Skip to 0 minutes and 10 secondsLet's look at the intermittent infusion equations. This equation represent the concentration at any time after constant rate IV infusion. Here the K0 is the zero order infusion rate. V is volume distribution. k small k is elimination rate constant. and small t is any time after the infusion. The peak concentration is described by C peak is equal to K0 divided by kV times e to the minus K cap T. Here you notice that at the peak concentration that's when the cap T where replaces the small T. And the trough concentration is equal to Peak concentration times e minus K times t minus tau with tau - cap T and that these are notations of the symbols.

Skip to 1 minute and 27 secondsIntermittent infusion to the steady state. If we infuse the drug on a intermittent basis and the following multiple doses here is the infusion time Every 12 hours for example and for greater than or more than 5 half-lives then the plasma concentration would reach a steady state and at the steady state you have peak concentration and that you have trough concentration. So peak concentration at steady state how do we express that? The peak concentration at steady state is equal to K 0 is the 0 infusion rate times 1 minus e to the minus K T cap T divided by k elimination rate constant times v, volume distribution times 1 minus e to the minus K tau tau is the dosing interval.

Skip to 2 minutes and 33 secondsAnd the trough concentration steady-state. Once you have the peak concentration trough concentration is always easy to divide because the trough concentration is equal to the peak concentration times e to the minus K T now the T is replaced by tau minus cap T and again these are the notations of the symbols. Now following multiple intermittent infusion we are able to derive the volume of distribution by this formula. This is simply a rearrangement of the previous formula and the dosing interval in order to maintain a therapeutic range is defined by this formula. tau is equal to natural log of peak concentration over trough concentration divided by K plus the infusion time.

Skip to 3 minutes and 41 secondsSo again here are the notations for these symbols Continue on multiple intermittent infusion. So if we wish to achieve a peak concentration knowing the elimination rate constant of the drug knowing the volume of distribution of the drug knowing the dosing infusion time rather the cap T And knowing how frequent we are going to perform the intermittent infusion then we will be able to divide a dose and therefore the infusion rate is equal to the dose divide by cap T, the infusion time.

# Single and Multiple Intermittent Infusion Equations

Prof. Lee introduces single and multiple intermittent infusion equations in this step. He starts with single intermittent infusion.

To begin with, he illustrates how to calculate the concentration at any time after constant rate IV infusion. Following that, he also demonstrates how to derive the peak concentration after the first infusion, and get the trough concentration after the first dose.

Besides, we can know the concept of steady-state from the diagram in this video.

For multiple intermittent infusion equations, there are five key parameters, including peak concentration at steady-state, trough concentration at steady-state, volume of distribution, dosing interval, and recommended dose.

Therefore, knowing the elimination rate constant, the volume of distribution, the dosing infusion time, and how to perform the intermittent infusion, we will be able to derive the recommend dose.

Ultimately, the infusion rate is equal to the dose divide by cap T, the infusion time.

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