ORIGINAL PAPERS

Post-mortem cooling of the human head: an infrared thermology study

AHMED KHALLAF and ROWLAND WYN WILLIAMS

Department of Mathematics and Computing, The Polytechnic of Wales, Treforest, Pontypridd, Mid Glamorgan, United Kingdom CF3 1DL

The post-mortem cooling of the human head, over the first fifteen hours after death, was measured by infrared thermol- ogy. A detailed temperature map of the head and face was obtained by the use of image processing techniques and the cooling behaviour of twelve preselected facial features was observed. The two main findings of the study were a difference in cooling pattern between the upper and the lower part of the head, and a consistency in the cooling pattern of the lower part of the head in all the cases studied. A comparison of various model fits to the raw data was undertaken and the "best" bodies, models and features were determined on a statistical basis. The formula that best fitted the raw data was a novel double application of Newton's law. The features with the least error in data fitting were the chin and zygoma; that with the most error was the mouth. Key W o r h : Post-mortem cooling; Time of death; Thermol- ogy; Infrared; Image processing. Journal of the Forensic Science Society 1991; 31 : 7-1 9 Revision received 18 June 1990; accepted 20 December 1990

Introduction In spite of advances in knowledge over the last few decades, the time of death can present major problems to forensic practitioners [I]. For estimating time since death, it is generally agreed that only from the study of body cooling and, in particular rectal cooling, can any semblance of accuracy be expected. Different researchers have selected different parts of the body for observation, but so far no replacement has been found for the rectal cooling method. Unfortunately, this method is known to have an inherent margin of error which could approach 100% [2].

The measurement of temperature has varied in sophistication from feeling the coldness of the body by hand [3], through the use of several kinds of thermometer [4], to highly advanced devices such as microwave systems [5].

Simple methods for interpreting the results have varied from reference to "standard cooling curves" ([6] and as constructed by us in Figure I), performing a short mathematical calculation or applying a general "rule of thumb". Some workers have applied a single exponential (Newtonian) model [7,8], an extended exponential and linear model [3,9-111, or the

31 f I I I I I I 1

0 2 4 6 8 10 12 14

Time after death (h)

FIGURE 1 Cooling curves for unclothed adults in a room at 15.S°C.

double exponential cooling formula [12]. Others have utilised virtual temperature difference and cooling time [ l l ] or have relied on formulae based on the Heat Transmission Theory (the infinite cylinder or sphere models) [13,14] and/or some modification(s) of these formulae. The factors that can naturally affect the rate of body cooling and hence the calculation of time of death were also considered in the above methods and formulae. These included body size and physique, body position, environmental temperature and body temperature at death.

The studies of Marshall and co-workers [15-171 and his summary of the situation [IS] greatly advanced our knowledge of the rectal cooling process. In spite of this, the situation is still as perceived by Knight in 1979 when he wrote "Although one might be right on a considerable number of occasions, one never knows that one is right and one never knows the potential span of one's error, so that being dogmatic in evidence is unwise and unjustified". [19]. In 1977, Simonson, Voigt and Jeppesen reported a study of simul- taneous and continuous measurements of the post-mortem temperature fall in a group of organs which included the rectum, liver, skin, muscles and brain [20]. These authors stated that of all the measurements taken, the brain temperature was the most useful. They reasoned that the head, and hence the brain, are approximately globe shaped, varying little in size from individual to individual and that clothing normally plays no part in the cooling process.

Infrared thermology is a non-invasive and extremely sensitive technique of temperature measurement especially when combined with computerised

8 JFSS 1991; 31(1): 7-19

TABLE 1

. St

udy

of f

ive

case

s of

dea

th f

rom

nat

ural

cau

ses,

sho

win

g ro

utin

e m

easu

rem

ents

and

cha

ract

eris

tics o

f th

e h

bo

dies

. P ". 2

Hei

ght

Wei

ght

Hea

d ci

rc

Tem

p at

C

ase

Age

Se

x (c

m)

(kg)

(c

m)

deat

h "C

C

ause

of

deat

h B

ody

char

acte

rist

ics

k

1

88

F 15

3 41

.7

56

-

Bro

ncho

pne

umon

ia

Thi

n an

d fr

ail.

Eye

s de

eply

2

sunk

. Hai

r co

veri

ng e

ars.

M

outh

clo

sed

7 h

55 m

aft

er

deat

h. C

hin

thin

and

pr

otru

ding

. Nec

k ve

ry th

in.

2 61

M

18

5 89

.3

63

41.5

P

onti

ne in

farc

tion

O

bese

. M

outh

clo

sed

6 h

40 m

af

ter d

eath

. Bal

d an

d sc

alp

hair

rec

edin

g. C

hin

thic

k.

Nec

k sh

ort a

nd th

ick.

3

87

F 15

1 43

-6

53

36.8

?C

onge

stiv

e he

art f

ailu

re

Thi

n an

d fr

ail.

Eye

s su

nken

. M

outh

clo

sed

9 h

40 m

aft

er

deat

h. H

air

cove

ring

ear

s.

Chi

n w

ide.

Nec

k ve

ry th

in.

Wea

ring

den

ture

s.

4 69

M

15

5 45

.6

53

-

Sub

acut

e in

test

inal

obs

truc

- T

hin

and

frai

l. E

yes

deep

ly

tion

(m

alig

nant

) su

nk. M

outh

clo

sed

6 h

afte

r de

ath.

Sca

lp h

air

rece

ding

. Fa

ce th

in a

nd f

acia

l mus

cles

w

aste

d. N

eck

thin

. 5

82

F

168

89-3

54

-

Hae

mop

eric

ardi

um

Obe

se. F

ace

feat

ures

thic

k an

d m

yoca

rdia

l in

farc

tion

, di

stor

ted.

Chi

n w

ide.

co

rona

ry a

rter

y di

seas

e.

Nas

opha

ryng

eal

tube

in s

itu.

M

ost o

f lo

wer

hal

f of

fac

e co

vere

d w

ith p

last

er.

\O

image processing. This combined usage has already proved its usefulness in the study of living patients.

Experimental An in-depth study of five cases of death from natural causes was carried out at the Cardiff Royal Infirmary in April 1987, using a complete thermo- graphy system. Routine measurements, including body weight, height and head circumference are shown in Table 1.

The shrouded body was laid in a supine position and the head was raised on a solid rubber block, except for Case 5 where the body configuration dispensed with the necessity of raising the head. A "half profile" view of the head and face was recorded on video tape. Figure 2, which is a map of the twelve selected features, also shows the line denoting the artificial division of the head and face into the upper and lower parts. The "hot" features were forehead, inner canthus, temple, external auditory meatus, nasal fold, side of mouth and mouth; the "cold" features were eyeball, earlobe, zygoma, nose and chin. The video-tapes were viewed and the required images were captured onto the GEMS system of the PDP-11 minicomputer. The raw digitised data were then transferred to a VAX computer for analysis.

FIGURE 2 Features map of the human head showing position of the head during the case study. 1 Forehead; 2 Inner canthus; 3 Eyeball; 4 Temple; 5 Meatus; 6 Earlobe; 7 Zygoma;

8 Nasal fold; 9 Nose; 10 Side of mouth; 11 Chin; 12 Mouth.

10 JFSS 1991; 31(1): 7-19

Preliminary analysis Although all the bodies arrived in the mortuary at least one hour after death, the processing of the images clearly demonstrated that each of the features on the head had started at a different temperature and that there was a distinct difference in the pattern of heat loss between hot and cold features. Table 2 shows an example of the Case 1 raw data. The spread in measured site temperatures was less than 3%. Figure 3 shows the cooling pattern in Case 1 where, for clarity, each graph shows only three of the features. This general pattern was observed in all the other cases, although the spread of results was not nearly as marked. The top line in each of the graphs shows a thinlsmall body rectal sigmoid curve (from Figure I), plotted for comparison purposes. Case 1 demonstrates the results of fitting of the models used to the raw data and also illustrates the limitations of our methods at this early stage of our research procedure.

Although the kinks in these graphs may be attributable to the earlier short rise in ambient temperature, we observed similar kinks in other cases without such a rise; in one case there was even a drop in ambient temperature. Such kinks were mostly observed between nine and twelve hours after death. The general shape of the cooling curves seemed to correspond to the second and third stage of a sigmoid curve. There was no strong indication of a plateau stage.

Gross comparison using only forehead, inner canthus, temple, nasal fold and side of mouth, indicated different thermological behaviour. The upper part of the head, although invariably starting hotter, cooled more quickly than the lower part with eventual cross-over in temperatures reflecting a different cooling rate. However, if the tip of the nose was used as a temperature reference point, we were able to plot adjusted graphs, levelling out most of the local changes in air flow and minor fluctuations of the ambient temperature. Using the difference between a feature temperature and the nose temperature, a relative consistency was noted; the lower part of the head showed a more uniform pattern of cooling than the upper part. Adjusted plots for the four lower face features showed each of the features on the graph was in the same relative order (nasal fold, side of mouth, zygoma and chin). There was always a cross-over between the zygoma and chin, but the crossing time varied between the cases [21]).

This part of the study, in contrast to most published studies on cadaver cooling, concentrated on relative rather than absolute temperatures.

Formulae used to represent cooling The similarities between facial and rectal cooling curves suggested the use of models currently applied to rectal data. Four well-known models were

JFSS 1991; 31(1): 7-19 11

TA

BL

E 2

. C

oolin

g ta

ble

for

Cas

e 1.

Tim

e si

nce

deat

h (h

rs)

Fea

ture

/tem

pera

ture

("

C)

2-17

3.98

5-25

7.92

8.75

9.90

11.15

11.58

11-98

12-68

13.05

Fore

head

In

ner

cant

hus

Eye

ball

Tem

ple

Mea

tus

Ear

lobe

Z

ygom

a N

asal

fol

d N

ose

Side

of

mou

th

Chi

n M

outh

4

Am

bien

t te

mpe

ratu

re

Rel

ativ

e hu

mid

ity (

%)

considered: the Newtonian model (a single exponential formula); Marshall's model; the infinite cylinder and sphere heat transmission theory models.

A novel "Double Newton's law formula with a switch time" was also devised to account for a phenomenon observed in the study. By the time each experiment started, it could safely be assumed that the bodies had almost, or completely, passed through any possible plateau period and this was confirmed by close examination of the shape of the curves obtained (Figure 3). For most of the cases studied, there was a clear change in the pattern of the features temperature curves at a certain stage during cooling. Each of these curves was found to consist of two logarithmic lines, having a different slope, and corresponding to segments two and three of the standard sigmoid curve. Newton's law was applied to each of these two segments separately and the time of change in the gradient between the two was defined as the "switch time", i.e., when the pattern of heat loss changed.

Using t as time in hours since death, t , as the switch time, and 8 as the temperature difference between each feature temperature and the ambient

28-

24 - 3 *-Ambient a Ambient e 2 0 1 - - - - , - , T 1 ,--

1 . . . . . . - . - Ambient Time aftt

0 2 4 6 8 10 12 14 death (h)

FIGURE 3 Cooling curves for Case 1. For key to features, see Figure 2.

JFSS 1991; 31(1): 7-19 13

temperature, a formal mathematical definition of the Double Newton formula is

with d 5 b, where H(t) denotes the Heaviside function. In order for each segment of the curves to join at the switching time, the quantity c has to satisfy the equation

where a, b, d and t , are positive constants. The ranges of parameters used here are a from 1 to 20 and t, from 2 to 12. Two versions referred to as K+ and K* were required to fit most of the case study data.

For formula K+, b = d + z , with d ranging from 0.01 to 0-50 and z from 0-00 to 0.49.

With formula K*, d = b *z, with z ranging from 0.02 to 1.00 and b from 0.01 to 0.50.

Data fitting procedures For every selected feature in each case, the five cooling curves were fitted to the raw data from the case study and plotted together in one graph to illustrate the difference between the curves, in order to allow a comparison between the several models and to demonstrate the degree of error encountered in fitting each of the curves. The temperature of the features at death were unknown, but could be estimated from studies on live people, the results of which will be published in the near future. From their derivation, the formulae require a constant reference temperature. Taking the weighted mean of the ambient temperature provided less error from small fluctuations than taking actual temperature differences, as had been done in former studies and also in our early studies.

To fit the Newton formula to the raw data, the logarithm of the temperature I3 was taken and the resultant data correlated with the times of observation through a linear regression procedure. For the other formulae, a non-linear minimisation technique was used through a NAg routine to minimise the squares of difference between calculated and raw data [22]. Graphs were prepared of the compound output for the fitted data with the raw data; an example for the first four features in Case 1 is shown in Figure 4. Due to compression, merging of some of the model curves has taken place signifying little difference between those particular formulae. Each of the graphs shows the jagged raw data curve as well as the formulae curves. All the formulae were found to fit the raw feature data well, although the Double Newton formula was generally somewhat high initially, signifying overshoot. A line was drawn vertically on the graph paper at 1.5 hours after the known time of death to indicate a possible plateau stage, as after

14 JFSS 1991; 31(1): 7-19

FIGURE 4 Cooling curves for K model (1), Newton, Marshall cylinder and sphere model (2) and raw data (3). (a) Forehead; (b) inner canthus; (c) eyeball; (d) temple.

reviewing the varying plateau duration times given by other scientists, a possible plateau duration of 1.5 hours was considered to be reasonable for our study. All features and cases were treated in the same fashion and both the standard error (SE) and the root mean square error (RMS) of fit for all combinations were obtained.

Statistical analysis of the fitted data A standard statistical analysis of the RMS and SE data fitting errors, with a view to estimating the "best" and the "worst" of the bodies, models and features, is displayed in Table 3. The overall mean and standard deviation are also shown.

Table 3 shows that the error for Case 1 of about 0.4"C is much worse than for the other bodies, which are at the 0.2-0-3°C level. The order of the features from best to worst, based on the errors obtained, was the same irrespective of RMS or SE calculations. The best features were the chin and the zygoma, with errors below 0.21°C, whilst the worst was the mouth with errors above 0.4"C. It is noticeable that for both the RMS and SE errors the double Newton's formula gave the best fit and that there was not much to

JFSS 1991; 31(1): 7-19 15

TABLE 3. Summary of data fitting errors.

RMS SE

Best case 1 2 3 4 5

Average

Best model K model Marshall Cylinder Sphere Newton

Average

Best features Chin Zygoma Nose Eyeball Nasal fold Forehead Meatus Temple Inner canthus Side of mouth Earlobe Mouth

Average

All data Mean SD

choose between the other models, though the order in RMS and SE errors changed due to the number of parameters used. The overall error was approximately 0-29°C which we considered to be small. Although Case 1 had higher error values in comparison with the other bodies, we could not find a definite reason to explain this. Case 5 proved useful although it was far from an ideal case. We have not considered the temperature loss which must have occurred in the interval between time of death and the time the body arrived in the mortuary, one hour or more later.

16 JFSS 19%; 31(1): 7-19

Discussion and conclusions Apart from two fits (out of 300), all models could be closely fitted to the raw data. Newton's law applied as expected, assuming that our data covered a post-plateau region. The graphs were consistent with the human body being a solid and homogeneous mass, losing heat in a regular and constant way. The Marshall model demonstrated a pattern akin to Newton, except for a short plateau at the beginning of the curve, from zero time. This plateau was more pronounced with some of the cold features. The Marshall zero time temperature was nearer to reality than the Newton and also it was the only model to show a plateau consistently. The Cylinder and the Sphere formulae behaved similarly except that the former generally gave a higher zero time temperature.

The Double Newton formula gave a higher temperature at zero time than in the case of a single Newton model when applied to the whole data. The reason is that it utilised two standard Newton curves for the second and the third segments of the sigmoid curve and did not account for an initial plateau giving rise to zero time overshoot. Also, the Double Newton formula demonstrated a switch time where the two curves met, i.e., when the pattern of cooling changed to the more gentle, and flatter, pattern of heat loss. Some difficulties were encountered; occasionally the fit was reduced to a single Newton curve and in Case 5 two sets of raw data could not be fitted, due to the sharp adjustment of the temperature profile at the switch time.

In all cases, the Newton, Cylinder and Sphere models behaved almost in the same manner, while the Marshall and the Double Newton formulae were distinct from each other, and from the former models in their profiles. An approximate idea of a plateau duration could be estimated from observing the Marshall model. The temperatures predicted by all the models bar the Double Newton were close to each other at the end of a plateau stage. All temperatures at this time were comparable to feature temperatures of living people, as was later confirmed by the experiment mentioned above.

This study showed the power of the combined use of infrared thermology and image processing systems for simultaneous multi-point temperature measurements during post-mortem cooling of the head. We have also demonstrated that at time of death, facial features have different tempera- tures and lose heat at their own specific rate. It may be possible to utilise the relationship between two or more features to estimate time since death.

The pattern of cooling of the upper and the lower parts of the head and the consistency of the cooling of the lower part as well as the cross-point between the zygoma and the chin were shown. The significance of cross-over points is not yet apparent.

The Double Newton formula best fitted the raw data corresponding to the

JFSS 1991; 31(1): 7-19 17

second and third segment of the rectal sigmoid curve, albeit in a small number of trial cases, and with the reservations we have mentioned. Various models may be used to estimate time of death and although the Double Newton formula has some occasional problems such as overshoot, we are confident that it can be accommodated through the plateau interval of a full three-stage sigmoid cooling curve. The models were fitted to the raw data with the time of death taken as the zero time, but there is latitude in the fitting procedures to allow for time of death to be an unknown. In future work, the predicted time of death from such fits may be compared with the known time of death. Further exploration may show the value of using the post-mortem cooling of the human head in the estimation of time of death.

Acknowledgements The authors gratefully acknowledge Novamedix Ltd for the free loan of the Inframetrics 600 System, the mortuary staff of the Cardiff Royal Infirmary for all their help, and are indebted to the staff of the Information Technology Centre and School of Computing technical team at the Polytechnic of Wales for their prompt attention to our requirements.

References 1. Polson CJ, Gee DJ and Knight B. The Essential of Forensic Medicine, 4th

edn. Oxford: Pergamon Press, 1985: 5-39. 2. Knight B. Legal Aspects of Medical Practice, 3rd edn. Edinburgh: Churchill

Livingstone, 1982: 118-126 and Figures 10, 11. 3. De Saram GSW, Webster G and Kathirgamatamby N. Post-mortem tem-

perature and the time of death. Journal of Criminal Law and Criminology 1955; 46: 562-577.

4. Engel JM and Ring EFJ. Applied thermology. Verlag Chemie Publication, Weinheim, 1985.

5. Louay M, Al-Alousi LM and Anderson RA. Post-mortem interval by microwave thermography. The Police Surgeon 1986; 30: 30-42.

6. Burgess SH and Hilton JE. The New Police Surgeon. London: Hutchinson Benham Ltd, 1978.

7. Molnar GW. Newton's law of cooling applied to Newton's ingot of iron and to other solids. Physiologist 1969; 12: 137-151.

8. Molnar GW. Newton's thermometer: a model for testing Newton's law of cooling. Physiologist 1969; 12: 9-19.

9. Nokes LDM, Hicks B and Knight B. The post-mortem temperature plateawfact or fiction? Medicine, Science and the Law 1985; 25: 263-264.

10. James WRL and Knight B. Errors in estimating time since death. Medicine, Science and the Law 1965; 15: 111-116.

11. Fiddes FS and Patten TD. A percentage method for representing the fall in body temperature after death. Journal of Forensic Medicine 1958; 5: 2-15.

12. Brown A, Hicks B, Knight B and Nokes LDM. Determination of time since death using the double exponential cooling model. Medicine, Science and the Law 1985; 25: 223-227.

13. Hiraiwa K and Ohiro Y. Estimation of post-mortem interval from rectal

18 JFSS 1991; 31 (1): 7-19

temperature by use of computer. Medicine, Science and the Law 1980; 20: 115-125.

Joseph AEA and Schickele E. A general method for assessing factors controlling post-mortem cooling. Journal of Forensic Medicine 1970; 15: 364-391.

Marshall TK and Hoare FE. Estimating the time of death (a). Journal of Forensic Sciences 1962; 7: 56-81.

Marshall TK. The use of body temperature in estimating the time of death and its limitation. Medicine, Science and the Law 1969; 9: 178-182.

Brown A and Marshall TK. Body temperature as a means of estimating the time of death. Journal of Forensic Sciences 1974; 4: 125-133.

Marshall TK. The problem of timing death from the body temperature. The Police Surgeon 1979; 16: 21-28.

Knight B. The determination of the time since death. The Police Surgeon 1979; 16: 29-32.

Simonson J, Voigt J and Jeppesen N. Determination of the time of death by continuous post-mortem temperature measurements. Medicine, Science and the Law 1977; 17: 112-122.

Khallaf A and Rosser BL. Thermographic study of post-mortem cooling of the human head: a preliminary report. Journal of the American Academy of Thermology and the International College of Thermology 1988; 3: 53-58.

Khallaf A. Post-mortem cooling of the human head using infrared thermol- ogy and image processing. M Phil thesis, Polytechnic of Wales, 1989.