Forensic Pharmacokinetics of Blood Alcohol Concentration (BAC)
Blood Alcohol Concentration (BAC), also termed Blood Alcohol Content or blood ethanol concentration, measures the mass of ethyl alcohol (ethanol, $\text{C}_2\text{H}_5\text{OH}$) present in a specified volume of blood, conventionally expressed as grams of ethanol per $100\text{ mL}$ of blood (grams percent, $\% \text{w/v}$). In clinical toxicology and forensic traffic jurisprudence, BAC serves as the universal objective metric of physiological alcohol impairment.
The Classical Widmark Kinetic Equation
In 1932, Swedish forensic scientist Erik M. P. Widmark formulated the foundational pharmacokinetic single-compartment model predicting blood ethanol absorption and elimination:
$$\text{BAC}(t) = \left[ \frac{A}{W \cdot r} \times 100 \right] - (\beta \cdot t)$$
Where the variables denote:
- $A$: Total mass of pure ethanol ingested, measured in grams ($\text{g}$).
- $W$: Total body mass of the subject, measured in grams ($\text{g}$). ($1\text{ lb} \approx 453.592\text{ g}$, $1\text{ kg} = 1000\text{ g}$).
- $r$: Gender-specific Widmark volume of distribution factor ($\text{L/kg}$ or unitless ratio), quantifying the fraction of total body weight consisting of aqueous tissue into which alcohol dissolves.
- $\beta$: Metabolic elimination rate of ethanol from the bloodstream per hour (linear clearance rate, typically $\beta \approx 0.015\%\text{ per hour}$).
- $t$: Total elapsed time in hours since the onset of alcohol consumption ($t \ge 0$).
Gender Divergence in Volume of Distribution ($r$)
Ethanol is a polar, water-soluble hydrophilic molecule that dissolves readily in aqueous body water but does not partition into lipid adipose tissue. Because average female body composition exhibits a higher percentage of adipose tissue and lower total body water ($TBW$) relative to males of identical body weight, Widmark established distinct distribution constants:
- Male Distribution Constant: $r_{\text{male}} \approx 0.68$ (range $0.60 - 0.75$).
- Female Distribution Constant: $r_{\text{female}} \approx 0.55$ (range $0.50 - 0.62$).
Consequently, an identical mass of alcohol consumed by a female will yield a substantially higher peak BAC than in an identically weighted male.
Standard Drink Quantification
Under United States public health guidelines, one standard drink contains exactly $14.0\text{ grams}$ ($0.6\text{ fluid ounces}$ or $17.7\text{ mL}$) of pure ethanol:
- Beer: $12\text{ fl oz}$ ($355\text{ mL}$) of standard lager at $5.0\%\text{ ABV} = 14.0\text{ g ethanol}$.
- Wine: $5\text{ fl oz}$ ($148\text{ mL}$) of table wine at $12.0\%\text{ ABV} = 14.0\text{ g ethanol}$.
- Distilled Spirits: $1.5\text{ fl oz}$ ($44\text{ mL}$) shot of $80\text{-proof}$ liquor at $40.0\%\text{ ABV} = 14.0\text{ g ethanol}$.
Hepatic Zero-Order Elimination Rate ($\beta$)
Unlike most pharmaceutical xenobiotics that clear via first-order kinetics (proportional to concentration), ethanol metabolism in the liver follows zero-order (Michaelis-Menten saturated) kinetics at clinically relevant blood concentrations. The primary hepatic enzyme, alcohol dehydrogenase ($\text{ADH}$), becomes fully saturated at low concentrations ($\text{BAC} \ge 0.02\%$), resulting in a constant linear clearance rate:
$$\beta_{\text{average}} \approx 0.015\%\text{ to } 0.017\%\text{ BAC per hour}$$
To determine the post-drinking duration required to achieve complete physiological sobriety ($\text{BAC} = 0.000\%$):
$$t_{\text{sober}} = \frac{\text{BAC}_{\text{peak}}}{\beta} = \frac{\text{BAC}_{\text{peak}}}{0.015}$$
Clinical & Legal Impairment Spectrum
Neurochemical depression of the central nervous system ($\text{GABA}_A$ receptor agonism and $\text{NMDA}$ glutamate inhibition) correlates directly with systemic BAC:
- $0.020\% - 0.039\%$: Mild euphoria, relaxation, minor loss of fine motor coordination.
- $0.040\% - 0.079\%$: Lowered inhibitions, delayed braking reaction times, impaired peripheral vision and divided attention.
- $0.080\%$ (US Legal Limit): Gross motor coordination loss, slurred speech, marked sensory processing impairment. Driving is illegal in all 50 US states.
- $0.150\% - 0.250\%$: Severe dysphoria, motor ataxia, blackout risk, vomiting.
- $\ge 0.350\%$: Critical risk of fatal respiratory depression, coma, and autonomic arrest.