Uncertainty in Widmark calculations: ABV variation in packaged versions of the most popular beers in the UK

Forensic practitioners regularly use the Widmark equation to determine theoretical blood alcohol concentrations for use in cases involving alcohol. It is important with these calculations to determine the uncertainty associated with any result. Previous work has investigated the uncertainty in percent alcohol by volume (%ABV) from beers produced by small independent breweries in the UK but did not study the top selling beers in the UK. The top selling lagers and ales/bitters in the UK were identified by sales volume and the %ABV determined. These data was then used to determine the percent coefficient of variation (%CV) that should be used by forensic practitioners when constructing alcohol technical defence reports for use in forensic cases. These samples, from what may be described as ‘big’ brewers, were determined to have a smaller root mean square error (RMSE) (±0.1%v/v, n?=?35), and %CV than those previously reported for beers produced by small, independent breweries in the UK. The results from this study shows that different RMSE's should be used for %ABV when determining the uncertainty of results from Widmark calculations depending if the drinks consumed have been from either ‘big’ brewers or small, independent breweries.     

Alcohol content of beer and malt beverages: forensic consideration

Beer consumption is commonly an issue in a medico-legal setting, requiring estimates either of a likely blood alcohol concentration (BAC) for a given pattern of consumption or vice versa. Four hundred and four beers and malt beverages available for sale in the State of Washington were tested by gas chromatography for their alcohol content. Considerable variability in the alcoholic strength was found, even within the same class. Overall the range of concentrations was 2.92%v/v to 15.66%v/v. The mean alcohol concentration for ales was 5.51%v/v (SD 1.23%v/v), and for lagers, 5.32% (SD 1.43%v/v). Some specialty brews had characteristically higher or lower mean concentrations: ice beers 6.07%v/v, malt liquor 7.23%v/v, light beer 4.13%v/v, seasonal ales 6.30%v/v. Six brands of lager and four light beers account for the majority of all beer sales in the United States, and the mean alcohol concentration for these products was measured as 4.73%v/v and 4.10%v/v respectively. Few of the beers (17%) were labeled with respect to alcohol content, and in some cases, there was a significant disparity between the concentration listed on the label, and the measured alcohol concentration. Toxicologists need to exercise caution when performing Widmark type calculations, using all available information to select the most appropriate estimate for alcoholic strength of a beer or malt beverage.     

Concentration-time profiles of ethanol in capillary blood after ingestion of beer.

Blood ethanol profiles were determined in experiments with healthy volunteers after they had drunk beer. When 330 ml of light beer (1.8% w/v ethanol) was consumed in 5 min by four men and four women, the average peak blood-alcohol concentration (BAC) reached was 8 mg/100 ml (range 2-11). After nine men had drunk 660 ml of beer (3.0% w/v or 3.6% w/v ethanol) in 25 minutes on an empty stomach, the average peak BAC was 32 mg/100 ml (range 26-44) and 37 mg/100 ml (range 23-54) respectively. When the same two beers were consumed by another nine men together with a meal, the peak BAC was 24 mg/100 ml (range 20-29) and 28 mg/100 ml (range 20-39) respectively. The peak BAC occurred earlier when beer was ingested together with food; mean 32 min (range 30-50) compared with 41 min (range 30-70) with an empty stomach. The rate of disappearance of alcohol from blood (beta-slope) was 12 mg/100 ml/h in the fed state and 15 mg/100 ml/h when subjects were fasted. The apparent volume of distribution of ethanol (Vd) was 0.65 l/kg (SD 0.07) for the empty stomach condition but exceeded unity when beer was ingested together with food. It seems that part of the dose of alcohol when consumed with food never reaches the systemic circulation.     

Revised equations allowing the estimation of the uncertainty associated with the Total Body Water version of the Widmark equation

Widmark calculations are the most commonly used alcohol calculations to estimate a) the amount of alcohol consumed based on blood alcohol concentration (BAC) and b) BACs at a set time after consumption of a known amount of alcohol. These calculations are vital in forensic casework. Previous work has demonstrated that using general error propagation-based equations the variability associated with alcohol calculations can be estimated, but these equations have only been determined for the volume of distribution version of the Widmark equation. However, recent investigations have shown that the total body water (TBW) version of the Widmark equation is more reliable than the version that utilizes the apparent volume of distribution of ethanol. To date, there is no general error propagation equation to determine the variability associated the TBW version of the Widmark equation. Using previously published studies of 185 individuals in which alcohol elimination rate (β) and ethanol's volume of distribution were determined, we have shown that there is a negative correlation (?0.247) between the alcohol elimination rate (β) and TBW. Using these data, we were able to produce equations allowing the estimation of the variability of the results calculated using the TBW version of the Widmark equation. This will allow forensic practitioners to give the best determination of the variability associated with Widmark calculations currently possible.     

The Contribution of Body Mass and Volume of Distribution to the Estimated Uncertainty Associated with the Widmark Equation

The Widmark equation is used forensically for the determination of the amount of ethanol (alcohol) that may have been consumed and also to determine the blood alcohol concentration (BAC) of an individual at a specific time. It is important to be able to estimate the uncertainty associated with Widmark equations. To date, there has been no detailed determination of contribution to the final uncertainty of Widmark calculations of the volume of distribution of ethanol (V_d), using anthropometric equations, or the contribution of an individual’s body mass. Using published data, published literature, and freedom of information data, we determined that the variability (%CV) associated with V_d was ~10% (Watson et al. and Forrest anthropometric equations) and that the %CV associated with estimated body mass was ~15% compared to ~3% when body mass was directly measured. These data allow an estimation of the overall uncertainty of Widmark calculations using general error propagation. The estimated total uncertainty for BAC calculations increased from ~11% (volume consumed) and ~22% (BAC) to ~19% (volume consumed) and ~37% (BAC) when using measured body mass compared to estimated body mass. These results demonstrate that forensic practitioners should be mindful of the increase in estimated uncertainty in calculated Widmark equation results when estimated body mass is used rather than measured body mass. These data further improve the knowledge around the uncertainty of results calculated with the Widmark equation.     

Estimating the uncertainty associated with Widmark's equation as commonly applied in forensic toxicology

No computation is performed more frequently by forensic toxicologists than that involving Widmark's equation. The equation is employed to estimate either the number of drinks consumed or the corresponding blood or breath alcohol concentration. Despite the wide use of Widmark's equation, rarely is an uncertainty estimate also provided. Estimates from Widmark's equation involve at least seven uncertain random variables. Uncertainty estimates are presented that rely on methods of general error propagation compared to a method developed by Widmark. Assuming reasonable variable and uncertainty estimates, the error propagation method yielded for N=10.4 drinks, a combined uncertainty (standard deviation) of 1.3 drinks (CV=12.3%). Similarly, estimating the blood alcohol concentration yielded for 0.120 g/100 ml, an uncertainty of 0.0255 g/100 ml (CV=21.2%). Widmark's uncertainty method yielded 1.6 drinks (CV=15.4%). The derivation of Widmark's uncertainty estimate is also presented, showing that he considered only rho and beta to be uncertain. Widmark estimates for the number of drinks should include a 2CV estimate of approximately 25% while the blood alcohol concentration estimate should include a 2CV estimate of approximately 42%. Including valid estimates of uncertainty should enhance the legal admissibility and confidence for Widmark estimations.     

The effect of storage at various temperatures on blood alcohol concentration

There is a paucity of data available on the effect of storage on blood alcohol concentration (BAC) at elevated temperatures. Changes in serum alcohol concentration (SAC) and BAC were studied. Serum samples spiked with alcohol in the presence or absence of preservative were stored at 26.7 °, 32.2 ° or 37.8 °C respectively. Serum alcohol concentrations were determined daily on days 1 through 14, and on days 21 and 35. Under these controlled conditions, no significant change in SAC was observed at the aforementioned temperatures. Whole blood samples submitted from outside agencies were initially analyzed (day 1), then stored for 35 days at different elevated temperatures before a second analysis. The average loss in BAC was 19.20 ± 15.6, 9.95 ± 5.7, and 15.60 ± 6.9% when the samples were stored at 26.7, 32.2 and 37.8 °C, respectively. The alcohol loss from whole blood samples may be attributed to chemical oxidation rather than to elevated temperatures. It is, therefore, concluded that a whole blood sample obtained from a living individual and stored in a locker, glove compartment or other environment where the temperature is elevated, may lose 10–19% of its alcohol content over 35 days of storage. On the other hand, when a serum or plasma sample is exposed to the same environment, no significant change in SAC was observed. The utility of this information is significant to the forensic toxicologist. The results of this study suggest that a whole blood sample analyzed after exposure to elevated temperature may have had, originally, a higher BAC.     

酒的种类对乙醇代谢动力学的影响

目的乙醇代谢动力学受诸多因素影响,关于酒的种类对其影响少见报道。方法本研究让志愿者在相同的饮酒时间内,饮用含相同乙醇量的啤酒、白酒,将所得数据用药代动力学计算程序DAS Ver1.0进行处理。结果乙醇的体内过程符合一级吸收、非线性消除、一室模型,权重为1。啤酒与白酒相比,吸收速度快,峰浓度高,达峰时间早,消除速度快。结论酒的种类对乙醇代谢动力学有影响,如果根据乙醇的代谢动力学规律来推测饮酒个体某一时刻的BAC,或根据BAC推测实际饮酒量,应该充分考虑到酒的种类对乙醇代谢动力学的影响。     

A study concerning the blood/breath alcohol conversion factor Q: concentration dependency and its applicability in daily routine

The conversion factor Q, obtained by division of blood alcohol concentration (BAC) by breath alcohol concentration (BrAC) is a widely discussed topic due to its great variance. By Austrian law, regulations frequently require an estimation of a corresponding BAC by a measured BrAC. It is known that Q depends among other things, on the alcohol kinetic state of the person being tested, which mathematically can be transformed to a dependency on the BrAC. Theoretically calculated Q values per BrAC level form a hyperbola shaped curve, thus decreasing with increasing BrAC values. Applying Austrian forensic standards for BAC and BrAC measurements, these calculations were verified in a study under practical conditions with BAC and BrAC data of 390 individuals. Q decreases from 2629 (+/- 455) for BrAC levels < 0.1 mg/l to 2229 (+/- 160) for a BrAC range of 0.4-0.5 mg/l and increases again to 2428 (+/- 124) for BrAC levels > 0.6 mg/l. Since these results were obtained under realistic practical conditions they can be directly applied in routine forensic expert opinion and can eliminate avoidable variances in the calculation of Q.     

法医DNA标准物质备选细胞STR等位基因片段长度的定值

目的 研究建立法医DNA标准物质备选细胞基因组STR基因座等位基因片段长度标准定值的方法.方法 利用有机法提取HPF和HSSM细胞基因组DNA并进行STR复合扩增,将产物进行电泳检测.利用Gene Mapper软件分析电泳结果,记录STR基因座等位基因的数值,并对目前我国公安系统应用较为广泛的DNATyperTM15、IdentifilerTM两种试剂盒扩增产物进行相应的DNA片段长度(bp)统计以及定值.结果 HPF为男性个体细胞,HSSM为女性个体细胞.HPF和HSSM细胞DNATyperTM15系统等位基因片段长度范围分别为126.26±0.05～367.53±0.20bp和125.33±0.07～370.08±0.17bp,IdentifilerTM系统等位基因片段长度范围分别为117.22±0.04～340.02±0.08bp和117.21±0.03～323.86±0.09bp.结论 对STR基因座等位基因片段长度进行标准定值,可为法医DNA标准物质提供有效的溯源途径.     

Evaluation of the Analytical Performance of a Fuel Cell Breath Alcohol Testing Instrument: A Seven‐Year Comprehensive Study

Abstract: Between 2003 and 2009, 54,255 breath test sequences were performed on 129 AlcoSensor IV–XL evidential instruments in Orange County, CA. The overall mean breath alcohol concentration and standard deviation from these tests was 0.141 ± 0.051 g/210 L. Of these test sequences, 38,580 successfully resulted in two valid breath alcohol results, with 97.5% of these results agreeing within ±0.020 g/210 L of each other and 86.3% within ±0.010 g/210 L. The mean absolute difference between duplicate tests was 0.006 g/210 L with a median of 0.004 g/210 L. Of the 2.5% of duplicate test results that did not agree within ±0.020 g/210 L, 95% of these had a breath alcohol concentration of 0.10 g/210 L or greater and 77% had an alcohol concentration of 0.15 g/210 L or greater. The data indicate that the AlcoSensor IV–XL can measure a breath sample for alcohol concentration with adequate precision even amid the effects of biological variations.     

过敏性休克豚鼠血浆咽喉肺组织中P物质的观测

目的探讨过敏性休克法医学鉴定的诊断指标。方法制备豚鼠过敏性休克的动物模型,应用放射免疫法测定其血浆中P物质浓度;免疫组化SABC法和BI-2000图像分析系统对咽喉和肺组织的P物质免疫反应进行染色观测,计算阳性指数(PI)。结果与对照组含量(87．70pg±7．60pg／μl)相比,过敏性休克豚鼠血浆中P物质含量 (131．01pg±18．93pg／μl)增加,其差异具有极显著意义(P<0．01);呼吸道内P物质免疫阳性反应增强,实验组咽喉和肺组织PI值分别为63．59±14．51和55．98±14．8,对照组咽喉和肺组织PI值分别为33．32±8．04和20．51±6．76, 两组差异具有极显著意义(P<0．01)。结论 P物质在过敏性休克豚鼠血浆浓度增加和呼吸系统组织中免疫阳性反应增强,可能有助于过敏性休克的法医病理学诊断。     

Measurement of Postmortem 1,5‐anhydroglucitol in Vitreous Humor for Forensic Diagnosis

In forensic diagnosis, postmortem blood glucose is known to be susceptible to change after death. However, the 1,5‐anhydroglucitol (1,5‐AG) concentrations in plasma and cerebrospinal fluid (CSF) reflect the mean blood glucose level for a short period of time. In this study, we compared the postmortem 1,5‐AG concentrations in vitreous humor and CSF in 47 subjects to evaluate the utility of this concentration in the vitreous humor for forensic diagnosis. The postmortem 1,5‐AG concentrations in vitreous humor (mean±SD: 20.2 ± 8.7 μg/mL) and CSF (16.8 ± 8.7 μg/mL) did not differ significantly and showed a strong correlation (r² = 0.87, p < 0.01). These results suggest that the vitreous humor 1,5‐AG concentration provides useful information on the antemortem blood glucose level, in addition to the HbA1c value and the CSF 1,5‐AG concentration.     

酒精在人体内的代谢动力学研究

将16名健康男性志愿者随机分为两组，分别按含酒精0．65g／kg和0．80g／kg体重的剂量给予酒精饮料，于酒后不同时间点采取静脉血样。用乙醇脱氨酶（ADH）氧化分析法测血样酒精浓度（BAC），所得浓度-时间数据经用药代动力学软件分析拟合。结果表明，酒精在人体内的代谢符合非线性消除伴一级吸收的一室开放模型。据此，作者建立了描述酒精在人体内动态变化规律的数学模型。经验证，该模型符合度良好，可用于司法实践。     

The Accuracy of Handheld Pre‐Arrest Breath Test Instruments as a Predictor of the Evidential Breath Alcohol Test Results

Drunk driving is a serious threat to public safety. All available and appropriate tools for curbing this threat should be employed to their full extent. The handheld pre‐arrest breath test instrument (PBT) is one tool for identifying the alcohol‐impaired driver and enforcing drunk driving legislation. A set of data was evaluated (n = 1779) where the PBT instrument was employed in drunk driving arrests to develop a multivariate predictive model. When maintained and operated by trained personnel, the PBT provides a reasonable estimate of the evidential test result within the relevant forensic range (95% prediction interval:  ± 0.003 g/210 L). ROC analysis shows that a multivariate model for PBT prediction of the evidentiary alcohol concentration above versus below the legal limit of 0.08 g/210 L has excellent performance with an AUC of 0.96. These results would be of value in evidential hearings seeking to admit the PBT results in drunk driving trials.     

血中酒精浓度的回推算研究

目的研究血中酒精浓度值（BAC值）的推算关系。方法对327位自愿受试者饮酒后测定其血中酒精时浓曲线进行分析,计算血中酒精清除率。结果血中酒精消除呈线性,327例血液中酒精消除线性相关系数为0.985±0.019,最小绝对值为0.98,最大绝对值1.000,消除斜率绝对值平均为（0.136±0.037）mg/mL/h,最小绝对值为0.075mg/mL/h,最大绝对值0.266mg/mL/h。结论血液中酒精浓度的推算可根据线性消除关系回推,血液中酒精浓度按照每小时下降0.10mg进行回推算。     

Evaluation of breath alcohol instruments II. In vivo experiments with Alcolmeter Pocket Model

The precision and accuracy of an Alcolmeter Pocket Model breath alcohol instrument have been investigated in experiments with human subjects under controlled conditions. The instrument response was zero in all tests with breath samples from alcohol-free subjects. The standard deviations of ethanol determinations in breath were ±0.0722 mg/ml during ethanol absorption and ±0.0416 mg/ml during ethanol elimination. The standard deviation during the elimination phase increased with ethanol concentration in the sample, being ±0.0416 mg/ml on average at a mean concentration of 0.420 mg/ml, corresponding to a coefficient of variation of 9.9%.The blood alcohol estimates using the Alcolmeter were somewhat too high during active absorption of ethanol, and too low during elimination, when a constant blood-breath alcohol ratio of 2100:1 was used to calibrate the instrument. During the elimination phase of ethanol kinetics and at a mean blood alcohol concentration of 0.50 mg/ml, the mean Alcolmeter result was 0.456 ± 0.169 mg/ml with 95% confidence, i.e. varying between 0.287 and 0.625 mg/ml 95 times out of 100 tests at this critical blood alcohol level.     

Proficiency Testing as a Basis for Estimating Uncertainty of Measurement: Application to Forensic Alcohol and Toxicology Quantitations

Abstract: While forensic laboratories will soon be required to estimate uncertainties of measurement for those quantitations reported to the end users of the information, the procedures for estimating this have been little discussed in the forensic literature. This article illustrates how proficiency test results provide the basis for estimating uncertainties in three instances: (i) For breath alcohol analyzers the interlaboratory precision is taken as a direct measure of uncertainty. This approach applies when the number of proficiency tests is small. (ii) For blood alcohol, the uncertainty is calculated from the differences between the laboratory’s proficiency testing results and the mean quantitations determined by the participants; this approach applies when the laboratory has participated in a large number of tests. (iii) For toxicology, either of these approaches is useful for estimating comparability between laboratories, but not for estimating absolute accuracy. It is seen that data from proficiency tests enable estimates of uncertainty that are empirical, simple, thorough, and applicable to a wide range of concentrations.     

Comparison of ethyl glucuronide in hair with phosphatidylethanol in whole blood as post-mortem markers of alcohol abuse

Ethyl glucuronide (EtG) is a direct metabolite of ethanol and has been used as a marker of alcohol abuse in both urine and hair. This study investigated the value of EtG testing in post-mortem hair for diagnostic improvement of alcohol abuse in forensic medicine. Material from 70 consecutive medico-legal autopsies was collected in accordance with the recommendations on ethics by the Swedish National Board of Forensic Medicine. A method for determination of EtG in hair samples was developed using ultra performance liquid chromatography/electrospray tandem mass spectrometry (UPLC/ESI-MS/MS; LOQ, 2.5 pg/mg). The result of the EtG analysis was compared with the findings of phosphatidylethanol (PEth) in femoral whole blood, as measured by high performance liquid chromatography with an evaporative light-scattering detector (HPLC-ELSD; LOQ, 0.22 micromol/l). Evaluation of liver histology and anamnestic evidence of alcohol abuse of the deceased were taken in consideration for the interpretation. Measurable levels of EtG were present in 49 of the 70 autopsy cases whereas PEth was present in 36. Thirty-nine cases had EtG levels above the cutoff limit (> or = 30 pg/mg) compared with 29 for PEth (> or = 0.7 micromol/l). Fifteen cases had EtG as exclusive indicator for alcohol abuse compared with four cases for PEth. These findings suggest that measurements of EtG in hair may provide improved diagnostic information on alcohol abuse, due to a long retrospective time-window for detection and stability of EtG in hair in the decaying cadaver. However, an EtG level below the cutoff does not completely exclude previous alcohol abuse.     

Forensic Analysis of Explosives Using Isotope Ratio Mass Spectrometry (IRMS)—Part 1: Instrument Validation of the DELTAplusXP IRMS for Bulk Nitrogen Isotope Ratio Measurements

Abstract: A significant amount of research has been conducted into the use of stable isotopes to assist in determining the origin of various materials. The research conducted in the forensic field shows the potential of isotope ratio mass spectrometry (IRMS) to provide a level of discrimination not achievable utilizing traditional forensic techniques. Despite the research there have been few, if any, publications addressing the validation and measurement uncertainty of the technique for forensic applications. This study, the first in a planned series, presents validation data for the measurement of bulk nitrogen isotope ratios in ammonium nitrate (AN) using the DELTA^plusXP (Thermo Finnigan) IRMS instrument equipped with a ConFlo III interface and FlashEA? 1112 elemental analyzer (EA). Appropriate laboratory standards, analytical methods and correction calculations were developed and evaluated. A validation protocol was developed in line with the guidelines provided by the National Association of Testing Authorities, Australia (NATA). Performance characteristics including: accuracy, precision/repeatability, reproducibility/ruggedness, robustness, linear range, and measurement uncertainty were evaluated for the measurement of nitrogen isotope ratios in AN. AN (99.5%) and ammonium thiocyanate (99.99+%) were determined to be the most suitable laboratory standards and were calibrated against international standards (certified reference materials). All performance characteristics were within an acceptable range when potential uncertainties, including the manufacturer’s uncertainty of the technique and standards, were taken into account. The experiments described in this article could be used as a model for validation of other instruments for similar purposes. Later studies in this series will address the more general issue of demonstrating that the IRMS technique is scientifically sound and fit‐for‐purpose in the forensic explosives analysis field.