Medicinal Chemistry Applet

Cp vs time - iv bolus

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Introduction

Plotting plasma concentration (Cp) against time for a drug administered by an iv bolus provides a curve that follows first-order kinetics.  Intraveneous administration is the simplest form for these types of calculations since issues such as oral bioavailability can be ignored.  The Cp vs time plot is normally generated from clinical data and is the first step in determining the pharmacokinetic profile of a drug.  The relationship between Cp and time is shown in the equation below (Equation 1).  The equation can be expressed with either the half-life (t½) of the drug or the elimination rate constant (kel).

     (1)

The drug half-life may be approximated directly from the Cp vs time curve.  This value corresponds to the time required for the drug concentration to be halved and is constant over the entire curve.  The more common way to determine t½ is to generate a linear plot of ln Cpo against time (Equation 2).  The slope of the resulting line is -kel, and t½ = 0.693/kel.

     (2)

For a very closely related discussion, see also the applet on ln Cp vs time plots.

Applet

This applet plots data for up to three different drugs with arbitrary initial concentrations and t½ values.  Data points are generated and plotted from t = 0 until approximately five half-lives have elapsed.  The units of both axes are the same as the units of the input values for Cpo and t½.  Common units would be µg/mL and hours, respectively.

Drug
(Color)		 half-life
(t½)		 plasma conc.
(Cpo)
Drug 1 (red)
Drug 2 (blue)
Drug 3 (green)
calculation may be slow

Problem information - also see the ln Cp vs time applet

Advances within a class of drugs, such as cephalosporins, provide nice examples for this applet.  Since their discovery in the late 1940s, cephalosporins have undergone a series of improvements.  Examples from three generations of cephalosporins are shown below.  The pharmacokinetic data for each drug were taken from Goodman and Gilman's The Pharmacological Basis of Therapeutics, a standard reference on drugs and their activity.  Cpo values were approximated based on a single-compartment model with the formula Cpo = Do/Vd.  The Vd values are adjusted to a 70 kg patient.


cephalosporin Vd
(L)		 dose
(g)		 t½
(h)		 Cpo
(µg/mL)
cephalothin (1) 18 2 0.6 110
cefotetan (2) 10 2 3.6 200
ceftriaxone (3) 14 2 7.3 140


Problems

The treatment in these questions is virtually identical to that of the ln Cp vs time applet.

  1. Enter the cephalosporin data into the applet fields and graph all three compounds.  Be sure to use the bolded data from the table, and check that the rate constant and concentration data are placed in the proper text boxes.

  2. If all three cephalosporins are active at concentrations greater than 25 µg/mL, how long will each drug be effective after a single iv injection?

  3. Having a long half-life is generally considered to be advantageous for a drug.  For what types of drugs would it be particularly beneficial to have a long half-life?

  4. A very long half-life is not necessarily good.  What type of drug activity would be an extended half-life be unfavorable?

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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