U.S. Naval AirDevelopmen

CenterJohnsville, Pennsylvan*

NADC-MR-6623 14 Jwwc 1ý67

Calculation of Time-Temperatute HistoT ,and Prediction of Injury to S:lin Expos.,

to Thermal Radiation

Naval Air Systems CommandAirTask R360 FR1O2/2021/ROI 101 01

(RB-6-0!)

DISTRIBUTION OF THIS DOCUMENT IS UNLIMI

RECEIVEDAUG 4 1967

CFSTI

"\IUG 1 1967

Limitations concerning ý'ie distribution of L --this report and revelaf',on of ;its contlentsr-'.ar on the ;nside c this cover.

DEPARTMENT OF THE NAVYU. S. NAVAL AIR DEVELOPMENT CENTER

JOHNSVILLEWARMINSTER. PA. 16974

Aeros, ... edical Research Department

NADL-MR-6623 14 June 1967

Calculation of Time-Temperature Historiesand Prediction of Injury to Skin Exposed

to Thermal Radiation

Naval Air Systems CommandALrTask R360 FRI02/2021/RO 101 01

(RB-6-0O)

DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED

Prepared by: 7John A. Weaver

Approved by: Carl F. Schmidt, M.D.Research DirectorAerospace Medical Research Department

Released by: E.M. WurztI, CAPT, MC. USNDirectorAerospace Medical Research Department

VStIWIARY

'This report gives a general description of a digital computer program

used in connection with the study of injury of skin exposed to thermal energy.

All of the information necessary for a detailed understanding of the program

is included; however, the material is presented in a manner such that the novice

in the field of computer science may make use of the program if he so desires.

For this reason emphasis is placed on the operating instructions for the pro-

gram. A short discussion of the pertinent theory and equations as they apply

to the human skin is included at the beginning of this report.

iii

TABLE OF CONTENTSPage

SUMMARY ---------------------------------------------------- ii

INTRODUCTION ----------------------------------------------- 1

THEORY OF PROBLEM AND EQUATIONS -.--------------------------- 1

PROGRAM DESCRIPTION ---------------------------------------- 5

OPERATING INSTRUCTIONS ------------------------------------- 12

General ---------------------------------------------- 12

Input ------------------------------------------------ 12

Output ----------------------------------------------- 16

REFERENCES ------------------------------------------------ 27

LIST OF FIGURES

Figure Title Page

1 Typical Time-Temperature History of SkinExposed to a Square-Wave Pulse of Thermal Energy ---- 2

2 Fortran Statement Listing of Program ----------------- 6a,b,c

3 Flow Chart for Computation of rime-TemperatureHistories ------------------------------------------- 9

4 Damage Rates Derived from Radiative Data ------------- 11

5 Flow Chart for Computation of the ThermalTissue Damage Integral ------------------------------ 13

6 Macro Flow Chart of Logic--------------------------- 14

7 Example3 of Input Data Cards ------------------------ 15

8 Example of Array Printout --------------------------- 17

9 Example of Integration Printout --------------------- 19

10 Example of Punched Data Cards ----------------------- 20

lii

L!5T 0' FIGURES (Cont'd)

Figure Title Page

11 Example of Tissue Temperature Plot--------------------- 22

12 Example of Surface Temperature andTissue Temperature Plot -------------------------------- 24

13 Example of Surface Time-TemperatureHistory Printout --------------------------------------- 25

I

iv

INTRODUCTION

This report contains a description of a digital computer program

that can be used to evaluate theoretical equations associated with the time-

temperature histories of skin exposed to various levels of thermal radiation

and to predict the injury due to such exposures (1). The program is written

for a Control Data Corporation 3200 Computer System using the Fortran 3200

language. In the study of thermal tissue damage it is of interest to obtain

the time-temperature history at some depth below the surface of the skin such

as at the dermis-epidermis interface and also to obtain the time-temperature

history at the surface of the skin. For this reason the computer program in-

corporates the feature of obtaining the time-temperature history at depth and

at the surface.

THEORY OF PROBLEM AND EQUATIONS

The time-temperature history of skin exposed to a square-wave pulse of

thermal energy is characterized by a temperature rise from some initial tempera-

ture of the surrounding environment T0O at time t=o when irradiation at a flux

of magnitude, Q, begins. The temperature continuc: to rise to some peak tempera-

ture at time t = T, the time at which the radiation ceases. The temperature then

drops, rapidly at first, then more slowly, approaching T as t approaches in-

finity. Figure I shows a typical example of a time-temperature history as com-

puted for a specific exposure.

The following equation suggested by Buettner (2) describes the desired

time-temperature history:

60

58

56

54- U--m surf

524

4a.-

46

on__ /0pfo Deptgg W~D h) --S4-

Apommef Lows ORO~ of

Riedetion

34 I3Z5f

0 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68TIME - SECONDS

Figure 1. Typical Time - Temperature History of Skin Exposed to a Square-Wave Pulse of Thermal Energy.

2

SC -f.- ))I.TT2a e-x2/ 4 a2t - x (1-6 2at +

2 • Za -vT e- x2 /4a 2 (t-T) _ x(I-8 ( X

/a7 2 Eq. 1

where Tx a tissue temperature at depth x below the surface (C)

Q a effect je radiation on the surface of skin (Cal/cm2 sec)

k = thermal conductivity (Cal/cm sec *Q

P = density of skin (g/cm3 )

c = specific heat (Cal/g 0C)

a2 = k/oc = "temperature diffusivity" (cm 2/sec)

t - time (sec)

T = time at which thermal radiation ceases (exposure time) (sec)

x = depth below the surface of the skin (cm)

T 0 initial surrounding temperature ( *C) U eY2

8(U) - integral of the probability curve Error

ve e0 Function

Equation 1 can be derived directly from the general differential equation for heat

conduction in one dimension

6T 26T Eq. 2-•= a 6x-" q

assuming a constant heat flow and an initial isothermal condition (vertical temp-

erature gradient equals zero) and the heat absorbed at the surface of the skin

transferred inward by conduction.

Prediction of dermal injury resulting from exposure to thermal radiation

of any given magnitude and duration depends entirely upon the resultant time-

temperature history. Total tissue damage done during any g-ven episode must

3

include the damage done during cooling after the radiation ceases as well as

the damage done during heating. Equations 3 and 4 express damage as temporal

integral of rates of tissue injury depending upon the tissue temperatire, and

increasing logarithmically with this temperature (3,4,S).

Q a T dt t d- dt Eq. 3t1

Sa Pe- AE/RTx dt + 2 Pe 'E/R Tx dt Eq. 4ti

where 'i = total tissue damage = 1.0 at point of complete transepidermal

necrosis

dQ/dt ý damage rate at given temperature, T

dt = time interval for which given temperature prevailed (sec.)

T = time at which thermal radiation ceases (exposure time)(sec.)

tI = time at which the injurious temperature level t44 0 C) is

reached (sec.)

t2 = time at which temperature falls below the injurious level

(44 0C) (sec.)

P = constant of integration

AE = energy of inactivation

R a gas constant

T x tissue temperature at depth x in %u at time tx

The first term on the right hand side of Eq. 4 is the damage done during heat-

ing, hereafter designated i'H the second term is the damage dore during coo ling.

hereafter designated •C; the sum of these two teres is the total damage done,

hereafter designated r and is equal to unity at the point of complete trans-

epidermal necrosis.

4

PI1RAO;Nq DLSCRIP'I ION

The complete program can he roughly brokei, into seven parts. Figure 2

is a listing of the Fortran statements of the entir' progr:im.

The first part of the program reads into the computer the necessary

data required for cilculation of time-temperature histories. This includes

data such as the number of time-temperature histories to he computed, various

labels used on graph outputs, constants of intevrtition, etc.

The second part of the progran computes the individual time-temperature

histories as arrays of time-temperature points. Each time poitrt ii stored in the

arra:' 1IMEýN) and the associated temperature point is stored in the array T(N).

In addition, an array A(N) containing the square root of values of thermal con-

ductivity is stored. Each of the Lhree arrays has a maximum dimension of 200

floating point values. For each time-temperature history to be zomiited, a

data card is read in containing the following variables:

Q = effective radiation on the sirface of the skin

X = depth below the surface of s0in (x = o at the surface)

DT = time interval btLween points in the tire-temperature history

TAU = time at which therma' radiation ceases = i 'exposure time)

TIM1E(l) = initial starting point in time at which first temperature pcint

is computed

Al square root of value of thermal conductivity during heating phase

A2 square root of ýalue of thermal conductivity used to compute

first temperature point during the cooling phase.

ZEROTI.'MP i nitnial urrourd - tet.perature r I0

P I LSQRT

"E(AU ?4144 U. me C1-9 0001AI tAl. 244b)

Its ee'ial 4-eLiti l.6)9004.111

L4.413111.40)I: So NOV1A*A0 St4101*i Stftillrik-bAt.ae 1101ifmle1

r 11A14 1100 tu"AlIUN

)IU* W$a.ahlEg4 C./lSApblCIOCI viouQIAIOAII

A(M) a &I

it1jot l* lw I IuA.IO0e

I0-ii "*I l'P 11po v-Il

lilt t~.'.kj') TO) 1

13 I OU We [I.%4

I~ IF l~if 1L 1..0 4*11- %0 .- ~lif 10%IO104 F ( M4.011: Lt 1644014111'43 IN OOS,169

1006 11 a a *F&.3#/

60IN I1.P'Z'/) Z9.3,$99 PIUNT 0/Z kIAtA

PQ1NT S0013 1.,

SIO 1`0016*u

I./)IFRo ?49-30

1113 LEL13- 11-

bill-of NAL SLIOU.iE 1)SL))

100 (1) TI) 11113911. elh SSVTCHF III

1112 IE)4INT4 001.IIIIN O~l

PRll ?41- 11.1009 101113 LaL-

LY - 1U SIL a %Il.Qv1`)AIISTZ.-)u 'V'1u4i.ie SbTA-919.00 '.YAaBs.?% SVTA,11101.90

bISO I,)TI)I 60St'O)l SSOlCN f4)

IFS (ST to- (It 0)111.1 hZIldF 1

1010r 2.0 Forra Statementi Listing ofPr1r)2011POIN 44019 PHIN Mo

r Continuation of Figure 2.III uo~e'IAI *tp#1-to If II IJI.M?.) I

I1 PI NT 41.111 9.. 1

Lo0 Ito 16

to7 .. 1 "i.0

G.O ft0 1 1

1 O 1.'I

II0it "1110 w)1.SJ

SO. F0144J3-IPA,??..i TFl

'30 Ito lb

eft fRINT ageI ii

9.0l 101 ~1I19 09lk91t'0.41

If0 If99 9 I ,/.119.4f jI 14.'e I~ i*.p14 014)34no

F161641 -C!

TEUTSO.01919.1 "s.

V1934 FOM ,FM.OMGf3M3C

1908 GO 143 (401019tw.?o SGWTCIU4

41S POINT7 3000.3500 FOIINAI 41013616 GO It, it49.J.&OZI 9.!?,4MI1`1431

C CAO~l PU9.CI

lost F0.4194 IF0%. .I3.3Fl.3sFA,.33

1067 00094*3 I I f 1.31otoo3 GOo 1" iI.600SUSSTC0f 410

C LAIKLS

If I313C.LI.11.9. 101.1671144 ATIC au.

AL. ol XIICOIU.

701 If (AlIC.L3I.G.V21 103,104703 XTIC a 5.29.

AL . '13C91,.1

?a?12 Ia ITICIfiIAt.L1.411C3 de3

2 ATIC * 1A

3 ATIC 0 [A 8 ATIC-1.4 AL S 31COI0.

701 110 to) 1111.0420ILILAI3JSA~TCt1

ALOW 8 *AIIC

202 PAWs 202 Soo 14) 209.203 A a -19.0IIIci2u.

2o'? OPAU19 29Y s. uTO 10 03219* CALL LABECL l1.2.0,L90411

CALL LABIL 43.I.SLWI41

211 A *-37.P11C.21i

233 VAUWA 213 $00 to 211III CALL IAdEL 1..@MS234 a a *3%.@AI IC/20.

3F4e'LOf~IAY4A1?.%91D9S!I 2319.23421* PAUS.E 216 V001 TV 214231S CALL I AB.EL 11.1.0,0404)

A a - ATIC/09.0

I . l1'9.0

211 LIL - LILTIII)tF(l'LOtYIIA.Y.60.0l 220.220

PAP V*1119 ol2 Soo0 To pal

6b

Continuation of Figure 2.

11S C'LL 1,"L~k AIALL

1^ 04OW d'S 6..l TO gpolj1,04 CALL tAMIL 14A.?.V.LNUjl

CALL 1,A1411 (::I.:0L1 1CALL I AmL IAI0LWU~y 111M.i AAW1l*1I

AIa .%IhiI hAI.OfII 1.Oil LOWI .1S hilt

0001"AUl.% b0WI0

o4:CALLi Mit 'AL I.1.0.dIl

ICALL I AMLt 1A..'.U.CI

u C% ALL 04Li,~D1O

'%A mý 14:0:00:1 "1.CALL ALL 1AlI 6 "

If til 1,1fAVV(1:AI0901I 1 %4 0'.0

0,46 CALL 1 AMILL 41,1.U,LROION0

0 1C-OPOAI IF.£... 1d0A

CALL L414LL 16-1#1061-4

'P3 AUst SoO % Ii3 hi £a.?CALL IL'"tl. hI.P0.LWIIII14

It'4Cu04,tlt.dAA.IAJI Al

CALL IA"L ?,.lIJ

?*.?3 640As it #t- SWl 140 .'e A

;!%a CALL khI 1".10#11.1.41311)'

CALL 1414LL (Ne-0.431A~

t LU.It I-

I oft IFlpbt IIR014.IO-l..0.11)II -1010.1£1o is AU%t j'3 Aul'o Ij I).1 10 001 01 i I.i.

II IhItAY I I I 1 1 11 1.11111 .0I I I 0I11-JiI? C'I.' I ."

.. ) IFOl(."I'IvAT.?%U I 101b.0lot1-14 IF ft I IN. I I

Iij un I, ilm.II1 Iv%ý, qil~ffiAIAt EIASlh 1.0.101 1a IItC I.11 .At 0"I.0%. .0. 3.)..k. I I14

o 4 4.d

,I ,si II,.co.t.

6c

It is necessary to use some value other than zero for TIME(1) in order that the

vaJue of the exponent containing TIME(N) as a divisor does not aprr.ach infinity

since in this event an exponent overflow error would occur. Hence a value of

TIME(l) very nearly equal to zero should be chosen so that the sum of TIME(1)

plus some integer number times DT is very nearly equal to TAU. Again it is neces-

sary that the sum of TIME(1) plus some integer number times DT does not exactly

equal TAU in order to prevent errcr.

In solving E1 . I on the computer, the following approximation is used:

pc= 1 Eq. S2

Hence a 2 k

or a VV Eq. 6

The r-imputation of the time-temperature history is divided into two intervals.

0 < TIME(N) < TAU and TIME(N) > TAU, which correspond to the heating phase and

cooling phase respectively. Before the calculation of each temperature point, a

check is nade to see if TIME(N) < TAU. If this is the case, Eq. 1 is solved for

the first two terms on the right hand side, the third term being imaginary. When

TIME(N) exceeds TAU in value (during the cooling phase), tie entire equation is

solved. During the heating phase a constant value of the square root of thermal

conductivity, Al, is used; however, during the c-oling phase the value of the

square root of thermal conductivity, A2, is decremented by 0.0001 after the cal-

culation of the first temperature point and is continually decremented for each

ttmperature point thereafter

The prograi uses an approximation formula to compute the value of the

complementary Error Function, I - e(U). The approximation formula for the Error

Function 8(U) is given by Haitings (6).

e(u) - I -2U 3U 4 5U U 6. 16(l~a 1 U~a2 U *a 3U *a4 U*a SU *a 6 U IEq.

7

Since the complementary Error Function is equal to one minus the Error Function

we have, Com. e(U) - I-8(U)

Com. 8(U) x COMERF = + [l+a1U+a 2 j2+a 3 J3,a4U4 +asUS+abU6 1l6 Eq. 8

where a, x 0.0705230784

a 2 a 0.0422820123

a 3 = 0.0092705272

a4 = 0.0U01520143

aS = 0.0002765672

a6 = 0.0000430638

During and following calculation of the tlme-terperature history the

following three specific valves of T(N) are stored separately for later use:

TPK = peak temperature obtained

TMINUP = value of the temperature closest to 44°C (injurious temperature

level) during the heating phase.

TWINDN - last value of temperature in the T(N) array.

Also the number of elements in the array T(N) between ININtIP and ThINDN inclusivw

is stored in NO for later use. Figure 3 is a flow chart of time-temperature

history computation.

The last five parts of the program are essentially connected with out-

put and are selected by means of sense switches located on the computer console.

Thus any, all, or none of the five parts can be selected in turn. Ihe operation

of any one of the parts may be skipped in the program ,.y setting the proper

sense switch to the "ON" position. Briefly the fie parts are concerned with:

(1) printed output of the T(N), TimeV%), ind A(%) arrays, (., numerical solution

a

SET .?U- , 01 8

C&LCULOU ~ ~ SI TIN Si.IPAT Gas.as

Figure ~ ~ 1111 3.1111#1 Floe: Chr o opuaino im. emp~lmeraueHsois

9

of the thermal tissue damage integral and printed output of results, (3) card

punch of time-temperature history just computed, (4) plot of time-temperature

history just computed, and (5) plot of time-temperature history for surface

temperatures (x = o). Here we discuss the numerical , lution of the thermal

tissue damage equation. The others are discussed under output in the Operating

Instructions.

Equations 3 and 4 yield the following equation for tissue damage

rates as a functior of temperature Tx,

dQ pe-AE/RTx Eq. 9

where the symbols have been previously defined. The values of P, M., and R

were determined as follows from the graph in Figure 4 (4);.124

P - P1 a 2.1850 x 10

and AE/R - ERI - 93,534.9 for tissue temperature, T , less than 500C and

P a P2 a l.S23C x 10*51

and AE/k - ER2 - 39,109.8 for tissue temperature, T, equal to or Kreater

than 50C.

The damage rate for each temperature value in the 3rraY iWO between

ThINUP and ThINDN is computed according to Eq. 9, depending on whether the value

of the temperature is less than, greater than, cr equal to S6"C. values of

temperature below TMINUP do not make a significant contributicn to Lhe total

damage integra'. The heating damage integral (for values of ,.4 iture between

TMINUP and IPk), HI, and the cooling danage integral ,for values of temperature

between TPK and TMINDN), C[, are computed according to the trave:oidal rule for

integration;

10

614104

41

TEMPCEqATUNE -C

Figure 4. Damage Rates Derived frcm Radiative Data

dt dfl 2dfl &2 E&.210

where 9 - damage integral

dt = DT a time interval between temperature points

dQ/dtm - damage rate at given temperature

Following the computation of the damage integral during heating, HI, and CI,

the integral during cooling, the sum HI + Cl, the total damage is stored in

Fl. Figure 5 is a flow chart of the integral computation.

OPERATING INSTRUCTIONS

General

In addition to a deck of Hollerith cards containing all the Fortran

statements, control cards are necessary for the operation of the program. How-

ever, since the number and format of the control cards may vary somewhat in dif-

ferent computer installations, they will not be considered here. Details on the

appropriate control cards can be obtained at each installation. A binary deck

containing the incremental plotter routine to operate the plotter (7,8) completes

the card requirements.

Various modes of output may be selected by means of sense switches.

The operation of each output is inhibited by p!acing the proper sense switch in

the "ON" position. Figure b is a macro flow chart of the logic between various

sections.

The first datA card (Figure 7A) contains the variable L. the number of

graphs to be plotted or the number of time-temperature histories to be computed.

12

S4 at

Ml:

I ••

Figure S. Flow Chart for Computation of the Thersal Tissue Dimge Integral

13

fanIWO WWPsmCftckpL*"

Toul."NA'diem

so

sp sm am

Ttm soto

BUT* ,WT vp Omp" 6am

Pew. ftaff

TT

on W9

WO

ma Sao

Laddu

Figure 6. Macro Flow Lhart of Logic.

ILl [1l21314 1516"17 l8 19 Ih112'166666i toeo.e~eseeofOO esOO sOO~lO aaOeell so68eo 6636O6eO .leee~e,

is$$ $lt e$l , I, I II nI.iP.I...... I. @Of.I.I.II.I$@@ II..ts@III#&

888131 3111 1 1 3 111J 3 3JI811 3 1 11 3838 1 3 3 1 38 11113

11 1081 ssPssss 444 0 iiss1issssigs, isis 14s is 1its i

110111 'llltllll~lltlllllgllllllllglfltllllggllIulgutll~ll~

"A 7

333301313-3 1.33133J 3313 141ieG[ Sl t4 3)6.S 3l 313

~~~iii* T IIA I '6466666666666666 666366*66 666666T

....... 0 .00 .........

IiIBICI J P2 MRtt itR1818888888818 *:l8881|11g8888088lll81881118ll8181 1 is I

164646464444 66444s 61*64641i 464466illle46 i~4364446411s,

sis~ssi~•Ssssssssssm:i 63lsl3s33sfl3fl~siii~s~ss sss isss s

1666666~ll 66666 lilli's66.63366ls66iil.6l6isisi 66i 66il

il lili IIlll1111 I g i i g ig,,, ill g i li l Siliiiigilliii3iliigigi g il

8li18888888 88818 8118 8188 d? * III 18818811 ll) 81118888811111i 18S15

Figure 7. 1xamples of Input Data18ards.o!IolII6o!IoN6o4o Ilflo 106s 441144is0*

36666 3655655t5656o 6,5355,i35553566366563355P1335

666666666666666666666666666666666666666666666666

666166|66 |eS 666|h666 66| 6 sesaiesuIIa|aale|esssessglee,. alssees 666636666665666366666166161165666666666665666666616

Fi~ gur 7.i Examples of ••••••Input Data Cards.~ii~iiii••iii

ll lil l lll il lll i$| •ll~l~ ll l ll l| l ll~~ll ll~l llisll l

L is a three-digit integer punched in columns 1-3 on the card and is read in I

forsat. L is decremented by I after the computation of each history and tested

for zero. When L=0 the program is terminated.

The second data card (Figure 7B) contains in array called LILY which

has 12 four-digit labels used to label the ordinate axis of the graphed outputs.

The first value, LILY(1), is punched in columns 1-4 on the card in the form

.35, and is read in A format. Successive values of LILY are punched in successive

columns of four, thus using columns I throiigh 48 for the entire array.

The third data card (Figure 7C) contains three variables, D, B, C, used

in labeling the graphed outputs. They are the date expressed in month, day, and

year form, thus, 00/00/00. Each value is three digits ia length and the three

variables occupy columns 1 through 9 with the following form, D = A00, B=/00,

and C=/00, The values are read in A format.

The fourth data card (Figure 7D) contains the values Pl, P2, ERl, and

ER2. P1 and P2 are punched in columns 1-11 and 12-22 respectively and read in

E format. ERl and ER2 are punched in columns 23-30 and 31-38 respectively and

are read in F format.

The remaining data cards (Figure 7E) contain the values of Q, X, DT,

TAU, TIME(l), Al, A2, ZEROTEIMP, cnd PIESQRT. All the values are read in F format

and occupy thc following columns; Q in columns 1-8, X in col=ns 9-16, DT in

columns 17-24, TAU in columns 25-32, TIME(l) in columns 33-40, Al in columns

41-49, A2 in columns S0-58, ZEROTEMP in columns 59-66 and PIESQRT in columns

67-77. All values cover the expected range of the values with a sign position.

Ou-put

The first part of the output, the printed output of the three arrays

T(N), TIME(N), and A(N), is controlled by sense switch #1. Figure 8 is an

16

* * *..*.0000000 @00000000-0

**OS@*@M NOOS e * 0 t. N* a, 1- *

Pb4ISPf AS:

* ~ ~ ~ ~ 0 0. 000000 @0. .0.00000 .

I it 011 0l

4 0 0 0 000&400

*4*44 0000ioo

%::000600000000

0 IfoobH :;:1 : :!: :110, i om 00" oon ool0

* 17

(example of the array printout. The values of Q, Al, A2, and TAU are printed

at the top of the page for identification purposes, followed by the appro-

priate headings for each of the arrays. The arrays are each split in half

and printed in six columns across thc page. It will be noted that there is no

variation in the value of the square root of thermal conductivity during the

heating phase (0 < TIME < TAU), while the square root of thermal conductivity

during the cooling phage (TIME > TAU) is continually decremented by 0.0001 at

each time-temperature point as mentioned before.

The second part of the output, the printed output of the results of

the numerical solution of the thermal tissue damage integral, is controlled

by sense switch #2. Figure 9 is an example of the integration printout. The

printout consists of the values of Q, Pl, P2, ERl, ER2, TPK, TMINUP, and

ThINDN for checking and identification purposes, along with the results of

the integration Fl, HI, and CI. It is seen that the integration printout

directly follows the array printout. Since TPK should occur at TIME = TAU,

ThINUP should be the value of temperature nearest to 44°C during the heating

phase, and TMINDN should be the last value in the T(x) array, these values can

easily be checked against the array printout.

The third part of the output punching the T(N) array on cards is con-

trolled by sense switch #3. Figure 10 is an example of the punched data cards.

Each array is preceded by a card containing the following data: PT in columns

l-S, NO in columns 6-8, ThINUP in columns 9-15, TMINDN in columns 16-22, TPK

in columns 23-29, and Q in columns 30-35. (Figure 1OA) The array from TMINIP

to TMINDN inclusive is punched, eleven values of temperature per card, each

value having a maximum of six digits and decimal point, three places to the

18

IFI

00 fe , *0 0

* S@@ SO @@@SIto.@SO -. Pto

# A IA

.*0 i ... .. .:s. s .

191

0I TOOK 0

,I tllll OItt! 1l llll1 ol $ 1 tISOl soI Ito I t iltls tIIfilt e Soist 11111 11IIIgotl t I 11III1got1

44444444 4 r44r444444444444n44a44a4a44.4-.44444.444m 4444444444

sIflo msssIIl•smsifIIasIIIs•••••••••••• IiIssIsishisai suIiIsI•Issss Issls'iIss3i3iiI~

hIltl ItlItll tl t Il itl1ln l Ill tl ,,llllO itll tltll ttlllll itittll t'll llll lllillltl~ltll ill

A

0 0 O00 0 o 0 O I 0 0

151 6 I 6 I7 I IIlilt*3. 111111111 t i tm a vamp1wa10 bu11111 ill l 1t 1 6,44101,1101111111111I110 I11

i~ llllllllllllOlll lltl i 11111 itt lt iglt ilttlflt ll Dillllllltllllliiifti ll ~ii 0'l'

,,OasesOs~sIlaSISIOeesg0,OsifI0S48008ISSdS0IdiIdISSShSSI~ISSaaS isilsitsssss

11. 4 .. cu . . . , .....

Figure 10. Exasple of Puriched Data Cards.

10

right of the decimal point. (Figure 10B). This feature was originally included

in the program to provide data output acceptable for use in another program.

The fourth part of the output, a plot of the entire tissue temperature

array T(N) from T to TMINDN by means of an incremental plotter is controlled

by sense switch #4. Figure 11 is an example of a tissue temperature plot. The

ordinate of the plot is labeled T(x) and has a range from 25-75"C with the

appropriate labeling. This graph procedure is used to plot time-temperature

histories at a depth x below the surface where a TPK of less than 75"C is

desirable. Hence, since the initial surrounding temperature (TO) is always

32.5SC, the range of the ordinate is sufficient to plot tissue temperatures at

depth. The length of the abscissa is computed for each plot depending on the

size of TIME(N). If TIME(N) is less than 4.5 sec the length of the abscissa

is 5.0 sec long; if TIME(N) is less than 2.25 sec the length of the abscissa is

2.5 sec long. If TIME(N) is greater than 4.5 sec, the length of the abscissa

is equal to ten times the following truncated value: [(TIME(N)/9.)+I.] The

abscissa is labeled TIME(sec.) and covers the appropriate range. The upper

right hand corner of the plot contains the date of the plot and the values of Q,

Al, A2, and TAU for identification purposes. One time-temperature history is

plotted per each graph.

The fifth and last part of the output, a plot of surface time-temperature

histories, is controlled by sense switch #5. The graph is exactly the same as

that for tissue time-temperature histories except that the range of the ordi-

nate is increased to 25-90*C to handle the higher TPK of the surface time-

temperature histories.

Since there are five sense switches each with "ON" and "OFF" positions,

there are thirty-two different modes of operation of the program. The program

21

70

Dose 03/23/6665 o-, 1.880

Ai - .0375A2 - .0355

600 T - .523

55

~50M

I-45

40

35

.50 1.00 1.50 2.00 2.50 3.00Time Wsec.

Figure 11. Exanple of Tissue Temperature Plot.

22

is designed to operate in each of the thirty-two modes; however only a few of

the rissible modes are used in actual practice. Some of these are briefly

discussed because of their importance.

1. All sense switches in "OFF" position - normal mode of operation.

The three arrays T(N), TIME(N), and A(N) are printed, followed by a printout

of the results of the tissue damage integral as shown in Figure 9. The T(N)

array is punched on cards according to the format shown in Figure 10 and a

graph with increased ordinate size (25"-90*C) is drawn containing both surface

temperatures (the plot with the larger TPK) and tissue temperatures (the plot

with the smaller TPK) as shown in Figure 12. Each surface time-temperature

history is printed out as shown in Figure 13 with a label at the bottom identify-

ing the history as a surface temperature history. The first four input data

cards are arranged as mentioned before; however the remaining cards containing

values of Q, X, DT, TAU, TIME(l), Al, A2, ZEROTEMP, and PIESQRT are arranged in

the following order. Each card containing values of Q, X, DT, TAU, TIME(l), Al,

A2, ZEROTEMP and PIESQRT for a time-temperature history at some depth x below

the surface of the skin is immediately followed by a card containing exactly

the same values except that the value of X is zero (0.0). Thus the value of L

is equal to the number of such paired cards or the number of graphs drawn but

equal to one-half the jiumber of time-temper3ture histories computed.

2. Sense switch #3 in "ON" position, all the other switches in "OFF"

position - Operation is exactly as in case 1 above except the punching of

T(N) array is inhibited.

3. Sense switch 05 in "ON" position, all the other switches in "OFF"

position - Operation is exactly as in Case I above except a graph with normal

23

90

865

O6D 03/23/66

n .376A, a .0374

60 k, a .0345

55

50

.n 45,

40o

35

A A A a

2.00 400 600 8.00 10.00 12.00 14.00To me (seQ

Figure 12. Example of Surface Temper4ture and Tissue Temperature Plot.

24

1mvx5*1j:j~xx:ts:3:x

;Z a

II I 7I 0177

.. .. .. . 2 3

02

ordinate size (2$s-75"C) is drawn containing only one plot, that of a time-

temperature history at depth x below the surface of the skin. The value of

L is equal to number of data cards after the fourth one or the number .' eraphs

drawn or the number of time-temperature histories computed.

4. Sense switch I4 in "ON" position, all other switches in "OFF" poIi-

tion. Only surface time-temperature histories are computed and printed out

as shown in Figure 13. Integration and punching of surface time-temperature

histories onto data cards are always automatically omitted whenever surface

time-temperature histories are computed. In this case a large graph is drawn

with one surface time-temperature hi~tory plotted per graph. The value of L

is determined as in Case #3.

5. All sense switches except #2 in "ON" position, sense switch #2 in

"OFF" position. The only operation performed is the evaluation of the thermal

tissue damage integral, the results printed out one after another consecutively

down the page.

The operational analysis of the other modes of operations can easily be

understood by reference to the flow chart in Figure 6. It should be noted that

the computer can distinguish between surface time-temperature history data

(x-O.O) and time-temperature history at depth data only by means of the sequenc-

ing called for n the program. Thus, for instance, if the operator .oads in

surface time-temperature history data and places sense switch 95 in the "0" posi-

tion the computer will treat the data as time-temperature history at depth data.

It is the responsibility of the operator to make the input data consistent with

what is called for by the sense switch settings.

26

REFERENCES

1. Weaver, John A. and Stoll, Alice M. Mathematical Model of Skin Exposed to

Thermal Radiation. Aerospace Medical Reiearch Department, J. S. Naval Air

Development Center, Johnsville, Warminster, Pa. Report NADC-MR-6708, 1967.

2. Buettner, K., Professor, Department of Atmospheric Sciences, University of

Washingtor, Seattle, Washington 98105. Unpublished data.

3. Henriques, F. C., Jr., Studies of Thermal injury: V. The Predictability

and the Significance of Intrmally Induced Rate rrocesses Leading to Irre-

versible Epidermal Injury. Arch. Path. 43, 489-502, 1947.

4. Stoll, Alice M. and Greene, L. C. Relationship Between Pain and Tissue

Damage Due to Thermal Radiation. J. Appl. Physiol. 14, (3) 373-382, 1959.

5. Stoll, Alice M. A Computer Solution for Determination of Thermal Tissue

Damage Integrals from Experimental Data. IRE Trensactions on Medical

Electronics, Vol. ME-7, October 1960, p. 355-358.

6. Hastings, Cecil, Jr. Approximations for Digital Computers; Princeton

University Press, Princeton, New Jersey, p. 187.

7. Michehl, Ed. Corporate Marketing, Control Data, Palo Alto, Cal.; Incre-

mental Plotter Routine; Platy, Axis and Line Generation; Swap Ident. 3E5.01.

8. Michehl, Ed. Corporate Marketing, Controrl Data, Palo Alto, Cal.; Incre-

mental Plotter Routine; Xymove, Interface Between Platy and 3293, Label Gen-

erator; Swap Ident. 3E5.02.

27

UNCLASSlk-iLtu

Swuty lasifist DOCBUMENT CONTROL DATA -R&DM eI~ty Edwiseafiefo of dli.. budy of ~betaet mW hudientd mannido moet 6% .Mmd otan evei~i bnpie to sh"0#1i(

CALCULATION OF TIME-TEMPERATURE HISTORIES AND PREDICTION OF INJURY TO SKIN EXPOSEDTO ThERMAL RADIATION

4. OESCRIPTIVC NOTES (1T~qw of aopo mE n inclusive dot".)Phase Report

S. AUTHOR(S) (Lost nim. hoof name, ilitial)

Weaver, John A.

4. REPC RT DATE OTOANOOFP01 7bNoorpo

14 June 1967 2So. CONTRACT ON GRANT NO. S0. omgegNHATeNu REPORT NUMIDER(S)

&PtojacT NO. AirTask R360 FR102/2021/R01 101 01 (RB-6-O1) NADC-MR-6623

C. SbZT5NER'PORT No(S) (Any oii, numbesbv fiat mor be aeefewd

d._________________ ____________

10. A VA IL AILITY/LIMITATION NOTICES

Distribution of this Document is Unlimited.

II.- SUPPLEKMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

13 ABSTRACT

This report gives a general descripti'on of a digital computer program usedin connection with the study of injury of skin exposed to thermal energy. Allo". the information necessary for a itailed understanding of the program is in-cluded; however, the mate-rial is presented in a manner such that a novice i~n thefield of computer science may make use of the program if he so desires. For thisreason emphasis is placed on the operating instructions for the program. A shortd.scussion of the pertinent theory and equations as they apply to the human skinis included at the beginning of this report.

D FORM A7DD -JAN 64 1473UNC ASIFIEn

Security Classification

UNCLASSII ILEDSecurity Classification

14. LINK A LINK 9 LINK CKEY WORDS ROLM f Wr ROLE WT ROLE[ WT

1' Thermal Injury2. Digihal Computer Program

INSTRUCTIONS1. ORIGINATING ACTIVITY: Enter the name and address imposed by security classification, using standard statementsof the contractor, subcontractor, grantee, Departmei•t of De- such asfense activity or other organization (corporate author) issuing (i "Qutaliled requesteras my obtain copies of thisthe repoit. report from DDC."2a. REPORT SECURETY CLASSIFICATION: Enter the over- (2) "Foreign announcement and dissemination of thisall security classification of the report. Indicate wfiether"Restricted Data" is included. Marking is to be in accord. report by DDC is not authorized,"ance with appropriato security regulations. (3) "U. S. Government agencies may obtain copies of

this report directly from DDC. Other qualified DDC2b. GROUP: Automatic downgrading is specified in DOD Di- users shall rquest throughrective 5200. 10 and Armed Forces Industrial Manual. Enterthe groop number. Also, when applcable, show that optional ."markings have heen used for Group 3 and Group 4 as atahor- '4) "U. S, military agencies may obtain copies of thisized. report directly from DDC Other qualified users

3. REPORT TITLE: Enter the complete report title in all shall request throughcapital leters. Titles in all cases should be unclassified. ,If a meaningful title cannot be selected without classifica-tion, show title classification in all capitals in parenthesis (5) "All distribution of this report Is controlled. Qual-immediateýy following the title. ified DDC users shall request through

4. DESCRIPTIVE NOTES. If appropriate, enter the type of ,to_

report, e.g., interim, prcgress, summary, annual, or final. If the report has been furnished to the Office of TechnicalGive the inclusive dates when a specific reporting period is Services, Departme.st of Commerce, for sale to the public, indi-covered. cate this fact and enter the price, if known.S. AUTHOR(S): Enter the name(s) of author(s) as shown on IL SUPPLEMENTARY NOTES- Use for additional explans-or in the report. Entei aset name, first name. middle initial, tory notes.If military, show rank and branch of service. The name ofthe principal oethor ia an absolute runimum requirement. 1. SPONSORING MILITARY ACTIVITY: Enter the name of

the departmental project office or laboratory sponsoring (payr6. REPORT DATE. Enter the date of the report as day, ing for) the research and development. Include address.month. year, or month, year. If more than one date appearson the report, use date of publication. 13. ABSTRACT: Enter an abstract giving a brief and factual

summary uf the document indicative of the report, even though7 a. TOTAL NUMBER OF PAGES: The total page count it may also appear elsewhere in the body of the technical re-should follow normal pagination proced'Ires, Le., enter the port. If additional space is required, a continuation sheet shallnumber of pages containing information. he attached.7b. NUMBER OF REFERENCES, Enter the total number of It is highly desirable that the abstract of classified reportsreferences cited in the report. be unclassified. Each paragraph of the abstract shall end withSa. CONTRACT OR GRANT NUMBER: If appropriate, enter an indication of the military security classification of the in-the applicable number of the contract or grant under which formation in the paragraph, represented as (TS). (S), (C) or (U).the report was written. There Is no limitatJon on the length of the abstract. How-8b, Sc, & 8d. PROJECT NUMBER; Enter the appropriate ever, the suggested length is from 150 to 225 words.military department identification, such as project number,subproject number, system numbers, task number, etc. 14. KEY WORDS: Key words are technically meaningful tems

or short phrases that characterize a report and may be used as9a. ORIGINATOR'S REPORT NUMBER(S): Enter the offi- index entries for cataloging the re0ort. Key words musa becial report number by which the document will be identified selected so that no security classification is required. Identi-and controlled by the originating activity. This number must flate, such as equipment model designation, trade name, militarybe unique to this report. project code name, geographic location, may be used as key9b. OTHER REPORT NUMBER(S): If the report has been words but will be followed by an Indication of technical con-assigned any other report numbers (either by the originator text. The assignment of links, roles, and weights is optional.or by the sponsor), also enter this number(a).10. AVAILABILITY/LIMITATION NOTICES: Enter any lim-itations on further dissemination of the report, other than those

DD ION 1473 (BACK) UNCLASSIFIED