32 Introduction
Pharmacokinetics is the study of what the body does to a drug: how it is absorbed, distributed, metabolized, and excreted (ADME) (Grogan and Preuss 2023). These processes set how the drug’s concentration rises and falls over time, and so which dose and schedule keep it in a safe, effective range (Ernstmeyer and Christman 2023).
Motivation
Pharmacokinetics answers questions about time. How much morphine must a doctor load into a syringe to relieve pain for 8 hours? How long must a dialysis session run to reduce urea (a waste product) by a given percentage? How long must a researcher wait before a thyroid scan after exposure to radioactive iodine? Each asks how fast something changes, not where it ends up. The name combines pharmaco (drug) and kinetics (rate).
A dose is an amount of drug (mg); the plasma concentration is that amount per liter of plasma, the liquid part of blood (mg/L). The drug cannot be tracked in every organ and cell, so a compartment model treats a region of the body as one well-mixed volume with a single concentration and writes a mass balance for the drug in it: rate in − rate out = accumulation. The model predicts how the concentration changes with time.
Learning Objectives
After this module, a student can:
Engineering
- Write a mass balance for a well-mixed compartment.
- Solve the one-compartment model for a single dose, and use the solution to find a concentration, an elimination rate constant, or an elimination half-life.
- Relate the clearance, the volume of distribution, and the rate constant, and compute any one from the other two.
- Choose an infusion rate from the steady-state relation to hold a target concentration.
- Apply a two-compartment model, in which a central compartment feeds a second compartment, to iodine uptake by the thyroid.
Biology
- Name the ADME processes and describe how each shapes the concentration-time curve.
- Compute the volume of distribution from a dose and the initial plasma concentration, interpret it as an apparent volume, and relate a large or small \(V_d\) to tissue binding.
- Explain what the therapeutic window and therapeutic index are, and why a narrow-window drug requires careful dosing and blood-level monitoring.
- Identify the kidney as the principal organ of drug excretion, and describe clearance as the volume of plasma cleared of drug per unit time.
Before You Start
- First-order differential equations and the exponential function (differential equations). The one-compartment model is a first-order linear differential equation whose solution is an exponential. It requires separating variables, integrating once, and using \(e^{-kt}\) and the natural logarithm.
Module Roadmap
- The one-compartment model: a single dose, half-life, clearance, and steady state.
- The kidney: clearance and urea balance in dialysis.
- Iodine metabolism: the thyroid scan, a two-compartment model.
- Practice problems: exercises on the module’s topics.
ADME: what the body does to a drug
Absorption sets how fast the concentration rises, distribution how quickly it falls as the drug spreads into tissue, and metabolism and excretion how fast it declines afterward. Metabolism and excretion together are called elimination, which the one-compartment model describes.
Absorption is the entry of the drug into the bloodstream from the site of administration. The route determines how much of the dose reaches the circulation and how quickly. A drug injected intravenously is placed directly into the blood and is fully and immediately available; a drug swallowed as a tablet must dissolve, cross the wall of the gastrointestinal tract, and survive a first pass through the liver, so it enters the blood gradually and often incompletely (Grogan and Preuss 2023).
Distribution is the spreading of the absorbed drug from the blood into the tissues. Drugs distribute differently: some remain largely in the plasma, while others concentrate in fat, muscle, or specific organs. The volume of distribution \(V_d\) describes this behavior; the one-compartment model defines and measures it.
Metabolism is the chemical transformation of the drug, mostly in the liver, into other molecules called metabolites. Enzymes convert the drug, which is often fat-soluble, into more water-soluble products that the kidney can excrete (Susa et al. 2026).
Excretion is the removal of the drug and its metabolites from the body, most commonly by the kidneys into the urine, and for some drugs by the liver into bile or through the lungs and skin (Grogan and Preuss 2023). The clearance \(CL\) quantifies removal: the volume of plasma cleared of drug per unit time. The one-compartment model defines it, and it follows from the filtration of blood in the kidney.
The therapeutic window
A drug works only within a range of plasma concentrations. The minimum effective concentration is the plasma concentration below which a drug produces no useful therapeutic effect. The minimum toxic concentration is the level above which harmful effects appear. Between them lies the therapeutic window, the range of plasma concentrations within which the drug is both effective and safe (Ernstmeyer and Christman 2023). A dosing schedule must keep the concentration inside this window. A drug that is cleared quickly leaves the window and must be dosed again sooner; a drug that is cleared slowly accumulates across doses and can reach the toxic range.
The width of the window varies between drugs and is summarized by the therapeutic index, the ratio of a toxic dose to an effective dose. Ibuprofen and penicillin have a large therapeutic index: their effective and toxic levels are far apart, so an approximate dose suffices. Warfarin, digoxin, and lithium have a small therapeutic index: their effective and toxic concentrations are close together. The dose must be chosen carefully, and the concentration is often measured directly in the blood and the dose adjusted to match (Ernstmeyer and Christman 2023).
A single dose cannot hold the concentration in the window. It decays exponentially from its starting level and eventually falls below the minimum effective concentration, so sustained therapy requires repeated administration. A drug that is cleared quickly falls below that level sooner. The one-compartment model quantifies this decay.