Editing Blood alcohol content (section)

=== By intake ===
{{Main|Pharmacology of ethanol#Modeling}}
Blood alcohol content can be quickly estimated by a model developed by Swedish professor Erik Widmark in the 1920s.<ref name=Ed>{{cite web |last1=Ed Kuwatch |title=Fast Eddie's 8/10 Method of Hand Calculating Blood Alcohol Concentration: A Simple Method For Using Widmark's Formula |url=http://www.dui-law.com/810art.htm|archive-url=https://web.archive.org/web/20031202155933/http://www.dui-law.com/810art.htm |archive-date=2003-12-02 }}</ref> The model corresponds to a [[pharmacokinetic]] single-compartment model with instantaneous absorption and [[zero-order kinetics]] for elimination. The model is most accurate when used to estimate BAC a few hours after drinking a single dose of alcohol in a fasted state, and can be within 20% [[Coefficient of variation|CV]] of the true value.<ref>{{cite conference |last1=Zuba |first1=Dariusz |last2=Piekoszewski |first2=Wojciech |title=Uncertainty in Theoretical Calculations of Alcohol Concentration |book-title=Proc. 17th Internat. Conf. on Alcohol, Drugs and Traffic Safety |date=2004 |url=https://www.researchgate.net/publication/255499090}}</ref><ref>{{cite journal |last1=Gullberg |first1=Rod G. |title=Estimating the uncertainty associated with Widmark's equation as commonly applied in forensic toxicology |journal=Forensic Science International |date=October 2007 |volume=172 |issue=1 |pages=33–39 |doi=10.1016/j.forsciint.2006.11.010 |pmid=17210238}}</ref> It is not at all realistic for the absorption phase, and is not accurate for BAC levels below 0.2 g/L (alcohol is not eliminated as quickly as predicted) and consumption with food (overestimating the peak BAC and time to return to zero).<ref>{{cite journal |last1=Searle |first1=John |title=Alcohol calculations and their uncertainty |journal=Medicine, Science and the Law |date=January 2015 |volume=55 |issue=1 |pages=58–64 |doi=10.1177/0025802414524385 |pmid=24644224|pmc=4361698 }}</ref><ref name="Jones2011">{{cite journal |last1=Jones |first1=AW |title=Pharmacokinetics of Ethanol - Issues of Forensic Importance. |journal=Forensic Science Review |date=July 2011 |volume=23 |issue=2 |pages=91–136 |pmid=26231237 |url=https://www.researchgate.net/publication/280602837}}</ref> The equation varies depending on the units and approximations used, but in its simplest form is given by:<ref>{{cite journal |last1=Maskell |first1=Peter D. |last2=Jones |first2=A. Wayne |last3=Heymsfield |first3=Steven B. |last4=Shapses |first4=Sue |last5=Johnston |first5=Atholl |title=Total body water is the preferred method to use in forensic blood-alcohol calculations rather than ethanol's volume of distribution |journal=Forensic Science International |date=November 2020 |volume=316 |pages=110532 |doi=10.1016/j.forsciint.2020.110532|pmid=33099270 |s2cid=224966411 }}</ref>
:<math>EBAC = \frac{A}{V_d}-\beta\times T</math>
where:
*{{mvar|EBAC}} is the estimated blood alcohol concentration (in g/L)
*{{mvar|A}} is the mass of alcohol consumed (g).
*{{mvar|T}} is the amount of time during which alcohol was present in the blood (usually time since consumption began), in hours.
*{{mvar|β}} is the rate at which alcohol is [[Elimination (pharmacology)|eliminated]], averaging around 0.15 g/L/hr.<ref>{{cite journal |last1=Jones |first1=Alan Wayne |title=Evidence-based survey of the elimination rates of ethanol from blood with applications in forensic casework |journal=Forensic Science International |date=July 2010 |volume=200 |issue=1–3 |pages=1–20 |doi=10.1016/j.forsciint.2010.02.021|pmid=20304569 }}</ref>
*{{mvar|V<sub>d</sub>}} is the [[volume of distribution]] (L); typically body weight (kg) multiplied by 0.71 L/kg for men and 0.58 L/kg for women<ref name="MaskellVd">{{cite journal |last1=Maskell |first1=Peter D. |last2=Heymsfield |first2=Steven B. |last3=Shapses |first3=Sue |last4=Limoges |first4=Jennifer F. |title=Population ranges for the volume of distribution ( V_d ) of alcohol for use in forensic alcohol calculations |journal=Journal of Forensic Sciences |date=September 2023 |volume=68 |issue=5 |pages=1843–1845 |doi=10.1111/1556-4029.15317|pmid=37345356 |doi-access=free }}</ref><ref name="MaskellMass">{{cite journal |last1=Maskell |first1=Peter D. |last2=Cooper |first2=Gail A. A. |title=The Contribution of Body Mass and Volume of Distribution to the Estimated Uncertainty Associated with the Widmark Equation |journal=Journal of Forensic Sciences |date=September 2020 |volume=65 |issue=5 |pages=1676–1684 |doi=10.1111/1556-4029.14447|pmid=32421216 |s2cid=218677989 }}</ref> although estimation using TBW is more accurate.<ref>{{cite journal |last1=Maskell |first1=Peter D. |last2=Jones |first2=A. Wayne |last3=Heymsfield |first3=Steven B. |last4=Shapses |first4=Sue |last5=Johnston |first5=Atholl |title=Total body water is the preferred method to use in forensic blood-alcohol calculations rather than ethanol's volume of distribution |journal=Forensic Science International |date=November 2020 |volume=316 |pages=110532 |doi=10.1016/j.forsciint.2020.110532|pmid=33099270 |s2cid=224966411 }}</ref>

A standard drink, defined by the WHO as 10 grams of pure alcohol,<ref name="WHO_AUDIT_EN">{{Cite web|url=https://apps.who.int/iris/bitstream/handle/10665/67205/WHO_MSD_MSB_01.6a.pdf?sequence=1&isAllowed=y|title=AUDIT The Alcohol Use Disorders Identification Test (Second Edition)|date=2001|website=WHO|format=pdf|access-date=2020-01-02}}</ref> is the [[Standard_drink#Definitions_in_various_countries|most frequently used measure in many countries]]. Examples:
* An 80&nbsp;kg man drinks 20 grams ethanol. After one hour:
<math display="block"> EBAC = 20/(0.71 \cdot 80) - (0.148 \cdot 1) \approx 0.204 \text{g/L} = 0.0204% \text{BAC}</math>
* A 70&nbsp;kg woman drinks 10 grams of ethanol. After one hour:
<math display="block"> EBAC = 10/(0.58 \cdot 70) - (0.156 \cdot 1) \approx 0.090 \text{g/L} = 0.0090% \text{BAC}</math>

In terms of [[fluid ounce]]s of alcohol consumed and weight in pounds, Widmark's formula can be simply approximated as<ref name=Ed/>
:<math>EBAC=8\times\text{fl oz}/\text{weight in pounds}-\beta\times T</math>
for a man or
:<math>EBAC=10\times\text{fl oz}/\text{weight in pounds}-\beta\times T</math>
for a woman, where EBAC and {{mvar|β}} factors are given as g/dL (% BAC), such as a {{mvar|β}} factor of 0.015% BAC per hour.<ref name=Ed/>