Estimation of blood alcohol concentration (BAC)

A case was presented of a young man who engaged in a bout of binge drinking.

"A.M., 22 year old Indian student of a private college, received news that his childhood sweetheart wanted to end their relationship.

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In a fit of depression, he bought a bottle of vodka, retreated to his hostel room, and sometime between 8pm to midnight he ingested about two thirds of a bottle (1L) of vodka. His room-mate who was out had spoken to him over the phone at 1130pm and had found him incoherent. When he arrived back to the hostel at 0045am, he found A.M. unconscious, and called for an ambulance."

The question is whether we can estimate the blood alcohol level when he was found. What do we know, and what assumptions can we make?

In this case, we may assume he consumed about 640mLs of vodka. The equivalent in terms of cans of beer can be found here, and is approximately 16.5 cans of beer. If we can make assumptions about his volume of distribution (body weight, BMI), and about the bioavailability (0.8), we can begin to estimate the possible maximum BAC, as well as the BAC at any time we are interested in, if consumption and absorption were relative rapid.

The interactive graph here allows you to visualize the BAC-time profile following binge drinking. 

The two models (mixed order, and zero order) estimates that at the time he was found, BAC might have been about 3.4 mg/mL and 2.7 mg/mL, respectively. Both these estimates are above the legal limit for driving and consistent with severe degree of intoxication (see Chart). From the plots we can also estimate when he was likely to rouse, and recover from the intoxication.

Back extrapolation of blood alcohol concentrations - a forensic exercise

A case was presented of an alleged rape of an woman intoxicated with alcohol. The question was how to back extrapolate from a measure blood sample taken a number of hours after the alleged rape to the time of the alleged rape. The case is reproduced here for discussion:

A 33 year old Chinese bar hostess (45kg, slim built), drank heavily from about 7pm on eve of public holiday. Began to feel sick, and drowsy at about 10pm. Vomited after last drink at about 11pm.

Some well meaning friends brought her to hotel room where she passed out.

At about 1am, the accused found her unconscious and took advantage of her.

She roused at about 1pm next day. Was able to collect her thoughts, inferred what had happened, called friends, and reported to police at about 4pm when blood sample for alcohol was obtained. Sample was 0.4mg/mL.

The simplest method is to assume that alcohol elimination follows zero order kinetics over the concentration range that are relevent here. The generally accepted 95% confidence interval for the beta-slope of elimination is 0.09 - 0.29 mg/mL per hour. Since the alleged rape occured 15 hours prior to the blood sample, the expected blood alcohol concentration (BAC) concentration at the time of the alleged rape will be approximately 0.4mg/mL + (15 hours x the beta slope). Therefore, depending on whether you apply the lower or higher boundaries of the 95% confidence interval, you will obtain BAC of either 0.4 + (15 x 0.09) or 0.4 + (15 x 0.29). The 95% confidence interval for the expected BAC at the time of the alleged rape would therefore be 1.75mg/mL to 4.75mg/mL. These are concentrations consistent with a fairly extreme level of intoxication and impairment of judgement.

The above is using a simple back-extrapolation method based on zero order alcohol kinetics. To try a graphical method of back extrapolation using a mixed zero to first order model, you can  go here. 

To view the correlation between BAC and cognitive degradation, please go here.

Genetic polymorphism in Oct1.... and metformin exposure

Global genetic variation in select opiate metabolism genes

Global genetic variation in select opiate metabolism genes...

Ethanol elimination kinetics: a zero- to first order approach

Ethanol is primarily metabolized in the body by alcohol dehydrogenase to acetaldehyde. This is a very low Km reaction, so at most alcohol concentrations achieved after social drinking, it is very often assumed to obey a near zero order type of elimination kinetics.

In reality however, ethanol elimination kinetics, like every other drug follows a zero- to first order type of elimination profile. The above concentration-time curve illustrates the elimination kinetics from very high to very low ethanol concentrations.

During the zero order phase, there is a relatively fixed rate of ethanol elimination (NB. not elimination rate constant), but becomes clearly exponential at much lower concentrations. 

All this might be merely of academic interest if not for the fact that ethanol concentrations are very often back-extrapolated to a prior time (e.g. time of an accident or assault) because of forensic investigations. If the wrong model is used, the back-extrapolation can be quite erroneous.

Most often the back-extrapolations have been simplistically done assuming a zero order model, applying a fixed rate of elimination. We can see from the plot below, that the use of a zero order model, when the measured concentration is relatively low (less than 0.1 mg/mL) can lead to significant over-estimates of a prior concentration.

Is drug clearance a pharmacokinetic constant?

We of course know that the clearance of a drug, regardless of metabolic or renal, may be affected by various environmental and physiologic changes, but from a pharmacokinetic model point of view, we generally regard the Clearance for an individual to be a relative constant,.... as long as the drug 'exhibits linear or first order kinetics'.

In reality, this is only a convenient though fallacious assumption. In reality, Clearance is always concentration dependent. The question is how much, or how little?

Regardless of the processes involved, clearance can be represented by the expression Vmax/(Km+C), where C is the concentration of drug, the Vmax and Km are the rate max and concentration at 0.5Vmax respectively. From the expression it is obvious that Clearance is always concentration dependent. It is only fixed at the extreme ends of the range, where either C = 0, when Clearance becomes the 'intrinsic Clearance', or at the other extreme where concentration is infinitely high.

The maximum concentration-dependence is seen when the concentrations are approximately 0.1Km to 10Km, when there is a 'linear' relationship between Clearance and concentration. This is the range where we empirically label the kinetics as being 'zero-order'. Outside of this range, particularly where the concentrations are less than 0.1Km, the concentration dependance reduces towards a minimum.

So Clearance is always concentration dependent. Most therapeutic drug concentrations are in the range that is fairly low compared to the Km of the elimination processes (or we hope they are), so we comfort ourselves in being able to make the assumption that the drug pharmacokinetic behaviour is consistent with first order kinetics. But this is merely a convenient assumption. Most drugs are likely show various degrees of a mixed first to zero order pharmacokinetic behaviour.

A minority of drugs tend towards an overtly zero order behaviour, e.g. ethanol, omeprazole, phenytoin...... In the next post, we will examine the pharmacokinetic behaviour of one such drug, ethanol.

Effect of Vd change on pharmacokinetic parameters

With the interactive graph provided in the previous post you can vary the body weight by using the slider. Here, simplistically, the body weight directly changes the volume of distribution, so effectively the slider just changes the Vd.

What you will observe is that as you change the body weight, the half-life changes, and correspondingly, the time to reach steady state. The accumulation index also changes, because it is affected by the ratio of half-life/dose interval. The AUC and steady state concentrations remain unchanged because these are affected by Clearance and not Vd. The peaks and troughs changes, and these may affect the efficacy-toxicity balance of the dosage regimen if either efficacy or toxicity is affected by peaks or troughs.

In the display above, the body weight was altered from 70kg to 140kg. The half-life and time to reach steady state both corresponding doubled. While the AUC remained unchanged, the peaks have been lowered while the trough has increased. Whether the dosage regimen needs to be adjusted will depend on the therapeutic ratio of the drug, and the therapeutic objectives.