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16 January 2006

Blood alcohol content calculations

How much can you drink before you exceed the legal limit? And could it be that the morning after you are not merely hung over, but still drunk?

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How much can you drink before you exceed the legal limit? And could it be that the morning after you are not merely hung over, but that the alcohol level in your blood is still so high that you might still be drunk? Dr Izak Loftus, forensic and anatomical pathologist from the Pathcare-group explains how these calculations work.

When you drink, your blood alcohol levels are not skyhigh within minutes. When alcohol is consumed and the blood alcohol concentration (BAC) is constantly monitored, it is apparent that there is a phase where the blood alcohol levels increase rapidly, and that it is followed by a phase in which the blood alcohol levels drop again.

During the first phase, while the blood alcohol levels are still increasing, the alcohol is being absorbed more quickly from the intestinal tract into the bloodstream, than when it is being eliminated by the liver from the bloodstream. The blood alcohol levels reach a peak and then decrease in the second phase, when the elimination through the liver takes place more quickly than the absorption.

Different types of patterns are seen in different people, and also in the same person at different times, when graphically depicted. It is because of these known variations that may exist, that the calculations should not be oversimplified or treated dogmatically.

A few basic formulae and calculations are important if you want to calculate how much you can drink. But I need to emphasise at the outset that there may be many exceptions to the rule. This is therefore merely a rule of thumb, and it might not be very accurate, writes Dr Loftus.

In order to calculate how much you can drink, you need to consider several calculations, such as the amount of alcohol in a drink, how much alcohol you are consuming, and how quickly alcohol is metabolised by the body.

Calculation 1: The amount of alcohol in a drink
As a rule of thumb it can be accepted that a glass of wine, a beer and a single unit of spirits contain the same amount of alcohol, namely 10 grams.

Sometimes it is necessary to calculate more accurately how much alcohol there is in a specific drink.

If the strength of a drink is expressed as a percentage of total volume, the amount of alcohol in grams can be calculated by considering the specific weight of the alcohol. For example, for the calculations below, a 100 ml glass of white wine with an alcohol content of 12% was used.

100 ml of white wine will contain 12 ml of alcohol. The specific weight of alcohol is 0,79, therefore 1 ml of alcohol will weigh 0,79 g. The alcohol content of 100 ml of white wine, 12 X 0,79 will be 9,48 g.

Calculation 2: The amount of alcohol that you have consumed (the Widmark formula)
A Swede, Erik Widmark, created a formula that assists us in determining how much alcohol a person has consumed. This formula is controversial, and several variations have been suggested. However, I do believe that the original does provide a guideline. It is important to remember that this formula is only useful after the completion of alcohol absorption, and when equilibrium has been reached between blood and body tissue.

The Widmark formula is used to determine in grams the specific amount of alcohol consumed by an individual to cause a specific alcohol concentration within a specific time. It is important to remember that this calculation does not refer to any alcohol that has already been eliminated, or any alcohol that has been consumed, but may not yet be absorbed by the body.

The formula is as follows: A = p x c x r, where
A = The amount of alcohol in grams in the body at a given time to be able to cause the particular blood alcohol concentration,
p = The mass of the person in kilograms,
c = The blood alcohol concentration in g/1000 g blood. It is determined by recalculating the BAC (g/100ml) to g/100g, and then multiplying it by 10.
r = The Widmark or distribution factor.

BAC is expressed in South Africa with regards to a specific blood volume (100 ml) With the recalculation into a specific blood volume, the specific weight of the blood (1,056) must be considered. 100 g of blood represents 94,7 ml of blood, or expressed differently, 100 ml blood weighs 105,6 g.

The reason why this formula must be multiplied by a factor of 10, is a result of its European origin. In Germany, the alcohol levels are expressed as promille, in other words g/1000 l. In order to express c in g/1000 g, the BAC (g/100ml), is multiplied by 10 and divided by 1,056.

Alcohol is water-soluble; the water content of any organ or tissue will therefore determine how much alcohol can dissolve in it. Tissue with a high water content can have more alcohol dissolved into it. Men have, or are supposed to have, a higher muscle mass than women. Women, on the other hand, have a higher fat content. This is the reason why, if all other factors were theoretically equal, a man would have a lower blood alcohol concentration than a woman, after consuming a similar amount of alcohol. This factor is also known as the distribution factor, or “r” factor in the Widmark formula. It varies between 0,5 and 0,9, but we usually accept 0,7 for men and 0,6 for women.

Because the specific weight factor (1,056) plays such a small role (especially in a formula that is already subject to so many variables), it is often left out and the formula is used as follows: A = p x c x r x 10 (with the BAC expressed in g/100 ml). For the rest of the description I actually use the complete formula as set out above.

As an example, we use a man with a mass of 70 kg and a blood alcohol level of 0,08 g/100 ml. Based on the Widmark formula, this particular blood level represents the following amount of alcohol that has been consumed:

A = p x c x r
= 70 x (0,08 x 10/1,056) x 0,7
= 37,12 g
This is therefore roughly about 4 units

Calculation 3: How quickly the body can break down alcohol
About 85-90% of alcohol is metabolised by the liver. The enzyme alcohol dehydrogenase (ADH), plays a very important role in this process. The products produced by this process, includes acetyldahide, one of the causes of a “hangover”.

The rest of the alcohol is eliminated unchanged through the lungs, the kidneys and sweat. Alcohol is eliminated at a constant tempo. The tempo of elimination is between 0,01 tot 0,02 g/100 ml per hour. Usually the average value (0,015 g/100 ml/h), is used and is known as the ß60 value.

The speed of the elimination is more or less constant for a given individual and is not significantly affected by cold, exercise, sleep or any other factors, including medicines or injuries. Liver diseases also do not have a significant effect, except in a late stage when the patient is experiencing liver failure.

The concentration of blood alcohol also does not influence the tempo of elimination. This tempo will be constant, regardless of whether the BAC is 0,15 or 0,25 g/100ml.

In the case of someone who parties until the early morning hours, and went to sleep at two o’ clock in the morning with a blood alcohol concentration of 0,2 g/100 ml, it means that if he drives to work at seven o’çlock in the morning, his alcohol levels will still be far above the legal limit.

C = Ci - (ß60 x t),
Where
Ci = concentration at time of going to bed at 02:00,
C= concentration at time of driving to work at 07:00
t = time duration in hours between these two occurrences
ß60 = 0,015 g/100 ml/h.

We therefore find:

C = Ci - (ß60 x t)
= 0,20 g/100 ml - (0,015 g/100 ml/hx5h)
= 0,20 g/100 ml - 0,075 g/100 ml
= 0,125 g/100 ml

We accept that no alcohol was consumed after 02:00 in the morning. The person may ascribe many of his symptoms to a “hangover”, but in effect he is still under the influence – with a BAC of 0,125 g/100 ml!

Sleep has no effect on the breakdown of the alcohol. The only advantage is that it probably prevents the person from landing in dangerous situations. The fact that he has rested, as well as the Mellanby effect, probably make him appear and feel more sober.

Maybe as good citizens it is more important to take a look at how many grams of alcohol the body can break down in an hour. Let us again take a man weighing 70 kg, and we assume his alcohol level decreases by 0,015 g/100ml every hour. Or differently put, in one hour he eliminates (A) alcohol in grams by:

A = p x c x r
= 70 x (0,015 x10/1,056) x 0,7
= 7,0 g alcohol or almost one glass of wine

I cannot emphasise enough that these are merely guidelines and should be interpreted as such. If you want to sit and drink while clutching a calculator, that’s your decision, but then maybe you should ask yourself whether it might not be better not to drink anything before you get in behind the steering wheel.

Dr Izak Loftus, forensic and anatomical pathologist, Pathcare-group, for Health24. (January, 2006)

 
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