PHAR 7633 Chapter 14

Multiple IV Bolus Dose Administration

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Cpmax and Cpmin

More useful equations can be derived from this general equation. These are equations to calculate the maximum and minimum plasma concentration after many doses. That is as n approaches ∞, Rn (= e-n • kel • τ) approaches 0 and with t = 0 or t = τ. These are the limits of the PLATEAU CONCENTRATIONS.

Equation 14.6.1 Cp Immediately after Many Doses

Equation 14.6.2 Cp Immediately before Many Doses

An example may be helpful: t1/2 = 4 hr; IV dose 100 mg every 6 hours; V = 10 liter

What are the Cpmax and Cpmin values when the plateau values are reached

therefore

therefore the plasma concentration will fluctuate between 15.5 and 5.48 mg/liter during each dosing interval when the plateau is reached.

Accumulation Factor

In Equation 4.6.1 the ratio, Dose/V represents the initial concentration after the first dose. Thus the ratio between the highest, initial concentration at steady state, Cpmax and the highest concentration after the first dose, Cp01 can be expressed as the ratio.

Equation 14.6.3 Accumulation Factor

The accumulation factor describes how much drug accumulates during a multiple dosing regimen and gives a direct measure of how much higher the concentrations are during a dosing interval as steady state and the concentration during the first dosing interval.

It is interesting to note that if the dose is given every drug elimination half-life the accumulation factor is two since R equal to e-kel • τ equals one half.

If dosing every half-life Cpmax is twice the Cp01 value and Cpmin is equal to the Cp01 value.

For the example above R is equal to 0.354 and the accumulation factor can be calculated.

To complete the example above we can calculate the plasma concentration at any time following multiple IV bolus administration (using Equation 14.5.11 on the previous page) AND we can calculate the Cpmax and Cpmin values (using Equation 14.6.1 and 14.6.2 above).

Figure 14.6.3 Plot of Cp versus Time showing Time to Approach
50% of Plateau during Multiple Dose Regimen

Click on the figure to view the interactive graph
Interactive graph as a Semi-log Plot

Time to Cpmax/Cpmin

Just as in the case of a continuous infusion it takes some time to get to the plateau where the concentrations vary between Cpmax and Cpmin during each dosing interval. As before, it can be shown that the time to reach a certain fraction of the plateau concentration is dependent on the drug elimination half-life only, much the same as for the approach to steady state during an IV infusion. Thus we may again have a problem with an excessive time required to reach the plateau. Administration of a loading dose will achieve steady state concentrations rapidly.

In the previous example Cpmax was 15.5 mg/liter

A suitable loading dose can be calculated as Cpmax • V = 15.5 x 10 = 155 mg as a bolus which would give Cp = 15.5 mg/liter. This loading dose could be followed by 100 mg every 6 hours to maintain the Cpmax and Cpmin values at 15.5 and 5.5 mg/liter, respectively.

In summary:

The IV bolus loading dose to quickly achieve a required drug concentration, Cpmax, can be calculated as Cpmax • V

Rewriting Equation 14.6.1 with Dose expressed more explicitly as the Maintenance Dose.

Equation 14.6.4 Cpmax

Equation 14.6.5 Loading Dose

or

Equation 14.6.6 Maintenance Dose

Using Cpmax and Cpmin to Calculate a Suitable Dosing Regimen

We can try another example of calculating a suitable dosing regimen. Consider that we know V = 25 liter and kel = 0.15 hr-1 for a particular drug and for this drug we need to keep the plasma concentration between 35 mg/liter (MTC) and 10 mg/liter (MEC).

What we need is the maintenance dose, the loading dose, and the dosing interval.

Dividing Equations 14.6.1 by Equation 14.6.2

Equation 14.6.7 Cpmax and Cpmin provides 1/R

therefore

taking the ln of both sides

Solving for Τ gives

A dosing interval of 8 hours would be more reasonable and keeps the concentration between the limits of MTC and MEC. Thus with τ' = 8 hr and kel = 0.15 hr-1

From Equation 14.6.4

Equation 14.6.8 Maintenance Dose

Maintenance dose = 35 x 25 x (1 - 0.301) = 612 mg

Again we can round the value to a more realistic value, a maintenance dose of 600 mg every 8 hours.

This regimen should be quite suitable as the maximum and minimum values are still within the limits suggested. All that remains is to calculate a suitable loading dose.

This loading dose could be round (down) to a more suitable 850 or 800 mg. Let's use 800 mg.

The dosing regimen is then a loading dose of 800 mg followed by a maintenance dose of 600 mg every 8 hours.

To check this regimen

Concentrations from the loading dose

NOTE the use of the loading dose in this equation and that the Cpmax is below the MTC.

Concentrations from the maintenance dose

and

Here we use the maintenance dose. Note, the Cpmax and Cpmin are below and above the MTC and MEC, respectively.

This answer can be expressed graphically.

Figure 14.6.4 Plasma Concentration after Multiple IV Bolus Doses

Calculator 14.6.1 Calculate a suitable multiple IV bolus dosage regimen for specified Cpmin and Cpmax

Patient (weight Kg) is to receive a drug by multiple IV bolus doses. For optimal treatment drug concentration should be kept between Cpmax mg/L and Cpmin mg/L. This drug has an apparent volume of distribution of L/Kg and an elimination rate constant of hr-1 (Clearance = L/kg.hr).

First calculate the dosing interval, tau.

Tau hour.

Enter a new (rounded) value for tau. hr.

The next step is to calculate a suitable maintenance and loading dose.

Start with a loading dose of mg as an IV Bolus and a maintenance dose of mg as an IV Bolus every hour.

Calculator 14.6.2 Calculate Cpmin and Cpmax after Multiple IV Bolus Doses

Patient (weight Kg) has received mg of a drug as an IV Bolus every hours. This drug has an apparent volume of distribution of L/Kg and an elimination rate constant of hr-1 (Clearance = L/kg.hr). Calculate the Cpmin and Cpmax at steady state.

Cpmin mg/L

Cpmax mg/L

Practice problems involving Cpmax and Cpmin at steady state after uniform multiple dose IV bolus doses. Another practice problems involving Cpmax and Cpmin at steady state after uniform multiple dose IV bolus doses. A third practice problems involving Cpmax and Cpmin at steady state after uniform multiple dose IV bolus doses.

Other practice problems involving the calculation of Cp at three times during a uniform dosing interval with Linear or Semi-log graphical answers or calculation of Cp at three times during a non-uniform dosing interval with Linear or Semi-log graphical answers

Student Objectives for this Chapter

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