16.3 Half-Life & Basic Kinetic Calculations

15.3 Half-Life & Basic Kinetic Calculations

Quick Answer: Elimination half-life (t½) is the time for drug concentration to drop by half. Use it to estimate how long to wash out, when steady state is near, and how renal impairment may stretch dosing intervals. Intern Written kinetics stay at conceptual formulas and clean arithmetic—not full multi-compartment modelling. FIB items may ask for remaining concentration, number of half-lives, or hours to a stated fraction remaining; enter the exact number the stem’s units require.

Kinetics link compounding numeracy (Standard 3.4) to monitoring sense (Standard 3.3): knowing when levels matter is as important as how to calculate a volume.

What half-life means

For first-order elimination (the usual exam assumption for these rules of thumb):

• After 1 × t½: 50% remains
• After 2 × t½: 25% remains
• After 3 × t½: 12.5% remains
• After 4 × t½: 6.25% remains → about 94% eliminated
• After 5 × t½: 3.125% remains → about 97% eliminated

Half-life is a time (hours, days). It is not a concentration and not a dose.

Worked example A — remaining fraction

A drug has t½ = 6 hours. Starting concentration 80 mg/L (assume no further doses, distribution complete).

After 12 hours (2 half-lives): 20 mg/L remains.

FIB practice: if asked “concentration after 12 h in mg/L,” enter 20.

Worked example B — time to ~94% elimination

t½ = 8 hours. Time for ~4 half-lives ≈ 4 × 8 = 32 hours.

If the stem asks how many hours until roughly 6% remains, answer 32 (hours).

Worked example C — how many half-lives?

Concentration falls from 64 mg/L to 4 mg/L.

• 64 → 32 → 16 → 8 → 4 = 4 half-lives

If t½ = 3 h, time elapsed = 12 h.

Steady state (~4–5 half-lives)

On repeated fixed dosing with linear kinetics, plasma levels rise until input equals elimination. Steady state (Css) is effectively approached after about 4–5 elimination half-lives of continuous or regular therapy—not after 4–5 doses unless the dosing interval equals the half-life.

Worked example D — time to steady state

Drug t½ = 12 hours, given regularly every 12 hours.

• 4 × t½ = 48 h; 5 × t½ = 60 h → expect near steady state in about 2–2.5 days

If t½ = 6 hours:

• 4–5 half-lives ≈ 24–30 hours

Exam interpretation: measuring a level after one dose of a long half-life drug does not represent steady-state Css. Timing of levels (trough versus peak) still matters clinically; half-life only tells the accumulation timeline.

Basic Css and loading-dose concepts (no advanced PK required)

You should recognise relationships, not derive multi-compartment AUCs.

Maintenance rate and clearance

At steady state, roughly:

$\text{Dosing rate} \approx CL \times C_{ss}$

So if clearance falls (for example severe renal impairment for a renally cleared drug), the same dosing rate produces a higher Css—maintenance doses often need reduction or intervals lengthened.

Loading dose concept

A loading dose fills the volume of distribution to a target concentration quickly:

$LD \approx C_{target} \times V_d$

(Bioavailability F may appear as LD ≈ (Ctarget × Vd) / F for oral products.)

Worked example E — loading dose arithmetic

Target concentration 10 mg/L, Vd 30 L, IV (F = 1).

• LD = 10 × 30 = 300 mg

FIB: 300 (mg).

Worked example F — why load?

If t½ is 24 hours, waiting for steady state on maintenance alone may take 4–5 days. A loading dose reaches therapeutic levels early, while maintenance keeps Css. Exam stems test the idea more than obscure constants.

Dosing interval intuition

• Drugs with short t½ may need more frequent dosing (or formulations that slow input) to avoid large peak–trough swings.
• Drugs with long t½ can often be given less frequently once loaded, but take longer to clear after stopping and longer to reach Css.

Renal impairment and half-life (qualitative + simple numbers)

If a drug is largely renally cleared, falling eGFR can reduce clearance, prolong t½, and raise accumulation risk at unchanged doses.

Worked example G — qualitative

A renally cleared drug has t½ 4 hours in normal function. In severe impairment, t½ might lengthen substantially (exact factor is drug-specific—use AMH-style guidance in practice). Exam reasoning:

• Longer t½ → longer time to steady state if started without a load
• Longer t½ → higher troughs if the interval is not adjusted
• Stopping the drug → slower washout (more half-lives of calendar time)

Worked example H — washout comparison

Normal t½ 4 h → ~4 half-lives ≈ 16 h to ~94% gone.
If t½ becomes 12 h → ~4 half-lives ≈ 48 h to the same residual fraction.

You do not invent a new half-life number without data; you interpret direction when the stem states impairment and a renally cleared agent.

Linking kinetics to dosing-interval questions

Typical Intern Written patterns:

1. When can I re-challenge / when is most drug gone? → count ~4 half-lives for ~94% elimination (unless the stem defines another threshold).
2. When are steady-state levels meaningful? → after ~4–5 half-lives on a stable regimen (and correct sample timing).
3. Why reduce dose in renal failure? → lower CL → higher Css if rate unchanged; t½ may rise.
4. Loading versus maintenance → load uses Vd × target; maintenance matches elimination (CL × Css).

Worked example I — multi-step half-life

Peak (post-distribution) level 32 mg/L, t½ 5 hours. What is the level after 15 hours if no further drug is given?

• 15 h = 3 half-lives
• 32 → 16 → 8 → 4 mg/L

Worked example J — percent eliminated

After 2 half-lives, fraction remaining = 25%, so fraction eliminated = 75%.

After 4 half-lives, remaining 6.25%, eliminated 93.75% ≈ 94%.

FIB technique for kinetic numbers

• Decide whether the blank wants concentration, hours, number of half-lives, or dose (mg).
• Halve concentrations once per half-life—do not divide by the half-life value itself (a common error: “t½ = 6 h so divide concentration by 6”).
• Time elapsed ÷ t½ = number of half-lives only when units match (both hours).
• Keep linear first-order assumptions unless the stem signals saturation kinetics.
• Round only as the stem requires; many pure halving sequences stay exact (80 → 40 → 20).

Putting Standard 3.4 calculations together

Chapters 14–15 form the compounding and calculation band of the blueprint (~8% combined weight with formulation). In practice and on exam day:

• Section 16.1 turns a prescribed dose into mg and mL and day supply
• Section 16.2 turns labelled strengths into recipes and safe dilutions
• Section 16.3 turns half-life into timing and accumulation literacy

Use scrap paper, SI units, and magnitude checks on every FIB. Exact arithmetic under time pressure is a registrable pharmacist skill—not optional numeracy.