- Email: [email protected]
Precision of estimating the time since death by vitreous potassium—Comparison of 5 different equations
Forensic Science International 269 (2016) 1–7
Contents lists available at ScienceDirect
Forensic Science International journal homepage: www.elsevier.com/locate/forsciint
Precision of estimating the time since death by vitreous potassium— Comparison of 5 different equations Jan Ortmann, Philipp Markwerth, Burkhard Madea* Institute of Forensic Medicine, University of Bonn, Stiftsplatz 12, D-53111 Bonn, Germany
A R T I C L E I N F O
Article history: Received 22 April 2016 Received in revised form 22 August 2016 Accepted 10 October 2016 Available online 17 October 2016 Keywords: Potassium Vitreous humor Precision of death time estimation
A B S T R A C T
The precision of death time estimation by vitreous potassium using 5 different formulas is compared on a random sample of 600 cases. Mean differences, standard deviations and 95% limits of confidence between real and extrapolated time since death were calculated. The best results were obtained using equations with “mean” slopes of about 0,17 or 0,19 mmol/l per hour. Equations with a steeper or flatter slope reveal already great mean deviations between real and extrapolated time since death and do not allow a reliable death time estimation. ã 2016 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Estimation of the time since death is a daily task in Forensic Medicine. Gold standard in the early postmortem interval (PMI) is Henssge’s nomogram based on the two-exponential formula of body cooling by Marshall and Hoare together with data on supravital reactions, postmortem lividity and rigor mortis [so called compound method; [13,25,26]]. There is also a huge literature on chemical methods proposed for estimating the time since death which however play obviously no role in forensic practice [26,31,32]. Beside blood, cerebrospinal fluid, synovial fluid, especially vitreous humor were investigated [8–10,20,24]— not only in forensic pathology but animal medicine as well [27,33]. One of the most investigated analytes is the potassium concentration in vitreous humor [[1–3,8,9,11,12,14–19,21– 23,28,29,34–37,39], for review see Refs. [26] and [39]]. The linear rise of vitreous potassium over the postmortem interval is as well-known as the different statements concerning the slope and intercept of the regression line (Table 1). Some reasons for the different regression parameters – especially the slope – have already been discussed in other publications such as
* Corresponding author. E-mail address: [email protected] (B. Madea). http://dx.doi.org/10.1016/j.forsciint.2016.10.005 0379-0738/ã 2016 Elsevier Ireland Ltd. All rights reserved.
- the ambient temperature [6,7,22,30][6,7,22,30,75] - the duration of terminal episode [1,22] - composition of the random sample: hospital cases, coroner cases [11,22] - much steeper slope in cases with elevated urea values [9,21,22] - possible influence of the blood alcohol level at the moment of death [22] - distribution of the cases over the PMI - instrumentation used to measure concentrations [4,10,37] - age (steeper slope in infants than in adults) [24,39] - linear relationship between vitreous K+ and the PMI. This is obviously not a straight line but is biphasic with a steeper slope in the first 6 h than for prolonged times [8,9] - sampling methods, preanalytical treatment of samples and instrumentation used for analysis [4,5,10,20,37,38] - which is the dependent and which is the independent variable in the regression between vitreous K+ and time since death [21,28,29]. In casework therefore the question arises which intercept and which slope to use for extrapolating the time since death. Coe [9], one of the pioneers in vitreous humor analysis, recommended in his historical review on vitreous potassium as a measure of the postmortem interval the well known Sturner formula [35] for estimating the time since death, although, the slope in Sturner’s material is the flattest reported in the literature (Table 1).
2
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7 Table 1 Intercept and slope of the regression of vitreous potassium and postmortem interval according to different authors. Author
n
Intercept
Slope
Sturner [35]
54
Adelson et al. [1] Hansson et al. [11] Lie [19] Coe [8]
209 108 88 160
5.96a mmol/l 5.6 mmol/l 5.36 mmol/l 8 mmol/l
Adjutantis and Coutselinis [2] Stephens and Richards [34] Madea et al. [22]
1427 170
0.132a mmol/l h 0.14 mmol/l h 0.17 mmol/l h 0.17 mmol/l h 0.14 mmol/l h 0.332 mmol/l h (first 6 h) 0.1625 mmol/l h (over 6 h) 0.55 mmol/l h (for the first 12 h) 0.238 mmol/l h 0.19 mmol/l h
4.99 mmol/l 6.19 mmol/l 6.342 mmol/l 5.88 mmol/l
a Our own calculations on Sturner’s material with differences to Coe’s [9] statement. In cases with vitreous potassium of both eyes, the mean value was used for regression analysis.
Table 2 Regressions and formulas of five different studies used for calculating time since death. Author
Regression
Formula
Sturner Madea et al. James et al. Munoz et al. Jashnani et al.
Y = 0,14x + 5,6 Y = 0,19x + 5,88 Y = 0,23x + 4,2 Y = 0,17x + 5,60 Y = 0,929x + 2,616
PMI = 7,14[K+] PMI = 3,92[K+] PMI = 4,32[K+] PMI = 3,92[K+] PMI = 1,076[K+]
39,1 30,9 18,35 19,04 2,815
Postmortem interval
Investigated country
104 h postmortem 120 h postmortem Unknown 29 h postmortem 50 h postmortem
USA Germany Australia Spain India
Table 3 Mean differences, standard deviations and 95% limits of confidence (in hours) between real and extrapolated time since death for 600 cases in the postmortem interval up to about 100 h postmortem using the different equations from Table 3.
n= Mean difference Standard deviation 95% confidence limits
Sturner
Madea et al.
James et al.
Munoz et al.
Jashnani
600 9,19 15,31 30,62
600 0,18 10,03 20,06
600 4,13 8,54 17,08
600 0,22 8,31 16,62
600 10,01 13,37 26,74
Coe [9] states that the results by this formula are most satisfactory when the ambient temperature in which the body has lain is below 50 F and emphasises the results even under these conditions may be quite inexact. The 95% limits of confidence will be much greater than 4.7 h (the standard deviation originally
calculated by Sturner up to 104 h postmortem) in the first day and will increase with increasing postmortem interval. However, clear values for the precision of estimating the time since death (95%—limits of confidence) using the Sturner formula were missing.
Fig. 1. Potassium concentration, postmortem interval and number of cases used for calculation of the time since death.
Fig. 2. Vitreous K+ values of 600 cases over the PMI with regression lines of the five studies used for calculating time since death.
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7
In our opinion, vitreous potassium is only of limited value in estimating the time since death in the first 24 h postmortem since other methods (body cooling, electrical excitability of skeletal muscle, chemical excitability of iris) are working quite satisfactory in this postmortem period, but the value of vitreous potassium may increase with increasing postmortem interval since the other methods for determining the time since death are of no use in the later postmortem interval (because electrical excitability has expired and the body temperature has reached the ambient temperature). Already 25 years ago we compared two different formulas of death time estimation by vitreous potassium on an independent random sample of 100 cases [23]. The very flat slope in Sturner’s equation is the reason for a systematic over-estimation of the time since death with much wider 95% limits of confidence compared to the results using an own equation with a steeper slope of vitreous potassium. Meanwhile further formulas for extrapolating the time since death have been recommended [26,39]. The formulas are from different countries, different continents and different climate zones. Especially Zilg et al. [39] studied a much longer postmortem
3
interval than other authors (up to 409 h postmortem); due to this long postmortem interval the rise in vitreous potassium was not linear but followed an exponential curve. This curve became eventually asymptotic after about a week. Since data on the precision and reliability of different formulas are missing in the literature it was the aim of the present paper to assess the suitability and precision of death time estimation using 5 different equations (Table 2). 2. Material and methods We have studied in the last 30 years the rise of vitreous potassium in 600 cases of mainly sudden natural or traumatic death. Time since death in the cases included in this study was known quite exactly (15 min). Vitreous humor was withdrawn at the same time postmortem from both eyes where possible. Both specimens were determined independently using ion sensitive electrodes as previously described [22]. However, investigations were carried out in different laboratories. Therefore data on the intra-day and inter-day precision are not available. All cases were
Fig. 3. Deviations between extrapolated and real time since death (d t in hours) over the postmortem interval for 600 independent cases. Systematic overestimation of the time since death using the Sturner formula, systematic underestimation of the time since death using Jashnani’s formula.
4
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7
independent from a previous study [22]. Time since death was extrapolated for all 600 cases using the formulas in Table 2. These formulas were selected since they are from different continents and are obviously used in daily casework. For calculation the mean value of both eyes was used. From the deviation between real and extrapolated time since death statistical parameters of precision of death time estimation were calculated (mean deviation, standard deviation, 95% confidence limits). The composition of the random sample (number of cases in which postmortem interval) becomes evident from Fig. 1. Most cases are from PMI’s below 65 h and potassium concentrations below 15 mmol/l. In Fig. 2 the 600 potassium values over the postmortem interval and the 5 regression lines used for extrapolating the time since death are shown. Furthermore the confidence intervals were calculated for different potassium values (5–10 mmol/l; 10–15 mmol/l; 15–20 mmol/l) and
postmortem intervals (<30 hpm; 30–60 hpm; >60 hpm) to check if they increase with increasing pmi. 3. Results Using the Sturner [35] equation and the equation by Jashnani et al. [16] there is a systematic deviation between real and extrapolated time since death (Table 3, Fig. 3). The mean difference is +9 h using Sturner’s equation and 10 h using Jashnani et al.’s equation. The mean difference is only 0,18 h in the own equation and 0,22 h using the equation of Munoz et al. [29]. The reason for the systematic underestimation using Jashnani’s formula may be due to the following factors: - the authors studied only the first 50 h postmortem.
Fig. 4. Deviations between extrapolated and real time since death (d t in hours) over the postmortem interval for 3 different postmortem intervals (<30; 30–60;> 60 h).
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7
5
- composition of the random sample (mostly included cases involving sepsis or tuberculosis, followed by intrapulmonary hemorrhages in acute febrile illness and pneumonia). - the higher ambient temperature in India compared to Central Europe.
mean differences between real and extrapolated time since death and standard deviations for 3 potassium concentration ranges are shown also in Table 4.
The reason for the systematic overestimation of the time since death using Sturner’s formula is the flat slope. When the confidence interval are calculated for different potassium concentrations (5–10 mmol/l; 10–15 mmol/l; 15– 20 mmol/l) or postmortem intervals (<30 hpm; 30–60 hpm; >60 hpm) the confidence intervals are increasing with increasing PMI (Fig. 4) or potassium concentration (Fig. 5) respectively. The
When different formulas for extrapolating the time since death using vitreous potassium are used the geographic background should be taken into consideration. For Central Europe the formulas from Munoz et al. and the own one give quite reliable results, however the 95% limits of confidence are 20 h in the time interval up to 100 h postmortem. By taking into account influencing factors like ambient temperature or electrolyte
4. Discussion
Fig. 5. Deviations between extrapolated and real time since death (d t in hours) over the potassium concentration for 3 different concentration ranges (5–10; 10–15; 15– 20 mmol/l).
6
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7
Table 4 Mean differences, and standard deviations (in hours) between real and extrapolated time since death for different potassium concentrations. Sturner Potassium concentration mmol/l [K+] Number of cases Mean difference Standard deviation
<10 436 3,275 5,677
Madea 10–15 103 19,99 9,004
>20 65 31,73 30,33
<10 436 2,253 4,386
James 10–15 103 5,522 8,166
>20 65 8,08 23,69
<10 436 3,433 4,199
disturbances due to renal insufficiency a rise of precision may be achieved. Zilg et al. [39] were successful to prove the influence of ambient temperature on the rise of vitreous potassium: the higher the average ambient temperature, the steeper the increase in potassium. A further major finding of their study was that decedent’s age significantly affected the rise in vitreous potassium concentrations: the younger the subject, the more rapid the increase. They developed a formula for death time estimation taking into account the vitreous potassium concentration, ambient temperature and age of the decedent. As has already been shown by other authors [39] the standard deviations between real and extrapolated time since death are increasing with increasing postmortem interval or potassium concentration. A further rise of precision may be achieved by multiple linear regression analysis taking into account not only the potassium concentration but further vitreous humour electrolytes as well. However, the resulting increase of precision will not be very high [26]. Therefore vitreous potassium is only rarely used as an aid in estimating the time since death in daily forensic casework or at court. Nevertheless we have seen cases where the question was to check if the decedent was less or more than 1 week dead or less than 3 or more than 5 days. In these cases vitreous potassium may be of help for the police investigations.
[12]
5. Conclusions
[19]
When using vitreous potassium to estimating the time since death equations with a steeper slope than that reported by Sturner and otherwise a flatter slope than that reported by Jashnani should be preferred to avoid systematic over- or underestimations of the time since death. For Central Europe estimating the time since death with a slope of about 0.19 mmol/l h and an intercept of 5.88 mmol/l reveals an estimation of the time since death with no systematic deviations. However, the 95% limits of confidence are about 20 h up to 100 h postmortem. For Central Europe the formulas by Munoz et al. [29] and Madea et al. [22] give quite reliable results. In other climate zones formulas with steeper (high ambient temperature) or flatter (low ambient temperature) slopes may be advantageous.
[20]
References [1] L. Adelson, I. Sunshine, N.B. Rushforth, M. Marnkoff, Vitreous potassium concentration as an indicator of postmortem interval, J. Forensic Sci. 8 (1963) 503–514. [2] G. Adjutantis, A. Goutselinis, Estimation of the time of death by potassium levels in the vitreous humour, Forensic Sci. Int. 1 (1972) 55–60. [3] B.A.W. Balasooriya, C.A.S. Hill, A.R. Williams, The biochemistry of vitreous humour: a comparative study of the potassium, sodium and urate concentration in the eyes at identical time intervals after death, Forensic Sci. Int. 26 (1984) 85–91. [4] S.A. Blana, F. Musshoff, T. Hoeller, R. Fimmers, B. Madea, Variations in vitreous humor chemical values as a result of pre-analytical treatment, Forensic Sci. Int. 210 (2011) 263–270. [5] F. Bortolotti, J.P. Pascali, G.G. Davies, F.P. Smith, R.M. Brissie, F. Tagliaro, Study of vitreous potassium in correlation with the time since death in the postmortem
[6] [7] [8] [9] [10] [11]
[13] [14] [15]
[16] [17]
[18]
[21]
[22]
[23]
[24]
[25] [26] [27]
[28]
[29]
[30] [31]
Munoz 10–15 103 6,74 8,127
>20 65 4,705 21,26
<10 436 0,178 4,105
Jashnani 10–15 103 1,228 8,192
>20 65 2,762 20,48
<10 436 4,719 5,545
10–15 103 16,83 9,867
>20 65 34,72 20,83
range from 2 to 110 hour using capillary ion analysis, Med. Sci. Law 51 (2011) S20–S23. M. Bray, The eye as a chemical indicator of environmental temperature at the time of death, J. Forensic Sci. 29 (1984) 396–403. M. Bray, The effect of chilling, freezing, and rewarming on the postmortem chemistry of vitreous humor, J. Forensic Sci. 29 (1984) 401–411. J.I. Coe, Postmortem chemistries on vitreous humour, Am. J. Pathol. 51 (1969) 741–750. J.I. Coe, Vitreous potassium as a measure of the postmortem interval: an historical review and critical evaluation, Forensic Sci. Int. 42 (1989) 201–213. J.I. Coe, F.S. Apple, Variations in vitreous humour chemical values as a result of instrumentation, J. Forensic Sci. 30 (1985) 828–835. L.M.A. Hansson, U. Uotila, R. Lindfors, K. Laiho, Potassium content of the vitreous body as an aid in determining the time of death, Forensic Sci. 11 (1966) 390–394. J.B. Henry, F.A. Smith, Estimation of the postmortem interval by chemical means, Am. J. Forensic Med. Pathol. 1 (1980) 341–347. C. Henssge, B. Madea, Estimation of the time since death, Forensic Sci. Int. 165 (2007) 182–184. W. Hughes, Levels of potassium in the vitreous humour after death, Med. Sci. Law 150 (1965) 150–156. R.A. James, P.A. Hoadley, B.G. Sampson, Determination of postmortem interval by sampling vitreous humour, Am. J. Forensic Med. Pathol. 18 (2) (1997) 158– 162. K.D. Jashnani, S.A. Kale, A.B. Rupani, Vitreous humor: biochemical constituents in estimation of postmortem interval, J. Forensic Sci. 55 (6) (2010) 1523–1527. N. Lange, S.T. Swearer, W.Q. Sturner, Human postmortem interval estimation from vitreous potassium: an analysis of original data from six different studies, Forensic Sci. Int. 66 (1994) 159–174. E. Lendoiro, C. Cordeiro, M.S. Rodriguez-Calvo, D.N. Vieira, J.M. SuárezPenaranda, M. López-Rivadulla, J.I. Monoz-Barús, Applications of tandem mass spectrometer (LC-MSMS) in estimating the postmortem interval using the biochemistry of the vitreous humour, Forensic Sci. Int. 223 (2012) 160–164. J.T. Lie, Changes of potassium concentration in vitreous humour after death, Am. J. Med. Sci. 254 (1967) 136–142. B. Madea, Is there recent progress in the estimation of the postmortem interval by means of thanatochemistry? Forensic Sci. Int. 151 (2005) 139–149. B. Madea, A. Rödig, Time of death dependent criteria in vitreous humor: accuracy of estimating the time since death, Forensic Sci. Int. 164 (2006) 87– 92. B. Madea, C. Henssge, W. Honig, A. Gerbracht, References for determining the time of death by potassium in vitreous humour, Forensic Sci. Int. 8 (1989) 231– 243. B. Madea, N. Herrmann, C. Henssge, Precision of estimating the time since death by vitreous potassium: comparison of two different equations, Forensic Sci. Int. 46 (1990) 277–284. B. Madea, H. Käferstein, N. Hermann, G. Sticht, Hypoxanthine in vitreous humour 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. B. Madea, Methods for determining the time since death, For. Sci. Med. Pathol. (2016) (Epub ahead of print). B. Madea (Ed.), Estimation of the Time Since Death, 3rd ed., CRC Press, Taylor & Francis Group, Boca Raton, London, New York, 2016. P.S. McLaughlin, B.G. McLaughlin, Chemical analysis of bovine and porcine vitreous humors: correlation of normal values with serum chemical values and changes with time and temperature, Am. J. Vet. Res. 48 (1987) 467–473. J.I. Munoz, J.M. Suárez-Penaranda, X.L. Otero, M.S. Rodgríguez-Calvo, E. Costas, X. Miguéns, et al., A new perspective in the estimation of post-mortem interval (PMI) based on vitreous, J. Forensic Sci. 46 (2) (2001) 209–214. J.I. Munoz Barús, J.M. Suárez-Penaranda, X.L. Otero, M.S. Rodríguez-Calvo, E. Costas, X. Miguénes, L. Concheiro, Improved estimation of postmortem interval based on differential behavior of vitreous potassium and hypoxanthine in death by hanging, Forensic Sci. Int. 125 (2002) 67–74. 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. F. Schleyer, Postmortale klinisch-chemische Diagnostik und Todeszeitbestimmung mit chemischen und physikalischen Methoden, Thieme, Stuttgart, Germany, 1958.
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7 [32] F. Schleyer, Determination of the time since death in the early postmortem interval, in: F. Lundquist (Ed.), Methods of Forensic Science, vol. 2, Interscience Publishers, John Wiley and Sons, New York, 1963, pp. 253–293. [33] O. Schoning, A.C. Strafuss, Determining time of death of a dog by analysing blood, cerebrospinal fluid and vitreous humour colected postmortem, Am. J. Vet. Res. 41 (1980) 955–957. [34] R.J. Stephens, R.G. Richards, Vitreous humour chemistry: the use of potassium concentration for the prediction of the postmortem interval, J. Forensic Sci. 32 (1987) 503–509. [35] W.Q. Sturner, The vitreous humour: postmortem potassium changes, Lancet 1 (1963) 807–808.
7
[36] W.Q. Sturner, G.E. Gantner, The postmortem interval: a study of potassium in the vitreous humor, Am. J. Clin. Pathol. 42 (1964) 137–144. [37] F. Tagliaro, G. Manetto, F. Cittadini, D. Marchetti, F. Bortolotti, M. Margio, Capillary zone electrophoresis of potassium in human vitreous humour: validation of a new method, J. Chromatogr. B 733 (1999) 273–279. [38] A. Thierauf, F. Musshoff, B. Madea, Post-mortem biochemical investigations of vitreous humor, Forensic Sci. Int. 192 (2009) 89–92. [39] B. Zilg, S. Bernard, K. Alkass, S. Berg, H. Druid, A new model for the estimation of time of death from vitreous potassium levels corrected for age and temperature, Forensic Sci. Int. 254 (2015) 158–166.
Contents lists available at ScienceDirect
Forensic Science International journal homepage: www.elsevier.com/locate/forsciint
Precision of estimating the time since death by vitreous potassium— Comparison of 5 different equations Jan Ortmann, Philipp Markwerth, Burkhard Madea* Institute of Forensic Medicine, University of Bonn, Stiftsplatz 12, D-53111 Bonn, Germany
A R T I C L E I N F O
Article history: Received 22 April 2016 Received in revised form 22 August 2016 Accepted 10 October 2016 Available online 17 October 2016 Keywords: Potassium Vitreous humor Precision of death time estimation
A B S T R A C T
The precision of death time estimation by vitreous potassium using 5 different formulas is compared on a random sample of 600 cases. Mean differences, standard deviations and 95% limits of confidence between real and extrapolated time since death were calculated. The best results were obtained using equations with “mean” slopes of about 0,17 or 0,19 mmol/l per hour. Equations with a steeper or flatter slope reveal already great mean deviations between real and extrapolated time since death and do not allow a reliable death time estimation. ã 2016 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Estimation of the time since death is a daily task in Forensic Medicine. Gold standard in the early postmortem interval (PMI) is Henssge’s nomogram based on the two-exponential formula of body cooling by Marshall and Hoare together with data on supravital reactions, postmortem lividity and rigor mortis [so called compound method; [13,25,26]]. There is also a huge literature on chemical methods proposed for estimating the time since death which however play obviously no role in forensic practice [26,31,32]. Beside blood, cerebrospinal fluid, synovial fluid, especially vitreous humor were investigated [8–10,20,24]— not only in forensic pathology but animal medicine as well [27,33]. One of the most investigated analytes is the potassium concentration in vitreous humor [[1–3,8,9,11,12,14–19,21– 23,28,29,34–37,39], for review see Refs. [26] and [39]]. The linear rise of vitreous potassium over the postmortem interval is as well-known as the different statements concerning the slope and intercept of the regression line (Table 1). Some reasons for the different regression parameters – especially the slope – have already been discussed in other publications such as
* Corresponding author. E-mail address: [email protected] (B. Madea). http://dx.doi.org/10.1016/j.forsciint.2016.10.005 0379-0738/ã 2016 Elsevier Ireland Ltd. All rights reserved.
- the ambient temperature [6,7,22,30][6,7,22,30,75] - the duration of terminal episode [1,22] - composition of the random sample: hospital cases, coroner cases [11,22] - much steeper slope in cases with elevated urea values [9,21,22] - possible influence of the blood alcohol level at the moment of death [22] - distribution of the cases over the PMI - instrumentation used to measure concentrations [4,10,37] - age (steeper slope in infants than in adults) [24,39] - linear relationship between vitreous K+ and the PMI. This is obviously not a straight line but is biphasic with a steeper slope in the first 6 h than for prolonged times [8,9] - sampling methods, preanalytical treatment of samples and instrumentation used for analysis [4,5,10,20,37,38] - which is the dependent and which is the independent variable in the regression between vitreous K+ and time since death [21,28,29]. In casework therefore the question arises which intercept and which slope to use for extrapolating the time since death. Coe [9], one of the pioneers in vitreous humor analysis, recommended in his historical review on vitreous potassium as a measure of the postmortem interval the well known Sturner formula [35] for estimating the time since death, although, the slope in Sturner’s material is the flattest reported in the literature (Table 1).
2
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7 Table 1 Intercept and slope of the regression of vitreous potassium and postmortem interval according to different authors. Author
n
Intercept
Slope
Sturner [35]
54
Adelson et al. [1] Hansson et al. [11] Lie [19] Coe [8]
209 108 88 160
5.96a mmol/l 5.6 mmol/l 5.36 mmol/l 8 mmol/l
Adjutantis and Coutselinis [2] Stephens and Richards [34] Madea et al. [22]
1427 170
0.132a mmol/l h 0.14 mmol/l h 0.17 mmol/l h 0.17 mmol/l h 0.14 mmol/l h 0.332 mmol/l h (first 6 h) 0.1625 mmol/l h (over 6 h) 0.55 mmol/l h (for the first 12 h) 0.238 mmol/l h 0.19 mmol/l h
4.99 mmol/l 6.19 mmol/l 6.342 mmol/l 5.88 mmol/l
a Our own calculations on Sturner’s material with differences to Coe’s [9] statement. In cases with vitreous potassium of both eyes, the mean value was used for regression analysis.
Table 2 Regressions and formulas of five different studies used for calculating time since death. Author
Regression
Formula
Sturner Madea et al. James et al. Munoz et al. Jashnani et al.
Y = 0,14x + 5,6 Y = 0,19x + 5,88 Y = 0,23x + 4,2 Y = 0,17x + 5,60 Y = 0,929x + 2,616
PMI = 7,14[K+] PMI = 3,92[K+] PMI = 4,32[K+] PMI = 3,92[K+] PMI = 1,076[K+]
39,1 30,9 18,35 19,04 2,815
Postmortem interval
Investigated country
104 h postmortem 120 h postmortem Unknown 29 h postmortem 50 h postmortem
USA Germany Australia Spain India
Table 3 Mean differences, standard deviations and 95% limits of confidence (in hours) between real and extrapolated time since death for 600 cases in the postmortem interval up to about 100 h postmortem using the different equations from Table 3.
n= Mean difference Standard deviation 95% confidence limits
Sturner
Madea et al.
James et al.
Munoz et al.
Jashnani
600 9,19 15,31 30,62
600 0,18 10,03 20,06
600 4,13 8,54 17,08
600 0,22 8,31 16,62
600 10,01 13,37 26,74
Coe [9] states that the results by this formula are most satisfactory when the ambient temperature in which the body has lain is below 50 F and emphasises the results even under these conditions may be quite inexact. The 95% limits of confidence will be much greater than 4.7 h (the standard deviation originally
calculated by Sturner up to 104 h postmortem) in the first day and will increase with increasing postmortem interval. However, clear values for the precision of estimating the time since death (95%—limits of confidence) using the Sturner formula were missing.
Fig. 1. Potassium concentration, postmortem interval and number of cases used for calculation of the time since death.
Fig. 2. Vitreous K+ values of 600 cases over the PMI with regression lines of the five studies used for calculating time since death.
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7
In our opinion, vitreous potassium is only of limited value in estimating the time since death in the first 24 h postmortem since other methods (body cooling, electrical excitability of skeletal muscle, chemical excitability of iris) are working quite satisfactory in this postmortem period, but the value of vitreous potassium may increase with increasing postmortem interval since the other methods for determining the time since death are of no use in the later postmortem interval (because electrical excitability has expired and the body temperature has reached the ambient temperature). Already 25 years ago we compared two different formulas of death time estimation by vitreous potassium on an independent random sample of 100 cases [23]. The very flat slope in Sturner’s equation is the reason for a systematic over-estimation of the time since death with much wider 95% limits of confidence compared to the results using an own equation with a steeper slope of vitreous potassium. Meanwhile further formulas for extrapolating the time since death have been recommended [26,39]. The formulas are from different countries, different continents and different climate zones. Especially Zilg et al. [39] studied a much longer postmortem
3
interval than other authors (up to 409 h postmortem); due to this long postmortem interval the rise in vitreous potassium was not linear but followed an exponential curve. This curve became eventually asymptotic after about a week. Since data on the precision and reliability of different formulas are missing in the literature it was the aim of the present paper to assess the suitability and precision of death time estimation using 5 different equations (Table 2). 2. Material and methods We have studied in the last 30 years the rise of vitreous potassium in 600 cases of mainly sudden natural or traumatic death. Time since death in the cases included in this study was known quite exactly (15 min). Vitreous humor was withdrawn at the same time postmortem from both eyes where possible. Both specimens were determined independently using ion sensitive electrodes as previously described [22]. However, investigations were carried out in different laboratories. Therefore data on the intra-day and inter-day precision are not available. All cases were
Fig. 3. Deviations between extrapolated and real time since death (d t in hours) over the postmortem interval for 600 independent cases. Systematic overestimation of the time since death using the Sturner formula, systematic underestimation of the time since death using Jashnani’s formula.
4
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7
independent from a previous study [22]. Time since death was extrapolated for all 600 cases using the formulas in Table 2. These formulas were selected since they are from different continents and are obviously used in daily casework. For calculation the mean value of both eyes was used. From the deviation between real and extrapolated time since death statistical parameters of precision of death time estimation were calculated (mean deviation, standard deviation, 95% confidence limits). The composition of the random sample (number of cases in which postmortem interval) becomes evident from Fig. 1. Most cases are from PMI’s below 65 h and potassium concentrations below 15 mmol/l. In Fig. 2 the 600 potassium values over the postmortem interval and the 5 regression lines used for extrapolating the time since death are shown. Furthermore the confidence intervals were calculated for different potassium values (5–10 mmol/l; 10–15 mmol/l; 15–20 mmol/l) and
postmortem intervals (<30 hpm; 30–60 hpm; >60 hpm) to check if they increase with increasing pmi. 3. Results Using the Sturner [35] equation and the equation by Jashnani et al. [16] there is a systematic deviation between real and extrapolated time since death (Table 3, Fig. 3). The mean difference is +9 h using Sturner’s equation and 10 h using Jashnani et al.’s equation. The mean difference is only 0,18 h in the own equation and 0,22 h using the equation of Munoz et al. [29]. The reason for the systematic underestimation using Jashnani’s formula may be due to the following factors: - the authors studied only the first 50 h postmortem.
Fig. 4. Deviations between extrapolated and real time since death (d t in hours) over the postmortem interval for 3 different postmortem intervals (<30; 30–60;> 60 h).
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7
5
- composition of the random sample (mostly included cases involving sepsis or tuberculosis, followed by intrapulmonary hemorrhages in acute febrile illness and pneumonia). - the higher ambient temperature in India compared to Central Europe.
mean differences between real and extrapolated time since death and standard deviations for 3 potassium concentration ranges are shown also in Table 4.
The reason for the systematic overestimation of the time since death using Sturner’s formula is the flat slope. When the confidence interval are calculated for different potassium concentrations (5–10 mmol/l; 10–15 mmol/l; 15– 20 mmol/l) or postmortem intervals (<30 hpm; 30–60 hpm; >60 hpm) the confidence intervals are increasing with increasing PMI (Fig. 4) or potassium concentration (Fig. 5) respectively. The
When different formulas for extrapolating the time since death using vitreous potassium are used the geographic background should be taken into consideration. For Central Europe the formulas from Munoz et al. and the own one give quite reliable results, however the 95% limits of confidence are 20 h in the time interval up to 100 h postmortem. By taking into account influencing factors like ambient temperature or electrolyte
4. Discussion
Fig. 5. Deviations between extrapolated and real time since death (d t in hours) over the potassium concentration for 3 different concentration ranges (5–10; 10–15; 15– 20 mmol/l).
6
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7
Table 4 Mean differences, and standard deviations (in hours) between real and extrapolated time since death for different potassium concentrations. Sturner Potassium concentration mmol/l [K+] Number of cases Mean difference Standard deviation
<10 436 3,275 5,677
Madea 10–15 103 19,99 9,004
>20 65 31,73 30,33
<10 436 2,253 4,386
James 10–15 103 5,522 8,166
>20 65 8,08 23,69
<10 436 3,433 4,199
disturbances due to renal insufficiency a rise of precision may be achieved. Zilg et al. [39] were successful to prove the influence of ambient temperature on the rise of vitreous potassium: the higher the average ambient temperature, the steeper the increase in potassium. A further major finding of their study was that decedent’s age significantly affected the rise in vitreous potassium concentrations: the younger the subject, the more rapid the increase. They developed a formula for death time estimation taking into account the vitreous potassium concentration, ambient temperature and age of the decedent. As has already been shown by other authors [39] the standard deviations between real and extrapolated time since death are increasing with increasing postmortem interval or potassium concentration. A further rise of precision may be achieved by multiple linear regression analysis taking into account not only the potassium concentration but further vitreous humour electrolytes as well. However, the resulting increase of precision will not be very high [26]. Therefore vitreous potassium is only rarely used as an aid in estimating the time since death in daily forensic casework or at court. Nevertheless we have seen cases where the question was to check if the decedent was less or more than 1 week dead or less than 3 or more than 5 days. In these cases vitreous potassium may be of help for the police investigations.
[12]
5. Conclusions
[19]
When using vitreous potassium to estimating the time since death equations with a steeper slope than that reported by Sturner and otherwise a flatter slope than that reported by Jashnani should be preferred to avoid systematic over- or underestimations of the time since death. For Central Europe estimating the time since death with a slope of about 0.19 mmol/l h and an intercept of 5.88 mmol/l reveals an estimation of the time since death with no systematic deviations. However, the 95% limits of confidence are about 20 h up to 100 h postmortem. For Central Europe the formulas by Munoz et al. [29] and Madea et al. [22] give quite reliable results. In other climate zones formulas with steeper (high ambient temperature) or flatter (low ambient temperature) slopes may be advantageous.
[20]
References [1] L. Adelson, I. Sunshine, N.B. Rushforth, M. Marnkoff, Vitreous potassium concentration as an indicator of postmortem interval, J. Forensic Sci. 8 (1963) 503–514. [2] G. Adjutantis, A. Goutselinis, Estimation of the time of death by potassium levels in the vitreous humour, Forensic Sci. Int. 1 (1972) 55–60. [3] B.A.W. Balasooriya, C.A.S. Hill, A.R. Williams, The biochemistry of vitreous humour: a comparative study of the potassium, sodium and urate concentration in the eyes at identical time intervals after death, Forensic Sci. Int. 26 (1984) 85–91. [4] S.A. Blana, F. Musshoff, T. Hoeller, R. Fimmers, B. Madea, Variations in vitreous humor chemical values as a result of pre-analytical treatment, Forensic Sci. Int. 210 (2011) 263–270. [5] F. Bortolotti, J.P. Pascali, G.G. Davies, F.P. Smith, R.M. Brissie, F. Tagliaro, Study of vitreous potassium in correlation with the time since death in the postmortem
[6] [7] [8] [9] [10] [11]
[13] [14] [15]
[16] [17]
[18]
[21]
[22]
[23]
[24]
[25] [26] [27]
[28]
[29]
[30] [31]
Munoz 10–15 103 6,74 8,127
>20 65 4,705 21,26
<10 436 0,178 4,105
Jashnani 10–15 103 1,228 8,192
>20 65 2,762 20,48
<10 436 4,719 5,545
10–15 103 16,83 9,867
>20 65 34,72 20,83
range from 2 to 110 hour using capillary ion analysis, Med. Sci. Law 51 (2011) S20–S23. M. Bray, The eye as a chemical indicator of environmental temperature at the time of death, J. Forensic Sci. 29 (1984) 396–403. M. Bray, The effect of chilling, freezing, and rewarming on the postmortem chemistry of vitreous humor, J. Forensic Sci. 29 (1984) 401–411. J.I. Coe, Postmortem chemistries on vitreous humour, Am. J. Pathol. 51 (1969) 741–750. J.I. Coe, Vitreous potassium as a measure of the postmortem interval: an historical review and critical evaluation, Forensic Sci. Int. 42 (1989) 201–213. J.I. Coe, F.S. Apple, Variations in vitreous humour chemical values as a result of instrumentation, J. Forensic Sci. 30 (1985) 828–835. L.M.A. Hansson, U. Uotila, R. Lindfors, K. Laiho, Potassium content of the vitreous body as an aid in determining the time of death, Forensic Sci. 11 (1966) 390–394. J.B. Henry, F.A. Smith, Estimation of the postmortem interval by chemical means, Am. J. Forensic Med. Pathol. 1 (1980) 341–347. C. Henssge, B. Madea, Estimation of the time since death, Forensic Sci. Int. 165 (2007) 182–184. W. Hughes, Levels of potassium in the vitreous humour after death, Med. Sci. Law 150 (1965) 150–156. R.A. James, P.A. Hoadley, B.G. Sampson, Determination of postmortem interval by sampling vitreous humour, Am. J. Forensic Med. Pathol. 18 (2) (1997) 158– 162. K.D. Jashnani, S.A. Kale, A.B. Rupani, Vitreous humor: biochemical constituents in estimation of postmortem interval, J. Forensic Sci. 55 (6) (2010) 1523–1527. N. Lange, S.T. Swearer, W.Q. Sturner, Human postmortem interval estimation from vitreous potassium: an analysis of original data from six different studies, Forensic Sci. Int. 66 (1994) 159–174. E. Lendoiro, C. Cordeiro, M.S. Rodriguez-Calvo, D.N. Vieira, J.M. SuárezPenaranda, M. López-Rivadulla, J.I. Monoz-Barús, Applications of tandem mass spectrometer (LC-MSMS) in estimating the postmortem interval using the biochemistry of the vitreous humour, Forensic Sci. Int. 223 (2012) 160–164. J.T. Lie, Changes of potassium concentration in vitreous humour after death, Am. J. Med. Sci. 254 (1967) 136–142. B. Madea, Is there recent progress in the estimation of the postmortem interval by means of thanatochemistry? Forensic Sci. Int. 151 (2005) 139–149. B. Madea, A. Rödig, Time of death dependent criteria in vitreous humor: accuracy of estimating the time since death, Forensic Sci. Int. 164 (2006) 87– 92. B. Madea, C. Henssge, W. Honig, A. Gerbracht, References for determining the time of death by potassium in vitreous humour, Forensic Sci. Int. 8 (1989) 231– 243. B. Madea, N. Herrmann, C. Henssge, Precision of estimating the time since death by vitreous potassium: comparison of two different equations, Forensic Sci. Int. 46 (1990) 277–284. B. Madea, H. Käferstein, N. Hermann, G. Sticht, Hypoxanthine in vitreous humour 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. B. Madea, Methods for determining the time since death, For. Sci. Med. Pathol. (2016) (Epub ahead of print). B. Madea (Ed.), Estimation of the Time Since Death, 3rd ed., CRC Press, Taylor & Francis Group, Boca Raton, London, New York, 2016. P.S. McLaughlin, B.G. McLaughlin, Chemical analysis of bovine and porcine vitreous humors: correlation of normal values with serum chemical values and changes with time and temperature, Am. J. Vet. Res. 48 (1987) 467–473. J.I. Munoz, J.M. Suárez-Penaranda, X.L. Otero, M.S. Rodgríguez-Calvo, E. Costas, X. Miguéns, et al., A new perspective in the estimation of post-mortem interval (PMI) based on vitreous, J. Forensic Sci. 46 (2) (2001) 209–214. J.I. Munoz Barús, J.M. Suárez-Penaranda, X.L. Otero, M.S. Rodríguez-Calvo, E. Costas, X. Miguénes, L. Concheiro, Improved estimation of postmortem interval based on differential behavior of vitreous potassium and hypoxanthine in death by hanging, Forensic Sci. Int. 125 (2002) 67–74. 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. F. Schleyer, Postmortale klinisch-chemische Diagnostik und Todeszeitbestimmung mit chemischen und physikalischen Methoden, Thieme, Stuttgart, Germany, 1958.
J. Ortmann et al. / Forensic Science International 269 (2016) 1–7 [32] F. Schleyer, Determination of the time since death in the early postmortem interval, in: F. Lundquist (Ed.), Methods of Forensic Science, vol. 2, Interscience Publishers, John Wiley and Sons, New York, 1963, pp. 253–293. [33] O. Schoning, A.C. Strafuss, Determining time of death of a dog by analysing blood, cerebrospinal fluid and vitreous humour colected postmortem, Am. J. Vet. Res. 41 (1980) 955–957. [34] R.J. Stephens, R.G. Richards, Vitreous humour chemistry: the use of potassium concentration for the prediction of the postmortem interval, J. Forensic Sci. 32 (1987) 503–509. [35] W.Q. Sturner, The vitreous humour: postmortem potassium changes, Lancet 1 (1963) 807–808.
7
[36] W.Q. Sturner, G.E. Gantner, The postmortem interval: a study of potassium in the vitreous humor, Am. J. Clin. Pathol. 42 (1964) 137–144. [37] F. Tagliaro, G. Manetto, F. Cittadini, D. Marchetti, F. Bortolotti, M. Margio, Capillary zone electrophoresis of potassium in human vitreous humour: validation of a new method, J. Chromatogr. B 733 (1999) 273–279. [38] A. Thierauf, F. Musshoff, B. Madea, Post-mortem biochemical investigations of vitreous humor, Forensic Sci. Int. 192 (2009) 89–92. [39] B. Zilg, S. Bernard, K. Alkass, S. Berg, H. Druid, A new model for the estimation of time of death from vitreous potassium levels corrected for age and temperature, Forensic Sci. Int. 254 (2015) 158–166.