Cp vs time - oral dosing

Medicinal Chemistry Applet

Cp vs time - oral dosing

Introduction

Orally-available drugs are the most common type of pharmaceuticals. They allow a patient to easily self-administer the drug without the help of a trained medical professional. A cost of this convenience is that the patient must follow the drug regimen as it has been prescribed by either the physician or drug instruction insert. Extreme cases of lack of patient compliance can lead to major problems such as overdosing. Regardless, orally-available pharmaceuticals give a patient great freedom in administering medication.

Unlike drugs that are delivered intravenously, orally delivered drugs go through a relatively slow absorption phase before they can enter the blood stream. Onset of the pharmacalogical effect is not instantaneous, but depends on the rate of absorption. Of course, as soon as any drug is absorbed from the gastrointestinal tract, it immediately is subject to the various elimination processes. Therefore, the plasma concentration (C_p) of the drug is a function of both its rate of absorption, described by the absorption rate constant k_ab, and its rate of elimination, k_el. Assuming that both absorption and elimination are first-order processes, C_p at any given time can be determined through Equation 1. In this equation, F is the bioavailability of the drug, D refers to the mass of the oral dose, V_d is the volume of distribution, and t is the elapsed time since the administration of dose D.

(1)

Pharmacokinetic parameters such as V_d and k_el are generally determined from a ln C_p vs time plot from a single iv bolus. k_ab is only available through oral delivery data. k_ab may be estimated from oral C_p vs time data with Equation 2 by extrapolating the linear, elimination portion of the graph back to t = 0. At t = 0, the theoretical C_p^o value is equivalent to the y-intercept term and, with the other variables in hand, k_ab may be determined.

(2)

With a single oral dose, C_p will rise with time, reach a peak, and then drop once the rate of elimination is greater than the rate of absorption. C_p peaks at C_max at a time of t_max. At this time, dC_p/dt = 0. Rearrangement of Equation 3, the derivative of Equation 1 with respect to time, and setting dC_p/dt to 0 affords Equation 4. With this equation, if k_el and k_ab are known, t_max may be estimated for a single oral dose.

(3)

(4)

Applet

This applet calculates the C_p of an orally-delivered drug using a single-compartment model. Multiple oral doses at a fixed time interval are an option. The calculation continues for a time of seven half-lives after the last oral dose. If V_d is entered with units of liters and dose is in milligrams, the units of C_p will be µg/mL. Multiplication factors, if any, will be listed at the very top of the y-axis. While the time unit is explicitly listed as hours, if k_el, k_ab, and the dosage interval are entered with minute units, the x-axis will be in minutes.

Problem information

Indomethacin is a non-steriodal anti-inflammatory drug that can be used to treat pain in patients suffering from rheumatoid arthritis, osteoarthritis, and bursitis/tendinitis. It is available as 25 and 50 mg oral tablets and is commonly taken three times per day (t.i.d.). The t_max for indomethacin is 1.3 h. Indomethacin has an effective concentration range of 0.3-3.0 µg/mL and shows toxicity (nausea, vomiting, headaches) above 5.0 µg/mL.

The pharmacokinetic parameters of indomethacin are shown below.

k_el = 0.29 h^-1
V_d = 0.39 L/kg
F = 100%

Problems

By trial and error using the applet, determine the approximate k_ab of indomethacin. (Enter values for k_ab repeatedly until the graph shows a t_max of approximately 1.3 h.) Only use a single oral dose.

The "standard" patient mass is 70 kg. Would a 25 mg t.i.d. regimen be suffient to maintain an effective dose of indomethacin for a 70 kg patient? Use the k_ab you found in question 1 with at least 7 oral doses.

Would a 50 mg t.i.d. regimen reach toxicity for a 35 kg patient? Follow the same guidelines as with question 2.

Under the best circumstances, oral dosing should try to mimic the steady-state C_p (C_ss) of an intravenous infusion. Reset the parameter table. Examine each parameter and determine which one, if any, is most effective at minimizing the ups and downs of the oral dosage curve.

Reference

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

back to applets page