Following the acquisition of MR data, the time course of the metabolite concentrations has to be described by mathematical functions (Figure 14.6, step 1).

Figure 14.5 (a, b): Calibration curves for two different metabolites together with a comparison of calculated and true times of death. The experimental data are fitted with functions that are as simple as possible. The fitting procedure also gives error ranges of the calibration curve (upper and lower curve): (a) shows the decay of N-acetyl-aspartate (NAA) and N-acetyl-aspartylglutamate (NAAG) due to auto-lytic degradation; (b) demonstrates the increase of butyrate, most likely due to bacterial metabolism. The scattering of the data is surprisingly small (Scheurer et al., 2003). (c) Comparison of predicted times versus true times. In the sheep model, this comparison proves the feasibility of PMI estimations up to 250 hours postmortem. Reproduced with permission from Scheurer et al. (2005)

Figure 14.5 (a, b): Calibration curves for two different metabolites together with a comparison of calculated and true times of death. The experimental data are fitted with functions that are as simple as possible. The fitting procedure also gives error ranges of the calibration curve (upper and lower curve): (a) shows the decay of N-acetyl-aspartate (NAA) and N-acetyl-aspartylglutamate (NAAG) due to auto-lytic degradation; (b) demonstrates the increase of butyrate, most likely due to bacterial metabolism. The scattering of the data is surprisingly small (Scheurer et al., 2003). (c) Comparison of predicted times versus true times. In the sheep model, this comparison proves the feasibility of PMI estimations up to 250 hours postmortem. Reproduced with permission from Scheurer et al. (2005)

Figure 14.6 Schematic representation of the mathematical calculation of the predicted PMI. The time course of the experimental data points is described by a mathematical function (solid line, step 1). In addition, this fitting procedure of the scattered experimental points leads to error ranges (broken lines). Subsequently, a measured concentration of a metabolite (black arrows, step 2) is projected on the calibration curve, resulting in a predicted PMI. The error range for the PMI is obtained as indicated by the grey arrows (step 3)

Figure 14.6 Schematic representation of the mathematical calculation of the predicted PMI. The time course of the experimental data points is described by a mathematical function (solid line, step 1). In addition, this fitting procedure of the scattered experimental points leads to error ranges (broken lines). Subsequently, a measured concentration of a metabolite (black arrows, step 2) is projected on the calibration curve, resulting in a predicted PMI. The error range for the PMI is obtained as indicated by the grey arrows (step 3)

Since the exact biochemical mechanisms are not yet known, it is reasonable to chose functions with the smallest number of parameters that still lead to an appropriate description of the time course (Scheurer et al., 2005). Two examples of the concentration changes over time with applied model functions and cor responding confidence intervals are shown in Figures 14.5a and 14.5b. The concentration of NAA+NAAG is described by a decreasing exponential function - it may serve as an indicator for the period below 70 h. Butyrate starts to increase at about 50 h postmortem and reveals an unequivocal function up to 400 h that is parameterized by a quadratic function.

As soon as such a calibration curve is established, a measured metabolite concentration (Figure 14.6, step 2) corresponds to a specific point in time when the metabolite is expected to have this concentration. Figures 14.5a and 14.5b illustrate that a description of the experimental data by mathematical functions allows a definition of error ranges. These error ranges can now be used to estimate the error of the resulting PMI, as shown in the third step of Figure 14.6. It is obvious that equivocal, scattered or flat parts of the time course cannot be used as a calibration curve. Therefore, from the 30 visible metabolites, just about 10 are fitted by mathematical functions and 5 of them are used for further analysis (Scheurer et al., 2005).

Since experimental data from different metabolites will not predict exactly the same PMI, it is necessary to combine the predictions obtained from different metabolite curves by a robust procedure. In addition, and in order to restrict the fit to meaningful (i.e. unequivocal) parts of the measured time course, limits for concentrations and times are applied - full details about this procedure can be found in Scheurer et al. (2005) but to summarize: final estimations for the PMI are calculated on the basis of PMIs from the different metabolites, weighted by their accuracy as determined by Figure 14.6 (step 3).

Figure 14.5c compares, for every measurement time, predictions combined from five metabolites (acetate, alanine, trimethylamine, butyrate and propion-ate) weighted according to their variances with true PMIs (regression analysis below 250 h: y = 0.898x + 6.5). The correlation coefficients of the predicted time versus true PMI are r = 0.93 for the whole time period (0-300 h) and r = 0.97 for the time period below 250 h. Predicted times combined from these five metabolites correlate very well with true times postmortem up to 250 h. In contrast, PMIs of >250 h are systematically underestimated in this model system. It is surprising that this result is almost independent for various combinations of metabolites (r = 0.87-0.97, mean 0.92), showing that the influence of the choice of metabolites is almost negligible. Obviously, a larger number of metabolites leads to smaller variances, however the robustness of the method is convincing. Eventually, a combination of acetate, alanine, butyrate, trimethyl-amine and propionate is used for evaluation of the experimental data (Scheurer et al., 2005).

In order to test the applicability of the sheep model to human bodies, four selected human cases from the Institute of Forensic Medicine were examined

(Ith et al., 2002; Scheurer et al., 2005). The human cases were selected in order to match the ambient conditions of the animal model, i.e. were found in closed areas and the skull and brain were not injured. The forensic PMI was estimated by traditional forensic methods, i.e. by evaluating livor and rigor mortis, putrefaction signs and criminological information. After arriving at the Institute of Forensic Medicine the bodies were stored at 4°C for 20-70 h before being examined by MRS. To make human data comparable to the sheep model, storage times in the cold have been subtracted from the total forensic PMI based on the experience that bacterial decomposition is massively reduced at low temperatures. The MR data acquisition was done the same way as for the sheep heads.

Figure 14.7 shows good qualitative agreement between the sheep model and human cases. The same metabolites occur at comparable points in time, in particular metabolites that are not found in vivo can be found postmortem (Ith et al., 2001) in sheep as well as in human spectra. This is not self-evident since the bacterial colonization in an animal body could be different from humans. This qualitative agreement leads to the conclusion that the sheep model can be used to construct calibration curves, which then could be used for estimating PMIs in humans.

The four substances trimethylamine, propionate, butyrate and isobutyrate are generally not observed in healthy human brain tissue, however they are known as products of microbial activity. In addition, trimethylamine is almost exclusively found in bacterial metabolism (Brand and Galask, 1986). Succinate, another substance specifically seen in brain abscesses (Kim et al., 1997; Sabatier et al., 1999), could also be measured in sheep and human brain postmortem.

When calibration curves from sheep data are used to estimate PMIs in the four human cases (Figure 14.8), the estimated PMI can be compared with 'true' PMIs that have been mainly determined from criminal evidence. The comparison shows an acceptable agreement (Scheurer et al., 2005), however the large error bars of forensic PMIs demonstrate that the determination of PMIs in forensic medicine is often very imprecise, covering time spans of several days or even weeks. This is an inherent problem and illustrates that a real 'gold standard' for validation of the MRS data is largely missing. It takes a prohibitively long time to wait for a large number of the rare cases where a human body is found after a long time, while it is still possible to restrict the time of death to a reasonable period. It will be necessary to collect these rare cases in order to validate the time curves established in the sheep model, however it is completely unrealistic to define the calibration curves directly in humans.

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