The situation is definitely an extremely complex one, and you should probably forget about having an exact equation to define it.
When talking about the effects of a substance on the organism there are several factors to take into account. These are generally put together under the term pharmacodynamics.
Some of the factor to take into account are:
- The dose of the substance
- The route of administration
- The metabolism of the substance
- The target organ
The problem is, not all ethanol you drink will go to the brain, and it will not necessarily go there immediately, or all at the same time. All of this will change the effects on the brain. Also, there are several confounding factors, some of which I have tried to list.
I have summarized here a few information about ethanol metabolism, taken mostly from Principles of Forensic Toxicology - Chapter 10 by Barry Levine and Yale H. Caplan
Ethanol is normally taken through drinking, which means that it will have to pass through the gastrointestinal (GI) tract (i.e. stomach and intestine) before getting into the bloodstream. This route permits practically 100% of absorption of ethanol in the body, with the major site of absorption being the small intestine, absorbing ~75% of a dose of ethanol. The rest will be absorbed in the stomach and in the other parts of the intestine.
The absorption in the GI tract is dependent on the type of beverage: for instance carbonated alcoholic beverages are absorbed faster than "plain" ones.
The alcohol content also is important: a very diluted drink is absorbed slower than one with 10-30% of ethanol, as the latter will generate a bigger concentration gradient between the GI tract and the circulation, so it will diffuse faster. However, >30% ethanol will enhance mucus formation, which will slow down absorption. Furthermore, absorption depends on the status of the GI tract: preexisting conditions (e.g. inflammation) can modify the rate at which the alcohol enters the bloodstream.
But, we are still far away from the brain! After being absorbed, ethanol goes into the vena cava, and passes through the liver, where it can be metabolized (destroyed) by an enzyme called alcohol dehydrogenase (ADH), which converts ethanol into acetaldheyde, effectively reducing the ethanol concentration in the blood.
This is a well-known phenomenon for many drugs, and it is called first pass effect
Importantly, the human stomach also expresses ADH, so this first pass effect can start even before reaching the liver! The effects of ADH in the stomach obviously depends on how long the ethanol stays in there. So, it will be lower for an empty stomach then after a big meal.
Food, in fact, is also a well known factor that reduces the amount of ethanol in the blood.
For instance, these graphs show blood ethanol content in four healthy subjects after a 10 hour fast (filled circles) or after breakfast (empty circles), after drinking the same dose of 0.80 g ethanol/kg body weight, in 30 minutes.
From: Food-Induced Lowering of Blood-Ethanol Profiles and Increased Rate of Elimination Immediately After a Meal - Jones AW and Jönsson KA - J Forensic Sci., 1994.
As you can see, eating strongly decrease the ethanol blood content. Also see how there is quite a bit of variation between the different subjects (if you open the paper you will also see the graphs from other 6 subjects).
Also, you can look for instance at this paper (just got a random study, there seems to be a ton of them around):
First pass metabolism of ethanol. - Lieber CS et al. - Alcohol Alcohol Suppl., 1994
Coming out of the liver, ethanol goes into the right side of the hearth, and from there to the lungs. This poses no particular issue for most drugs, but ethanol is volatile! So, part of the ethanol is released through respiration (in fact the "classic" way of saying if someone has drunk alcohol is to smell his breath). However, this only accounts for a minor decrease in blood ethanol levels.
Finally, ethanol can start going around the body. Being a water-soluble molecule it will tend to diffuse into water-containing parts of our body (i.e. you will not find much ethanol in fat), which include the brain.
In the meantime, however, the process of elimination has started: ethanol can be excreted in urine, sweat and breath, although the major route of elimination is epathic metabolism by ADH, accounting for >90% of ethanol elimination.
There is a neat formula to express all of this, called the Widmark equation:
$A$ = number of drinks consumed
$W$ = body weight (important because of the content of water in the body)
$r$ = Widmark constant (depends on sex, age, etc.)
$C_t$ = blood ethanol concentration at time t
$\beta$ = acohol elimination rate
$t$ = time since the first drink
$z$ = volume of alcohol per drink
You can find examples of this formula in this PDF about Widmark equations
And now to the brain: ethanol does indeed have various effects on neurons. Short term effect essentially involve depression of neuronal activity, ethanol being able to modulate GABA signalling in the brain. Long term effect range from reduced neurogenesis (i.e. birth of new neurons) to reduced volume of certain brain areas, probably due to loss of neurons, to inflammation in the brain.
Again, the situation is very complex and it depends on the frequency of drinking, the amount of each drink and many other factors. A single dose of ethanol will probably have irrelevant effects on your neurons... as the amount needed (in one shot) for serious neurotoxicity will probably send you into ethilic coma. The exact mechanisms for these effects are only partially known and very likely to be derived by the interaction of numerous diverse effects.
This article explains some of the mechanisms for loss of neurons in the cerebellum.
Mechanisms of ethanol-induced degeneration in the developing, mature, and aging cerebellum. - Jaatinen and Rintala - Cerebellum, 2008
These mechanisms include: (i) excitotoxicity; (ii) dietary factors, especially thiamine depletion; (iii) glial abnormalities; (iv) changes in growth factors; (v) apoptotic mechanisms; (vi) oxidative stress; and (vii) compromised energy production.
I will not go into the details of all of this, but it should be clear by now that all the things I mentioned so far (and many other factors I did not talk about) make it extremely difficult to give an exact quantification of the number of cells killed by ethanol. Surely the relationship is not linear, in fact, for instance, positive effects of small doses of alcohol have been reported numerous times.
A few more references on effects of alcohol on the brain:
Long-lasting reduction in hippocampal neurogenesis by alcohol consumption in adolescent nonhuman primates. - Taffe et al. - PNAS, 2010
Adolescent binge alcohol exposure alters hippocampal progenitor cell proliferation in rats: effects on cell cycle kinetics. - McClain et al. - J Comp Neurol., 2011
Brain volume decrease
Decreased volume of the brain reward system in alcoholism. - Makris et al. - Biol Psychiatry, 2008
Amygdala volume associated with alcohol abuse relapse and craving. - Wrase et al. - Am J Psychiatry., 2008
Hyperhomocysteinemia as a new risk factor for brain shrinkage in patients with alcoholism. - Bleich et al. - Neurosci Lett., 2003
per mil(I assume
promilis the German spelling). I apologize if you meant another thing, in which case feel free to revert the edit! $\endgroup$