Cp vs time - iv bolus with metabolite formation

Medicinal Chemistry Applet

Cp vs time - iv bolus with metabolite formation

Introduction

Special thanks for this exercise go to my colleague, Durwin Striplin, a physical chemist who derived Equation 4 from the diagram in Scheme 2.

Elimination is a term that refers to the removal of a drug (D) from circulation. In simple treatments, elimination can be summarized in the umbrella term of k_el, the elimination rate constant (Scheme 1). This term is the sum of all the elimination processes that affect the drug. A slightly more complicated discussion breaks down the elimination processes into two categories: excretion by the kidneys and metabolism by the liver. Each metabolite (M) can then be excreted by the kidneys (Scheme 2).

Scheme 1 - simple drug elimination model

Scheme 2 - elimination model with excretion and metabolism

Drug metabolism is normally classified as either Phase I or Phase II. Phase I includes hydrolyses, oxidations, and reductions. Phase II includes conjugation of the drug with other compounds such as glutathione or glucuronic acid. Generally, the effect of either Phase I or Phase II metabolism is to increase the polarity, or water-solubility, of the drug. With increased polarity, the drug metabolite is more readily excreted through the kidneys and into the urine. Unfortunately, not all metabolites are simply excreted. Some metabolites are biologically active with effects that can be similar to or different from the original drug. Identifying and tracing drug metabolites and their pharamcokinetics and pharmacodynamics is a key aspect in the FDA approval process.

Based on Scheme 2, the rate of change in concentration of the drug and metabolite can be expressed through Equations 1 and 2. Equation 1 simplifies to the standard one-compartment, first-order expression for drug elimination. Integration of Equations 1 and 2 affords Equations 3 and 4. Once the required rate constants are known, the C_p of the metabolite can be determined at any time following an iv bolus with an drug concentration of [D]_o.

(1)

(2)

(3)

(4)

Applet

This applet plots data for the C_p of a drug and a metabolite. Common units for each parameter are shown in the form below.

Problem information

Morphine (1) is an analgesic is widely used to manage severe pain in hospitals. The major metabolite for morphine is morphine-6-glucuronide (2) (Figure 1). While the metabolism and elimination of morphine is not trivial, a few assumptions can simplify the analysis.

Figure 1 - Pharmacokinetic parameters for morphine (1) and morphine-6-glucuronide (2)

Morphine has a t_1/2 of 1.9 h, corresponding to a k_el of 0.36 h^-1. This k_el is the sum of the k_ex and k_m. Since only approximately 5% of morphine is excreted unchanged by the kidneys, we can assume that k_ex is 0.02 h^-1 (5% of k_el). We will further assume that the remainder of k_el is for metabolism of 1 to 2, so k_m is 0.34 h^-1. Metabolite 2 has a k_ex of about 0.17 h^-1.

Problems

Assuming that morphine (1) has a V_d of 230 L for a 70-kg patient and a typical iv bolus dose is 10 mg, generate the C_p vs time graph for these parameters.

Morphine-6-glucuronide (2) is twice as potent as an analgesic as morphine itself. At approximately what time point is the analgesic effect in the patient primarily from the activity of the metabolite and not morphine?

With patients suffering from renal failure, the rate of elimination of metabolite 2 is much lower and k_mex drops to about 0.014 h^-1. Generate the C_p vs time graph and note the change in the x-axis. Which patient (healthy kidney or failed kidney) requires more morphine for effective pain control?

Equation 4 has at least one problem. It quietly assumes that the V_d of the metabolite is the same as the original drug. The problem is in the [D]_o term. Replace the [D]_o term with its equivalent, dose (drug)/V_d (drug). Now, derive a version of Equation 4 that will use the proper V_d of the metabolite. Of course, to use this new equation, one needs to know the V_d of the metabolite.

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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