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Minimum time since death when the body has either reached or closely approximated equilibrium with ambient temperature
Forensic Science International 281 (2017) 63–66
Contents lists available at ScienceDirect
Forensic Science International journal homepage: www.elsevier.com/locate/forsciint
Original Research Paper
Minimum time since death when the body has either reached or closely approximated equilibrium with ambient temperature S. Potentea,b,* , M. Kettnerb,**, M.A. Verhoffb , T. Ishikawaa a b
Department of Legal Medicine, Osaka City University, Medical School, Asahimachi 1-4-3, Abenoku, Osaka 545-8585, Japan Department of Legal Medicine, Goethe-University Frankfurt, Medical School, Kennedyallee 104, 60596 Frankfurt am Main, Germany
A R T I C L E I N F O
Article history: Received 31 May 2017 Received in revised form 5 September 2017 Accepted 12 September 2017 Available online 28 October 2017 Keywords: Death time Nomogram Time since death Equilibrium
A B S T R A C T
In temperature based death time estimation the construction of a death time interval using the conventional Nomogram method (NM) is not permissible for bodies in which rectal temperature (Tr) has reached or closely approximated equilibrium with ambient temperature (Ta). We provide a logic approach to compute a minimum time since death with high probability. We also provide a simple graphical solution to be used at the crime scene for preliminary estimation. Special attention is advised in regards to cases with Ta > 23 C as well as borderline cases. Proof by induction, application to test cases and one example of use are presented. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The Gold standard for the estimation of death time in the early postmortem period is the Nomogram method (NM) [1–3]. The NM is based on the mathematical description of body cooling developed by Marshall and Hoare [4–8] which utilizes ambient temperature (Ta), rectal temperature (Tr) and body weight (BW) [9]. Corrective factors (CF) are applied to BW [10] to calculate the virtual body weight (vBW), when conditions differ from standard cooling conditions, namely the uncovered, naked body in supine position on a thermally indifferent surface without air flow, solar irradiation or dampness. CF may in turn be adjusted for BW [11,12]. The NM provides a death time interval of 2 SD (95.45%) width in the form of a Gaussian distribution, which may be altered for certain ranges of cooling (see below) and Ta and for non standard cooling conditions (CF 6¼ 1.0). Resulting death time intervals may be further limited due to findings in the so-called compound method [2] or due to non-medical limitations [13,14], taking confidence interval limits into account. The originally published confidence intervals [15,16] have been subject of debate recently [17–20]. The formula is modified for Ta > 23 C to account for limitations in the underlying dataset by de Saram [21,22] by adjusting factor A (1.11 instead of 1.25) and the degree of cooling to which the NM is applicable (critical Q, see below).
In the NM, the degree of cooling is defined by the standardized temperature Q, which assumes values between 1.0/100% (no cooling) and 0.0/0% (equilibrium with Ta). The relationship between Tr, Ta and Q is simple and for every two given factors the third may be derived: Q¼
ðT r T a Þ ð37:2 T a Þ
ð1Þ
For progressed cooling with Q < 0.2 for Ta < 23 C and Q < 0.5 (Qc) for Ta > 23 C, the NM must not be used. We will call this “critical Q” (Qc). The original NM provides the smallest possible 95.45% (2 SD) death time interval, centered symmetrically around the expected value in the form of a Gaussian distribution. The interval width for Ta < 23 C depends both on Q and CF (=1.0 or 6¼1.0). For Ta < 23 C it is constant. The expected value is determined by a combination of Q and vBW. Given the known distribution, it is possible to state probabilities for other chosen intervals. When the original death time interval (‘from time X to Y’) of 95.45% probability is opened on one side (‘before time Y’ or ‘after time Y’), this time frame's probability amounts to 97.725%. The proposed method utilizes this by calculating a hypothetical borderline scenario followed by the construction of a minimum time frame of death. 2. Method 2.1. Logic proof
* Principal corresponding author. ** Corresponding author. E-mail addresses: [email protected] (S. Potente), [email protected] (M. Kettner). http://dx.doi.org/10.1016/j.forsciint.2017.09.012 0379-0738/© 2017 Elsevier B.V. All rights reserved.
We will prove by induction that for any advanced cooling case with Q < Qc (0.2 for Ta < 23 C, 0.5 for Ta > 23 C) and with known
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S. Potente et al. / Forensic Science International 281 (2017) 63–66
vBW, the minimum time since death, with a probability of >97.725%, equals the expected value (m) minus 2 standard deviations (SD, s ), as calculated according to NM for the respective critical rectal temperature Tc. For Tr > Ta, Tr is reduced over time (cooling) until it reaches equilibrium with Ta, according to the second law of thermodynamics. According to Eq. (1), this cooling towards equilibrium results in diminishing Q which is calculated using the fixed “starting” Tr at death, Ta and Tr. Therefore, for any valid Ta, the “critical rectal temperature” Tc can be calculated, for which Q is exactly critical (0.2 for Ta < 23 C, 0.5 for Ta > 23 C). For any case with Q Qc, the death time interval equals m 2s (normal distribution). Normal distribution allows for the calculation of probability for various ranges, such as 1, 2 or 3 s . The time frame from 1 to [m 2s ] holds 97.725%, since the probability for 1 to [m + 2s ] is added to the initial [m 2s ] interval. According to Eq. (1), the reduction of Tr in the process of cooling results in a reduction of Q. Lower Q, according to the NM formula, results in lower m, which, according to normal distribution results in a shift in probability towards “the past”. Therefore, given Ta, vBW and assuming one point in time before temperature measurement, for lower Tr there is a higher probability of death having occurred before that point in time than compared with higher Tr. Consequently, with Tr and Q diminishing over time (cooling), Tc (calculated for Qc) represents the utmost usable Tr. For Tr = Tc, the minimum death time frame (holding 97.725%) is (1 to [m 2s ]) with values calculated for Q and vBW according to NM. Hence for Q < Qc and therefore Tr < Tc, the minimum death time frame of 1 to [m 2s ] holds more than 97.725%. Should elevated Tr at death be known or suspected, it can be accounted for by adjusting the value for Tr at death (37.2 C) in the calculation of Q and Tc. The provided graphical solution (see below) however, must not be used to establish low Q for these cases, since it implicitly assumes 37.2 C as Tr at death!
utilizing 0.2 for Qc: T c ¼ ð0:2 ð37:2 19:9ÞÞ þ 19:9 23:4
ð4Þ
For Tc = 23.4 C, Ta = 19.9 C and vBW = 94.7 kg the auxiliary death time interval is then computed as: 39:9 h ð7:0 h; due to low Q and use of CFÞ or 32:9 to 46:9 h prior to measurement: Statement: With a probability of 97.725% the daughter died before the 30th 1.00 pm (at least 32.9 h prior to measurement). Therefore she was already dead with a high probability when the roommate returned from work, but failed to check on her health. 2.3. Graphical solution Since Ta and Tr enter the NM equation in the form of Q only, it follows, that once Q is established as or set to Qc, the actual minimum time since death is dependent on vBW only. In a simple chart (see Fig. 1) the two computational steps are combined: First, Ta and Tr are entered on their respective scales and each pair connected. When the intersection of the two lines falls into the grey area, one may utilize the NM as usual (Q > Qc). If said intersection falls below the line marked as Tc, then Q < Qc is established. Both 23 C as threshold value for Ta and an important transitional range of Ta/Tr values are flagged for special attention (see “discussion” for details). In the next step, the minimum time since death (in hours prior to measurement or in rough half-day steps) for the vBW may be read from the graph on the lower right. The range of vBW was chosen to accommodate even extreme BW/CF combinations. Three lines are provided: the uppermost line represents cooling in “standard conditions” for Ta < 23 C (CF = 1.0) already including 4.5 h deviation. The next line below represents Ta < 23 C with non-standard conditions (CF 6¼1.0) including 7.0 h. The lowest line represents Ta > 23 C including 2.8 h, where CF does not have
2.2. Calculation In cases of known Ta, with Q < Qc, we first calculate Tc by assuming Qc as 0.2 for Ta < 23 C or 0.5 for Ta > 23 C: Qc ¼
Tc Ta 37:2 T a
ð2Þ
and solve for Tc: T c ¼ Q c ð37:2 T a Þ þ T a
ð3Þ
Then, for Tc, Ta, vBW and time of measurement we construct an auxiliary death time interval. Using only the upper margin (minimum hours since measurement) we then state that death occurred these X or more hours prior to measurement (“earlier than X”), with 97.725% probability. Case example: A woman phoned her daughter's roommate at work (morning of 30th), asking him to check on her daughter since she could not be reached. After finishing work, he returned to the apartment at 3.30 pm but did not check on the daughter. Instead, he went out with a friend, returned to the apartment and went to bed, again without checking. Only the next day, on the 31st around 4 pm did he finally check and found her dead. The mother accused the roommate of failure to render assistance and claimed her daughter might have been saved, if he had checked on her when he returned from work. With the 31st 9.45 pm for time of measurement, Tr = 20.2 C, Ta = 19.9 C, Q = 0.017 and (virtual) BW = 94.7 kg (1.1 * 87 kg) the critical rectal temperature Tc is calculated according to Eq. (3),
Fig. 1. Chart for minimum time since death estimation, completed for example case (arrows): Filling in Ta and Tr on respective scales and combining the entries, Q is established as below Qc. Then the virtual body weight (body weight multiplied with correction factor) is entered (roughly 95 kg in example case) and the minimum time since death read for the lower curve (non standard conditions, for CF = 1.1 in the example case). In a typical scene scenario, after identification as “below critical temperature” and a rough assessment of a preliminary virtual body weight on the scene, a quick assessment in the order of “roughly 1.5 days minimum” may be performed alternatively.
S. Potente et al. / Forensic Science International 281 (2017) 63–66
to be accounted for. See “discussion” for notes on use and interpretation. Charts for metric (kg, C) and imperial (lbs, F) measurements, including means of documentation and manuals for completion, are included in the electronic supplementary materials. 3. Results In addition to the above proof by induction the method was tested on 12 cases (see Fig. 2). For three logger cases (top three cases) the times of death were known and fell into the respected estimated minimum time frames when calculated for the first logged Tr value below Tc. 9 autopsy cases with cooling on the scene below 0.2 for Q were subjected to the method. All cases produced results, however the informative value varied. For cases 11.540 (example case) and 11.195 a specific date of interest could be established as chronologically after the minimum death time. In 11.195 the deceased failed to attend a family gathering and was later found dead, raising the question of possible rescue. With the family meeting (and notice of his apparent absence) after the minimum time since death, this was not the case. In case 11.413 an elderly lady was ‘house sitting” for a family on vacation when she fell down the stairs and died. She had been contacted daily by phone on an agreed time but one day could not be reached. This did not prompt an immediate reaction from the caller. The old lady was found dead many hours later. Even though a minimum time frame was established, the chronological proximity to the failed response could not be clarified. The rapid onset of injuries however and their severity make survivability unlikely. In case 12.849, loud noises and music from an apartment late at night led neighbors to call for the police. Upon arrival however, silence had set in and no further action was taken. The tenant, a professional DJ, was later found dead with haemorrhages on the
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head and fists, with the apartment in disarray, doors and plates smashed, raising suspicion of a crime. Autopsy and toxicology revealed a combination of amphetamine intoxication and asthma attack as cause of death. It was concluded that amphetamines had led to the person “raving” violently in the apartment, smashing objects with his fists and banging his head against walls and furniture after which he collapsed and the music finished independently before the police arrived. Even though a minimum time frame was established, the question of whether he was still alive when the police arrived for the first time, could not be answered. In case 11.716 witnesses could only roughly remember having seen the deceased alive “one or two days before he was found”. As additional information, the minimum time since death was estimated as 46 hours. 4. Discussion As a direct logic derivative of the NM, the method incorporates the same possible errors. Determination of Ta for longer time periods is generally problematic but even more so for high ambient temperatures, where day–night fluctuations must often be accounted for. Distinct, stepwise ranges of Ta and Q are particularly problematic when shifting from lower to higher Ta as may be exemplified for a borderline case with Ta of “roughly” 23 C: Tc for Ta of 23 C (with Qc = 0.2) is 25.84 C, while for Ta of 23.1 C (with Qc = 0.5) it is 30.15 C. Therefore, for more than 4 C of rectal cooling, conventional NM calculation would have been possible assuming an only slightly lower Ta. Also, Q is below Qc between 23.1 and 25.84 C Tr for both example Ta-values, but the resulting minimum times since death may differ to the magnitude of days for either 23 C or 23.1 C, depending on vBW and as reflected in the lines for high and low Ta in the chart. The problematic general ranges for Ta and Tr were highlighted in the chart to indicate the need for extra caution. For borderline Ta in
Fig. 2. Overview of test cases. Black dot on white circle: known time of death. “L” – last sign of life. Grey dot on black circle: date of interest. Minimum time since death presented as bars, relative to time of measurement on the left margin. A combined alignment chart for vBW and minimum time since death in hours is depicted at the bottom.
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close proximity to 23 C, we advise to assume two Ta scenarios, below and above 23.0 C, and properly report the procedure. However, we do not generally advise against the use of the method in Ta > 23 C. There may well be scenarios with minimum death time in question, where Ta may be assumed as both high and stable for a longer period of time, such as death in temperature controlled environments. Overall, the method may assist with a wide range of scenarios for which conventional temperature based methods do not provide solutions. It may provide some baseline information at the scene both for general casework and homicide investigations. Further value depends on the preconditions of the case at hand, namely the amount and quality of available information. As one extreme, a minimum time frame may exculpate an accused person. In cases of missing and later found dead persons it may assist in the evaluation of response time and search efforts, as sometimes questioned by the family. In other cases, relatives themselves may blame themselves for apparently reacting “too late” and they may find comfort in the results of the estimation. The probability of >97.725% for the estimated time frame cannot be further quantified. The method is applied quickly and easily on scene using the provided chart. A more detailed and precise written statement can be given later, including more precise calculation as well as a time line, overview of statements, findings and such. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. forsciint.2017.09.012. References [1] C. Henssge, Death time estimation in case work. I. The rectal temperature time of death nomogram, Forensic Sci. Int. 38 (3–4) (1988) 209–236. http://www. ncbi.nlm.nih.gov/pubmed/3192144. [2] C. Henssge, L. Althaus, J. Bolt, A. Freislederer, H.T. Haffner, C.A. Henssge, B. Hoppe, V. Schneider, Experiences with a compound method for estimating the time since death. I. Rectal temperature Nomogram for time since death, Int. J. Legal Med. 113 (6) (2000) 303–319. https://www.ncbi.nlm.nih.gov/pubmed/ 11100425. [3] B. Madea, Methods for determining time of death, Forensic Sci. Med. Pathol. 12 (4) (2016) 451–485, doi:http://dx.doi.org/10.1007/s12024-016-9776-y. [4] T.K. Marshall, F.E. Hoare, Estimating the time of death. The rectal cooling after death and its mathematical expression, J. Forensic Sci. 7 (1) (1962) 56–81. [5] T.K. Marshall, Temperature methods of estimating the time of death, Med. Sci. Law 5 (4) (1965) 224–232. http://www.ncbi.nlm.nih.gov/pubmed/5849645.
[7] T.K. Marshall, F.E. Hoare, Estimating the time of death: the use of the cooling formula in the study of post-mortem body cooling, J. Forensic Sci. 7 (1962) 189–210. [8] T.K. Marshall, The use of body temperature in estimating the time of death and its limitations, Med. Sci. Law 9 (3) (1969) 178–182, doi:http://dx.doi.org/ 10.1177/002580246900900304. http://msl.sagepub.com/content/9/3/178. short. [9] T. Riepert, G. Lasczkowski, J. Becker, R. Urban, [Extremely varied rectal temperatures in 10 fatalities after a house fire-a contribution to the significance of body weight in cadaver cooling], Arch. Kriminol. 191 (3–4) (1993) 107–113. http://www.ncbi.nlm.nih.gov/pubmed/8390233. [10] M. Hubig, H. Muggenthaler, I. Sinicina, G. Mall, Body mass and corrective factor: impact on temperature-based death time estimation, Int. J. Legal Med. 125 (3) (2011) 437–444, doi:http://dx.doi.org/10.1007/s00414-011-0551-z. [11] C. Henssge, Rectal temperature time of death nomogram: dependence of corrective factors on the body weight under stronger thermic insulation conditions, Forensic Sci. Int. 54 (1) (1992) 51–66. http://www.ncbi.nlm.nih. gov/pubmed/1618454. [12] B. Madea (Ed.), Estimation of the Time Since Death, 3rd ed., CRC Press, 2015. http://amazon.com/o/ASIN/1444181769. [13] F.M. Biermann, S. Potente, The deployment of conditional probability distributions for death time estimation, Forensic Sci. Int. 210 (1-3) (2011) 82–86, doi:http://dx.doi.org/10.1016/j.forsciint.2011.02.007. [14] M. Hubig, H. Muggenthaler, G. Mall, Conditional probability distribution (CPD) method in temperature based death time estimation: error propagation analysis, Forensic Sci. Int. 238 (2014) 53–58, doi:http://dx.doi.org/10.1016/j. forsciint.2014.02.016. [15] C. Henßge, Die präzision von todeszeitschätzungen durch die mathematische beschreibung der rektalen leichenabkühlung, Z. Rechtsmed. 83 (1) (1979) 49– 67, doi:http://dx.doi.org/10.1007/BF00201311. [16] A. Albrecht, I. Gerling, C. Henßge, M. Hochmeister, M. Kleiber, B. Madea, M. Oehmichen, S. Pollak, K. Püschel, D. Seifert, K. Teige, Zur anwendung des Rektaltemperatur-Todeszeit-Nomogramms am leichenfundort, Z. Rechtsmed. (103) (1990) 257–278. [17] M. Hubig, H. Muggenthaler, I. Sinicina, G. Mall, Temperature based forensic death time estimation: the standard model in experimental test, Leg. Med. 17 (5) (2015) 381–387, doi:http://dx.doi.org/10.1016/j.legalmed.2015.05.005. [18] M. Hubig, H. Muggenthaler, I. Sinicina, G. Mall, With reference to the letter to the editor by Henssge (Leg Med (Tokyo). 2015 Jul 29. http://dx.doi.org/10.1016/ j.legalmed.2015.05.005): “with reference to the article by Hubig et al.: Temperature based forensic death time estimation: The standard model in experimental test’ (Legal Med 2015 XX)”, Leg. Med. 17 (5) (2015) 304–305, doi: http://dx.doi.org/10.1016/j.legalmed.2015.08.006. [19] C. Henssge, With reference to the paper by Hubig et al. entitled ‘temperature based forensic death time estimation: the standard model in experimental test’ (Legal Med 2015 XX), Leg. Med. (2015), doi:http://dx.doi.org/10.1016/j. legalmed.2015.07.012. [20] M. Hubig, H. Muggenthaler, G. Mall, Confidence intervals in temperaturebased death time determination, Leg. Med. 17 (1) (2015) 48–51, doi:http://dx. doi.org/10.1016/j.legalmed.2014.08.002. [21] G. De Saram, G. Webster, N. Kathirgamatamby, Post-mortem temperature and the time of death, J. Crim. Law Criminol. Police Sci. 46 (1955) 562. http:// scholarlycommons.law.northwestern.edu/cgi/viewcontent.cgi?article=4412&context=jclc. [22] G.S.W. de Saram, G. Webster, N. Kathirgamatamby, Post-mortem temperature and the time of death, J. Crim. Law Criminol. Police Sci. 46 (4) (1955) 562–577, doi:http://dx.doi.org/10.2307/1139735. http://www.jstor.org/stable/1139735.
Contents lists available at ScienceDirect
Forensic Science International journal homepage: www.elsevier.com/locate/forsciint
Original Research Paper
Minimum time since death when the body has either reached or closely approximated equilibrium with ambient temperature S. Potentea,b,* , M. Kettnerb,**, M.A. Verhoffb , T. Ishikawaa a b
Department of Legal Medicine, Osaka City University, Medical School, Asahimachi 1-4-3, Abenoku, Osaka 545-8585, Japan Department of Legal Medicine, Goethe-University Frankfurt, Medical School, Kennedyallee 104, 60596 Frankfurt am Main, Germany
A R T I C L E I N F O
Article history: Received 31 May 2017 Received in revised form 5 September 2017 Accepted 12 September 2017 Available online 28 October 2017 Keywords: Death time Nomogram Time since death Equilibrium
A B S T R A C T
In temperature based death time estimation the construction of a death time interval using the conventional Nomogram method (NM) is not permissible for bodies in which rectal temperature (Tr) has reached or closely approximated equilibrium with ambient temperature (Ta). We provide a logic approach to compute a minimum time since death with high probability. We also provide a simple graphical solution to be used at the crime scene for preliminary estimation. Special attention is advised in regards to cases with Ta > 23 C as well as borderline cases. Proof by induction, application to test cases and one example of use are presented. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The Gold standard for the estimation of death time in the early postmortem period is the Nomogram method (NM) [1–3]. The NM is based on the mathematical description of body cooling developed by Marshall and Hoare [4–8] which utilizes ambient temperature (Ta), rectal temperature (Tr) and body weight (BW) [9]. Corrective factors (CF) are applied to BW [10] to calculate the virtual body weight (vBW), when conditions differ from standard cooling conditions, namely the uncovered, naked body in supine position on a thermally indifferent surface without air flow, solar irradiation or dampness. CF may in turn be adjusted for BW [11,12]. The NM provides a death time interval of 2 SD (95.45%) width in the form of a Gaussian distribution, which may be altered for certain ranges of cooling (see below) and Ta and for non standard cooling conditions (CF 6¼ 1.0). Resulting death time intervals may be further limited due to findings in the so-called compound method [2] or due to non-medical limitations [13,14], taking confidence interval limits into account. The originally published confidence intervals [15,16] have been subject of debate recently [17–20]. The formula is modified for Ta > 23 C to account for limitations in the underlying dataset by de Saram [21,22] by adjusting factor A (1.11 instead of 1.25) and the degree of cooling to which the NM is applicable (critical Q, see below).
In the NM, the degree of cooling is defined by the standardized temperature Q, which assumes values between 1.0/100% (no cooling) and 0.0/0% (equilibrium with Ta). The relationship between Tr, Ta and Q is simple and for every two given factors the third may be derived: Q¼
ðT r T a Þ ð37:2 T a Þ
ð1Þ
For progressed cooling with Q < 0.2 for Ta < 23 C and Q < 0.5 (Qc) for Ta > 23 C, the NM must not be used. We will call this “critical Q” (Qc). The original NM provides the smallest possible 95.45% (2 SD) death time interval, centered symmetrically around the expected value in the form of a Gaussian distribution. The interval width for Ta < 23 C depends both on Q and CF (=1.0 or 6¼1.0). For Ta < 23 C it is constant. The expected value is determined by a combination of Q and vBW. Given the known distribution, it is possible to state probabilities for other chosen intervals. When the original death time interval (‘from time X to Y’) of 95.45% probability is opened on one side (‘before time Y’ or ‘after time Y’), this time frame's probability amounts to 97.725%. The proposed method utilizes this by calculating a hypothetical borderline scenario followed by the construction of a minimum time frame of death. 2. Method 2.1. Logic proof
* Principal corresponding author. ** Corresponding author. E-mail addresses: [email protected] (S. Potente), [email protected] (M. Kettner). http://dx.doi.org/10.1016/j.forsciint.2017.09.012 0379-0738/© 2017 Elsevier B.V. All rights reserved.
We will prove by induction that for any advanced cooling case with Q < Qc (0.2 for Ta < 23 C, 0.5 for Ta > 23 C) and with known
64
S. Potente et al. / Forensic Science International 281 (2017) 63–66
vBW, the minimum time since death, with a probability of >97.725%, equals the expected value (m) minus 2 standard deviations (SD, s ), as calculated according to NM for the respective critical rectal temperature Tc. For Tr > Ta, Tr is reduced over time (cooling) until it reaches equilibrium with Ta, according to the second law of thermodynamics. According to Eq. (1), this cooling towards equilibrium results in diminishing Q which is calculated using the fixed “starting” Tr at death, Ta and Tr. Therefore, for any valid Ta, the “critical rectal temperature” Tc can be calculated, for which Q is exactly critical (0.2 for Ta < 23 C, 0.5 for Ta > 23 C). For any case with Q Qc, the death time interval equals m 2s (normal distribution). Normal distribution allows for the calculation of probability for various ranges, such as 1, 2 or 3 s . The time frame from 1 to [m 2s ] holds 97.725%, since the probability for 1 to [m + 2s ] is added to the initial [m 2s ] interval. According to Eq. (1), the reduction of Tr in the process of cooling results in a reduction of Q. Lower Q, according to the NM formula, results in lower m, which, according to normal distribution results in a shift in probability towards “the past”. Therefore, given Ta, vBW and assuming one point in time before temperature measurement, for lower Tr there is a higher probability of death having occurred before that point in time than compared with higher Tr. Consequently, with Tr and Q diminishing over time (cooling), Tc (calculated for Qc) represents the utmost usable Tr. For Tr = Tc, the minimum death time frame (holding 97.725%) is (1 to [m 2s ]) with values calculated for Q and vBW according to NM. Hence for Q < Qc and therefore Tr < Tc, the minimum death time frame of 1 to [m 2s ] holds more than 97.725%. Should elevated Tr at death be known or suspected, it can be accounted for by adjusting the value for Tr at death (37.2 C) in the calculation of Q and Tc. The provided graphical solution (see below) however, must not be used to establish low Q for these cases, since it implicitly assumes 37.2 C as Tr at death!
utilizing 0.2 for Qc: T c ¼ ð0:2 ð37:2 19:9ÞÞ þ 19:9 23:4
ð4Þ
For Tc = 23.4 C, Ta = 19.9 C and vBW = 94.7 kg the auxiliary death time interval is then computed as: 39:9 h ð7:0 h; due to low Q and use of CFÞ or 32:9 to 46:9 h prior to measurement: Statement: With a probability of 97.725% the daughter died before the 30th 1.00 pm (at least 32.9 h prior to measurement). Therefore she was already dead with a high probability when the roommate returned from work, but failed to check on her health. 2.3. Graphical solution Since Ta and Tr enter the NM equation in the form of Q only, it follows, that once Q is established as or set to Qc, the actual minimum time since death is dependent on vBW only. In a simple chart (see Fig. 1) the two computational steps are combined: First, Ta and Tr are entered on their respective scales and each pair connected. When the intersection of the two lines falls into the grey area, one may utilize the NM as usual (Q > Qc). If said intersection falls below the line marked as Tc, then Q < Qc is established. Both 23 C as threshold value for Ta and an important transitional range of Ta/Tr values are flagged for special attention (see “discussion” for details). In the next step, the minimum time since death (in hours prior to measurement or in rough half-day steps) for the vBW may be read from the graph on the lower right. The range of vBW was chosen to accommodate even extreme BW/CF combinations. Three lines are provided: the uppermost line represents cooling in “standard conditions” for Ta < 23 C (CF = 1.0) already including 4.5 h deviation. The next line below represents Ta < 23 C with non-standard conditions (CF 6¼1.0) including 7.0 h. The lowest line represents Ta > 23 C including 2.8 h, where CF does not have
2.2. Calculation In cases of known Ta, with Q < Qc, we first calculate Tc by assuming Qc as 0.2 for Ta < 23 C or 0.5 for Ta > 23 C: Qc ¼
Tc Ta 37:2 T a
ð2Þ
and solve for Tc: T c ¼ Q c ð37:2 T a Þ þ T a
ð3Þ
Then, for Tc, Ta, vBW and time of measurement we construct an auxiliary death time interval. Using only the upper margin (minimum hours since measurement) we then state that death occurred these X or more hours prior to measurement (“earlier than X”), with 97.725% probability. Case example: A woman phoned her daughter's roommate at work (morning of 30th), asking him to check on her daughter since she could not be reached. After finishing work, he returned to the apartment at 3.30 pm but did not check on the daughter. Instead, he went out with a friend, returned to the apartment and went to bed, again without checking. Only the next day, on the 31st around 4 pm did he finally check and found her dead. The mother accused the roommate of failure to render assistance and claimed her daughter might have been saved, if he had checked on her when he returned from work. With the 31st 9.45 pm for time of measurement, Tr = 20.2 C, Ta = 19.9 C, Q = 0.017 and (virtual) BW = 94.7 kg (1.1 * 87 kg) the critical rectal temperature Tc is calculated according to Eq. (3),
Fig. 1. Chart for minimum time since death estimation, completed for example case (arrows): Filling in Ta and Tr on respective scales and combining the entries, Q is established as below Qc. Then the virtual body weight (body weight multiplied with correction factor) is entered (roughly 95 kg in example case) and the minimum time since death read for the lower curve (non standard conditions, for CF = 1.1 in the example case). In a typical scene scenario, after identification as “below critical temperature” and a rough assessment of a preliminary virtual body weight on the scene, a quick assessment in the order of “roughly 1.5 days minimum” may be performed alternatively.
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to be accounted for. See “discussion” for notes on use and interpretation. Charts for metric (kg, C) and imperial (lbs, F) measurements, including means of documentation and manuals for completion, are included in the electronic supplementary materials. 3. Results In addition to the above proof by induction the method was tested on 12 cases (see Fig. 2). For three logger cases (top three cases) the times of death were known and fell into the respected estimated minimum time frames when calculated for the first logged Tr value below Tc. 9 autopsy cases with cooling on the scene below 0.2 for Q were subjected to the method. All cases produced results, however the informative value varied. For cases 11.540 (example case) and 11.195 a specific date of interest could be established as chronologically after the minimum death time. In 11.195 the deceased failed to attend a family gathering and was later found dead, raising the question of possible rescue. With the family meeting (and notice of his apparent absence) after the minimum time since death, this was not the case. In case 11.413 an elderly lady was ‘house sitting” for a family on vacation when she fell down the stairs and died. She had been contacted daily by phone on an agreed time but one day could not be reached. This did not prompt an immediate reaction from the caller. The old lady was found dead many hours later. Even though a minimum time frame was established, the chronological proximity to the failed response could not be clarified. The rapid onset of injuries however and their severity make survivability unlikely. In case 12.849, loud noises and music from an apartment late at night led neighbors to call for the police. Upon arrival however, silence had set in and no further action was taken. The tenant, a professional DJ, was later found dead with haemorrhages on the
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head and fists, with the apartment in disarray, doors and plates smashed, raising suspicion of a crime. Autopsy and toxicology revealed a combination of amphetamine intoxication and asthma attack as cause of death. It was concluded that amphetamines had led to the person “raving” violently in the apartment, smashing objects with his fists and banging his head against walls and furniture after which he collapsed and the music finished independently before the police arrived. Even though a minimum time frame was established, the question of whether he was still alive when the police arrived for the first time, could not be answered. In case 11.716 witnesses could only roughly remember having seen the deceased alive “one or two days before he was found”. As additional information, the minimum time since death was estimated as 46 hours. 4. Discussion As a direct logic derivative of the NM, the method incorporates the same possible errors. Determination of Ta for longer time periods is generally problematic but even more so for high ambient temperatures, where day–night fluctuations must often be accounted for. Distinct, stepwise ranges of Ta and Q are particularly problematic when shifting from lower to higher Ta as may be exemplified for a borderline case with Ta of “roughly” 23 C: Tc for Ta of 23 C (with Qc = 0.2) is 25.84 C, while for Ta of 23.1 C (with Qc = 0.5) it is 30.15 C. Therefore, for more than 4 C of rectal cooling, conventional NM calculation would have been possible assuming an only slightly lower Ta. Also, Q is below Qc between 23.1 and 25.84 C Tr for both example Ta-values, but the resulting minimum times since death may differ to the magnitude of days for either 23 C or 23.1 C, depending on vBW and as reflected in the lines for high and low Ta in the chart. The problematic general ranges for Ta and Tr were highlighted in the chart to indicate the need for extra caution. For borderline Ta in
Fig. 2. Overview of test cases. Black dot on white circle: known time of death. “L” – last sign of life. Grey dot on black circle: date of interest. Minimum time since death presented as bars, relative to time of measurement on the left margin. A combined alignment chart for vBW and minimum time since death in hours is depicted at the bottom.
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close proximity to 23 C, we advise to assume two Ta scenarios, below and above 23.0 C, and properly report the procedure. However, we do not generally advise against the use of the method in Ta > 23 C. There may well be scenarios with minimum death time in question, where Ta may be assumed as both high and stable for a longer period of time, such as death in temperature controlled environments. Overall, the method may assist with a wide range of scenarios for which conventional temperature based methods do not provide solutions. It may provide some baseline information at the scene both for general casework and homicide investigations. Further value depends on the preconditions of the case at hand, namely the amount and quality of available information. As one extreme, a minimum time frame may exculpate an accused person. In cases of missing and later found dead persons it may assist in the evaluation of response time and search efforts, as sometimes questioned by the family. In other cases, relatives themselves may blame themselves for apparently reacting “too late” and they may find comfort in the results of the estimation. The probability of >97.725% for the estimated time frame cannot be further quantified. The method is applied quickly and easily on scene using the provided chart. A more detailed and precise written statement can be given later, including more precise calculation as well as a time line, overview of statements, findings and such. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. forsciint.2017.09.012. References [1] C. Henssge, Death time estimation in case work. I. The rectal temperature time of death nomogram, Forensic Sci. Int. 38 (3–4) (1988) 209–236. http://www. ncbi.nlm.nih.gov/pubmed/3192144. [2] C. Henssge, L. Althaus, J. Bolt, A. Freislederer, H.T. Haffner, C.A. Henssge, B. Hoppe, V. Schneider, Experiences with a compound method for estimating the time since death. I. Rectal temperature Nomogram for time since death, Int. J. Legal Med. 113 (6) (2000) 303–319. https://www.ncbi.nlm.nih.gov/pubmed/ 11100425. [3] B. Madea, Methods for determining time of death, Forensic Sci. Med. Pathol. 12 (4) (2016) 451–485, doi:http://dx.doi.org/10.1007/s12024-016-9776-y. [4] T.K. Marshall, F.E. Hoare, Estimating the time of death. The rectal cooling after death and its mathematical expression, J. Forensic Sci. 7 (1) (1962) 56–81. [5] T.K. Marshall, Temperature methods of estimating the time of death, Med. Sci. Law 5 (4) (1965) 224–232. http://www.ncbi.nlm.nih.gov/pubmed/5849645.
[7] T.K. Marshall, F.E. Hoare, Estimating the time of death: the use of the cooling formula in the study of post-mortem body cooling, J. Forensic Sci. 7 (1962) 189–210. [8] T.K. Marshall, The use of body temperature in estimating the time of death and its limitations, Med. Sci. Law 9 (3) (1969) 178–182, doi:http://dx.doi.org/ 10.1177/002580246900900304. http://msl.sagepub.com/content/9/3/178. short. [9] T. Riepert, G. Lasczkowski, J. Becker, R. Urban, [Extremely varied rectal temperatures in 10 fatalities after a house fire-a contribution to the significance of body weight in cadaver cooling], Arch. Kriminol. 191 (3–4) (1993) 107–113. http://www.ncbi.nlm.nih.gov/pubmed/8390233. [10] M. Hubig, H. Muggenthaler, I. Sinicina, G. Mall, Body mass and corrective factor: impact on temperature-based death time estimation, Int. J. Legal Med. 125 (3) (2011) 437–444, doi:http://dx.doi.org/10.1007/s00414-011-0551-z. [11] C. Henssge, Rectal temperature time of death nomogram: dependence of corrective factors on the body weight under stronger thermic insulation conditions, Forensic Sci. Int. 54 (1) (1992) 51–66. http://www.ncbi.nlm.nih. gov/pubmed/1618454. [12] B. Madea (Ed.), Estimation of the Time Since Death, 3rd ed., CRC Press, 2015. http://amazon.com/o/ASIN/1444181769. [13] F.M. Biermann, S. Potente, The deployment of conditional probability distributions for death time estimation, Forensic Sci. Int. 210 (1-3) (2011) 82–86, doi:http://dx.doi.org/10.1016/j.forsciint.2011.02.007. [14] M. Hubig, H. Muggenthaler, G. Mall, Conditional probability distribution (CPD) method in temperature based death time estimation: error propagation analysis, Forensic Sci. Int. 238 (2014) 53–58, doi:http://dx.doi.org/10.1016/j. forsciint.2014.02.016. [15] C. Henßge, Die präzision von todeszeitschätzungen durch die mathematische beschreibung der rektalen leichenabkühlung, Z. Rechtsmed. 83 (1) (1979) 49– 67, doi:http://dx.doi.org/10.1007/BF00201311. [16] A. Albrecht, I. Gerling, C. Henßge, M. Hochmeister, M. Kleiber, B. Madea, M. Oehmichen, S. Pollak, K. Püschel, D. Seifert, K. Teige, Zur anwendung des Rektaltemperatur-Todeszeit-Nomogramms am leichenfundort, Z. Rechtsmed. (103) (1990) 257–278. [17] M. Hubig, H. Muggenthaler, I. Sinicina, G. Mall, Temperature based forensic death time estimation: the standard model in experimental test, Leg. Med. 17 (5) (2015) 381–387, doi:http://dx.doi.org/10.1016/j.legalmed.2015.05.005. [18] M. Hubig, H. Muggenthaler, I. Sinicina, G. Mall, With reference to the letter to the editor by Henssge (Leg Med (Tokyo). 2015 Jul 29. http://dx.doi.org/10.1016/ j.legalmed.2015.05.005): “with reference to the article by Hubig et al.: Temperature based forensic death time estimation: The standard model in experimental test’ (Legal Med 2015 XX)”, Leg. Med. 17 (5) (2015) 304–305, doi: http://dx.doi.org/10.1016/j.legalmed.2015.08.006. [19] C. Henssge, With reference to the paper by Hubig et al. entitled ‘temperature based forensic death time estimation: the standard model in experimental test’ (Legal Med 2015 XX), Leg. Med. (2015), doi:http://dx.doi.org/10.1016/j. legalmed.2015.07.012. [20] M. Hubig, H. Muggenthaler, G. Mall, Confidence intervals in temperaturebased death time determination, Leg. Med. 17 (1) (2015) 48–51, doi:http://dx. doi.org/10.1016/j.legalmed.2014.08.002. [21] G. De Saram, G. Webster, N. Kathirgamatamby, Post-mortem temperature and the time of death, J. Crim. Law Criminol. Police Sci. 46 (1955) 562. http:// scholarlycommons.law.northwestern.edu/cgi/viewcontent.cgi?article=4412&context=jclc. [22] G.S.W. de Saram, G. Webster, N. Kathirgamatamby, Post-mortem temperature and the time of death, J. Crim. Law Criminol. Police Sci. 46 (4) (1955) 562–577, doi:http://dx.doi.org/10.2307/1139735. http://www.jstor.org/stable/1139735.