Temperature Based Death Time Estimation Research Articles

Quality measures for fully automatic CT histogram-based fat estimation on a corpse sample

In a previous article a new algorithm for fully automatic ‘CT histogram based Fat Estimation and quasi-Segmentation’ (CFES) was validated on synthetic data, on a special CT phantom, and tested on one corpse. Usage of said data in FE-modelling for temperature-based death time estimation is the investigation’s number one long-term goal. The article presents CFES’s results on a human corpse sample of size R = 32, evaluating three different performance measures: the τ-value, measuring the ability to differentiate fat from muscle, the anatomical fat-muscle misclassification rate D, and the weighted distance S between the empirical and the theoretical grey-scale value histogram. CFES-performance on the sample was: D = 3.6% for weight exponent α = 1, slightly higher for α ≥ 2 and much higher for α ≤ 0. Investigating τ, S and D on the sample revealed some unexpected results: While large values of τ imply small D-values, rising S implies falling D and there is a positive linear relationship between τ and S. The latter two findings seem to be counter-intuitive. Our Monte Carlo analysis detected a general umbrella type relation between τ and S, which seems to stem from a pivotal problem in fitting Normal mixture distributions.

Prism (II): 127 cooling dummy experiments

The Prism method for temperature based time since death estimation has been demonstrated as a proof of principle in 2021. Now it was validated experimentally. 10 cooling dummies (physical weights from 5.9 kg to 26.9 kg) were fabricated and fitted with temperature probes. A total of 127 dummy cooling experiments were conducted (total cooling time 2082 h, average cooling time 24.6 h) for both regular and elevated starting temperatures, covering ambient temperatures between − 14.0 °C and + 24.0 °C and for different cooling conditions. Cooling data was recorded, then cropped, smoothed, fed into the Prism workflow, and analyzed using dedicated scripts written in the Python programming language. Calculations did not take any additional information into account. No correction factors were needed. General Prism cooling weight curves were confirmed (false ambient temperature and elevated rectal temperature at the time of death). Sub-zero ambient temperature generated unexpectedly large cooling weights. Time since death estimation errors were − 0.29 h ± 5.24 h (whole course of cooling, all experiments) and were typically smaller in earlier stages of cooling. Prism performed relatively well, where conventional temperature based death time estimation struggles. In the future it may potentially be adapted to known conditions. Our results indicate that Prism’s cooling weight might serve as a highly individual, case-based data-driven umbrella parameter, replacing (subjectively) estimated parameters.

Prism – A novel approach to dead body cooling and its parameters

In temperature based death time estimation, the mathematical description by Marshall and Hoare is combined with the parameters defined and additional correction factors introduced by Henssge in the Nomogram method (summarized as MHH). Parameters and correction factors however leave room for subjectivity and disagreement. Elevation of rectal temperature at the time of death has been acknowledged as problematic for death time estimation in several studies, but has neither been solved nor systematically integrated into death time estimation methodology. Ambient temperature, when non-constant and/or unknown, may introduce additional errors. Further problems may arise if the fundamental relationship between torso dimensions and total body weight is not comparable to Henssge’s dummy cooling model. In this study we present a novel methodological approach to temperature based death time estimation, in which relevant parameters for calculations may be evaluated, corrected and generated using brute-force calculations. Consistency of death time over the course of cooling is used as brute-force target. The calculations produce momentary cooling weights, which are graphed over time. Cooling weight graphs can be analyzed to draw conclusions related to different parameters. The method was used on artificial ideal cooling data which was generated according to MHH for known parameters. Correctness of assumed parameters was confirmed by a linear horizontal path of the cooling weight graph. However, controlled false value input resulted in characteristic graph variations. Elevated rectal temperature at the time of death was detectable from the curve shape until hours after cooling below regular temperature at death. False high and false low ambient temperature produced positive and negative curve slopes. Overall, the method acts much like a prism which breaks up light into its elemental colors. It holds potential for application both in scientific settings and practical case work.

Temperature-based death time estimation in near equilibrium: Asymptotic confidence interval estimation

Temperature based death time estimation (TDE) is severely limited in situations where body core temperature has almost decreased to ambient temperature. The TDE method of Marshall/Hoare and Henßge (MHH) defines a lower bound TK for body core temperature below which the time p.m. should be stated to be >10h only.A recent study (Potente et al., 2017 [10]) established a new method, called variance-bias-tradeoff (VBT) complementing MHH in constructing a right-side-half-infinite 97.5%-confidence interval for such ‘near equilibrium’-situations. It seemingly proved the validity for all body core temperatures T<TK.The present study investigates VBT further and discovers that VBT-applicability has an upper limit in time since death. We show how to compute this upper limit explicitly in forensic casework and explain by the frequentist confidence interval probability interpretation why the former study (Potente et al., 2017 [10]) missed this upper limit.

Minimum time since death when the body has either reached or closely approximated equilibrium with ambient temperature

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.

Influence of hypo- and hyperthermia on death time estimation - A simulation study.

Numerous physiological and pathological mechanisms can cause elevated or lowered body core temperatures. Deviations from the physiological level of about 37°C can influence temperature based death time estimations. However, it has not been investigated by means of thermodynamics, to which extent hypo- and hyperthermia bias death time estimates. Using numerical simulation, the present study investigates the errors inherent in temperature based death time estimation in case of elevated or lowered body core temperatures before death. The most considerable errors with regard to the normothermic model occur in the first few hours post-mortem. With decreasing body core temperature and increasing post-mortem time the error diminishes and stagnates at a nearly constant level.

Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis.

Temperature-based death time estimation is based either on simple phenomenological models of corpse cooling or on detailed physical heat transfer models. The latter are much more complex but allow a higher accuracy of death time estimation, as in principle, all relevant cooling mechanisms can be taken into account.Here, a complete workflow for finite element-based cooling simulation is presented. The following steps are demonstrated on a CT phantom: Computer tomography (CT) scan Segmentation of the CT images for thermodynamically relevant features of individual geometries and compilation in a geometric computer-aided design (CAD) model Conversion of the segmentation result into a finite element (FE) simulation model Computation of the model cooling curve(MOD) Calculation of the cooling time(CTE) For the first time in FE-based cooling time estimation, the steps from the CT image over segmentation to FE model generation are performed semi-automatically. The cooling time calculation results are compared to cooling measurements performed on the phantoms under controlled conditions. In this context, the method is validated using a CT phantom. Some of the phantoms' thermodynamic material parameters had to be determined via independent experiments.Moreover, the impact of geometry and material parameter uncertainties on the estimated cooling time is investigated by a sensitivity analysis.

Calibration and parameter variation using a finite element model for death time estimation: The influence of the substrate.

The most established method for temperature based death time estimation is based on an empirical double exponential model. New physically based approaches using numerical simulation techniques are subject of current research. A major advantage of such models is the possibility to incorporate non-standard boundary conditions. The aim of this study was to investigate the influence of the substrate on the cooling rate of a body in the early postmortem phase. A finite element model was used for parameter variation in terms of different substrate materials. Simulation results showed a considerable influence of substrate material on the postmortem cooling rate of a body. From a thermodynamical point of view, comparability between measurements on a steel trolley and real cooling scenarios with common substrates like normal floors, asphalt or soil remains questionable. It could be shown that not only the type of substrate but also its composition can have a considerable influence on the postmortem body cooling rate.

Do multiple temperature measurements improve temperature-based death time estimation? The information degradation inequality.

The accuracy of the input parameter values limits the accuracy of the output values in forensic temperature-based death time estimation (TDE) like in many scientific methods. A standard strategy to overcome this problem is to perform multiple measurements of the input parameter values, but such approaches are subject to noise accumulation and stochastic dependencies. A quantitative mathematical analysis of advantages as well as disadvantages of multiple measurements approaches (MMAs) was performed. The results are A general stochastic model of MMA. The information degradation inequality quantifying gains and losses of MMAs. Example calculations of the information degradation inequality for the following two MMAs relevant to TDE: o Multiple successive rectal temperature measurements o Multiple synchronous body layer temperature measurements Neither multiple successive rectal temperature measurements nor multiple synchronous body layer temperature measurements seem to significantly improve death time estimation. MMAs are superior to the single measurement approach only in the very early body cooling phase.

Rectal temperature-based death time estimation in infants.

In determining the time of death in infants based on rectal temperature, the same methods used in adults are generally used. However, whether the methods for adults are suitable for infants is unclear. In this study, we examined the following 3 methods in 20 infant death cases: computer simulation of rectal temperature based on the infinite cylinder model (Ohno's method), computer-based double exponential approximation based on Marshall and Hoare's double exponential model with Henssge's parameter determination (Henssge's method), and computer-based collinear approximation based on extrapolation of the rectal temperature curve (collinear approximation). The interval between the last time the infant was seen alive and the time that he/she was found dead was defined as the death time interval and compared with the estimated time of death. In Ohno's method, 7 cases were within the death time interval, and the average deviation in the other 12 cases was approximately 80 min. The results of both Henssge's method and collinear approximation were apparently inferior to the results of Ohno's method. The corrective factor was set within the range of 0.7-1.3 in Henssge's method, and a modified program was newly developed to make it possible to change the corrective factors. Modification A, in which the upper limit of the corrective factor range was set as the maximum value in each body weight, produced the best results: 8 cases were within the death time interval, and the average deviation in the other 12 cases was approximately 80min. There was a possibility that the influence of thermal isolation on the actual infants was stronger than that previously shown by Henssge. We conclude that Ohno's method and Modification A are useful for death time estimation in infants. However, it is important to accept the estimated time of death with certain latitude considering other circumstances.

Confidence intervals in temperature-based death time determination.

Marshall and Hoare's double exponential model with Henßge's parameters is a well known method for temperature based death time estimation. The authors give 95%-confidence intervals for their method. Since body cooling is a complex thermodynamical process, one has to take into account a potential bias of the estimator. This quantity measures the systematic error of the estimators underlying model. For confidence interval radius calculation a bias of 0 is presupposed, therefore the actual probability of the true death time value to lie in the 95%-confidence interval can be much lower than 95% in case of nonvanishing bias. As in case of nonstandard conditions the confidence intervals have a probability of containing the true death time value which even in case of small corrective factor errors of Δ = ± 0.1 can be substantially smaller than the 95% claimed, the paper presents a formula for confidence intervals which keep a 95% probability in case of error Δc ⩽ ± 0.1.

Conditional probability distribution (CPD) method in temperature based death time estimation: Error propagation analysis

Bayesian estimation applied to temperature based death time estimation was recently introduced as conditional probability distribution or CPD-method by Biermann and Potente. The CPD-method is useful, if there is external information that sets the boundaries of the true death time interval (victim last seen alive and found dead). CPD allows computation of probabilities for small time intervals of interest (e.g. no-alibi intervals of suspects) within the large true death time interval. In the light of the importance of the CPD for conviction or acquittal of suspects the present study identifies a potential error source. Deviations in death time estimates will cause errors in the CPD-computed probabilities. We derive formulae to quantify the CPD error as a function of input error. Moreover we observed the paradox, that in cases, in which the small no-alibi time interval is located at the boundary of the true death time interval, adjacent to the erroneous death time estimate, CPD-computed probabilities for that small no-alibi interval will increase with increasing input deviation, else the CPD-computed probabilities will decrease. We therefore advise not to use CPD if there is an indication of an error or a contra-empirical deviation in the death time estimates, that is especially, if the death time estimates fall out of the true death time interval, even if the 95%-confidence intervals of the estimate still overlap the true death time interval.

Body mass and corrective factor: impact on temperature-based death time estimation

Model-based methods play an important role in temperature-based death time determination. The most prominent method uses Marshall and Hoare's double exponential model with Henssge's parameter determination. The formulae contain body mass as the only non-temperature parameter. Henssge's method is well established since it can be adapted to non-standard cooling situations varying the parameter body mass by multiplying it with the corrective factor. The present study investigates the influence of measurement errors of body mass m as well as of variations of the corrective factor c on the error of the Marshall and Hoare-Henssge death time estimator t (D). A formula for the relative error of t (D) as a function of the relative error of m is derived. Simple approximations of order 1 and 0 nevertheless yield acceptable results validated by Monte Carlo simulations. They also provide the rule of thumb according to which the quotient of the standard deviations D(t (D)) of the estimated death time and D(m) of the body mass is equal to the quotient of the estimated death time t (D) and the body mass m (D(t (D))/D(m) ≈ t (D)/m). Additionally, formulae and their approximations are derived to quantify the influence of Henssge's body mass corrective factor c on death time estimation. In a range of body masses between 50 and 150kg, the relative variation of the body mass corrective factor is approximately equal to the relative variation of the death time (Δt (D) = (t (D)/c)Δc). This formula is applied and compared to computations and to experimental cooling data with good results.

Concerning the paper by Mall et al., entitled ‘Temperature-based death time estimation with only partially environment conditions’ (Int J Legal Med (2005) 119:185–194)

Concerning the paper by Mall et al., entitled ‘Temperature-based death time estimation with only partially environment conditions’ (Int J Legal Med (2005) 119:185–194)

Temperature-based death time estimation with only partially known environmental conditions.

The temperature-oriented death time determination is based on mathematical model curves of postmortem rectal cooling. All mathematical models require knowledge of the environmental conditions. In medico-legal practice homicide is sometimes not immediately suspected at the death scene but afterwards during external examination of the body. The environmental temperature at the death scene remains unknown or can only be roughly reconstructed. In such cases the question arises whether it is possible to estimate the time since death from rectal temperature data alone recorded over a longer time span. The present study theoretically deduces formulae which are independent of the initial and environmental temperatures and thus proves that the information needed for death time estimation is contained in the rectal temperature data. Since the environmental temperature at the death scene may differ from that during the temperature recording, an additional factor has to be used. This is that the body core is thermally well isolated from the environment and that the rectal temperature decrease after a sudden change of environmental temperature will continue for some time at a rate similar to that before the sudden change. The present study further provides a curve-fitting procedure for such scenarios. The procedure was tested in rectal cooling data of from 35 corpses using the most commonly applied model of Henssge. In all cases the time of death was exactly known. After admission to the medico-legal institute the bodies were kept at a constant environmental temperature for 12-36 h and the rectal temperatures were recorded continuously. The curve-fitting procedure led to valid estimates of the time since death in all experiments despite the unknown environmental conditions before admission to the institute. The estimation bias was investigated statistically. The 95% confidence intervals amounted to +/-4 h, which seems reasonable compared to the 95% confidence intervals of the Henssge model with known environmental temperature. The presented method may be of use for determining the time since death even in cases in which the environmental temperature and rectal temperature at the death scene have unintentionally not been recorded.

Commentary

In temperature based death time estimation, the mathematical description by Marshall and Hoare is combined with the parameters defined and additional correction factors introduced by Henssge in the Nomogram method (summarized as MHH). Parameters and correction factors however leave room for subjectivity and disagreement. Elevation of rectal temperature at the time of death has been acknowledged as problematic for death time estimation in several studies, but has neither been solved nor systematically integrated into death time estimation methodology. Ambient temperature, when non-constant and/or unknown, may introduce additional errors. Further problems may arise if the fundamental relationship between torso dimensions and total body weight is not comparable to Henssge’s dummy cooling model. In this study we present a novel methodological approach to temperature based death time estimation, in which relevant parameters for calculations may be evaluated, corrected and generated using brute-force calculations. Consistency of death time over the course of cooling is used as brute-force target. The calculations produce momentary cooling weights, which are graphed over time. Cooling weight graphs can be analyzed to draw conclusions related to different parameters. The method was used on artificial ideal cooling data which was generated according to MHH for known parameters. Correctness of assumed parameters was confirmed by a linear horizontal path of the cooling weight graph. However, controlled false value input resulted in characteristic graph variations. Elevated rectal temperature at the time of death was detectable from the curve shape until hours after cooling below regular temperature at death. False high and false low ambient temperature produced positive and negative curve slopes. Overall, the method acts much like a prism which breaks up light into its elemental colors. It holds potential for application both in scientific settings and practical case work.