VelocideX
Bluelighter
- Joined
- May 26, 2003
- Messages
- 4,745
After a this thread I was spurred to create a simple differential equation model of absorption of stuff in the body.
Here's the assumptions I've made:
1) Pill reaches stomach as a whole. No "slow absorption" into the stomach. Stomach starts the problem with highest amount of substance
2) Stomach clears exponentially. Seems pretty reasonable to me, at least to a first approximation. I don't think its linear, and its got to tail off to 0 sometime, so you'd need some interpolation between a linear model and an exponential one. In any case, exponential IS linear in a small enough region.
3) Intestines receive stomach contents immediately. No time is allowed for "traversing the length of the intestines".
4) Intestines clear at a rate proportional to the amount of stuff in them. This assumes that no saturation is reached for whatever transporter mechanism exists. It would be accurate for low amounts of stuff, I guess
5) Amount of stuff entering blood is proportional to the amount in the intestines. This has to follow from the last one, it's just a conservation of stuff really
6) Blood clears proportional to how much is in it. Again, exponential decline. Seems reasonable to me; the concept of a blood half-life has no meaning without exponential decline.
You end up getting nice graphs like this
Amount of stuff in the intestines:
Amount of stuff in blood:
Admittedly I've just inserted random constants, but they're based on proportions I thought were sensible.
If anyone wants I can post the differential equation and the solutions. The solutions have a closed analytic form, though in its generality (no constant substitution) its a little hideous. Not too bad though, much better than I was expecting.
Here's the assumptions I've made:
1) Pill reaches stomach as a whole. No "slow absorption" into the stomach. Stomach starts the problem with highest amount of substance
2) Stomach clears exponentially. Seems pretty reasonable to me, at least to a first approximation. I don't think its linear, and its got to tail off to 0 sometime, so you'd need some interpolation between a linear model and an exponential one. In any case, exponential IS linear in a small enough region.
3) Intestines receive stomach contents immediately. No time is allowed for "traversing the length of the intestines".
4) Intestines clear at a rate proportional to the amount of stuff in them. This assumes that no saturation is reached for whatever transporter mechanism exists. It would be accurate for low amounts of stuff, I guess
5) Amount of stuff entering blood is proportional to the amount in the intestines. This has to follow from the last one, it's just a conservation of stuff really
6) Blood clears proportional to how much is in it. Again, exponential decline. Seems reasonable to me; the concept of a blood half-life has no meaning without exponential decline.
You end up getting nice graphs like this
Amount of stuff in the intestines:
Amount of stuff in blood:
Admittedly I've just inserted random constants, but they're based on proportions I thought were sensible.
If anyone wants I can post the differential equation and the solutions. The solutions have a closed analytic form, though in its generality (no constant substitution) its a little hideous. Not too bad though, much better than I was expecting.