ode23t solver was chosen for the simulation runs.

The TRM was challenged against 16 clothed studies for a range of conditions including clothing resistances

of 0.8 to 2.4 clo (i.e. light to heavily clothed), air temperatures of 10 to 45°C, and exercise levels of 2.6 to 8.8 MET

(one MET equals 58.2 W/m2 and represents the factor by which activity is above basal metabolism). The

environmental conditions and physical parameters from each experiment were used as input to the simulations.

Comparison plots between model and data are shown for core temperature and mean-weighted skin temperature

responses (see Figure 2 and Figure 3 of this supplementary document, respectively). The root mean square

deviation (RMSD) was also calculated between the experimental data points and model predictions for core

temperature and mean-weighted skin temperature (see Table 1 of this supplementary document). Additionaly,

Bland-Altman plots were generated for core temperature and mean-weighted skin temperature predictions (see

Figure 4 and Figure 5 of this supplementary document, respectively). The table and figures are located at the end of

this document. The TRM was shown to be accurate for the wide range of tested conditions.

2

TRM Equations

Heat Storage Equations

The geometric representation of the human body is shown in Figure 1 of this supplementary document. The

subscript i will denote the ith body segment, whereas j denotes the jth layer. The heat storage equation with one-

dimensional conduction and heat generations is

(A.1)

where ρi,j is the density [kg/L], ci,j is the specific heat capacity [J/kg/°C], Vi,j is the volume [L], is the volumetric

blood flow rate through the capillaries [L/s], and Ti,,j is composite temperature [°C] at the ith segment and jth

layer. Tartl,i is arteriole temperature of entering blood for the ith body segment. ρbl is the density [kg/L] and cbl is the

specific heat capacity [J/kg/°C] of blood. Thermal conductances between the j-1 th and jth layer and jth and j+1th layer

for the ith body segment, and [W/°C], are calculated according to Incropera and DeWitt’s

formulation (Incropera and DeWitt 1996), respectively. Tissue thermal conductivity, specific heat, and density

values are taken from Fiala et al. (1999). The mass fractions used to calculate the volume of each of the

compartments are taken from Stolwijk (1971).

Dry and Evaporative Heat Exchange in Air

The prediction of dry and evaporative heat exchange is adapted from Fiala et al. (1999). The total heat lost

from the environment to air at the skin surface, [W], is a combination of dry ( ) and evaporative

components ( ),

(A.2)

The exchange of dry heat at the skin surface, , factors in convection, radiation, and clothing insulation,

(A.3)

3

,, , , , 1 , 1 , , 1 , 1 , , , , ,( ) ( ) ( )i j

i j i j i j i j j i j i j i j j i j i j bl bl i j artl i i j met i j

dTc V G T T G T T c Q T T q

dt

,i jQ

,met i jq

, 1i j jG , 1i j jG

,env iq ,dry iq

,vap iq

, , ,env i dry i vap iq q q

,dry iq

, , , ,dry i cl i surf i O iq U T T

where and are the skin surface and operative environmental temperatures at the ith body segment [°C].

The value for is a weighted average of ambient air and radiant temperatures, and , respectively:

(A.4)

where and [W/°C] are the air convection and radiation coefficients at the ith body segment, respectively.

The heat-transfer coefficient equation for dry heat loss, [W/°C], is

(A.5)

The symbol, [ m2∙°C /W], represents the clothing heat resistance at the ith body segment and is the surface

area at the ith body segment. The area fractions used to calculate the surface area of each segment is taken from

Colin and Houdas (1965). The value for is calculated using Stefan-Boltzmann law:

(A.6)

where is the Stefan-Boltzmann radiation constant [W/m2/K4], is the surface emissivity which is assumed to be 1

(Werner and Blatteis 2001), and frad is a non-dimensional radiation fraction between 0 and 1 which assumes that not

all of the surface area experiences radiation heat exchange. In the model, frad is set equal to 0.9, which provided the

best results. The value for [W/°C] is determined as a function of effective air speed, Veff [m/s],

(A.7)

where Veff is raised to the ½, which is a typical exponent seen for convection coefficients (Kerslake 1972). The

coefficient, 4.4, is lower than what has been typically observed (Fiala et al. 1999). However, this value is adequate

when considering that only 50-80% of the body surface area typically exchanges heat with the environment (Fourt

4

,surf iT ,O iT

,O iT airT radT

, ,,

, ,

air i air rad i radO i

air i rad i

h T h TT

h h

,air ih ,rad ih

,cl iU

,

,

, , ,

11cl i

cl i

i cl i air i rad i

UIA f h h

,cl iI iA

,rad ih

2 2, , ,( 273) ( 273) ( 273) ( 273)rad i rad i surf i rad surf i radh f A T T T T

,air ih

, 4.4 60air i i effh A V

and Hollies 1970; Tikuisis 1995). The effective air speed is a combination of wind speed (Vwind) and air movement

due to activity (Vact):

(A.8)

For treadmill walking, Vact = 0.67*Vwalk where Vwalk [m/s] is the walking speed; and for cycling, Vact = 0.0043*fcyc

where fcyc [rpm] is the pedaling frequency (Lotens and Havenith 1991).

The prediction of evaporation is adapted from Fiala et al. (1999). The evaporative heat loss, , is

calculated as

(A.9)

where and represent the vapor pressure of air and skin at the ith body segment [mmHg], respectively. The

evaporative coefficient for the ith body segment, [W/mmHg] is

(A.10)

where = 2.2 is the Lewis constant for air [°C/mmHg] and [N.D.] is the moisture permeability index of

clothing at the ith body segment. The clothing area factor, [N.D.], which is the ratio of clothed to nude area is

calculated with the following empirical expression (McCullough and Jones 1984):

(A.11)

A heat and mass transfer balance at the skin is guaranteed with the following equation

(A.12)

5

eff wind actV V V

,vap iq

, , , ,vap i e cl i sk i airq U P P

airP ,sk iP

, ,e cl iU

,, ,

,

, , ,

1air m i

e cl icl i

i cl i air i rad i

L iU I

A f h h

airL ,m ii

,cl if

, ,1 0.305cl i cl if I

2

, , ,, , , ,

,

sk sat i sk ie cl i sk i air H O i sw i i

e sk

P PU P P Am A

R

where , , , and represent the rate of mass loss due to sweating [g/h/m2], heat of

vaporization of water [W∙h/g], skin moisture permeability [mmHg∙m2/(W)] and saturated vapor pressure at the skin

[mmHg] at the ith body segment. The vapor pressure at the skin surface, [mmHg], is then calculated as

(A.13)

The maximum evaporative capacity of the environment, [W], is calculated as (Givoni and Goldman 1972):

(A.14)

where [N.D.]

and [ m2∙°C/W] are the moisture permeability index and total thermal resistance of clothing and

air for the entire garment, respectively. The parameter, A [m2], is surface area of the entire nude body; and

[mmHg] represents the saturated vapor pressure at the mean-weighted skin temperature. The total rate of mass loss

due to sweating, [g/h/m2], is based on a linear regression relationship developed by the authors that is

dependent on changes in arterial and mean-weighted skin temperature:

(A.15)

where ( ), ( ) and ( ) represent the arterial (mean-weighted skin), initial arterial

(mean-weighted skin) and threshold change in arterial (mean-weighted skin) temperatures [°C], respectively. The

distribution of sweat loss to each compartment is taken from Stolwijk (1971).

Calculation of Skin Surface Temperature

The total heat loss from the environment to air at the skin surface due to dry and evaporative modes is

equal to the heat brought to the skin surface by conduction:

6

,sw im2H O ,e skR , ,sk sat iP

,sk iP

2 , , , , , ,,

, , ,

/1/

H O i sw i sk sat i e sk e cl i airsk i

e cl i e sk

A m P R U PP

U R

maxq

max ,m

air sk sat airT

iq L A P P

I

mi TI

,sk satP

swm

0 0

,0 , ,0 ,1 11046.1 32.353

ve or ve or

sw art art art thresh sk sk sk threshm T T T T T TA A

artTskT ,0artT ,0skT

,art threshT ,sk threshT

(A.18)

Solving for the temperature at the skin surface, [°C], yields the following equation:

(A.19)

where Ti,4 [°C] is the temperature at the ith segment of the skin layer and [W/°C] is the conductance between

the skin layer and skin surface at the ith segment.

Metabolic Heat Generation

The total heat generation due to metabolism, [W], is composed of the basal heat metabolism,

[W], and heat metabolism generated from inefficient work of exercise, [W]:

(A.21)

For model validation, the total basal metabolism was adjusted to achieve the correct initial core temperature.

The total work metabolism, MR, includes both inefficient (i.e. internal heat generation) and efficient (i.e.

mechanical work) components. The total metabolic load not converted to external mechanical work shows up as

internal heat. The efficiency, [%/100], at which the work load is converted into useful mechanical work then

determines the heat generation:

(A.24)

The distribution of heat to working muscles is taken from Stolwijk et al. (1971).

Heat Exchange in the Arterioles and Venules

The heat transferred by countercurrent exchange in the arteriole-venule, [W], is dependent on the

blood temperature exiting the arterioles, [°C], the blood temperature entering the venules, [°C], and the

countercurrent heat exchange coefficient, [W/°C]:

7

, , , , ,4 ,4 ,( )cl i surf i O i vap i i surf i surf iU T T q G T T

,surf iT

, , ,4 ,4 ,,

, ,4

cl i O i i surf i vap isurf i

cl i i surf

U T G T qT

U G

,4i surfG

metq ,met basq

,ineff workq

, ,met met bas ineff workq q q

, , 1ineff work met basq MR q

,cc iq

,artl iT ,venlin iT

,cc ih

(A.25)

The decrease in temperature of the blood in the arterioles is equal to the increase in temperature of

the blood in the venules due to countercurrent exchange:

(A.26)

(A.27)

The temperature of the blood leaving the venules is obtained by rearranging (A.27):

(A.28)

The temperature of blood leaving the arterioles is obtained by substituting (A.28) into (A.26) and solving for :

(A.29)

The temperature of blood entering the venules, , is a blood flow rate weighted function of each layer

temperature:

(A.30)

where the total volumetric blood flow rate to each segment: [L/s] is equal to the sum of

flow rates to each tissue layer. Equation (A.30) assumes the exiting capillary blood temperature to the venule

entrance has undergone rapid temperature equilibration with the tissue. The countercurrent heat exchange

formulation and coefficients are taken from Fiala et al. (1999).

Heat Exchange in the Central Artery and Vein

The blood exiting the lung capillaries supplies the blood in the arteries. The blood is dispersed throughout

the body to the various tissue groups. The blood flow leaving the lung, [L/s] must be equal to the blood flow

distributed to the tissues. Similarly, the blood flow leaving each of the tissue groups must be equal to the final

8

, , , ,cc i cc i artl i venlin iq h T T

,( )art artl iT T

, ,( )venl i venlin iT T

, , , , ,Bl Bl i venl i venlin i cc i artl i venlin ic Q T T h T T

, , ,art artl i venl i venlin iT T T T

, , ,( )venl i venlin i art artl iT T T T

,artl iT

,, ,

, ,

cc iBl Bl iartl i art venlin i

cc i Bl Bl i cc i Bl Bl i

hc QT T T

h c Q h c Q

,venlin iT

,1 ,2 ,3 ,4, ,1 ,2 ,3 ,4

i i i ivenlin i i i i i

i i i i

Q Q Q QT T T T T

Q Q Q Q

,1 ,2 ,3 ,4i i i i iQ Q Q Q Q

totQ

venous blood flow, [L/s]. Heat conservation in the arterial pool is dependent on the heat entering from the lungs

and leaving to the tissue arteries:

(A.31)

Simplifying (A.31), the heat conservation in the arterial pool becomes:

(A.32)

The rate of change of heat lost in the lungs through respiration, [W], is:

(A.33)

Rearranging gives the blood temperature in the lung:

(A.34)

Heat conservation in the venous pool is dependent on the heat entering from the tissue capillaries and the heat

leaving the veins to the lungs:

(A.35)

Rearranging gives:

(A.36)

Respiration Heat Exchange

Heat lost through respiration is a function of external air temperature and arterial blood temperature. The

total heat lost through respiration, [W], is equal to the sensible heat loss, [W], plus latent heat loss ,

[W]:

(A.37)

9

totQ

artBl Bl art Bl Bl tot lung Bl Bl tot art

dTc V c Q T c Q Tdt

( )art totlung art

art

dT Q T Tdt V

respq

( )resp Bl Bl tot ven lungq c Q T T

resplung ven

Bl Bl tot

qT T

c Q

10

,1

venBl Bl ven Bl Bl i venl i Bl Bl tot ven

i

dTc V c QT c Q T

dt

10

,1

i venl i tot venven i

ven

QT Q TdT

dt V

respq ,resp sensq

,resp latq

, ,resp resp sens resp latq q q

Sensible heat loss is modeled by air picking up heat as it flows down the wall of a tube (daSilva et al. 2002):

(A.38)

where [J/kg/°C] is the specific heat of air and [kg/s] is the mass flow rate which is

(A.39)

where is the air density [kg/m3] and is alveolar ventilation [m3/s] which is assumed to be directly

proportional to metabolic rate,

(A.40)

where the basal alveolar ventilation, , per body mass is 0.0014 [L/s/kg] (Duffin et al. 2000). Latent heat loss is

the transfer of heat by evaporation and is modeled by this (daSilva et al. 2002):

(A.41)

where

(A.42)

is the latent heat of vaporization = 2.258*103 [J/kg], is the universal gas constant = 8.3143 [J/mol/K], is

the molar mass of water = 18.016 [g/mol], is the saturation vapor pressure at the arterial temperature [Pa],

and is the partial vapor pressure of air [Pa].

Vasomotor Functions

The vasomotor relationship utilized in this paper is based on a formulation by Stolwijk (1971) where the

skin blood flow is:

(A.43)

10

,resp sens p art airq mc T T

pc m

a airm V

air aV

,,

meta a bas

met bas

qV Vq

,a basV

,resp lat B A a B Aair

mq V

* *

3 3

( ) ( )&( 273) ( 273)w art w air

B Aart air

M e T M e Tg gm R T m R T

R wM

*( )arte T

*( )aire T

,4 ,,4

,1bas i d i

ic i

Q a DLQ

a CS

where is the basal skin blood flow [L/s] and ( ) is the local skin weighted constant for dilatation

(constriction) [N.D.]. The vasodilatation drive, DL [L/s], is:

(A.44)

and the vasoconstriction drive, CS [N.D.] is:

(A.45)

where = 3.25 [L/s/°C] and = 0.5 [L/s/°C] ( = 100 [1/°C] and = 4.0 [1/°C]) are positive arterial

and mean-weighted skin vasodilatation (vasoconstriction) constants whose values have been altered from the

original (Stolwijk 1971). Additionally, the base 2 power term utilized in the original formulization was purposefully

excluded, and mean-weighted skin temperature rather than local skin temperature is used to calculate the

vasodilatation and vasoconstriction drives. The symbols, and , represent the arterial and mean-

weighted skin setpoint temperatures[°C]. The arterial and mean-weighted skin setpoint temperatures are set

equivalent to their respective thermoneutral temperatures (i.e. and ).

Cardiac Output

The total cardiac output, [L/s], is comprised of a basal andwork (or exercise) component:

(A.46)

where is the basal cardiac output [L/s] and is the cardiac output due to work [L/s]. Basal blood flow in

the muscle and fat regions is calculated in accordance with Fiala et al. (1999). In the core regions, it is assumed that

blood flow is only present for the head and torso segments (Fiala et al. 1999). Blood flow to the head core is

assumed to be a constant 0.0125 L/s, independent of temperature (Stolwijk 1971). Skin blood flow is calculated

according to (A.43). The remaining basal blood flow not in the muscle, fat, or skin regions pools into the torso core.

The work component of cardiac output is directly proportional to an increase in exercise

(A.47)

11

,4bas iQ ,d ia ,c ia

0 0, ,( ) ( )ve or ve or

dil art art set dil sk sk setDL x T T y T T

0 0, ,( ) ( )ve or ve or

con art art set con sk sk setCS x T T y T T

dilx dily conx cony

,art setT ,sk setT

, ,0art set artT T , ,0sk set skT T

totQ

tot bas workQ Q Q

basQ workQ

0.932work bas

BL BL

Q MR qc

where the expression, 0.932/(ρBL*cBL), relates power to volumetric blood flow [L/J] (Stolwijk 1971).

12

References

Armstrong LE, Johnson EC, Casa DJ, Ganio MS, McDermott BP, Yamamoto LM, Lopez RM, Emmanuel H (2010)

The American football uniform: uncompensable heat stress and hyperthermic exhaustion. J Athl Train 45

(2):117-127

Buller MJ, Tharion WJ, Cheuvront SN, Montain SJ, Kenefick RW, Castellani JW, Latzka WA, Roberts WS, Richter

MW, Jenkins OC, Hoyt RW (2013) Estimation of human core temperature from sequential heart rate

observations. Physiol Meas 34 (7):781-798

Colin J, Houdas Y (1965) Initiation of sweating in man after abrupt rise in environmental temperature. J Appl

Physiol 20 (5):984-990

daSilva RG, LaScala N, Jr., Filho AEL, Catharin MC (2002) Respiratory heat loss in the sheep: a comprehensive

model. Int J Biometeorol 46 (3):136-140

Duffin J, Mohan RM, Vasiliou P, Stephenson R, Mahamed S (2000) A model of the chemoreflex control of

breathing in humans: model parameters measurement. Respir Physiol 120 (1):13-26

Fiala D, Lomas KJ, Stohrer M (1999) A computer model of human thermoregulation for a wide range of

environmental conditions: the passive system. J Appl Physiol 87 (5):1957-1972

Fourt L, Hollies NRS (1970) Clothing: Comfort and Function. Marcel Dekker, New York

Gagge AP, Stolwijk JA, Saltin B (1969) Comfort and thermal sensations and associated physiological responses

during exercise at various ambient temperatures. Environ Res 2:209-229

Givoni B, Goldman RF (1972) Predicting rectal temperature response to work, environment, and clothing. J Appl

Physiol 32 (6):812-822

Holmer I (2006) Protective clothing in hot environments. Ind Health 44:404-413

Incropera FP, DeWitt DP (1996) Fundamentals of Heat and Mass Transfer. John Wiley & Sons, Inc., New York

Kerslake DM (1972) The Stress of Hot Environments. Cambridge University Press, Cambridge

Lotens WA, Havenith G (1991) Calculation of clothing insulation and vapour resistance. Ergonomics 34 (2):233-

254

McCullough EA, Jones BW (1984) A comprehensive data base for estimating clothing insulation. Institute of

Evironmental Research, Manhattan, KS

13

McLellan TM, Pope JI, Cain JB, Cheung SS (1996) Effects of metabolic rate and ambient vapour pressure on heat

strain in protective clothing. Eur J Appl Physiol 74:518-527

McLellan TM, Selkirk GA (2004) Heat stress while wearing long pants or shorts under firefighting protective

clothing. Ergonomics 47 (1):75-90

Stolwijk JA (1971) A mathematical model of physiological temperature regulation in man. NASA, Washington D.C.

Tikuisis P (1995) Predicting survival time for cold exposure. Int J Biometeorol 39 (2):94-102

Werner J, Blatteis CM (2001) Biophysics of heat exchange between body and environment. In: Physiology and

Pathophysiology of Temperature Regulation. World Scientific, New Jersey, pp 25-45

Wissler EH (1988) A review of human thermal models. In: Mekjavik IB, Banister EW, Morrison JB (eds)

Environmental Ergonomics. Taylor & Francis, London, pp 267-285

14

Table

Table 1. Test conditions and Root Mean Square Deviations (RMSD) between predicted and observed core temperature and mean-weighted skin temperature in hot and cool air for clothed exercising subjects. The symbols IT, im, Tair, rh, and act denote the clothing resistance, clothing permeability, air temperature, relative humidity, and activity level, respectively. RMSD values below 0.5 and 2.0°C for core temperature and mean-weighted skin temperature, respectively, are acceptable error thresholds (Wissler 1988). RMSD values meet the error criteria for each experiment for both core temperature and mean-weighted skin temperature.

# Reference

Tair

(

C)rh

(%)act

(MET)

IT

(clo)

im

(-)

RMSD

(C)

(C)

1 (Gagge et al. 1969) 10 40 8.8 0.8 0.45 0.09 1.642 (Gagge et al. 1969) 20 40 5.6 0.8 0.45 0.07 0.683 (Gagge et al. 1969) 20 40 8.8 0.8 0.45 0.15 1.194 (Gagge et al. 1969) 30 40 8.8 0.8 0.45 0.04 1.345 (McLellan and Selkirk 2004) 35 50 2.7 2.4 0.36 0.08 0.756 (McLellan and Selkirk 2004) 35 50 3.5 2.4 0.36 0.13 0.367 (McLellan and Selkirk 2004) 35 50 4.9 2.4 0.36 0.19 0.348 (McLellan and Selkirk 2004) 35 50 5.6 2.4 0.36 0.11 0.519 (McLellan et al. 1996) 40 15 2.9 1.88 0.33 0.08 0.3710 (McLellan et al. 1996) 40 65 2.9 1.88 0.33 0.13 0.2511 (McLellan et al. 1996) 40 15 4.3 1.88 0.33 0.23 0.2012 (McLellan et al. 1996) 40 65 4.3 1.88 0.33 0.17 0.2313 (Holmer 2006) 45 15 2.6 1.9 0.06 0.21 0.1014 (Armstrong et al. 2010) 33 50 6.5 0.9 0.42 0.10 ----15 (Armstrong et al. 2010) 33 50 6.5 1.15 0.4 0.21 ----16 (Armstrong et al. 2010) 33 50 6.6 1.5 0.35 0.31 ----

15

coreT skT

Figures

Figure 1. Schematic of body segments used in the model

16

0 20 40

37

38

391

T core

(°C

)

0 20 40

37

38

392

0 10 20 30

37

38

393

0 20 40

37

38

39

404

0 20 40 60 80

37

38

39

405

T core

(°C

)

0 20 40 60

37

38

39

406

0 20 40

37

38

39

407

0 10 20 30

37

38

39

408

0 20 40 60 80

37

38

399

T core

(°C

)

0 20 40

37

38

3910

0 20 40

37

38

3911

0 10 20 30

37

38

3912

0 10 20 30

37

38

39

4013

T core

(°C

)

Time (min)0 20 40 60

37

38

39

4014

Time (min)0 20 40 60

37

38

39

4015

Time (min)0 20 40

37

38

39

4016

Time (min)

Figure 2. Core temperature (Tcore) responses (solid lines) vs. experimental data (circular points) for clothed subjects exercising in hot and cool air. The input conditions and RMSD values for all clothing conditions are provided in Table 1.

17

0 20 402628303234

1T sk

in (°

C)

0 20 40

30

32

342

0 10 20 30

30

32

343

0 20 4032

33

34

354

0 20 40 60 80

34

36

38

5

T skin

(°C

)

0 20 40 60

34

36

38

6

0 20 40

35

407

0 10 20 30

35

408

0 20 40 60 8032

34

36

389

T skin

(°C

)

0 20 40

35

4010

Time (min)0 20 40

32343638

11

Time (min)0 10 20 30

35

4012

Time (min)

0 10 20 30

35

4013

T skin

(°C

)

Time (min)

Figure 3. Mean-weighted skin temperature (Tskin) responses (solid lines) vs. experimental data (circular points) for clothed subjects exercising in hot and cool air. The input conditions and RMSD values are provided in Table 1. For conditions #1 through #4, minimum and maximum mean-weighted skin temperature data for all subjects was reported for each condition. For these conditions, the RMSD values for mean-weighted skin temperature reported in Table 1were calculated using the data average at each time step. The mean-weighted skin temperature response for condition #1 is outside of the bounds but the RMSD for this case was still acceptable.

18

37 37.5 38 38.5 39 39.5-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Mean of Predicted and Observed Tcore (°C)

Pre

dict

ed m

inus

Obs

erve

d T

core

(°C

)

Figure 4. Bland-Altman plots for core temperature (Tcore) prediction. The solid lines show the LoA (0.28°C) and the dashed line shows the bias (0.052°C) of the RPE prediction. The LoA is below the 0.5°C threshold of acceptable RMSDs (Wissler 1988) and is more than adequate for a predictive core temperature model (Buller et al. 2013).

19

28 30 32 34 36 38 40-3

-2

-1

0

1

2

3

Mean of Predicted and Observed Tskin (°C)

Pre

dict

ed m

inus

Obs

erve

d T

skin

(°C

)

Figure 5. Bland-Altman plots for mean-weighted skin temperature (Tskin) prediction. The solid lines show the LoA (1.99°C) and the dashed line shows the bias (-0.030°C) of the RPE prediction. The LoA is below the 2°C threshold of acceptable RMSDs (Wissler 1988).

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