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Thaksaphon Thamarangsi

BAC and Widmark’s Formula

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Basic knowledge (1) • Alcohol: Ethanol vs Methanol• Metabolism of alcohol • Effect of alcoholic beverages on Central Nervous

System– Intoxication ---- Acetaldehyde– Dehydration – Hypoglycemia– Transient Vitamin B deficiency

• Blood alcohol concentration (BAC)• Blood-Breath-Urine

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What determines BAC?

• Let’s discuss

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Basic knowledge (2)

• Unit of wt 1 kg =1000 gm, 1 gm= 1000 mg• Unit of Volume 1 L = 10 dl =1000 ml• Unit of BAC

– weight / volume: mg/dl = 1000 * g/dl = 1000* g%/ml– Wt/wt: mg/ 100 mg of blood

• Beverage degree: what does it mean 5% alcohol content?

• D=M/V or M=V x D• Density of ethanol = 0.79 or 0.8

Concentration? (Practice 1: 0.1 kg of NaCl in 2 Liters of H2O , Conc in

mg/dl=?) Answer= 5000 mg/dl

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ndPractice 2-3

Practice 2: how many grams of ethanol in 1 bottle (0.75 L=75 CL=750 ml) of Black Label (42%)

Answer (248.9 gm)

Practice 3: Average Thai male youth drink 118 gm per drinking day, calculate this amount in terms of how many bottle (0.63 L) of Chang beer (6.4%) .

Answer (3.7 bottle)

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Basic knowledge(3)

• Male vs Female • Does alcohol equally distribute through

our body?• Is alcohol eliminated (from our body) at

constant rate ?

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Adapted from Wilkinson et al., Journal of Pharmacokinetics and Biopharmaceutics5(3):207-224, 1977

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ndEric Widmark

• N = f(W, r,Ct ,β , t, z)

N = amount consumed W = body weight

r = the volume of distribution (a constant)Ct = blood alcohol concentration (BAC)β = the alcohol elimination rate t = time since the first drink

z = the fluid ounces of alcohol per drink

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• N = Wr(C t + βt) 08. z

N = the number of drinks consumed W = body weight in ounces

r = volume of distribution (a constant relating the distribution of water in the body in L/Kg)Ct = the blood alcohol concentration (BAC) in Kg/Lβ = the alcohol elimination rate in Kg/L/hr t = time since the first drink in hours

z = the fluid ounces of alcohol per drink 08 08. = the density of ethanol ( . oz. per flui

d ounce)

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Widmark’s formula BAC = fully absorbed conc. - eliminated conc.Fully absorbed = unit = mg/dl= wt of ethanol consumed / (volume of body that

can hold alcohol)=

R= 0.68 for male , 0.55 for female Blood density =1.055

=

0.79 x Volume of ethanol

Body weight x R

Blood Density[ ]

0.79 x Volume of ethanol

Body weight x 0.68 (0.55)

1.055[ ]

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ndUnit Unit Unit

Fully absorbed = unit = mg/dl

0.79 x Volume of ethanol (ml)

Body weight (kg) x R

1.055[ ]

Then x 100 to be in mg/dl

0.79 x Volume of ethanol (ml)

Body weight (kg) x R

1.055[ ]

= gram / L =1000 mg / 10 dl=100 mg/dl

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ndPractice 4-5

Practice#4: A young lady (45 kg) rapidly consumed 3 bottles (630 ml) of Heineken beer (5%), what us her maximum BAC?

• Answer 318.22 mg/dl

Practice#5: A man of 70 kg consumed 325 ml of 40% distilled spirits

• Answer 227.6 mg/dl

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Useful formula Elimination rate = Time x Elimination rate

(Widmark’s Beta)

Beta = 0.017 % (0.010-0.024)

In another term = 15 - 17 mg/dl

Practice 6: how many hour would the subject in Practice 4, 5 eliminate all alcohol?

Answer (18.7 hours, 13.4 hours)

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Useful formula Elimination rate = Time x Elimination

rate (Widmark’s Beta)

BAC =0.79 x Volume of ethanol

Body weight x R

Blood Density[ ]

- Hour x Elim rate

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Practice 8

• An RTA injured man (65 kg) came to ER, time of accident 23.30, Breath test at 24.00 showed BAC =40.06 what is the BAC at the time of crash?

• Answer 48.56 mg/dl

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Practice 9

• An RTA injured man (65 kg) came to ER at 24.00, time of accident 23.30, reporting drinking of 2 cans (335 ml) of Leo beer (6%) between 21.00-23.00 (regularly & equally consumed over consumption period), what is the BAC at the time of crash?

• Answer 48.56 mg/dl