Does the body not clear drugs like caffeine at a constant rate? If you drink less caffeine does the body clear it less quickly? Or am I not understanding it? Caffeine half life is about 5 hours (via Google), so regardless of if I drink 100mg or 900mg of caffeine, half (50mg or 450mg) will be left in my body 5 hours later? That seems like a pretty drastic difference in the rate of clearance.
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Think about your liver and kidneys like the filtration system for a swimming pool. It processes a certain amount of fluid in a given time.
Suppose you dumped a bunch of dirt into a swimming pool all at once and mixed it up so it had a uniform concentration. When the filter processes a liter of water, it dumps the cleaner
water back into the pool, so the entire pool is a little bit cleaner. Now the next liter of water has a lower concentration of dirt, so the filter removes less total dirt the second time. Then the pool is slightly cleaner, and the third liter of water has less dirt… and so on.
Mathematically, this means that the rate at which dirt is removed is proportional to the total amount of dirt in the pool. (If you assume that the water has an efficient mixer so there aren’t clean regions and dirty regions of the pool.) The solution to an equation like that is exponential.
C(t) = C(0) * exp(-kt)
where C(t) is the concentration of dirt over time, and
k is called the decay constant (relates to how fast the filter can remove dirt)
Because exp(ln(2)) = 2, we can write the above equation more like
C(t) = C(0) * (1/2) ^ (t/H)
Where H is the half-life.
You can use a little algebra to see how k and H are related: k = ln(2) / H
Essentially, you’re right. Most drugs are not metabolized at a constant rate, but instead as a half-life, called 1st order metabolism. Only a few drugs metabolized at 0 order metabolism which is a constant rate.
Because that’s what we choose to measure with. Half life is nothing more than expressing how long it takes for half the substance to still exists somewhere or in something (body).
It’s a measurement of the time affecting the substance/element and not of sole weight or mass. We use the same unit for expressing how much time it takes for an radioactive element to decay into a different element. If expressed correctly it should state how much the original amount is and how much time it takes to become half of it.
So if one half-life of element A or substance has passed only the half or the original amount is still left. You can calculate the half-life for 1 pil, amount of grams, amount atoms (or just one) or other units that are usually used to indicate an amount.
So what you said: 400mg of caffeine will be 200mg in one half-life which is around 5 hours later.
With medications there are actually two pathways that the body uses. Zero order and first order elimination.
Zero order is simple, over a given time x, y amount of drug will be removed from your body. An example to think about is a famous person signing autographs. They can sign at a constant rate of 2 per minute. If they had 100 fans that’s 50 minutes. The same applies to certain drugs and your liver in zero order elimination. This is how ethanol, omeprazole, and a few others are eliminated.
First order elimination is how probably 95% of the medications are excreted. In this method the drugs are cleared at a rate depending on the initial concentration of the drug. A good example for this would be taking a water jug and putting holes in it. At first the water rushes out really fast, but as the water level drops, the flow slows.
This is a rough idea of the basic concepts behind the elimination of drugs in our bodies.
There are a few that use both methods for different metabolites (intermediates during elimination) but those are beyond this discussion, and in the end are limited by the slowest step (zero or first order).
Please note that in both of these are the RATE of elimination, and actually breaking down the drugs in your body is done by many enzymes and to understand it many of them are split into the zero and first order, however often most will have their own constant *k* that helps determine the actual value.
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At what point in the half-life elimination process can the effects of a drug be considered to have “worn off”?
Caffeine is rapidly absorbed into your bloodstream. (within 15 to 45 minutes after ingesting it) and it is cleared by a set of enzymes your liver produces. The rate of metabolism depends entirely on the speed at which your liver can produce those enzymes. Some people produce them quickly. others much more slowly. For a slow metabolizer of caffeine it can take fifteen hours or more to break it down to negligible amounts. For a fast metabolizer maybe nine hours. that is why the metabolic rate is measured in half lives, because there is a wide range. The dosage (amount of caffeine ingested) impacts how much of the effects of the drug you feel, but the rate at which it is cleared by your liver is largely driven by your genetics and nothing else. Once you ingest it, you just have to wait for your liver to break it down.
Most drugs are eliminated at a rate proportional to the concentration of the drug in the blood. If you do the math for that, it works out to match the “inverse exponential function”. That is a fancy way to say “half life”.
The time of elimination for each half still left is constant.
Does that make sense?
If you have 100mg of caffeine, 50mg will be filtered out in 5 hours. Over the next 5 hours, 25mg will be filtered out. Over the next 5 hours 12.5mg will be eliminated. And so on and so on.
Rate of drug clearance is measured in half life because the mechanism of clearance differs from drug to drug.
To explain in simple terms: Imagine the drug is a meal. And the clearance process(enzymes) are people with different favorite meal choice. Depending on the volume, type, and variety of meal (drug) on the table and the number (age, race, sex, etc) of the people (enzymes) having access to eat, the speed/clearance would differ.
Hence to make it easier to compare the clearance for drugs among a population, it’s easier to use half life than to use the time for total clearance.
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