Death Time Estimation in Case Work: Rectal Temperature Time of Death Nomogram PDF

Fore&c Science Internutbna& 33 (19881269-266 209 Elsevier Scientific Publishers Ireland Ltd. DEATH TIME ESTIMATION IN CASE WORK. I. THE RECTAL TEMPERATURE TIME OF DEATH NOMOGRAM C. HENSSGE Imtitut j?ir Rechtsmedkin der Univeraitit zu K6ln, Me...

Fore&c Science Internutbna& 33 (19881269-266 209 Elsevier Scientific Publishers Ireland Ltd. DEATH TIME ESTIMATION IN CASE WORK. I. THE RECTAL TEMPERATURE TIME OF DEATH NOMOGRAM C. HENSSGE Imtitut j?ir Rechtsmedkin der Univeraitit zu K6ln, MelatengMel 60/62, 05000 K61n JO lF.R. G.I (Received January 29th, 1988) (Accepted February 19th, 1988) A rectal temperature time of death nomogram was developed on the basis of physical consid- erations, the two-exponential term of Marshall and Hoare (J. Forensic Sci, 7 (19621 56-811, further studies of literature and our own experimental body coolings. The Nomogram Method is based on a single measurement of the rectal temperature. The result is obtained immediately at a scene of crime without any mental arithmetic. Support in the practical application of the method and data for the accuracy of estimated death time are given. Special problems and its limitations are discussed. The Nomogram Method is compared with other temperature methods of estimating the time since death. Key words: Time of death nomograms; Rectal cooling Introduction Whenever a body is found under suspicious circumstances the task of esti- mating the time since death should really be carried out by a forensic pathol- ogist. The contribution to clearing up a case depends on the accuracy and reliability of the methods available. In fact, most methods have insufficient accuracy and reliability. This is the reason why the importance of the foren- sic death time is so little. The methods of estimating the time of death based on body cooling are distinguished by some features in comparison with other methods: the cool- ing of a body is a predominantly physical process; the influence of biological processes (fever, hypothermia, postmortem heat production) and of physical facts (body build, composition of the body) is either negligible or recognizable and, consequently, can be taken into account. The process of cooling can be measured easily even on-line. Therefore, the data of literature is more exten- sive and more sophisticated and the main influencing factors are investigated better. We have continued these investigations by numerous experimental body toolings over the past 13 years and have summarized them all in the Nomogram Method. The method is based on a single temper- 0379-0733/33/$03.50 0 1988 Elsevier Scientific Publishers Ireland Ltd. Printed and Published in Ireland 210 ature measurement and it does not require any mental arithmetic or expen- sive devices, nevertheless, the result is obtained immediately at a scene of crime. The bases, our own experimental material and the practical experience in using this method are reported below. Basic Considerations Postmortem temperatwe plateau The cooling of a body is a predominantly physical process. Therefore, it is predominantly determined by physical rules. Even the so-called ‘Postmortem Temperature Plateau’ is physically determined and not a special feature of the dead human body. Each body which has a low thermal conductivity (e.g. the Cooling dummy, Fig. 15) has such a plateau during its first cooling phase providing non-stationary (unsteady) heat conduction. The postmortem tem- perature plateau leads to the sigmoidal shape of the cooling curve (Fig. l), [l-8]. (The postmortem heat production only contributes approx. l/6 to the plateau. tbl Fig. 1. Sigmoidal shape of cooling curve. A single exponential term like Newton’s Law of Cooling is insufficient to describe it mathematically. The two-exponential-term (Eqn. 1) of Marshall and Hoare provides a closed mathematical description. The quotient Z’r- T./T, - Tjstandardized temperature) is a good measure of the progress of cooling.  211 iUo&lling mathematicaily In 1962, Marshall and Hoare [3 - 51 published a formula in modelling rectal body cooling mathematically, which is in a different notation: T, - T, Q= = A x exp (B x t) + (1 - A) x exp (1) T0 - T. where Q = Standardized temperature; T, = rectal temperature at any time t; T, = rectal temperature at death (t = 0); T, = ambient temperature; A = constant; B = constant; t = death time. There are two exponential terms: the second (with the constant A as a part of the exponent) describes the postmortem temperature plateau. The first (with the constant B as exponent1 expresses the exponential drop of the temperature after the plateau according to Newton’s law of cooling (Fig. 11. The formula by Marshall and Hoare is the ultimate success in modelling body cooling for the applied purpose of estimation of the time since death. The formula only requires two constants (in addition to the body tempera- ture at death), but, nevertheless, it provides a sufficient mathematical description of real cooling curves of different parts of the body (e.g. rectal, brain) as well as of the Cooling Dummy (see below). As demonstrated by Brown and Marshall [ll] more than two exponential terms complicate the model (without better results). Though there are some difficulties in identifying the individual values of the only two constants in any specific case (see below) the question is not to look for a better model, but for the best way to identify the individual values of the constants A and B. The model of Marshall and Hoare is the basis of the Nomogram Method. Empiric Results under Chosen Standard Conditions of Cooling In our experimental body toolings the rectal temperature T, and the ambient temperature T, were measured on-line by an electronic device. The rectal temperature was measured at least 8 cm inside the sphincter ani and taken as the so-called deep rectal temperature [lo]. Rectal temperature at death T,, In the modelling of all experimental body toolings the rectal temperature at death T, was stated as 37.2OC even if there was a sign of fever (hospital cases). Chosen standard conditions of cooling The values of the constants A and B are dependent on the body build and the ambient cooling conditions including the thermal factors on the surface of the body. To investigate empirically rules of the dependency of the 212 constants on the body build only, the other influencing factors were at first kept uniform except for the ambient temperature which was relatively con- stant during an experiment, but at different levels between 5.8 and 22OCin different experiments. The ‘Chosen Standard Conditions of Cooling’we used in this sequence of experiments is the same as described in Refs. 3 - 5: ‘naked body - lying extended - on the back - on a thermally indifferent base - in still air - in a closed room - without any sources of strong heat radia- tion’. Constant B In the first sequence of experimental body toolings under almost identical conditions of the chosen standard (same investigator, room and random cir- cumstances) a strong correlation was found between the body weight to the power of - 0.625 and the value of B Fig. 21. The correlation between the 0.8 fold of the quotient ‘body surface/body weight’ (size factor according to Ref. 61 and the value of B [3-51 was less strong but not significantly in this sam- ple of 23 bodies which ranged between 30 kg and 112 kg body weight [10,12]. We concluded that the body build described as the relation of height and weight (by the size factor) does not give a more precise estimation of the cooling coefficient B than the more simple measure of the body weight only. Therefore, we prefered the simpler procedure to calculate the value of B from the body weight only. In addition, the quantity of fatty tissue of a body did not have any apparent influence on the value of B in accordance with theoretical aspects. In a combined series of 53 experimental body toolings.oo -.Ol -.02 -.03 -.04 1 -.05 I -.06 - B -.07 - -.08 - -09 - - 10 - -.l 1 -.12 1 -9 03.05 07.09.11 13 to be raised the - 625 power 1;2 9’0 5’7 4’0 3b 2’3 body weight (kg) Fig. 2. Relation between the exponent B and the body weight to the power of -0.626 under chosen standard conditions of cooling. Regression line and permissible variation of 95% (Eqn. 2).  213 from different investigators at different places, though under the ‘Chosen Standard Conditions of Cooling’ this correlation could be confirmed. The var- iance was greater than in the first series because of only similar, but not identical, cooling conditions. In consequence, the individual value of B can be computed under ‘Chosen Standard Conditions of Cooling’ by: B= - 1.2815 (kgd.62s1 + 0.0284 (21 The power of 0.625 seems to be an analogy to the rule of surface of Max Rubner: the surface is proportional to the body weight to the power of 0.67 according to the cubic root of the squared body weight, that’s the Rule of Meeh. If the individual value of B is experimentally investigated from the whole cooling curve of the body [lo] the body weight can be computed vice versa to Eqn. 2 by - 1.28151.6 kg = (31 B- 0.0284 In 46 cases this agreed with the real body weight within a standard devia- tion of * 6.1 kg. Constant A up to 2?1V ambient temperature The empiric investigation of the dependency of the constant A in experi- mental body cooling was much more difficult than that of the constant B, because A describes the postmortem temperature plateau and the tempera- ture at death was really unknown in our cases, since the bodies which were investigated came between 0.8 and 6 h post mortem. In the first series of experiments the duration of the plateau varied from between 5 h and 14 h corresponding to a fictitious period without any drop of the rectal tempera- ture between 1 h and 6 h [lo]. Nevertheless, there was a significant relation between the duration of the plateau and the rate of the temperature drop after the plateau: bodies with a low rate (high body weight) had also a longer plateau phase than bodies with a high rate (low body weight). There is a relationship between the values of the exponent of the first and the second term of the model. Within the investigated range of the ambient temperature between 5O and 22OC the value of the second exponent was found to be five times the value of the first exponent (Bl resulting in an approach of A = 1.25 [lo]. (The value of the second exponent is not a fixed one, e.g. - 0.4, as supposed in Refs. 3- 51. In ambient temperatures up to 23OC the time since death can now be cal- culated by: T, - T, Q= = 1.25 x exp U? x t) - 0.25 x exp (5 x B x t) (4) 37.2 - T. with B according to Eqn. 2. 214 Constant A above 2.9OC ambient temperature Using Eqn. 4 with the rectal cooling curves published by De Saram et al. in 1965 , which were obtained in ambient temperatures between 26O and 31°C the death time was systematically overestimated. The reason for this was solely an overestimation of the relative length of the plateau related to A = 1.25. By means of an approach of A = 1.11, (means: the value of the second exponent is ten times that of the first) corresponding to a relative shorter length of the plateau, the overestimation was removed. Theoretically the plateau also depends on the magnitude of the difference in temperature between the rectum and surroundings at death [7,10,14] so that the empiric result in modelling De Saram’s cooling curves establishes a real dependency of the value of A (relative length of the postmortem temperature plateau) on the ambient temperature. This dependency seems to be non-linear but pro- nounced in ambient temperatures above 23OC. Certainly a jump in the value of A from 1.25 to 1.11 at 23OC or at any other level of an ambient tempera- ture should not be expected but in lacking more experimental data of rectal cooling curves in higher ambient temperatures we have not any more accurate knowledge at present. In ambient temperatures above 23OC, the time since death may now be calculated according to Ref. 10: Tr - T, Q= = 1.11 x exp (B X t) - 0.11 x exp (10 x B x t) (51 37.2 - Ta Accuracy of calculated time since death In summarizing cases of different body weights the errors of computed death time should not be plotted against the progress of death time but against the progress of cooling, which is the real cause of the increase in errors. A good measure of the progress of cooling is the Standardized Tem- perature Q (Fig. 1 and Eqns. I,4 and 51. Its value is 1 at death and 0 when the rectal temperature has reached the ambient temperature. So a value of 0.5 e.g. means that the original difference between the rectal and the TABLE 1 DEATH TIME AT DEFINED LEVELS OF THE STANDARDIZED TEMPERATURE Q DEPENDENT ON THE BODY WEIGHT Level Body weight ikgl of Q SO 50 70 90 110 0.5 7 11 15 19 23 0.3 12 17 23 29 36 0.2 15 22 30 38 46  215 TABLE 2 STANDARD DEVIATION OF ‘CALCULATED - REAL DEATH TIME’ DEPENDENT ON THE PROGRESS OF COOLING Q OF 53 BODIES UNDER CHOSEN STANDARD CONDI- TIONS OF COOLING Q-range n Calculatkm according to Eqn 4 Rule of thumb 1.0 > Q > 0.9 117 1.3 1.4 0.9 > Q > 0.8 126 1.3 2.0 0.8 > Q > 0.7 142 1.4 2.5 0.7 > Q > 0.6 140 1.4 3.2 0.6 > Q > 0.5 155 1.4 4.0 0.5 > Q > 0.4 181 1.6 5.1 0.4 > Q > 0.3 208 1.6 6.7 0.3 > Q > 0.2 208 2.2 10.8 0.2 > Q > 0.1 224 3.1 16.1 0.1 > Q > 0.07 67 4.5 18.1 ambient temperature at death has been reduced to 50°~. Dependent on the body weight a defined value of Q corresponds to different times of death (Table 11. In our own experimental body toolings in ambient temperatures between 5O and 22OC the computed time of death, according to Eqn. 4 had errors which could be classified in three groups (Figs. 3,4; Table 2). These corresponded to values of Q between 1 and 0.5 - the permissible variation of 95% is f 2.8 h. For a more progressive cooling, corresponding to 81 , 6 2I S 1 di ’ -2 t’ -4 -6 / -8 -1 +, _ , 1.0 0.5 0.3 0.2 0.1 0 Q Fig. 3. Standard deviation se of calculated death time dependent on the progress of cooling Q. Chosen standard conditions of cooling. 53 bodies; body wts 9- 112 kg; age l-87 years; ambient temperature 6.8-22%; start of temperature measurement 0.8-6 h post mortem - end 10 - 75 h post mortem. The majority of bodies were cases of a sudden unexpected death with known time of death to within some minutes. Fig. 4. Histogram of the errors of calculated death time for 1 > Q > 0.5 in addition to Fig. 3. values of Q between 0.5 and 0.3 the permissible variation of 95% is k3.2 h. For values of Q between 0.3 and 0.2 the permissible variation of 95% is f 4.5 h. Below a value of 0.2 of Q we obtained in some cases very big errors. Therefore (in compliance with Ref. 271 the reliability of computing the time since death does not exist. In computing the time since death to Eqn. 5 of de Saram’s cooling curves in ambient temperatures between 26OC and 31°C the standard deviation was f 1 h [lo] corresponding to the permissible variation of 95Oh of approx. &2 h. Nevertheless, we recommend the use of the given permissible variation of 95% of our own experimental cooling curves in lower ambient temperatures, because of computation of death time ended at 8 h post mortem in De Saram’s material. Empiric Results Under Cooling Conditions Differing from the Chosen Standard Pilot ‘broken’ experiments For a clear decision as to whether there is a significant influence of cloth- ing, covering and wind on the body cooling [3- 5,361 or not [2,16] we made some special ‘broken’ experiments (Figs. 5 and 61 [lo]: A body cooled for the first several hours clothed or covered, and, after the clothing or covering was taken off the body, consecutively naked in still air (Chosen Standard) (Fig. 5). The graphs on the left show the original points of measurement with the computed cooling curves (lines) according to Eqn. 4 using the individual calculated values of the constant B which can be seen in the graphs on the right. These graphs demonstrate the cooling curves as the logarithm of the temperature difference between the rectum and the surroundings. Here, the given lines are the regression lines and the given figures are the slopes, which are identical to the constant B, of each of the two parts of the cooling  217 * clothed 1 naked 37 J 24.4 3s 30- 1.5 thick bedmead 1 naked thkk bedspread 1 naked 3.3 37. b 35- 3.0 30- 2.5 2s- 20 20. IS- 1s 101 *-. t 10 I, 1. ,, I- 0 10 20 2030 40 so -0 10 20 20 30 40 so Fig. 5. ‘Broken’ cooling experiments. Change from clothed to naked (upper graphs) and, resp. from covered by thick bedspread to naked (lower graphs). On the left: rectal and ambient tem- peratures (scale in the left margin) and, resp. temperature difference ‘rectum - ambient’ (scale in the right margin) in linear measures. On the right: logarithm of the temperature difference ‘rectal - ambient’. curves. These graphs give a clear answer to the question: The clothed body (upper graphs) cools with a slope of B - 0.04 which corresponds to the slope of a naked body of 109 kg according to Eqn. 3. After taking the clothing off the body the same body now cools with a slope of B = - 0.06 corresponding to 72 kg. The real body weight was 76 kg. The influence of the clothing (un- derwear, shirt, suit and thicker coat) is significant. The influence of a’covering like a thick bedspread (lower graphs of Fig. 5) is much more pronounced: the body cools with B = - 0.016 corresponding to 218 still alr ’ wind 35 *\ 0 \\ 1 30 25 stlll alr 1 wlnd 24.8 20 20 16 10 10 05 F0 00 1 1’ 7” ‘I.\ , 10 20 30 40 50 21s”c ! 10.2Yi Fig. 6. ‘Broken’ cooling experiments. Change from cooling in still air to permanently moving air (‘wind’; upper graphs). As a control experiment (lower graphs): Change of the ambient tempera- ture only from 21.6O to 10.2%. for further details see Fig. 5. 217 kg. After taking the covering off the body it cools with B = -0.06cor- responding to 72 kg. The real body weight was 73 kg. In analogy (Fig. 6, upper graphs), a body cooled firstly naked in still air (chosen standard), and, later on in permanently moving air by switching on a small fan (25 W,  219 mounted on the ceiling at a distance of approx. 2 m from the body surface giving only a very slight air movement). The slope B equals - 0.067 (64 kg) under the chosen standard conditions (still air) closely related to the real body weight of 65 kg. This changes to B = -0.084 under the condition of moving air corresponding to 49 kg. The conclusion of this experiment is that even a slight but permanent air movement accelerates the cooling of a naked body significantly. Conversely (lower part of Fig. 6): there is not any significant change to the slope of the cooling curve when the ambient temperature only changed rectangularly. As a control experiment this naked body of 71 kg body weight cooled in still air, firstly in an ambient temperature of approx. 21.5OC and, after a quick transfer to another room, later on, in approx. 10°C ambient temperature. The slope B changed from - 0.057 (76 kg) to - 0.063 (68 kg) which is insignificant. The principle of corrective factors of the body weight Example of the upper part of Fig. 5: the clothed body cools like the naked body 1.4 times heavier: 109 kg/76 kg = 1.4. This corrective factor of the body weight (Cl equals the body weight calculated from B of the real cooling curve (body wt.,,) divided by the real body weight (body wt.). body wt.alc C= 16) body wt. So, Eqn. 2 is now B= - 1.2815 [(C x kg) - 0.6251 + 0.0284 (2’1 where C = corrective factor of the body weight for taking into account any difference of the cooling conditions from the chosen standard. In case of the lower part of Fig. 5 (thick bedspreadk C =- 217kg = 30. 73 kg In case of the upper part of Fig. 5 (wind): 49 kg C= - = 0.75 65 kg In case of the lower part of Fig. 6 (chosen standard: rectangular change of the ambient temperature only): 220 76 63 C= - kg = 1.07 resp. C = kg = 0.96 71 kg 71 kg In comparison with the chosen standard (C = 11, thermic isolation conditions will result in a corrective factor greater than 1. Conditions with an acceleration of the cooling will result in a corrective factor smaller than 1. Cooling conditions comparable to the chosen standard will result in a correc- tive factor close to 1. Empiric cowective factors After the pilot experiments we made several series of cooling experiments under various cooling conditions, all differing from the chosen standard, and using naked bodies in permanently moving air, different types of dry clothing and covering (13,171, wet-through clothing, wet, naked body surface with or without wind and body cooling in still water. From each experimental body cooling curve the real value of B (in analogy to the graphs on the right in Figs. 5 and 61, the corresponding body weight TABLE 3 EMPIRIC CORRECTIVE FACTORS OF THE BODY WEIGHT* Dry Zn air Co77ective Wet-through In air/water clothing/covering” facto9 &thin&covering wet body srr$xce 0.35 Naked Flowing 0.5 Naked still 0.7 Naked Moving 0.7 1- 2 thin layers Moving Naked Moving 0.75 1- 2 thin layers Moving 0.9 2 or more thicker Moving Naked Still 1.0 l-2 thin layers still 1.1 2 thicker layers still 2-3 thin Iayers 1.2 More than 2 thicker Still l-2 thicker layers Moving or 1.2 layers 3 - 4 thin layers Still 1.3 More thin/thicker Without 1.4 layers influence - Thick bedspread 1.8 + clothing combined 2.4 Qnly the clothing or covering of the lower tmnk is relevant! ‘The listed Corrective Factors for higher thewnic isolution conditions (C = > 1.4) are only valid for b6dy weights between approx. 59 kg+ and 80 ks+. In cases of lower body weights higher factors are necessary; in cases of higher body weights lower factors are necessary. More detailed investigation has to come.  221 TABLE 4 STANDARD DEVIATION OF ‘CALCULATED - REAL DEATH TIME’ DEPENDENT ON THE PROGRESS OF COOLING Q OF 26 BODIES UNDER VARIOUS COOLING CONDI- TIONS. Q-range n Calculation according to Eqn 4 Rule of thumb 1.0 > Q > 0.5 464 1.3 3.9 0.5 > Q > 0.3 142 2.2 9.2 0.3 > Q > 0.2 42 3.4 18.3 according to Eqn. 3, and the resulting corrective factor according to Eqn. 6, were calculated. The more general results are to be seen in Table 3. For body cooling in still water the listed corrective factor of 0.5 was found only in water of lo- 20°C. Unexpectedly, the experiments in water at approx. O°C yielded dis- tinctly slighter temperature decreases according to corrective factors of about 0.75. This can be explained perhaps by a physically determined change of the thermal diffusivity of the fatty tissue. The corrective factor of naked bodies in ‘flowing water’ listed in Table 3 (0.351 is an evaluation according to Ref. 11 and is not based on our own experiments. Accuracy of calculated time since death In computing the time since death of the experimental body toolings under various cooling conditions, and the resulting error statistics (Table 41 we assumed a variation in the corrective factor of of: 0.1 around the real one. For example, if the investigated corrective factor was 1.4 in a case we also applied 1.3 and 1.5. This was made for using the error statistics in casework where the selection of a corrective factor is really somewhat uncertain. Dependent on the progress of cooling & we obtained the listed permissible variations (Table 4; Figs. 7 and 81. Application in Casework How is the death time obtained? According to the level of the ambient temperature the death time ought to be calculated either by Eqn. 4 or Eqn. 5. The equations cannot be solved to t, therefore an approximation is necessary. There are two ways to calcu- late the time since death at a scene of crime and neither require any mental arithmetic: (11By means of a hand-held computer [21,22]: We use the Hewlett Packard 71B. We wrote a program as a dialogue (Table 51. If you have a printer the result can be printed out. (2) By means of nomograms [17,20] 222 (h) 10 I 1 S dt ' [ -2 ---J -4 I -6 -8 * Ji , , , 1.0 0.5 0.3 0 2 0 1 0 Q Fig. 7. Standard deviation sdt of calculated death time dependent on the progress of cooling Q Various cooling conditions differing from the chosen standard. Twenty-six bodies. For further details see Fig. 3. TABLE 5 COMPUTERS (HANDHELD HP 71B) DIALOGUE FOR COMPUTING THE TIME SINCE DEATHGIVINGTHERESULTAFTERASHORTDELAY The computer asks Feed into it e.g. CASE? XYZ AMBIENT TEMPERATURE? 15 RECTAL TEMPERATURE? 27 BODY WEIGHT? 70 CORRECTIVE FACTOR? 1.0 Wait please 13.6 h + 2.8 h n -I 150 I 1 L L 100 1 Ld’ 5o _ -b: -4 -2 0 2 4 6 dt[ti Fig. 8. Histogram of the errors of calculated death time for 1 > Q > 0.5 in addition to Fig. 7.  223 (Figs. 9 and 101. F or the first step (Fig. 111 the points of the scales of the measured rectal temperature (e.g. 27OC in the left margin) and ambient tem- peratures (e.g. 15OC in the right margin) have been connected by a straight line. It crosses the diagonal of the nomogram at a special point. For the sec- ond step you have to draw a second straight line going through the centre of the circle, below left of the nomogram, and the intersection of the first line and the diagonal (Fig. 121. The second line crosses the semi-circles which represent the different body weights, each with a calibration of the death time. At the intersection of the semi-circle of the given body weight (e.g. 70 kg) the time since death can be read off (e.g. 13.5 h post mortem). The body weight used can be the real (chosen standard conditions of cooling) or the corrected body weight (corrective factors in Table 31. The second straight line touches the outermost semi-circle where the permissible variation of 95% can be seen respectively levelling off the range of reliability. This 95% error limit is the same as the result of the experimental body toolings under the chosen standard conditions of cooling (Table 21 respectively, under condi- tions differing from the chosen standard (Table 4). The latter are to be used if ‘using corrective factors’. Though the permissible variation of 95% was smaller in De Saram’s cases of ambient temperatures above 23OC we recom- mend using the error limits of ambient temperatures up to 23OC too. Reading off the time since death from the nomogram is very easy. Never- theless, there are some requirements in order to obtain reliable results. Firstly analyse the situation at the scene of crime The result of using the Nomogram Method is a reading off the time of death calculated by some rules from some points of contact which are them- selves either measured or evaluations. You can use right rules but get wrong results if the points of contact are wrong. The most important thing, and - certainly - often the most difficult one, is to adyse carefully the points of contact at the scene of crime. By using the nomogram you can quickly calculate some different times since death by taking some different points of contact as a basis. This is recommended if the points of contact are not closely defined and a range of any point of contact must be taken into account. The mean ambient temperature. Theoretically the formula requires a con- stant ambient temperature. In fact, the mean ambient temperature of the whole period between the time of death and the time of investigation is required. The actual measured ambient temperature at a scene of crime need not necessarily be the mean. The required mean ambient temperature of the period in question can often be evaluated, if necessary (body found out of a closed room), by contacting the weather station. It is a good strategy to evaluate an upper and a lower limit of the mean ambient temperature which might be possible on the basis of both the ambient temperature actually measured and the probable changes of it. Evaluating the corrective factor. The choice of a corrective factor of the body weight of any case is really only an approximation. It requires personal  224 PERMISSIBLE VARIATION OF 95% (Zh) \ \.44.x3 3i -.20 -26.ui \.wl.?. ',aj. -" A M i U T 5 0 I lb I 2b, 4b : 6b, 60 '100 1iOi 1601200 ' '+ 15 30 50 70 Go Ii0 140 180 10 Fig. 9. Nomogram for reading off the time of death from rectal, ambient temperature and body weight for ambient temperatures up to 23°C according to Eqn. 4. Without any corrective factor the nomogram is related to the chosen standard conditions of cooling.  225 PERMISSIBLE VARIATION OF 9S”& 23- “C A E KILOGRAM ?S :, 26 M Fig. 10. Nomogram for reading off the time of death from rectal, ambient temperature and body weight for ambient temperatures above Z3oC according to Eqn. 5. Without any corrective factor the nomogram is related to the chosen standard conditions of cooling.  PCRU(S9IEt.t VAAlITtON Of 05% (th) I- 5 ,1 'C R ‘I KlLf;CRIM U M FIRST STEP Rectal temperature: 27’C Ambient temperature: lS@C Fig. 11. The use of the nomograms. First step. experience. The data in Table 3 is only a support. Again it is a recommended strategy to select an upper and a lower corrective factor which might be possible. Range of death time by range of points of contact. Example: for a body of ‘75 kg actual body weight and a rectal temperature of 27OC you evaluate a mean ambient temperature between 17OC and 20°C and a corrective factor between 1.2 and 1.5 for special clothing. Using the nomogram you have to  227 PERMISSIBLE VARIATION OF 0596 (Zh) SECOND STEP Rectal temperature: 27OC Ambient temperature: 15OC Body weight: 70kg Result: about 13.5 hpm ? 2.8 h (95%) Fig. 12. The use of the nomograms. Second step. draw 2 x 2 straight lines (Fig. 13k connect 27OC rectal temperature with each 17 OC and 20°C. Now you have ito draw a second two lines crossing the semi-circles. Then you have to read ff the time since death on both lines at each two intersections of the followi kg semi-circles: 75 x 1.2 = 90 kg and 75 x 1.5 = 112.5 (110) kg. As a result ~youwill get four values of a death time: approx. 19, 23.5; 23 and 28.5 h post1mortem. So, you could state: the death  PERYlSSlU_E VARIATION OF 95% (th) Fig. 13. The use of the nomogram in a case with ranges of the ambient temperature (17-2OW and the Corrective factor (1.2-1.5) of a real body wt. of 75 kg corresponding to corrected body wts between 90 and 110 kg. occurred between 19 h and 28.5 h before the time of investigation, which means: 23.5 f 4.6 h. This example also demonstrates that the given permis- sible variation at the outermost semi-circle if 4.5 h, Fig. 13) includes some uncertainties. Where the method must not be used It must be emphasized that this method cannot be used in every case. Under some circumstances sketched in  223 TABLE 6 CONDITIONS UNDER WHICH THE METHOD MUST NOT BE USED (11 Strong radiation (sun, heater, cooling system). (21 Suspicion of general hypothermia. (3) The place where the body was found is not the same as the place of death. (41 Uncertain severe changes of the cooling conditions during the period between the time of death and examination. 16) Unusual cooling conditions without any experience of a corrective factor. Table 6 this method must not be used because the points of contact are really unknown. In almost all cases the criteria of Table 6 are recognizable providing a careful analysis of the apparent and the rather occluded circumstances. Example for a really recognizable but rather an occluded cir- cumstance which excludes the use of the method: a body was found by night in a closed room lying on the floor near the south-west window. Using the actual apparent points of contact - especially the darkness - a death time of early afternoon resulted. Even though at this time the body would have been set out directly sun radiation. Taking that into account and without any knowledge of the concrete influence of sun radiation we did not give any statement concerning the time of death. A usefuladdition:Cooling Dummy In some actual cases a body was found under special conditions where we had not any experience of a corrective factor. In order to decide the death time we started experimental body toolings under those particular condi- tions (e.g. Ref. 181.Because of obvious difficulties of such procedures the idea of a Cooling Dummy originated. We constructed a Cooling Dummy. It con- sists of a layer of coated material filled with a gel mixture of Glycerin (47.50/b), water (47.5O/bl and Agar (5Ohl which is somewhat elastic in temperatures below 4OOC. The dummy is heated to 37OC in an incubator. When taking it out of the incubator its ‘death’ occurs, so to speak. In numer- ous test toolings (Fig. 141 under different conditions, the Dummy provided cooling curves which were very similar to the corresponding curves of bod- ies, even in the first cooling phase, which is called the postmortal tempera- ture plateau (Fig. 1 and 151 [23,24]. By means of several test toolings under the chosen standard conditions of cooling (Fig. 151 the corresponding ‘body weight’ according to Eqn. 3 was investigated. A test cooling of the Dummy under cooling conditions differing from the chosen standard provides a ‘body weight’ differing from that, thus giving the true corrective factor according to Eqn. 6. So, we use the Dummy to find out the real corrective factor being true of unusual cooling conditions where we have not had any experience with dead bodies. Meanwhile, the Dummy was used for the reconstruction of the cooling rate of the body where it was found. 230 TEMPERATURE PROBES AMBIENT ‘RECTAL’ p DUMMY Fig. 14. Arrangement of a cooling test of the (37W heated Dummy. 1. I I I Tr - Ta ’I. , TO- Ta ,5.. I. I I. !. I :!, ’ i.I: I. -1 I ’a ‘0, ‘I 6: “‘I,.,..i;: o+ * 0 10 20 30 40 50 h p.m. Fig. 16. Cooling curves of a Dummy under chosen standard conditions of cooling. Six test cool- ings at three different places. Abscissa: time in hours after taking the Dummy out of the incuba- tor. Ordinate: standardized temperature.  231 TABLE 7 ERRORSOFCALCULATEDDEATHTIMEINCASESOFAFEVERATDEATH Example of a naked body of 70 kg body wt. in still air of 15’C. Measured rectal 40.2 OC Stated S7PC temperature OC at death at death Death time Calculated Error IM rm lIr) 37.1 4.8 0.8 -4 34 7.8 5.4 - 2.4 28 14.4 12.2 - 2.2 Special problems Besides the questions referred to evaluating the mean ambient tempera- ture and the corrective factor of any case there are some further problems. High ambient temperatures. As discussed in connection with the constant A in lower and higher ambient temperatures we have only a little of our own data of a body cooling in ambient temperatures above 23OC. So, Eqn. 5 and the corresponding nomogram (Fig. 101 is mainly based on the data from De Saram in 1955. Therefore experience in casework has yet to come. Fever at death. In our cooling experiments reported above we have had some (hospital) cases with fever at death. So, the errors due to a fever are included in the given permissible variations of 95%. The error due to a fever is greatest for the first postmortem hours and decreases later on. Because of the higher gradient between the rectal and the ambient temperature the drop of the rectal temperature is firstly steeper in comparison with the stated value of 37OC at death (Table 71. As long as the measured rectal tem- perature is 37.2OC or above, the decedent is ‘still alive’ according to the for- mula’s 37.2OC. When the rectal temperature becomes 37.1°C the real possibility of an error due to a fever is given. In the example in Table 7 the death time is 0.8 h in a case of 37.2OC at death. In a case with a real starting point of 40.2OC the death time would be 4.8 h and in using the nomogram with the stated starting point of 37.2OC an error of - 4 h would result. This is the maximum error in this case. But note: this error is recognized by rigor mortis, livores and the reduced mechanical and electrical excitability after a real time since death of approx. 5 h. Later on, when the rectal temperature decreases more and more, the error due to a fever diminishes to a level of approx. 2.5- 2 h (Table 71, which is within the given permissible variation of 95%. Artificial changes of the cooling conditions. If the changes of the cooling conditions are being supposed but really unknown in extent and direction the method must not be used (Table 61. If the changes are known they can often be taken into account without loss of reliability and without a significant reduction in accuracy. The one common situation is a change of the cooling conditions by the investigators before the temperature measurements can be made. Mostly, both the kind of change of the cooling conditions, and it’s time can be given. Example: a thick bedspread was taken off the body 1 h before the temperature measurement. Nevertheless, you are going to use the corrective factor of approx. 1.8 (Table 31 for calculating the death time. Though the drop of the rectal temperature starts to become steeper during the 1 h after the bedspread was taken off the body, the resulting error will be rather negligible because it is only additive (compare Fig. 5; 26-28 h post mortem). Certainly, if such a significant change of the cooling conditions has lasted some or even several hours this procedure is no longer possible. Often, the ambient temperature is changed by the operations of the inves- tigators such as opening windows and doors or using special lamps which generate great heat. Thus the measurement of the ambient temperature is misleading. Therefore we require the crime police to measure the ambient temperature at the beginning of their investigations, so that the evaluation of the mean ambient temperature is facilitated. It is strongly recommended not to use the method after the removal of the body to the mortuary if there are only reported information about the place where the body was found. On the other hand there are no arguments against the measurement of the rectal temperature and the investigations of the other methods (see part II of this paper) after the removal of the body into the mortuary providing the forensic investigator has inspected before the scene of crime in the above manner and the period of the transportation has not taken too much time. Reliability and accuracy The nomogram method has been applied to casework since 1978, first in Berlin at the Institute of Forensic Medicine under Professor Otto Prokop and, subsequently, in more and more European Institutes. In our own exten- sive experience of casework there is good reliability of the estimation of the time since death within the given permissible variation of 95% without any exception. Indeed, the real limits of the error seem to be smaller. In our opinion, the first essential to support this statement is that we keep strictly to the requirements for a careful analysis of the situation at the scene of crime firstly concerning the reasoned decision as to whether the method can be used or not. The same applies to the points of contact if the method can be used. Hitherto, there is no clear report of the errors in applying the Nomogram Method in casework. Such a report is in preparation. Some Comments on other Temperature Methods In our scientific investigation to obtain a reasoned temperature method suitable for casework we have examined other methods described in our  233 experimental material. The following comments are the results of this exami- nation described in more detailed elsewhere [S]. The rules of thumb In a comparison to the accuracy of calculated death times by using the rule ‘l°C fall in temperature per hour plus 3 h’ and by using the Nomogram Method on 53 naked bodies in still air as well as on 26 bodies under very dif- ferent cooling conditions, a clear advantage of the Nomogram Method resulted (Table 2 and 4);. In fact the Nomogram Method is as simple to use as the rule of the thumb. Certainly, in average cases (related to ambient temperature and body build and concomitant circumstances) the rule of the thumb provides good results. In some cases non-average points of contact compensate each other also accidentely giving good results. Nevertheless, in remaining cases there are big errors of the death time. These errors increase much more steeply with progress of cooling in comparison to the Nomogram Method (Table 2 and 41. The diversification of the rules of the thumb corresponding to different classes of the ambient temperature is, certainly, an improvement, but, nevertheless insufficient, because the other main influencing factors of body cooling are being unaffected. The d$‘ferential equation of an infinite circular cylinder This sophisticated model is valuable for theoretical aspects but, in our opinion, unsuitable for casework because it requires the concrete values of numerous constants [2,25,26] which are really unknown in individual cases. The percentage method This method has only one disadvantage but an important one: the post- mortem temperature plateau is omitted [8,10]. Nevertheless, the percentage idea was an advance embraced by the Nomogram Method (‘Standardized Temperature’). Methods with multiple temperature measurements These methods have one common aim: getting a measurement of the indi- vidual slope of the temperature drop of any case instead of its evaluating indirectly from the size factor [3--51 or the body weight with corrective fac- tors for concomitant circumstances (Nomogram Method). The methods of De Saram , Fiddes and Patten , Marshall [3- 51 and more recently Green and Wright [28,29] are based on the principle of measurement of the individ- ual slope by measuring the temperature at least twice. The most sophisti- cated method of this type is the method published by Green and Wright in 1985. Without any question: it would be an ultimate success after that of Marshall and Hoare in 1962 are being able to estimate the postmortem inter- val ‘from body temperature only’ without ‘a certain degree of approximation and perhaps the use of standard values and tables’ [28,29]. Therefore, we examined these methods, especially that of Green and Wright, on our all 224 experimental material as well as on the problematic part of our casework. In summarizing, we got worse results in comparison with the Nomogram Method. Beside good results we got a few results with very big errors unreliable because these few cases are not recognizable on the temperature measurements. As we see it, there are two main reasons for this. (11 There is only a small decrease in the rectal temperature in an interval of 1 h, especially in cases of obesity, thick clothing or high ambient tempera- ture: So, even a small mismeasurement of either one or both rectal tempera- tures in the order of O.lOC may lead to a relative great error of the resulting rate. In computing the time of death this small error of the rate is multiplied and may provide a big error in the calculated death time. In contrast, a small mismeasurement of the rectal temperature will provide only an additional error of the calculated death time in the Nomogram Method. For reducing this source of error Marshall recommended taking the second measurement 3 or 4 h apart as in [15,27]. To avoid any inaccuracy of the rate by small mismeasurements Green and Wright used recently a 11-fold measurement of the rectal temperatures each at an interval of 6 min over a period of 1 h for computing a regression line. (21 The actual measured rate of the rectal temperature decrease is only valid for the cooling conditions during the period of temperature measure- ment. When the cooling conditions - including the ambient temperature - have been changed before, even shortly before, the measurement of the rate is different from before. Nevertheless, it is used multiplicatively for the whole period between time of death and time of investigation. There is no way to take even well-recognized changes of the cooling conditions - includ- ing the ambient temperature - into account. The cooling conditions actually change. The question is, whether we can recognize and reconstruct it (more or less approximately1 or not. If not, there is not any suitable method. If it is, the method used should be open to take into account the changes, even approximately (compare the recommended strategy of the Nomogram Method, Fig. 131.So, the main advantage of the enlightened method of Green and Wright - measuring instead of evaluating the individual facts - is reduced by the impossibility of taking even known changes of the cooling conditions into account. We are continuing a more differentiated examination of this method. Brain temperature The postmortem temperature distribution inside the body can be described as inhomogenous. There is a temperature gradient mainly along the radius. Consequently, there is also a pronounced ‘Location Factor’ of the temperature inside the body. The length of the radius of any part of the body and the radial position of the temperature probe are mainly responsible for the actual temperature at a defined death time. The most important conclusion of that is to standardize the location of the temperature measure- ment. Inside the trunk the deep rectal temperature seems to be a sufficient  235 and useful standardization. Another useful location is apparently the centre of the head. The less the radius the steeper the temperature decrease. This is the main reason for a more exact estimation of the time since death certainly in a shorter period after death (approximately the first 10 h). Con- tinuing the investigation of Refs. 30- 33 we reported our encouraging results also about a combined brain-rectal temperature method which gave permissible variation of 95% of f 1.5 h up to 7 h post mortem, respectively, and f 2.5 h up to 11 h post mortem. References 1 Griiber, Erk and GriguII, W&meiibertrogung, Springer, Berlin, GGttingen, Heidelberg, 1967. 2 If. SeBier. Determination of the time of death by extrapolation of the temperature decrease curve. Acta Med Sot, ll(1968) 279-302. 3 T.K. Marshah and F.E. Hoare, Estimating the time of death. The rectal cooling after death and its mathematical expression. J. Forensic Sk, 7 (1962) 56-81. 4 TX. Marshall, The use of the cooling formula in the study of post mortem body cooling. J. Forensic Sk, 7 (1962) 189- 210. 5 T.K. Marshall, The use of body temperature in estimating the time of death. J. Forensic Sci, 7 (1962) 211-221. 6 H.A. Shapiro, The post-mortem temperature plateau. J. Forensic Med, 12 (1965) 137- 141. 7 A. Joseph and E. Schickele, A general method for assessing factors controlling postmortem cooling. J. Forensic Sk, 16 (1970) 364-391. 8 C. Hen/Ige, B. Madea and H. Joachim. Methoden zur Bestimmung der Todeszeit an der Leiche, Schmidt-RiimhiId-Verlag, Liibeck. 1988. 9 F. Lundquist, PhysicaI and chemical methods for the estimation of the time of death. Acta Med Leg. Sot., 9 (1956) N. spec.. 205-213. 10 C. Hen&e, Precision of estimating the time of death by mathematical expression of rectal body cooling (German, summ Engl). 2. Rechtsmed, 83 (1979) 49-67. 11 A. Brown and T.K. Marshall. Body temperature as a means of estimating the time of death. Forensic Sci, 4 (1974) 125- 133. 12 C. Henage, Die Pr&ision von Todeszeitschiitzungen durch die mathematische Beschreibung der rektalen Leichenabkiihiing. Krim. Forensische Wk., 36 (1979) 65-83. 13 E. Stipanits and C. Henage, Prbisionsvergleich von Todeszeitrtickrechnungen ohne und mit Beriicksichtigung von Einfluafaktoren (German, summ Engl). Beitr. GerichtL Med. XL111 (1985) 323 -329. 14 G. Almeida, Zur Frage der Todeszeitbestimmung aus der Abkiihlung von Leichen. Med Diss. Mfinchen, (1973). 15 G.S.W. De Saram, G. Webster and N. Kathirgamatamby, Post-mortem temperature and the time of death. J. Grim. Law. Criminal, 46 (1955) 562-577. 16 B. Mueller, Das Verhalten der Mastdarmtemperatur der Leiche unter verschiedenen iius- seren Bedingungen. Dtsch. 2. Ges. GetichtL Med. 29 (1938) 158- 162. 17 C. Henl]ge, Estimation of death-time by computing the rectal body cooling under various cooling conditions. (German, summ Engl). 2. Rechtsmed, 87 (1981) 147- 178. 18 C. Hen/3ge and B. Brinkamnn, Todeszeitbestimmung aus der Rektaltemperatur. Arch. Kri- minol, 174 (1984) 96- 112. 19 C. Henoge, B. Brinkmann and K. Piischel, Determination of time of death by measuring the rectal temperature in corpses suspended in water. (German, summ Engl). Z. Rechtsmed, 92 (1984) 256-276. 20 C. Hen/3ge, Temperatur-Todeszeit-Nomogramm fiir Bezugsstandardbedingungen der Lei- chenlagerung. Krim. Forensische Wiss., 46 (1982) 109- 115. 21 C. Heq3ge and B. Madea. Death-tune estimation from body temperature at a scene of crime (with practical demonstration). 11th Meeting of LA.F.S Vancouver, B.C. Canada, 1937. 22 C. Hen&e and B. Madea, Beading off the time of death on a Nomogram at a scene of crime. Digest Intern Meeting P.A.A.F.S. and Police Medical O#icers, Wichita, Kansas, U.S.A., 1937. 23 C. Hen/3ge, S. Hahn and B. Madea. Praktische Erfahrungen mit einem Abklilungsdummy. (German, summ Engl). Be&. GerichtL Med. XLIV (1933) 123-123. 24 C. Hex@ge, B. Madea. U. Schaar and C. Pitsken, Die Abkfihlung eines Dummy unter ver- schiedenen Bedfngungen im Vergleich sur Leichenabkfihlung. (German, summ Engl). Beitr. GevicRtL Med. XLV (1937) 14S- 149. 26 K. Hiraiwa, Y. Ohno, F. Kuroda. I.M. Sebstan and S. Oshida, Estimation of postmortem intervai from rectal temperature by use of computer. 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