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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
[email protected]: 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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