National University of Singapore · FACULTY OF PHARMACOLOGY

MDG5204 Chap.5 Clearance, Half-Life and Steady-State Dosing

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Chapter 5 of 11 · MDG5204

Clearance, Half-Life and Steady-State Dosing

Two numbers that summarise elimination

Clearance is the course's measure of how efficiently the body removes a drug. It is the irreversible loss of drug by metabolism and excretion combined, expressed as the volume of plasma cleared per unit time, and it equals the rate of elimination divided by the plasma concentration.

Half-life, the time for the plasma concentration to fall by half, is a derived parameter: it lengthens when the volume of distribution grows and shortens when clearance grows, and the constant that links them is 0.693.

The four-to-five rule

Each half-life removes half of what remains, so after one, two, three and four half-lives about 50, 75, 87.5 and 93.75% of a dose has gone.

Elimination is therefore nearly complete after four to five half-lives. The same number appears again with repeated dosing, because it also takes four to five half-lives for levels to build up to steady state.

Recognising that the two questions share one answer saves time in the examination.

Steady state and the plateau principle

When doses are repeated before the previous one is gone, drug accumulates until the amount eliminated per interval equals the amount given.

Concentrations then fluctuate around an average steady-state level, which the course calls the plateau principle, and the therapeutic aim is to keep that plateau inside the therapeutic window.

The average steady-state concentration equals the dose rate divided by clearance, so doubling the dose rate doubles it, while the time taken to reach it depends only on the half-life.

Loading dose, maintenance dose and monitoring

A loading dose reaches the target at once and depends on the volume of distribution; a maintenance dose keeps it there and depends on clearance, being the target concentration multiplied by clearance and the dosing interval.

A large loading dose can expose a patient abruptly to a high concentration, so it may be split or infused. Drugs with a narrow therapeutic window, potentially toxic drugs and poisonings are the indications the course lists for therapeutic drug monitoring.

In this chapter

What this chapter covers

  • 01

    Clearance as metabolism plus excretion and its units

  • 02

    Half-life and its dependence on volume of distribution and clearance

  • 03

    The four-to-five half-life rule for elimination and accumulation

  • 04

    Steady state, the plateau principle and the therapeutic window

  • 05

    Loading dose from volume and maintenance dose from clearance

  • 06

    Therapeutic drug monitoring and the drugs that need it

Worked example · free

What happens to half-life and dosing when clearance falls

Q [6 marks]. A drug has Vd = 50 L and CL = 10 L/h. Disease halves the clearance. Compare the half-life, the time to steady state and the dose rate needed for a target of 4 mg/L before and after. The step weighting shown here is an AskSia study allocation and is not a University marking scheme.
Figure 5.1.Figure 5.1. Each half-life removes half of what is left, so elimination is nearly complete after four to five half-lives. number of half-lives elapsed % of drug remaining 1: 50% 2: 25% 3: 12.5% 4: 6.25% 12 34 5
Figure 5.1. Each half-life removes half of what is left, so elimination is nearly complete after four to five half-lives.
  • 2Compute the half-life before and after.
  • 2State the time to steady state before and after.
  • 2Compute the dose rate before and after.
Before: half-life = 0.693 x 50 / 10 = 3.5 h. After, with CL = 5 L/h: 0.693 x 50 / 5 = 6.9 h, so the half-life doubles. Steady state takes about four to five half-lives, roughly 14 to 17 hours before and 28 to 35 hours after. The dose rate for 4 mg/L is target times clearance: 4 x 10 = 40 mg/h before, and 4 x 5 = 20 mg/h after. Keeping the old dose rate would double the steady-state level, and the patient would take longer to reach that higher level, which is why toxicity from reduced clearance can appear late.
Sia tip — Clearance sets the size of the maintenance dose; half-life sets how long you wait. Keep the two questions separate.
Glossary

Key terms

Plateau Principle
The levelling of concentrations with repeated dosing once elimination per interval equals the dose given.
Maintenance Dose
The dose repeated at fixed intervals to hold the steady-state concentration, equal to target concentration times clearance times interval.
Therapeutic Window
The concentration range that gives efficacy without unacceptable toxicity, bounded below by the minimum effective concentration.
Therapeutic Drug Monitoring
Measurement of plasma drug concentrations to keep treatment effective and safe.
Minimum Effective Concentration
The lowest plasma concentration at which the drug produces its intended effect.
FAQ

Clearance, Half-Life and Steady-State Dosing FAQ

Why does it take four to five half-lives to reach steady state?

Accumulation approaches the plateau in the same exponential way that elimination approaches zero, covering half the remaining distance each half-life. After four to five half-lives the level is within a few per cent of the plateau, which the course treats as steady state for practical purposes.

Does a bigger dose reach steady state sooner?

No. A bigger dose rate raises the steady-state level in proportion, but the time to reach it is set by the half-life alone. Only a loading dose shortens the wait, because it places the level at the target from the start rather than building it up.

Which drugs need their blood levels monitored?

Drugs with a narrow therapeutic index, where small changes cause failure or toxicity, such as warfarin, digoxin, lithium, phenytoin and theophylline; potentially toxic drugs such as vancomycin and the aminoglycosides; and poisonings such as paracetamol or salicylate overdose.

Study strategy

Exam move

Write the five dosing equations on a blank page every day for a week, then solve one regimen problem with your own numbers. Each time, say which quantity depends on volume and which on clearance before you calculate.

Working through Clearance, Half-Life and Steady-State Dosing in MDG5204? Sia is AskSia’s AI Pharmacology tutor — ask any MDG5204 Clearance, Half-Life and Steady-State Dosing question and get a clear, step-by-step explanation grounded in how MDG5204 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.

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