With Ben providing a nice substance abuse prelude, it seems like a good enough time to also explore other things related to death. Such as lethal doses - i.e. for things we scientists particularly indulge in (like coffee and alcohol and, yes - the free cookies at Departmental seminars). We'll start by looking at the fatality of coffee for this post, and here, for the scientist, the first place to look a little deeper into this is the vaulted MSDS (or Material Safety Data Sheet).
For those not initiated in this lingo, MSDS are those documents that provide risk assessment and health considerations for any and all reagents, compounds, molecules, chemistries you might care to use in a laboratory setting. Of course, the most press worthy value it often provides is the lethal dose. Which, according to wiki is:
the median lethal dose, LD50 (abbreviation for "Lethal Dose, 50%"), LC50 (Lethal Concentration, 50%) or LCt50 (Lethal Concentration & Time) of a toxic substance or radiation is the dose required to kill half the members of a tested population.
Anyway, for fun, and to shift focus if only momentarily away from the current remarkable events happening concerning pigs, viruses, and epidemiology, I thought it might be interesting to do some back of the envelope calculations to bring to you, our dear reader, a public service announcement on not only the value of washing your hands, and initially isolating yourself when exhibiting flu symptoms, but also to avoid things like drinking "X" many cups of coffee.
Anyway, this calculation is not as easy as it sounds because there's a certain amount of kinetics that needs to taken into consideration, but at the very least, let's first start with a few facts and figures to get the ball going.
Firstly, if we're going to focus on coffee, probably its most potent chemical component from an oral lethal dose point of view is the caffeine. However, from a purely empirical perspective, it might actually be its water content that will kill you in the end. In other words, if you drink lots of coffee and plan on doing it to induce a fatality, it might be interesting to see what scenarios are necessary for that death to be caused by too much caffeine versus too much water.
In any event, here are the numbers to concern ourselves with:
1. Average weight of a human: From wiki:
In the United States National Health and Nutrition Examination Survey, 1999-2002, the mean weight of males between 20 and 74 years of age was 191 pounds (86.6 kg, 13 st 9 lb); the mean weight of females of the same age range was 164 pounds (74.4 kg, 11 st 10 lb)
Let's use 80kg as an average.
2. A single cup of coffee on average contains about 250ml of water, and about 135mg of caffeine (link).
4. However, the other part of the equation is we need to evaluate involves rates of elimination.
The half-life of caffeine--the time required for the body to eliminate one-half of the total amount of caffeine--varies widely among individuals according to such factors as age, liver function, pregnancy, some concurrent medications, and the level of enzymes in the liver needed for caffeine metabolism. In healthy adults, caffeine's half-life is approximately 4.9 hours.
And for water - this was a little harder, because water turn over rates I found, tended to revolve around the idea of an individual not imbiding in crazy amounts of fluids. So, for the sake of our calculations, I'll go with the follow piece of information:
It's Not How Much You Drink, It's How Fast You Drink It! The kidneys of a healthy adult can process fifteen liters of water a day! You are unlikely to suffer from water intoxication, even if you drink a lot of water, as long as you drink over time as opposed to intaking an enormous volume at one time. As a general guideline, most adults need about three quarts of fluid each day. Much of that water comes from food, so 8-12 eight ounce glasses a day is a common recommended intake. You may need more water if the weather is very warm or very dry, if you are exercising, or if you are taking certain medications. The bottom line is this: it's possible to drink too much water, but unless you are running a marathon or an infant, water intoxication is a very uncommon condition.
O.K. so let's do the math.
First, an oral lethal dose for an 80kg human would extrapolate to 15,360mg of total caffeine. This technically is equivalent to the amount of caffeine absorbed from drinking 113 cups of coffee really really really quickly. However, the reality is that this figure would instead result in a fatality due to water intoxication since 113 cups is close to 30 litres of water.
So let's try a different tact: by focusing on a safe water ingestion figure (i.e. 15 litres per day when spread reasonably). This works out to 60 cups of coffee over a full day, or approximate one cup every 24 minutes. Anyway, this is some pretty nasty math to figure out (since it's a half life calculation with continual replenishing going on). Anyway, if you do the math, what you find is that at the end of a 24 hour period, that average body would have retained a little less than 2500mg. Not even close to the 15,000 or so milligrams needed to reach the lethal dose. Presumably still not a healthy thing to do, but withing the context of our LD50, it sounds doable.
And the funny thing is, by the next day, that 2500mg would have been metabolized or cleared itself and only about 50mg of this is left behind. Which means that the net total amount of caffeine still in a person's system if he or she were to continue drinking a cup of coffee every 24 minutes for a 48 hour period is 2550mg (2500mg + 50mg).
It turns out that your body is potentially quite capable of dealing with such a heavy coffee dosage, because that new 2550mg level becomes 53mg by the next 24hours - therefore three days of drinking a cup of coffee every 24 minutes will result in a net retention of 2553mg (2500mg + 53mg) and so on.
I haven't had a chance to extrapolate this over the full year (365 days), but I'm pretty sure that even a constant coffee drinking regime (1 cup every 24minutes for the full year) wouldn't work out to a retention amount above the lethal dose.
All to say that your body pretty much kicks ass in its remarkable metabolism. Now, it'll be interesting to maybe dig a little deeper with regards to how messed up a person gets with that base 2500mg inside them (as I'm sure the case will be). As well, not sure what the deal would be with 15 litres of expresso shots per day - that may just about be enough!
What about the caffeine in energy drinks?
Hah. With a housemate who was a toxicologist, I once figured out the LD50 of chocolate-covered espresso beans, which I was eating too many of. They're a much more efficienct way of getting caffeine into your system, and don't have all that pesky water. Turns out that the LD50 was something like 2 kg. Which is a lot, but you could certainly fit it in your stomach over the course of an hour or so.
Of course, you would wish you were dead long before you actually became dead...!
This probably won't affect your results much, but the mean is a poor measure to use for adult human weight because it's quite right-skewed (a 191-pound man who gained 125 pounds would lose a few years of life expectancy; one who lost 125 pounds would lose all of it).
If your looking for the equilibrium level, I think the half-life of 4.9 days works out to eliminating 5.5% of the caffeine in the body every 24 minutes. So at equilibrium, the intake of 135mg every 24 minutes would equal 5.5% of the total caffeine in the body, which works out to about 2450mg.
(Actually, I get only 2241mg after day 1, not sure how our models might be differing...)
Thanks Majolo - mine was literally a "back of the envelope" calculation so didn't have a calculator to do the full on first order analysis.
I think the proper term for the common calculation that is analagous to our needs (from a pharmocokinetic point of view) is called Multiple Dose Pharmocokinetic equation or something like that...
Is that how you got your other figure?
Another confounding factor in water intoxication is the concentrations of salts in the coffee, mostly sodium. There is slightly more sodium in coffee than standard tap water [5 mg/cup vs. 2 mg/cup]. Therefore the amount of fluid coffee to kill you would be slightly higher than the equivalent dosage of water, since it's usually the hyponatremia that gets you in water intoxication.
To complicate things, caffeine impacts kidney function, doesn't it? So is there a synergistic-lethal effect of caffeine dissolved in water? That sounds like rather nasty math, now that I think about it.
And I'm curious what the sub-lethal effects of carrying 2500mg of caffeine in one's bloodstream would be. I get jittery and have some minor GI tract issues if I drink too much coffee in too short a time, but I've never gotten anywhere near one cup per 24 minutes.
I took a decay function f(t)=(1/2)^(t/4.9) to give a half- life of 4.9 hours (not days, sorry for the typo). This gave 1-f(24/60)=0.055 for the 24-minute decay rate. For the level after one day I took the sum of 135*f(24*i/60), i going from 1 to 60 (you can simplify that as a geometric sum, but I have Mathematica handy). I might borrow this problem for a calculus exercise sometime.
Does anyone want to calculate the equivalent figures for espresso (1.7g/L caffeine)?
The math isn't quite as nifty, but just for fun:
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