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Improved estimation of postmortem interval based on differential behaviour of vitreous potassium and hypoxantine in death by hanging
Forensic Science International 125 (2002) 67–74
Improved estimation of postmortem interval based on differential behaviour of vitreous potassium and hypoxantine in death by hanging Jose´ I. Mun˜oz Baru´sa,*, Jose´ M. Sua´rez-Pen˜arandaa, Xose´ L. Oterob, Marı´a S. Rodrı´guez-Calvoa, Eduardo Costasa, Xoa´n Migue´nsa, Luis Concheiroa a
Institute of Legal Medicine, School of Medicine, C/San Francisco s/n, University of Santiago de Compostela, 15782 Galicia, Spain b Department of Statistics and IO, University of Santiago de Compostela, 15782 Galicia, Spain Received 16 April 2001; received in revised form 17 July 2001; accepted 30 October 2001
Abstract Many formulae are available to estimate the relation between the potassium ([Kþ]) and hypoxantine ([Hx]) concentration in the vitreous humour and the postmortem interval (PMI). Typically these have been based on a correlation test and linear regression using the postmortal interval as the independent variable and [Kþ] or [Hx] as the dependent variable in order to estimate the confidence interval. However, a recent study has shown that a more precise measurement of PMI can be obtained if [Kþ] is used as the independent variable. The regression lines obtained from the most recent deceased subjects with forensic relevance received for autopsy in the Institute of Legal Medicine are ½Kþ ¼ 5:589 þ 0:174PMI and ½Hx ¼ 26:459 þ 3:017PMI, by changing the variables, we obtain PMI ¼ 3:967½Kþ 19:186 (R2 ¼ 0:688, P < 0:001) and PMI ¼ 0:172½Hx þ 0:170 (R2 ¼ 0:518, P < 0:001). In this paper we propose the cause of death as an extra factor which modifies the relationship and gives even greater precision in estimating PMI. In cases of death by hanging the results are considerably improved with ½Kþ ¼ 5:224 þ 0:225PMI and ½Hx ¼ 15:161 þ 4:957PMI, respectively, and consequently, PMI ¼ 3:631½Kþ 17:334 (R2 ¼ 0:818, P < 0:001) and PMI ¼ 0:153½Hx 0:368 (R2 ¼ 0:757, P < 0:001): the slope is less and the precision is obviously enhanced. # 2002 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Postmortem interval; Vitreous humour; Potassium concentration; Hanging deaths
1. Introduction The relation between the increase of [Kþ] and [Hx] in the vitreous humour to the postmortem interval (PMI) has been a topic of study for many years. Numerous formulae in the literature correlate this relationship between both [Kþ] and [Hx] to PMI to a linear regression (Table 1) and this may be influenced by differences in statistical approach and techniques, as well as urea and creatinine levels [12,13]. The most precise statistical method to date is that of an inverse prediction by changing the variables [9,14,15]. However, to complement this advance in estimating PMI, we suggest the
* Corresponding author. Fax: þ34-981-5803-36. E-mail address: [email protected] (J.I. Mun˜oz Baru´s).
cause of death as an extra factor that may modify the relationship [16]. The aim of this paper is to investigate the influence of death by hanging on the relationship between both [Kþ] and [Hx] to PMI and to propose new formula based on a revised statistical approach. The influence of urea and creatinine levels is also investigated, and full data from our records is provided to facilitate comparative studies (Table 2).
2. Material and methods We studied 206 samples from 176 of the most recently deceased subjects with forensic relevance (samples from both eyes were taken from 30 corpses) received for autopsy in the Institute of Legal Medicine of the University of
0379-0738/02/$ – see front matter # 2002 Elsevier Science Ireland Ltd. All rights reserved. PII: S 0 3 7 9 - 0 7 3 8 ( 0 1 ) 0 0 6 1 6 - 8
J.I. Mun˜oz Baru´s et al. / Forensic Science International 125 (2002) 67–74
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Table 1 Formulae for determining PMI (h) with [Kþ] (mmol/l) or [Hx] (mmol/l) Equation obtaineda
Reference
Formula proposed
þ
y ¼ [K ] Sturner [1] Adelson et al. [2] Hansson et al. [3] Coe [4] Coe [4] Adjutantis and Coutselinis [5] Stephens and Richards [6] Madea et al. [7] James et al. [8] Mun˜ oz et al. [9] y ¼ [Hx] Rognum et al. [10]
¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼
0.14x þ 5.6 0.17x þ 5.36 0.17x þ 8 0.332x þ 4.99 (x < 6 h) 0.1625x þ 6.19 (x 6 h) 0.55x þ 3.14 0.238x þ 6.342 0.19x þ 5.88 0.23x þ 4.2 0.17x þ 5.60
y y y y
¼ ¼ ¼ ¼
4.2x 5.1x 6.2x 8.8x
1 2 3 4 5 6 7 8 9 10 11 12 13 14b 15 16 17 18b 19 20 21 22 23 24 25 26 27 28
7.6 7.6 7.6 7.6
at at at at
5 8C 10 8C 15 8C 23 8C PMI ¼ 0.31[Hx] þ 0.05 PMI ¼ 0.17[Hx] þ 0.17
Variable x is postmortem (h).
Table 2 Data provided for the study C
þ þ þ þ
PMI ¼ 7.14[Kþ] 39.1 – – – – – – PMI ¼ 5.26[Kþ] 30.9 PMI ¼ 4.32[Kþ] 18.35 PMI ¼ 3.92[Kþ] 19.04
y ¼ 1.29x þ 3.69 y ¼ 3.2x 0.15 y ¼ 3.01x þ 26.45
Madea et al. [11] James et al. [8] Our present data a
y y y y y y y y y y
PMI (h) 1.08 1.5 1.83 1.91 2 2.08 2.16 2.16 2.25 2.33 2.41 2.5 2.5 2.5 2.5 2.5 2.58 2.66 2.66 2.75 2.75 2.83 2.83 2.83 2.91 3 3 3.08
Table 2 (Continued ) C a
PMI (h)
Groupa
[Hx] (mmol/l)
[Kþ] (mmol/l)
A B B A B B B B B B B B B B B B A B B A B B B B B B B A B
– 38.04 37.10 25.36 – 20.97 25.95 43.68 – 47.68 55.14 30.79/– 45.60 42.81 –/42.04 31.67 26.38 32.04 31.65 32.89 – 10.67 13.36 34.39/33.88 22.21 24.25 32.66 46.42 –
5.6 6.5 6.8 5.4 6.2 5.9 5.7 5.7 6.6 5.7 6.2 6.5/6 7.3 6.3 6.8/6.5 6.3 6.1 5.9 5.8 6.1 5.9 5.7 5.9 6/6.1 4.4 5.7 6.6 6.0 6.4
þ
Group
[Hx] (mmol/l)
[K ] (mmol/l)
A A B B B A B B B B B B B B B B B B B A B B B B B B B A
13.52 17.88 18.19 66.11 24.34 16.58 29.73 18.20 – 27.88 26.58 55.40 28.16 –/– 25.38 – 32.87 21.88/– 26.17 22.63 – – 38.38 – 26.02 – 15.52 36.67
5.6 5.8 5.7 8.4 6 6.3 6 5.9 7.3 6.6 6.2 6.2 6.2 5.3/5.3 6 6.4 5.1 6.1/6 5.9 6 5.4 6.1 6.2 5.9 5.8 6.1 5.3 5.7
29 30 31 32 33 34 35 36 37 38 39 40b 41 42 43b 44 45 46 47 48 49 50 51 52b 53 54 55 56 57
3.08 3.25 3.33 3.5 3.5 3.5 3.5 3.63 3.66 3.66 3.66 3.7 3.75 3.83 3.86 3.93 4 4.05 4.08 4.25 4.5 4.5 4.5 4.66 4.75 4.75 4.75 4.98 5
J.I. Mun˜ oz Baru´ s et al. / Forensic Science International 125 (2002) 67–74 Table 2 (Continued )
69
Table 2 (Continued )
C
PMI (h)
Groupa
[Hx] (mmol/l)
[Kþ] (mmol/l)
C
PMI (h)
Groupa
[Hx] (mmol/l)
[Kþ] (mmol/l)
58 59b 60 61 62 63 64 65 66b 67 68 69 70 71 72b 73 74 75 76 77 78 79 80 81 82 83 84 85b 86 87 88 89 90 91 92b 93 94 95 96b 97 98 99 100 101 102 103 104b 105 106 107 108 109b 110 111 112 113 114b
5 5 5.08 5.25 5.25 5.25 5.5 5.66 5.66 5.66 5.75 5.75 5.91 5.91 5.95 6 6 6 6.16 6.25 6.25 6.25 6.33 6.5 6.5 6.5 6.58 6.75 6.75 6.75 7 7 7 7.08 7.33 7.5 7.5 7.5 7.83 8 8.25 8.33 8.5 8.5 8.58 8.75 9 9.08 9.25 9.66 9.91 10.08 10.33 10.9 11.16 11.25 11.41
B B A A A B A A A B B B A B B A B B B A B B B A B B B A B B B B B B B B B B B B B B B B A B B B B B B B B B A B A
28.29 33.59/38.39 51.22 65.27 33.29 53.91 58.57 24.63 44.95/45.63 – – – 67.08 75.73 –/– 55.56 92.18 – 52.53 18.66 44.17 – 43.60 34.27 67.46 – 79.65 72.22/58.83 59.20 71.98 78.59 – – 33.94 47.66/53.69 – – – –/– 53.19 56.06 53.28 – – 70.86 59.82 55.60/63.86 41.22 – – 45.01 75.45/– 64.13 – 81.86 79.74 –/–
6.7 6.5/6.3 7 7.5 6.2 7.2 6.6 5.7 6.7/6.9 6.3 6.4 7.2 6.3 6.5 7/6.8 7.4 8.9 6.4 7 5.7 6.2 6.5 7.2 5.1 6.8 8.2 7.4 7.6/7.5 6.1 7 6.2 6.5 6.9 6 6.8/7 6.9 6.7 6.9 7.6/6.6 7.2 6.8 7.4 7.6 7.3 6.7 6.3 7.5/7.5 6.6 7.6 7.9 6.5 6.7/6.7 7.1 8.1 8 8 7.9/7.8
115b 116 117 118 119 120 121 122 123b 124b 125 126 127 128 129 130 131 132b 133b 134 135b 136 137 138 139 140 141 142b 143b 144b 145 146 147b 148 149 150 151 152 153b 154 155 156 157 158 159b 160 161 162 163 164 165b 166b 167 168 169 170 171
11.5 11.5 11.68 12.25 12.5 12.66 13 13.25 13.25 13.75 14 14 14.45 14.5 14.68 15 15.25 15.33 15.38 15.51 15.83 16 16.16 16.41 16.5 16.66 16.83 16.88 16.91 17 17 17 17.13 17.5 17.58 17.75 17.76 17.86 17.91 18 18 18.69 18.75 19.31 19.41 19.5 19.5 19.61 20 20.25 20.25 20.75 21.58 21.75 22.25 22.25 22.95
A B B B B B B B B B A B B A B B B A A B B A A B B A B B B B B B B B B B B B B A B B B B B B B B B A B B B B B B B
68.31/71.3 – 75.52 64.21 57.48 48.11 – 46.90 –/48.39 85.93/– – 80.59 37.65 – 32.58 – 69.03 87.47/71.59 93.44/– 67.97 58.79/45.83 63.56 103.34 43.8 27.94 127.86 84.16 125.27/83.6 –/– 103.06/88.81 70.50 120.86 88.18/73.65 62.75 83.52 121.27 – 97.70 113.69/100.34 123.28 64.05 110.97 85.99 66.74 –/104.86 73.94 – 77.68 – 92.25 71.69/73.15 65.98/72.61 63.45 69.26 37.72 93.00 99.25
7.1/7 6.8 6.9 7.7 7 6.4 10.2 8 7.3/6.8 9.9/9.2 8.5 7.9 7.6 7.8 6.8 8.5 7.7 9/8.9 8.6/8.5 8.2 8.6/8.6 8.3 9.1 7.3 8.3 10.9 9.7 10.1/10 8/8.5 9.7/8.7 8.2 9.3 8.7/8 8.1 8 10.5 9.9 8.8 8.9/8 10.5 9.5 9.1 8 8.4 9.7/10.3 8.6 9.7 7.8 8 9.4 8.4/8.9 8.2/8 7.9 8 7.6 9.7 9.9
J.I. Mun˜ oz Baru´ s et al. / Forensic Science International 125 (2002) 67–74
70 Table 2 (Continued ) C
PMI (h) b
172 173 174b 175 176 a b
23.5 24 24.25 28 28.91
Groupa B B B B A
[Hx] (mmol/l)
[Kþ] (mmol/l)
73.81/67.82 – 73.21/– 121.07 –
10.8/10.1 10 10/9.4 9 11
Group A: hanging; group B: no hanging. [Kþ] and [Hx] determined in both eyes: left eye/right eye.
Santiago de Compostela (Spain). All cases were indexed with case number, sex, age, medical care, the cause of death, time of death, extraction time and toxicological screening. Samples were obtained by scleral puncture near the outer canthus using a 20 gauge needle and a 10 ml syringe. Suction was applied gradually and slowly to withdraw all extractable vitreous humour according to [11,17]. Samples from corpses whose time of death could not be established to within 15 min were excluded. Non-transparent specimens and those from new-born infants aged <6 months were considered unsatisfactory for analysis [11]. Each sample was centrifuged at 3000 rpm for 10 min [5], and only the supernatant part is was used in order to avoid obstructing the fine tubing used in most current analytical instruments [18]. The time between extraction and analysis was never more than 48 h, during which time samples were kept at 4 8C. Biochemical and toxicological parameters and analytical methods used are given below in Table 3. All results were obtained with a BM/747 (Boehringer Mannheim), except alcohol levels, which were determined with a 5890-series II (Hewlett-Packard) and hypoxanthine with Waters 996 PDA
Table 3 Analytical methods Parameter
Analytical methods
Potassium Urea Creatinine
Indirect potentiometry Kinetic UV assay for urea/urea nitrogen Jaffe´ method taking into consideration the sample blank (twin mode) High performance liquid chromatography Head space gas chromatography
Hypoxanthine Alcohol
and reverse phase column. The PMI in hours was expressed in the decimal system and statistical analysis carried out by applying simple linear regression using SPSS 9.0.1 for WindowsTM.
3. Results A total of 206 samples, from 141 men and 35 women, were used. All data are shown in Table 2. The minimum value of PMI was 1.08 h and the maximum 28.91 h, with an average of 9.6 h and S:D: ¼ 6:6. No significant difference arising from alcohol level was observed (P ¼ 0:711), nor were there significant differences between both eyes or between sex (P ¼ 0:787, 0.466). The linear regression formula we obtained with PMI as the independent variable and [Kþ] or [Hx] as the dependent were: ½Kþ ¼ 5:589 þ 0:174PMI (R2 ¼ 0:688, P < 0:001) and ½Hx ¼ 26:459 þ 3:017PMI (R2 ¼ 0:518, P < 0:001), respectively. All samples were classified into two groups: group A consisted of hanging deaths, while group B consisted of
Table 4 The regression lines and the formulae proposed (P < 0:001)a Groups All cases
Group A (hanging)
N
Regression line þ
Formula proposed þ
R
R2
1 R2
DW
Cook-d
No levels
176 134
[K ] ¼ 5.589 þ 0.174PMI [Hx] ¼ 26.459 þ 3.017PMI
PMI ¼ 3.967[K ] 19.186 PMI ¼ 0.172[Hx] þ 0.170
0.830 0.688 0.312 0.719 0.518 0.482
1.730 1.575
0.098 0.145
Urea 30 mg/dl
131 101
[Kþ] ¼ 5.572 þ 0.174PMI [Hx] ¼ 28.278 þ 2.850PMI
PMI ¼ 4.093[Kþ] 19.967 PMI ¼ 0.175[Hx] þ 0.112
0.843 0.711 0.289 0.707 0.500 0.500
1.659 1.551
0.127 0.173
No levels
35 30
[Kþ] ¼ 5.224 þ 0.225PMI [Hx] ¼ 15.161 þ 4.957PMI
PMI ¼ 3.631[Kþ] 17.344 PMI ¼ 0.153[Hx] 0.368
0.904 0.818 0.182 0.870 0.757 0.243
1.897 1.754
0.376 0.352
Urea 30 mg/dl
25 23
[Kþ] ¼ 5.193 þ 0.219PMI [Hx] ¼ 17.438 þ 4.567PMI
PMI ¼ 3.927[Kþ] 19.115 PMI ¼ 0.167[Hx] 0.910
0.927 0.860 0.140 0.874 0.764 0.236
2.283 1.879
0.335 0.304
141 104
[Kþ] ¼ 5.675 þ 0.162PMI [Hx] ¼ 28.155 þ 2.733PMI
PMI ¼ 4.083[Kþ] 19.885 PMI ¼ 0.178[Hx] þ 0.278
0.814 0.663 0.337 0.697 0.486 0.514
1.760 1.551
0.086 0.141
106 78
[Kþ] ¼ 5.672 þ 0.163PMI [Hx] ¼ 30.123 þ 2.573PMI
PMI ¼ 4.144[Kþ] 20.258 PMI ¼ 0.178[Hx] þ 0.426
0.822 0.676 0.324 0.676 0.457 0.543
1.634 1.583
0.117 0.165
Group B (no hanging) No levels Urea 30 mg/dl
a PMI in hours, [Kþ] in mmol/l and [Hx] in mmol/l; R correlation coefficient; R2 determination coefficient; 1 R2 proportion of the rest variance of the regression; DW Durbin–Watson and Cook-d is the maximum value of the Cook’s distance.
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Table 5 Confidence interval (95%) for different [Kþ] and [Hx]a All cases
Group A (hanging) Urea 30 (mg/dl)
No levels
Group B (no hanging) Urea 30 (mg/dl)
No levels
Urea 30 (mg/dl)
No levels
þ
[K ] (mmol/l) 6 9 12 15
4.615 16.516 28.417 40.317
0.745 0.891 1.980 3.152
4.593 16.874 29.154 41.435
0.863 1.009 2.240 3.570
4.441 15.334 26.227 37.120
1.181 1.399 2.966 4.681
4.446 16.227 28.007 39.788
1.309 1.589 3.326 5.227
4.614 16.865 29.114 41.364
0.892 1.070 2.408 3.842
4.608 17.042 29.475 41.909
1.043 1.207 2.724 4.357
[Hx] (mmol/l) 25 50 75 100 125
4.460 8.750 13.041 17.331 21.621
1.191 0.818 0.968 1.491 2.128
4.499 8.885 13.273 17.660 22.047
1.474 0.985 1.137 1.771 2.551
3.448 7.265 11.082 14.899 18.716
1.389 1.010 1.193 1.771 2.482
3.271 7.452 11.634 15.815 19.997
1.722 1.205 1.399 2.117 3.004
4.722 9.166 13.611 18.056 22.500
1.484 0.999 1.183 1.846 2.651
4.866 9.307 13.748 18.189 22.630
1.848 1.217 1.402 2.205 3.190
a
Results in hours.
non-hanging deaths. There was a significant difference for [Kþ] and [Hx] between the two groups (P ¼ 0:006 and 0.002, respectively). Accordingly, 35 samples (group A) and 141 samples (group B) were analysed for [Kþ] giving R2 ¼ 0:818 and 0.663, respectively (P < 0:001). In order to increase the precision of these results we established critical levels of urea and/or creatinine according to Madea and co-workers [7,13], and by using different values of urea and creatinine we found that best results were obtained by excluding cases with urea <30 mg/dl. The linear regression and the proposed formulae are shown in Table 4. The confidence intervals are given in Table 5.
4. Discussion We observed that in cases of death by hanging the relationship between PMI and [Kþ] or [Hx] is defined by two formulae which differs from that from death by other causes. There is significant difference between both groups (P ¼ 0:006 and 0.002, respectively) and the increase in the steepness of slope means that for each unit of PMI the value of [Kþ] is 72% greater and the value of [Hx] is 55% in cases of death by hanging (group A) than that for other deaths (group B). Also, the increase in the value of R, in group A, corresponds to an improvement of 23% and 55%, respectively, in the precision of PMI (Figs. 1 and 2).
Fig. 1. Regression lines using PMI as independent variable. Line A: deaths by hanging; line B: no hanging deaths. PMI in hours and [Kþ] in mmol/l.
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J.I. Mun˜ oz Baru´ s et al. / Forensic Science International 125 (2002) 67–74
Fig. 2. Regression lines using PMI as independent variable. Line A: deaths by hanging; line B: no hanging deaths. PMI in hours and [Hx] in mmol/l.
This might possibly be due to the rapidity of death which reduces agonal change in the chemistry of the vitreous humour and this, in turn, could also explain the increase in the value of R2 (1 R2 represents the rest variance of the regression, ‘‘not explained’’). The increase in the steepness of slope might be explained by the fact that in case any compression, resulting from the fatal tension of the noose on the neck, will interrupt the jugular system and cause a rapid rise in
venous pressure in the neck [16,19]. This pressure could lead to the congestion of capillaries and hence an increase of vascular leakage from the retinal capillaries and therefore a rise of potassium and hypoxantine into the vitreous humour. In the light of these results, we made an inverse prediction for [Kþ] and [Hx] by changing the variables according to Mun˜ oz et al. [9], and in this way obtained a line that is adjusted to the PMI (Figs. 3 and 4).
Fig. 3. Regression line using [Kþ] as independent variable. Only deaths by hanging are included. PMI in hours and [Kþ] in mmol/l.
J.I. Mun˜ oz Baru´ s et al. / Forensic Science International 125 (2002) 67–74
73
Fig. 4. Regression line using [Hx] as independent variable. Only deaths by hanging are included. PMI in hours and [Hx] in mmol/l.
The magnitude of the difference between both formulae is better understood if we consider two real cases from our data. In a case with known PMI ¼ 18:00 h with ½Kþ ¼ 10:5 mmol/l, the estimated PMI according to the general formula is 22.46 h, but using the formula we propose for cases of death by hanging the calculation is 20.78 h. Similarly, in a known PMI ¼ 11:16 h with ½Kþ ¼ 8 mmol/l, the estimated PMI obtained using the general formula would be 12.55, compared to 11.70 h. Moreover, for all cases a better precision is obtained (R2 ¼ 0:688 raising to 0.818) and a narrower confidence interval (Table 5). In the case with PMI ¼ 18:00 h with ½Hx ¼ 123:28 mmol/l, the estimated PMI obtained using the general formula would be 22.22, compared to 18.493 h; and in the case with PMI ¼ 11:16 with ½Hx ¼ 81:86 was obtained a PMI of 14.24 and 12.15 h, respectively. Moreover, for all cases a better precision is obtained (R2 ¼ 0:518 raising to 0.757). The exclusion of cases with urea <30 mg/dl further improves the precision of the equation. Different tests were made for several values of both metabolites and only the best results are shown (Table 4). Similar limitations were previously considered by others authors [4,7,9,13]. Testing the goodness-of-fit was made by calculating Cook’s distance and using the Durbin–Watson method. The results are included in Table 4, confirming the independence assumption and ruling out the existence of outliers. In conclusion, as a means of achieving greater accuracy in the determination of PMI from vitreous [Kþ] and [Hx], we propose a more precise formula whose specificity and greater precision, combined with the relative ease of ascertaining the cause of death, recommend its use in cases of death by hanging.
Acknowledgements This study was supported by Grants XUGA20807B98 and PGIDT99PXI20808B.
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Improved estimation of postmortem interval based on differential behaviour of vitreous potassium and hypoxantine in death by hanging Jose´ I. Mun˜oz Baru´sa,*, Jose´ M. Sua´rez-Pen˜arandaa, Xose´ L. Oterob, Marı´a S. Rodrı´guez-Calvoa, Eduardo Costasa, Xoa´n Migue´nsa, Luis Concheiroa a
Institute of Legal Medicine, School of Medicine, C/San Francisco s/n, University of Santiago de Compostela, 15782 Galicia, Spain b Department of Statistics and IO, University of Santiago de Compostela, 15782 Galicia, Spain Received 16 April 2001; received in revised form 17 July 2001; accepted 30 October 2001
Abstract Many formulae are available to estimate the relation between the potassium ([Kþ]) and hypoxantine ([Hx]) concentration in the vitreous humour and the postmortem interval (PMI). Typically these have been based on a correlation test and linear regression using the postmortal interval as the independent variable and [Kþ] or [Hx] as the dependent variable in order to estimate the confidence interval. However, a recent study has shown that a more precise measurement of PMI can be obtained if [Kþ] is used as the independent variable. The regression lines obtained from the most recent deceased subjects with forensic relevance received for autopsy in the Institute of Legal Medicine are ½Kþ ¼ 5:589 þ 0:174PMI and ½Hx ¼ 26:459 þ 3:017PMI, by changing the variables, we obtain PMI ¼ 3:967½Kþ 19:186 (R2 ¼ 0:688, P < 0:001) and PMI ¼ 0:172½Hx þ 0:170 (R2 ¼ 0:518, P < 0:001). In this paper we propose the cause of death as an extra factor which modifies the relationship and gives even greater precision in estimating PMI. In cases of death by hanging the results are considerably improved with ½Kþ ¼ 5:224 þ 0:225PMI and ½Hx ¼ 15:161 þ 4:957PMI, respectively, and consequently, PMI ¼ 3:631½Kþ 17:334 (R2 ¼ 0:818, P < 0:001) and PMI ¼ 0:153½Hx 0:368 (R2 ¼ 0:757, P < 0:001): the slope is less and the precision is obviously enhanced. # 2002 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Postmortem interval; Vitreous humour; Potassium concentration; Hanging deaths
1. Introduction The relation between the increase of [Kþ] and [Hx] in the vitreous humour to the postmortem interval (PMI) has been a topic of study for many years. Numerous formulae in the literature correlate this relationship between both [Kþ] and [Hx] to PMI to a linear regression (Table 1) and this may be influenced by differences in statistical approach and techniques, as well as urea and creatinine levels [12,13]. The most precise statistical method to date is that of an inverse prediction by changing the variables [9,14,15]. However, to complement this advance in estimating PMI, we suggest the
* Corresponding author. Fax: þ34-981-5803-36. E-mail address: [email protected] (J.I. Mun˜oz Baru´s).
cause of death as an extra factor that may modify the relationship [16]. The aim of this paper is to investigate the influence of death by hanging on the relationship between both [Kþ] and [Hx] to PMI and to propose new formula based on a revised statistical approach. The influence of urea and creatinine levels is also investigated, and full data from our records is provided to facilitate comparative studies (Table 2).
2. Material and methods We studied 206 samples from 176 of the most recently deceased subjects with forensic relevance (samples from both eyes were taken from 30 corpses) received for autopsy in the Institute of Legal Medicine of the University of
0379-0738/02/$ – see front matter # 2002 Elsevier Science Ireland Ltd. All rights reserved. PII: S 0 3 7 9 - 0 7 3 8 ( 0 1 ) 0 0 6 1 6 - 8
J.I. Mun˜oz Baru´s et al. / Forensic Science International 125 (2002) 67–74
68
Table 1 Formulae for determining PMI (h) with [Kþ] (mmol/l) or [Hx] (mmol/l) Equation obtaineda
Reference
Formula proposed
þ
y ¼ [K ] Sturner [1] Adelson et al. [2] Hansson et al. [3] Coe [4] Coe [4] Adjutantis and Coutselinis [5] Stephens and Richards [6] Madea et al. [7] James et al. [8] Mun˜ oz et al. [9] y ¼ [Hx] Rognum et al. [10]
¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼
0.14x þ 5.6 0.17x þ 5.36 0.17x þ 8 0.332x þ 4.99 (x < 6 h) 0.1625x þ 6.19 (x 6 h) 0.55x þ 3.14 0.238x þ 6.342 0.19x þ 5.88 0.23x þ 4.2 0.17x þ 5.60
y y y y
¼ ¼ ¼ ¼
4.2x 5.1x 6.2x 8.8x
1 2 3 4 5 6 7 8 9 10 11 12 13 14b 15 16 17 18b 19 20 21 22 23 24 25 26 27 28
7.6 7.6 7.6 7.6
at at at at
5 8C 10 8C 15 8C 23 8C PMI ¼ 0.31[Hx] þ 0.05 PMI ¼ 0.17[Hx] þ 0.17
Variable x is postmortem (h).
Table 2 Data provided for the study C
þ þ þ þ
PMI ¼ 7.14[Kþ] 39.1 – – – – – – PMI ¼ 5.26[Kþ] 30.9 PMI ¼ 4.32[Kþ] 18.35 PMI ¼ 3.92[Kþ] 19.04
y ¼ 1.29x þ 3.69 y ¼ 3.2x 0.15 y ¼ 3.01x þ 26.45
Madea et al. [11] James et al. [8] Our present data a
y y y y y y y y y y
PMI (h) 1.08 1.5 1.83 1.91 2 2.08 2.16 2.16 2.25 2.33 2.41 2.5 2.5 2.5 2.5 2.5 2.58 2.66 2.66 2.75 2.75 2.83 2.83 2.83 2.91 3 3 3.08
Table 2 (Continued ) C a
PMI (h)
Groupa
[Hx] (mmol/l)
[Kþ] (mmol/l)
A B B A B B B B B B B B B B B B A B B A B B B B B B B A B
– 38.04 37.10 25.36 – 20.97 25.95 43.68 – 47.68 55.14 30.79/– 45.60 42.81 –/42.04 31.67 26.38 32.04 31.65 32.89 – 10.67 13.36 34.39/33.88 22.21 24.25 32.66 46.42 –
5.6 6.5 6.8 5.4 6.2 5.9 5.7 5.7 6.6 5.7 6.2 6.5/6 7.3 6.3 6.8/6.5 6.3 6.1 5.9 5.8 6.1 5.9 5.7 5.9 6/6.1 4.4 5.7 6.6 6.0 6.4
þ
Group
[Hx] (mmol/l)
[K ] (mmol/l)
A A B B B A B B B B B B B B B B B B B A B B B B B B B A
13.52 17.88 18.19 66.11 24.34 16.58 29.73 18.20 – 27.88 26.58 55.40 28.16 –/– 25.38 – 32.87 21.88/– 26.17 22.63 – – 38.38 – 26.02 – 15.52 36.67
5.6 5.8 5.7 8.4 6 6.3 6 5.9 7.3 6.6 6.2 6.2 6.2 5.3/5.3 6 6.4 5.1 6.1/6 5.9 6 5.4 6.1 6.2 5.9 5.8 6.1 5.3 5.7
29 30 31 32 33 34 35 36 37 38 39 40b 41 42 43b 44 45 46 47 48 49 50 51 52b 53 54 55 56 57
3.08 3.25 3.33 3.5 3.5 3.5 3.5 3.63 3.66 3.66 3.66 3.7 3.75 3.83 3.86 3.93 4 4.05 4.08 4.25 4.5 4.5 4.5 4.66 4.75 4.75 4.75 4.98 5
J.I. Mun˜ oz Baru´ s et al. / Forensic Science International 125 (2002) 67–74 Table 2 (Continued )
69
Table 2 (Continued )
C
PMI (h)
Groupa
[Hx] (mmol/l)
[Kþ] (mmol/l)
C
PMI (h)
Groupa
[Hx] (mmol/l)
[Kþ] (mmol/l)
58 59b 60 61 62 63 64 65 66b 67 68 69 70 71 72b 73 74 75 76 77 78 79 80 81 82 83 84 85b 86 87 88 89 90 91 92b 93 94 95 96b 97 98 99 100 101 102 103 104b 105 106 107 108 109b 110 111 112 113 114b
5 5 5.08 5.25 5.25 5.25 5.5 5.66 5.66 5.66 5.75 5.75 5.91 5.91 5.95 6 6 6 6.16 6.25 6.25 6.25 6.33 6.5 6.5 6.5 6.58 6.75 6.75 6.75 7 7 7 7.08 7.33 7.5 7.5 7.5 7.83 8 8.25 8.33 8.5 8.5 8.58 8.75 9 9.08 9.25 9.66 9.91 10.08 10.33 10.9 11.16 11.25 11.41
B B A A A B A A A B B B A B B A B B B A B B B A B B B A B B B B B B B B B B B B B B B B A B B B B B B B B B A B A
28.29 33.59/38.39 51.22 65.27 33.29 53.91 58.57 24.63 44.95/45.63 – – – 67.08 75.73 –/– 55.56 92.18 – 52.53 18.66 44.17 – 43.60 34.27 67.46 – 79.65 72.22/58.83 59.20 71.98 78.59 – – 33.94 47.66/53.69 – – – –/– 53.19 56.06 53.28 – – 70.86 59.82 55.60/63.86 41.22 – – 45.01 75.45/– 64.13 – 81.86 79.74 –/–
6.7 6.5/6.3 7 7.5 6.2 7.2 6.6 5.7 6.7/6.9 6.3 6.4 7.2 6.3 6.5 7/6.8 7.4 8.9 6.4 7 5.7 6.2 6.5 7.2 5.1 6.8 8.2 7.4 7.6/7.5 6.1 7 6.2 6.5 6.9 6 6.8/7 6.9 6.7 6.9 7.6/6.6 7.2 6.8 7.4 7.6 7.3 6.7 6.3 7.5/7.5 6.6 7.6 7.9 6.5 6.7/6.7 7.1 8.1 8 8 7.9/7.8
115b 116 117 118 119 120 121 122 123b 124b 125 126 127 128 129 130 131 132b 133b 134 135b 136 137 138 139 140 141 142b 143b 144b 145 146 147b 148 149 150 151 152 153b 154 155 156 157 158 159b 160 161 162 163 164 165b 166b 167 168 169 170 171
11.5 11.5 11.68 12.25 12.5 12.66 13 13.25 13.25 13.75 14 14 14.45 14.5 14.68 15 15.25 15.33 15.38 15.51 15.83 16 16.16 16.41 16.5 16.66 16.83 16.88 16.91 17 17 17 17.13 17.5 17.58 17.75 17.76 17.86 17.91 18 18 18.69 18.75 19.31 19.41 19.5 19.5 19.61 20 20.25 20.25 20.75 21.58 21.75 22.25 22.25 22.95
A B B B B B B B B B A B B A B B B A A B B A A B B A B B B B B B B B B B B B B A B B B B B B B B B A B B B B B B B
68.31/71.3 – 75.52 64.21 57.48 48.11 – 46.90 –/48.39 85.93/– – 80.59 37.65 – 32.58 – 69.03 87.47/71.59 93.44/– 67.97 58.79/45.83 63.56 103.34 43.8 27.94 127.86 84.16 125.27/83.6 –/– 103.06/88.81 70.50 120.86 88.18/73.65 62.75 83.52 121.27 – 97.70 113.69/100.34 123.28 64.05 110.97 85.99 66.74 –/104.86 73.94 – 77.68 – 92.25 71.69/73.15 65.98/72.61 63.45 69.26 37.72 93.00 99.25
7.1/7 6.8 6.9 7.7 7 6.4 10.2 8 7.3/6.8 9.9/9.2 8.5 7.9 7.6 7.8 6.8 8.5 7.7 9/8.9 8.6/8.5 8.2 8.6/8.6 8.3 9.1 7.3 8.3 10.9 9.7 10.1/10 8/8.5 9.7/8.7 8.2 9.3 8.7/8 8.1 8 10.5 9.9 8.8 8.9/8 10.5 9.5 9.1 8 8.4 9.7/10.3 8.6 9.7 7.8 8 9.4 8.4/8.9 8.2/8 7.9 8 7.6 9.7 9.9
J.I. Mun˜ oz Baru´ s et al. / Forensic Science International 125 (2002) 67–74
70 Table 2 (Continued ) C
PMI (h) b
172 173 174b 175 176 a b
23.5 24 24.25 28 28.91
Groupa B B B B A
[Hx] (mmol/l)
[Kþ] (mmol/l)
73.81/67.82 – 73.21/– 121.07 –
10.8/10.1 10 10/9.4 9 11
Group A: hanging; group B: no hanging. [Kþ] and [Hx] determined in both eyes: left eye/right eye.
Santiago de Compostela (Spain). All cases were indexed with case number, sex, age, medical care, the cause of death, time of death, extraction time and toxicological screening. Samples were obtained by scleral puncture near the outer canthus using a 20 gauge needle and a 10 ml syringe. Suction was applied gradually and slowly to withdraw all extractable vitreous humour according to [11,17]. Samples from corpses whose time of death could not be established to within 15 min were excluded. Non-transparent specimens and those from new-born infants aged <6 months were considered unsatisfactory for analysis [11]. Each sample was centrifuged at 3000 rpm for 10 min [5], and only the supernatant part is was used in order to avoid obstructing the fine tubing used in most current analytical instruments [18]. The time between extraction and analysis was never more than 48 h, during which time samples were kept at 4 8C. Biochemical and toxicological parameters and analytical methods used are given below in Table 3. All results were obtained with a BM/747 (Boehringer Mannheim), except alcohol levels, which were determined with a 5890-series II (Hewlett-Packard) and hypoxanthine with Waters 996 PDA
Table 3 Analytical methods Parameter
Analytical methods
Potassium Urea Creatinine
Indirect potentiometry Kinetic UV assay for urea/urea nitrogen Jaffe´ method taking into consideration the sample blank (twin mode) High performance liquid chromatography Head space gas chromatography
Hypoxanthine Alcohol
and reverse phase column. The PMI in hours was expressed in the decimal system and statistical analysis carried out by applying simple linear regression using SPSS 9.0.1 for WindowsTM.
3. Results A total of 206 samples, from 141 men and 35 women, were used. All data are shown in Table 2. The minimum value of PMI was 1.08 h and the maximum 28.91 h, with an average of 9.6 h and S:D: ¼ 6:6. No significant difference arising from alcohol level was observed (P ¼ 0:711), nor were there significant differences between both eyes or between sex (P ¼ 0:787, 0.466). The linear regression formula we obtained with PMI as the independent variable and [Kþ] or [Hx] as the dependent were: ½Kþ ¼ 5:589 þ 0:174PMI (R2 ¼ 0:688, P < 0:001) and ½Hx ¼ 26:459 þ 3:017PMI (R2 ¼ 0:518, P < 0:001), respectively. All samples were classified into two groups: group A consisted of hanging deaths, while group B consisted of
Table 4 The regression lines and the formulae proposed (P < 0:001)a Groups All cases
Group A (hanging)
N
Regression line þ
Formula proposed þ
R
R2
1 R2
DW
Cook-d
No levels
176 134
[K ] ¼ 5.589 þ 0.174PMI [Hx] ¼ 26.459 þ 3.017PMI
PMI ¼ 3.967[K ] 19.186 PMI ¼ 0.172[Hx] þ 0.170
0.830 0.688 0.312 0.719 0.518 0.482
1.730 1.575
0.098 0.145
Urea 30 mg/dl
131 101
[Kþ] ¼ 5.572 þ 0.174PMI [Hx] ¼ 28.278 þ 2.850PMI
PMI ¼ 4.093[Kþ] 19.967 PMI ¼ 0.175[Hx] þ 0.112
0.843 0.711 0.289 0.707 0.500 0.500
1.659 1.551
0.127 0.173
No levels
35 30
[Kþ] ¼ 5.224 þ 0.225PMI [Hx] ¼ 15.161 þ 4.957PMI
PMI ¼ 3.631[Kþ] 17.344 PMI ¼ 0.153[Hx] 0.368
0.904 0.818 0.182 0.870 0.757 0.243
1.897 1.754
0.376 0.352
Urea 30 mg/dl
25 23
[Kþ] ¼ 5.193 þ 0.219PMI [Hx] ¼ 17.438 þ 4.567PMI
PMI ¼ 3.927[Kþ] 19.115 PMI ¼ 0.167[Hx] 0.910
0.927 0.860 0.140 0.874 0.764 0.236
2.283 1.879
0.335 0.304
141 104
[Kþ] ¼ 5.675 þ 0.162PMI [Hx] ¼ 28.155 þ 2.733PMI
PMI ¼ 4.083[Kþ] 19.885 PMI ¼ 0.178[Hx] þ 0.278
0.814 0.663 0.337 0.697 0.486 0.514
1.760 1.551
0.086 0.141
106 78
[Kþ] ¼ 5.672 þ 0.163PMI [Hx] ¼ 30.123 þ 2.573PMI
PMI ¼ 4.144[Kþ] 20.258 PMI ¼ 0.178[Hx] þ 0.426
0.822 0.676 0.324 0.676 0.457 0.543
1.634 1.583
0.117 0.165
Group B (no hanging) No levels Urea 30 mg/dl
a PMI in hours, [Kþ] in mmol/l and [Hx] in mmol/l; R correlation coefficient; R2 determination coefficient; 1 R2 proportion of the rest variance of the regression; DW Durbin–Watson and Cook-d is the maximum value of the Cook’s distance.
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Table 5 Confidence interval (95%) for different [Kþ] and [Hx]a All cases
Group A (hanging) Urea 30 (mg/dl)
No levels
Group B (no hanging) Urea 30 (mg/dl)
No levels
Urea 30 (mg/dl)
No levels
þ
[K ] (mmol/l) 6 9 12 15
4.615 16.516 28.417 40.317
0.745 0.891 1.980 3.152
4.593 16.874 29.154 41.435
0.863 1.009 2.240 3.570
4.441 15.334 26.227 37.120
1.181 1.399 2.966 4.681
4.446 16.227 28.007 39.788
1.309 1.589 3.326 5.227
4.614 16.865 29.114 41.364
0.892 1.070 2.408 3.842
4.608 17.042 29.475 41.909
1.043 1.207 2.724 4.357
[Hx] (mmol/l) 25 50 75 100 125
4.460 8.750 13.041 17.331 21.621
1.191 0.818 0.968 1.491 2.128
4.499 8.885 13.273 17.660 22.047
1.474 0.985 1.137 1.771 2.551
3.448 7.265 11.082 14.899 18.716
1.389 1.010 1.193 1.771 2.482
3.271 7.452 11.634 15.815 19.997
1.722 1.205 1.399 2.117 3.004
4.722 9.166 13.611 18.056 22.500
1.484 0.999 1.183 1.846 2.651
4.866 9.307 13.748 18.189 22.630
1.848 1.217 1.402 2.205 3.190
a
Results in hours.
non-hanging deaths. There was a significant difference for [Kþ] and [Hx] between the two groups (P ¼ 0:006 and 0.002, respectively). Accordingly, 35 samples (group A) and 141 samples (group B) were analysed for [Kþ] giving R2 ¼ 0:818 and 0.663, respectively (P < 0:001). In order to increase the precision of these results we established critical levels of urea and/or creatinine according to Madea and co-workers [7,13], and by using different values of urea and creatinine we found that best results were obtained by excluding cases with urea <30 mg/dl. The linear regression and the proposed formulae are shown in Table 4. The confidence intervals are given in Table 5.
4. Discussion We observed that in cases of death by hanging the relationship between PMI and [Kþ] or [Hx] is defined by two formulae which differs from that from death by other causes. There is significant difference between both groups (P ¼ 0:006 and 0.002, respectively) and the increase in the steepness of slope means that for each unit of PMI the value of [Kþ] is 72% greater and the value of [Hx] is 55% in cases of death by hanging (group A) than that for other deaths (group B). Also, the increase in the value of R, in group A, corresponds to an improvement of 23% and 55%, respectively, in the precision of PMI (Figs. 1 and 2).
Fig. 1. Regression lines using PMI as independent variable. Line A: deaths by hanging; line B: no hanging deaths. PMI in hours and [Kþ] in mmol/l.
72
J.I. Mun˜ oz Baru´ s et al. / Forensic Science International 125 (2002) 67–74
Fig. 2. Regression lines using PMI as independent variable. Line A: deaths by hanging; line B: no hanging deaths. PMI in hours and [Hx] in mmol/l.
This might possibly be due to the rapidity of death which reduces agonal change in the chemistry of the vitreous humour and this, in turn, could also explain the increase in the value of R2 (1 R2 represents the rest variance of the regression, ‘‘not explained’’). The increase in the steepness of slope might be explained by the fact that in case any compression, resulting from the fatal tension of the noose on the neck, will interrupt the jugular system and cause a rapid rise in
venous pressure in the neck [16,19]. This pressure could lead to the congestion of capillaries and hence an increase of vascular leakage from the retinal capillaries and therefore a rise of potassium and hypoxantine into the vitreous humour. In the light of these results, we made an inverse prediction for [Kþ] and [Hx] by changing the variables according to Mun˜ oz et al. [9], and in this way obtained a line that is adjusted to the PMI (Figs. 3 and 4).
Fig. 3. Regression line using [Kþ] as independent variable. Only deaths by hanging are included. PMI in hours and [Kþ] in mmol/l.
J.I. Mun˜ oz Baru´ s et al. / Forensic Science International 125 (2002) 67–74
73
Fig. 4. Regression line using [Hx] as independent variable. Only deaths by hanging are included. PMI in hours and [Hx] in mmol/l.
The magnitude of the difference between both formulae is better understood if we consider two real cases from our data. In a case with known PMI ¼ 18:00 h with ½Kþ ¼ 10:5 mmol/l, the estimated PMI according to the general formula is 22.46 h, but using the formula we propose for cases of death by hanging the calculation is 20.78 h. Similarly, in a known PMI ¼ 11:16 h with ½Kþ ¼ 8 mmol/l, the estimated PMI obtained using the general formula would be 12.55, compared to 11.70 h. Moreover, for all cases a better precision is obtained (R2 ¼ 0:688 raising to 0.818) and a narrower confidence interval (Table 5). In the case with PMI ¼ 18:00 h with ½Hx ¼ 123:28 mmol/l, the estimated PMI obtained using the general formula would be 22.22, compared to 18.493 h; and in the case with PMI ¼ 11:16 with ½Hx ¼ 81:86 was obtained a PMI of 14.24 and 12.15 h, respectively. Moreover, for all cases a better precision is obtained (R2 ¼ 0:518 raising to 0.757). The exclusion of cases with urea <30 mg/dl further improves the precision of the equation. Different tests were made for several values of both metabolites and only the best results are shown (Table 4). Similar limitations were previously considered by others authors [4,7,9,13]. Testing the goodness-of-fit was made by calculating Cook’s distance and using the Durbin–Watson method. The results are included in Table 4, confirming the independence assumption and ruling out the existence of outliers. In conclusion, as a means of achieving greater accuracy in the determination of PMI from vitreous [Kþ] and [Hx], we propose a more precise formula whose specificity and greater precision, combined with the relative ease of ascertaining the cause of death, recommend its use in cases of death by hanging.
Acknowledgements This study was supported by Grants XUGA20807B98 and PGIDT99PXI20808B.
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[10] T.O. Rognum, S. Hauge, S. Oyasaeter, O.D. Saugstad, A new biochemical method for estimation of postmortem time, Forensic Sci. Int. 51 (1991) 139–146. [11] B. Madea, H. Ka¨ ferstein, N. Hermann, G. Sticht, Hypoxanthine in vitreous humor and cerebrospinal fluid—a marker of postmortem interval and prolonged (vital) hypoxia? Remarks also on hypoxanthine in SIDS, Forensic Sci. Int. 65 (1994) 19–31. [12] J.I. Coe, F.S. Apple, Variations in vitreous humor chemical values as a result of instrumentation, J. Forensic Sci. 30 (1985) 828–835. [13] B. Madea, C. Henssge, Eye changes after death, in: B. Knight (Ed.), The Estimation Time Since Death in the Early Postmortem Period, 3rd Edition, Edward Arnold, London, 1996, pp. 106–137. [14] J.I. Mun˜ oz, J.M. Sua´ rez-Pen˜ aranda, X.L. Otero, M.S. Rodrı´guez-Calvo, E. Costas, X. Migue´ ns, L. Concheiro, La
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