So, in normal drug elimination (say, from an IV,) a drug would decay as a first (or possibly zero) order function, and from there we can get it’s half life, clearance, etc…
The graph to represent this usually has the drug plasma concentration start at some value (because it was given IV,) and then decay normally. But what if the graph starts at zero, like in an orally administered dose, but is still said to be from an IV (already I’m confused as to how that is,) and it never goes to zero. It goes up at an exponential rate until it hits a steady-state plasma-concentration, then stays there. I’m sure it goes back to zero eventually, but the part of the graph I’m seeing doesn’t show that. So how the heck can one figure out the elimination half-life if it’s not being eliminated? Every example I can find in my book or notes has the graph going the other way and eventualoly going to zero. What gives? The only thing I can come up with is that I take the half-life for how long it takes to get to it’s steady state value.
(Disclaimer: Yes, this is realted to some homework, but I figured that since I am asking for help on a general concept, not an actual problem, and would still have to do all the calculations and application of the knowledge myself, it was OK to start a thread about it. Mods can feel free to disagree and close it, though.)
I have studies enzyme kinetics and can derive a rate from a second order equation, but I haven’t done pharmacologic rates. Yet.
If you’re at a plasma steady state, and you know the rate of infusion, doesn’t that say something about the rate of clearance? It seems to me that at steady state, the rate of infusion would equal the rate of clearance. Form there, you would use some super-secret PharmD equation that would give you the half-life based in the clearance rate and the [P450] enzyme metabolizing the drug in question.
Well, clearance is not in the same units as the infusion rate. The infusion rate is in mg/hour, while the clearance is in l/hour. I did find an equation somewhere else equating clearance and infusion to a steady-state concentration. It’s nowhere in either the book or lecture notes, though, so I don’t know how the prof. will feel about me using it. It basically says that:
Infusion rate = clearance X steady-state concentration.
The units work out, so if nothing else, I can do that and get the clearance, but then I still need the volume of distribution to get the half-life by formulaic method. The volume of distribution is:
Vd = Dose/C[sub]0[/sub].
The dose and concentration (C[sub]0[/sub]) are both at time 0. I have a zero concentration at time zero, and no actual dose, jsut a dose rate.
(X-axis is time, y-axis is drug-plasma concentration.)
In that first graph, the alpha phase is the distribution of the drug, and the beta phase is the actual elimination. nd to get the concentration at time zero, you extrapolate back the beta phase instead of using the actual value in the alpha phase. But since my graph goes the wrong dammed way, I can’t do that.
My super-secret Pharm.D. smart friend looked at this and said:
This can’t happen.
The chart that goes down (your first link), that says “alpha phase” and “beta phase,” that is an elimination chart for an IV drug. The second chart is not an elimination chart. It is a steady state chart, most likely for an oral med, but could be an IV (she thinks that’s unlikely, though).
No; you’re assuming wrong. It never goes to zero, because it’s a steady state chart. If the patient continues to take the med per the regimen, this is what the blood concentration will look like as long as he continues to take the med (this is why it’s called a steady state).
You have to find another chart, namely, an elimination chart; or else figure out what the steady state concentration is and how long it took to get there; there’s a formula you can use to work back from there to determine the elimination half-life. So you need to figure out time to peak, concentration at peak, time to steady state, and concentration at steady state.
By the way, I want credit for this answer. I kind of even understood the science. I hope it helps.
