This was originally posted as a reply to this thread:
http://www.benzobuddies.org/forum/index.php?topic=5660.0
Strictly, it will not be earlier doses that are processed, but just a proportion of the amount of drug you have in your system. It just depends on the particular molecule coming into contact with your metabolic processes. So, it is all chance, and probability. But since there are huge numbers of these drug molecules floating around our system, we can predict how much (a proportion) of the drug is metabolised over a period of time. The only problem is that it varies from person-to-person. The usual way to describe this is how long it takes for half of the drug to be metabolised (assuming that you have stopped taking additional doses), we can work out the amount fairly simply. This will be expressed as a range because of our individual differences. So, Valium will take between 36-200 hours for half of it to be metabolised. Of what's remaining, half of that will be metabolised after a further 36-200 hours. So, you will have a quarter left in your system after 72-400 hours. The maths is as follows:
Since we cannot know our individual rates of metabolisation, we will have to instead calculate a range of possibilities. In the case of Valium, that's 36-200 hours. To calculate how much is left in our system, say, after 6 days:
144 hours in 6 days, divide by 36 hours, equals 4. (144/36=4). - This is our power.
Half-[...] (0.5) to the power of 4, equals 0.0625 (as a decimal). Multiply this by 100 to express it as a percentage, equals 6.25%. This is how much is left in our bodies after six days, assuming that we metabolise Valium at a half-[...] rate of 36 hours.
Now, if we instead assume that we metabolise Valium at half-[...] rate of 200 hours, then: 144 hours in six days, divide by 200 hours (144/200=0.72). This is our power!
Half-[...] (0.5) to the power of 0.72, equals 0.607 (as a decimal) Again, we multiply by 100 to gain a percentage figure, equals 60.7%.
So, you see, even after just six days, the range of possible blood levels is very large, and the gap grows even larger with more time.
Again (more succinctly):
6 days; half-[...] 36-200 hours
6x24=144 hours
144/36=4 (for a half-[...] of 36 hours)
0.5
4=0.0625
= 6.25%
144/200=0.72 (for a half-[...] of 200 hours)
0.5
0.72=0.607
= 60.7%
Range = 6.25 to 60.7%.
Another example:
Clonazepam; 2 days and 6 hours; half-[...] 18-50 hours
(2x24)+6=54 hours
54/18=3 (for a half-[...] of 18 hours)
0.5
3=0.125
= 12.5%
54/50=1.08 (for a half-[...] of 50 hours)
0.5
1.08=0.473
= 47.3%
Range after 54 hours: 12.5 to 47.3%
So, we can calculate possible ranges, but I don't think it really tells us anything, apart from our individual metabolic rates has huge effects upon our meds. Because of this variability, two people on the same benzo, at the same dose, can expect to have very different blood levels, even when not withdrawing!
As a matter of interest, the possible range for Valium left in our system after 30 days is: 0.000095% (that must be undetectable) to 8.25% (that must be easily detectable). This difference is enormous. Knowing this probably doesn't help any of us though.