Medicinal Chemistry Applet

Cp vs time - iv infusion with loading dose

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Introduction

A problem with drug infusions is that they can take a considerable amount of time to reach the steady-state concentration (C_ss) (see the iv infusion applet).  To solve this problem, a loading dose in the form of an iv bolus is normally administered before an iv infusion.  This effectively "jump starts" the infusion.  Instead of starting with a C_p of 0, the infusion starts with a C_p that is determined by the size of the bolus.  Ideally, the bolus will set C_p to the desired C_ss.  If so, C_p will be perfectly maintained at C_ss from t = 0 until the infusion is stopped.  If the iv bolus dose is too small, the C_p will be below C_ss and will slowly climb to C_ss during the infusion.  If the iv bolus dose is too large, the C_p will slowly fall to C_ss during the infusion.

The C_ss is determined by the rate of infusion (k_in) (units of mass/time - typically mg/h or similar), the elimination rate constant of the drug (k_el), and the volume of distribution of the drug (V_d) (eq. 1).  The proper loading iv bolus can be determined through Equation 2 in which the desired C_ss is used to find the dose (D_o) with the known V_d.  Essentially, C_p^o is the same as C_ss.  Importantly, if the exact loading dose is not used, Equation 2 will not be valid since C_p^o will not be equal to C_ss.  It any time during the infusion C_p can be readily calculated.  C_p will be a function of two contributing factors - dosing through the iv bolus and dosing through the infusion (eq. 3).  These can be independently determined and added together to find C_p (eq. 4).

     (1)

     (2)

     (3)

     (4)

Applet

This applet plots data for a drug that is administered by both a loading bolus and infusion.  The k_el, k_in, D_o, length of the infusion, and time after the infusion must be provided.  All varibles with time or mass units should have the same unit of measure.  If the mass units are in milligrams and the V_d is in liters, the concentration will be µg/mL (equivalent to mg/L).  The three lines generated correspond to the drug concentrations from the iv bolus alone (green), the infusion alone (blue), and the sum of the bolus and infusion (red).

Problem information

No problems for this applet.

Problems

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Reference

Goodman and Gilman's The Pharmacological Basis of Therapeutics, 10th ed.; Hardman, J. G., Limbird, L. E., Eds.; McGraw-Hill: New York, 2001.

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