Sometimes I encounter basic pharmacokinetic questions that don't seem to be readily answered in the immediately available literature. I've found FOAMed to be a useful way to make sure I'm doing this right (e.g., see a prior discussion of the appropriate loading dose based on intermittent maintenance dosing and half-life here).
Today I want to address a very simple question: suppose you are giving an IV loading dose of a drug followed by a maintenance infusion (let's say, for example, IV diltiazem). You've given a few IV doses of the drug to determine a safe and effective loading dose. How should this loading dose be used to estimate a rational continuous infusion rate?
Let's start with three basic equations (with the following abbreviations: concentration = therapeutic drug level; Vd = volume of distribution).
Equation #1:
Loading dose = (concentration)(Vd)
Equation #2:
Maintenance rate = (concentration)(clearance)
Equation #3:
Half-life = 0.7(Vd/clearance)
We can rearrange Equation #1 as follows:
Concentration = (Loading dose)/Vd
If we substitute this into Equation #2 for the maintenance rate, this yields Equation #4:
Maintenance rate = (Clearance)(Loading dose)/Vd
Now we can rearrange Equation 3 as follows to obtain Equation #5:
(Clearance / Vd) = 0.7/half-life
Finally, we can substitute Equation #5 into Equation #4 to yield:
This seems like a reasonably useful equation for clinical use, since in practice we often know the loading dose and the half-life.
So for example, let's imagine that 30 mg of IV diltiazem has the desired clinical effect. In that case, the infusion rate could be estimated based on the half-life of diltiazem being 4.5 hours:
Maintenance rate = (0.7 * 30 mg)/(4.5 hr) = 5 mg/hr
Does that make sense?
I find it odd that I can't readily find this equation anywhere, but it may be that I'm just not great at searching for equations.
Incidentally, you can also work this equation backwards. So an infusion rate of 15 mg/hour diltiazem would be equivalent to giving a patient a loading bolus of 96 mg. Yikes. That's a lot of diltiazem. This probably explains why patients who get titrated up to 15 mg/hr of diltiazem eventually accumulate the drug and deteriorate hemodynamically. Usually at 3 AM when nobody is paying a ton of attention.
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That is wonderful and very helpful. Thank you, Mr. Josh, for making our practice so simple.
Thanks for this phenomenal yet easy to conceptualize explanation of maintenance dose calculation.