# Chapter 14

# Multiple IV Bolus Dose Administration

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## Development of General Equation

We can now consider a general equation which could describe the plasma
concentration at any time after multiple IV bolus drug administration.

**Figure 14.5.1 Drug Concentration after Multiple Doses Showing Accumulation**

**Concentration at the end of the first dosing interval**

**Equation 14.5.1 Cp after the First Dose**

where

This gives the plasma concentrations at the end of first interval, where τ is
the dosing interval in hours.

**Concentration at the start of the second interval**

**Equation 14.5.2 Cp at the Start of the Second Interval**

**Concentration at the end of the second dose interval**

**Equation 14.5.3 Cp at the End of the Second Interval**

and so on.

It will help if we define the parameter, R = e^{-kel • τ}, which is the fraction of the initial plasma concentration remaining at the end
of the dosing interval.

Then

**Equation 14.5.4 Cp at the End of the Second Interval**

**Equation 14.5.5 Cp at the Start of the Third Interval**

this is a geometric series with each term R times the preceding term.

**Equation 14.5.6 Cp at the Start of the nth Interval**

**Equation 14.5.7 Cp at the End of the nth Interval**

these two sums are sums of geometric series and they can be simplified to give

**Equation 14.5.8 Cp at the Start of the nth Interval**

**Equation 14.5.9 Cp at the End of the nth Interval**

Starting with the first equation (Equation 14.5.8) we can calculate drug concentration in blood or plasma at any time following uniform multiple IV bolus administration.

**Equation 14.5.10 Cp at time,t, after the nth IV Bolus Dose**

where here t = time since the last dose.

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