BMS 123 · Common Core (Tronc commun)Section 4.4 · Drug excretion and clearance
Section 17 of 27
Clearance and half-life
Define clearance, use CL = 0.693 × Vd ÷ t½, and interpret a renal clearance value against the glomerular filtration rate.
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Why this matters
Clearance answers the question how fast does this patient remove the drug, and the answer sets the half-life, the dose interval, the duration of action and how quickly a toxic level can fall. The equation that links clearance to volume and half-life also shows why two drugs with the same clearance can behave completely differently, and why a failing organ changes the whole plan rather than one small detail. It is the number that turns pharmacology into a dose schedule.
What you need to know first
You need the apparent volume of distribution from Unit 2 and the three renal processes from section 4.1. The only mathematics here is one multiplication and one division; the hard part is reading what the result means.
Words to know (5)
Clearance (CL)
The volume of plasma cleared of drug per unit time; it estimates how fast the body removes a drug and is expressed as a volume per minute. A clearance of 120 mL/min means that 120 mL of plasma is cleared every minute.
Half-life (t½)
The time required for the plasma concentration of a drug to fall by half. A drug with a half-life of 8 hours is half gone after 8 hours and three-quarters gone after 16 hours.
Total systemic clearance
The sum of all organ clearances, chiefly hepatic and renal, that remove drug from the body. If hepatic clearance falls, total systemic clearance falls with it.
Renal clearance
The net volume of plasma cleared by the kidney: filtration plus secretion minus reabsorption. A drug that is only filtered has a renal clearance equal to the GFR.
Glomerular filtration rate (GFR)
The volume of fluid filtered by the glomeruli each minute, normally about 120–130 mL/min; it is the reference against which renal clearance is read. A renal clearance of 600 mL/min is far above the GFR and therefore implies active secretion.
One idea at a timeIdea 1 / 5
In one sentence Clearance estimates the volume of drug cleared from the body per unit of time, so it is expressed as millilitres per minute, not milligrams.
Clearance is a volume per unit time, not an amount
The notes define clearance (CL) as an estimate of the amount of drug cleared from the body per unit of time, and it can be estimated for each route of clearance. The units matter for understanding: clearance is a volume of plasma or blood cleared of drug each minute, not a mass of drug removed. A clearance of 120 mL per minute means that 120 mL of plasma is completely cleared of the drug every minute, whatever the concentration happens to be. Because the fraction removed per unit time stays roughly constant for most drugs, clearance describes the efficiency of elimination rather than the size of the dose. This is why clearance can be compared between patients, between drugs and against the filtration rate, while the number of milligrams removed per minute cannot be compared without also knowing the concentration.
For example
If a drug has a clearance of 60 mL/min, the body clears the drug contained in 60 mL of plasma each minute, whether the plasma level is high or low.
Think of it like
Clearance works like the flow rate of a water filter: it is a volume of fluid cleaned per minute, not a mass of dirt removed, so a dirty stream and a clean one pass through at the same number of litres per minute. The comparison has a limit, because clearance is not a fixed pipe — it is calculated from the fraction the organs remove, and that fraction can fall when the elimination routes saturate.
Pause and check yourself
Is clearance measured in milligrams or in millilitres per minute?
Show the answer
In millilitres per minute: it is a volume of plasma cleared per unit time, not a mass of drug. The mass removed depends on the concentration and on that volume.
Read detailed explanations
Where 0.693 comes from, and what first order means
The constant 0.693 looks arbitrary until you see what it measures. Most drugs are eliminated by a process that removes a constant fraction of whatever is present per unit time, rather than a constant amount. That behaviour is called first-order elimination, and it produces an exponential fall: after one half-life half remains, after two a quarter, after three an eighth. In mathematical form the concentration is an exponential function of time, and the rate constant in the exponent is the natural logarithm of 2 divided by the half-life. Since the natural logarithm of 2 is 0.693, the rate constant is 0.693 ÷ t½. Clearance is then simply that rate constant multiplied by the volume in which the drug is dissolved, which gives CL = 0.693 × Vd ÷ t½. The practical meaning is that half-life is a consequence, not a cause. It changes when clearance changes, when volume changes, or when both change. A few drugs, such as ethanol at high concentrations, show zero-order elimination instead, meaning a fixed amount is removed per unit time; their half-life is not constant and the simple equation does not apply.
The three CL-versus-GFR patterns in practice
Comparing renal clearance with the filtration rate is a compact diagnostic. The first pattern is clearance equal to GFR. Here the drug is filtered and then neither secreted nor reabsorbed, so the amount appearing in urine is simply the filtered load. The second pattern is clearance greater than GFR. Filtration alone cannot explain the result, so the proximal carriers must be adding drug to the tubule; this is typical of organic anions and cations that the kidney actively secretes, and it is why a strongly protein-bound acidic drug can still be cleared efficiently. The third pattern is clearance less than GFR. Some of the filtered drug must be returning to the blood, so reabsorption is significant; this is typical of lipid-soluble, uncharged molecules that diffuse back across the tubule. The same reasoning can be used quantitatively: renal clearance can be measured as the amount of drug appearing in urine per unit time divided by the plasma concentration, and that measured value can then be set beside the patient’s GFR. The comparison guides dose adjustment because a change in the dominant process predicts where the risk lies: a secreted drug is vulnerable to competition and saturation, while a reabsorbed drug is vulnerable to changes in urine pH and urine flow.
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Clearance, half-life and the decay curve
A plasma concentration–time curve with the half-life marked, beside the relationship that links clearance, volume of distribution and half-life.
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01 / 5Plasma concentration
If the drawing is wider than this panel, scroll it sideways. Labels stay readable; the numbered explanations below show the same ideas.
Plasma concentration
The amount of drug per unit volume of plasma at a given moment. It falls because drug is being distributed to tissues, metabolised and excreted. On this plate the distribution phase has already passed, so the curve shows elimination alone.
Teaching schematic; the drawn curve is an idealised first-order decay, not measured data. Real patients may show a distribution phase before the straight-line elimination phase.
Key points to remember
✓Clearance is the volume of plasma cleared per unit time, measured in millilitres per minute.
✓CL = 0.693 × Vd ÷ t½, where 0.693 is the natural logarithm of 2.
✓Total clearance is the sum of hepatic, renal, pulmonary and other clearances, with hepatic and renal the most important.
✓Renal clearance equals filtration plus secretion minus reabsorption.
✓Compared with GFR, renal clearance reveals the mechanism, and the elimination rate sets half-life, dose interval, duration of action and toxicity.
Go deeper
Worked example
Two drugs, one clearance equation. Drug A has Vd 10 L and half-life 2 h. Drug B has Vd 100 L and half-life 20 h. Both are given to the same patient. Calculate the clearance of each and explain what the numbers mean for dosing.
Use CL = 0.693 × Vd ÷ t½ for drug A: 0.693 × 10 ÷ 2 ≈ 3.5 L/h.
Use the same equation for drug B: 0.693 × 100 ÷ 20 ≈ 3.5 L/h.
Compare: the two drugs have the same clearance but very different volumes of distribution and half-lives; the body removes drug from plasma at the same rate, yet drug B leaves a large tissue reservoir slowly.
Interpret for dosing: drug A needs a shorter interval or a sustained-release form, while drug B can be given less often; the difference comes from Vd shaping t½, not from organ function.
State the general rule: clearance tells you how efficiently the organs work, and half-life tells you how the dose schedule must be arranged; the two are linked through Vd.
Identical clearances can produce half-lives twenty times apart when the volumes of distribution differ. That is why CL, Vd and t½ must always be read together rather than one at a time.
Common misconception
A frequent misunderstanding is that a drug with a high clearance must have a short half-life. It usually does, but not if its volume of distribution is very large: the same clearance working on a bigger volume takes longer to empty it.
Check your reasoning
A patient’s renal function falls and the measured clearance of a renally cleared drug drops by half. What happens to the half-life if Vd does not change, and what should follow for the dose interval?
Reveal an answer
Half-life is inversely related to clearance, so if clearance halves and Vd is unchanged, the half-life approximately doubles. The drug will accumulate if the interval is kept, so the interval usually has to be lengthened or the dose reduced, guided by monitoring of the patient and of drug levels where available.
Where this comes from
General Pharmacology II lecture notes — Lecture 4, Drug clearance · Section 3, clearance equation and total body clearance
General Pharmacology II lecture notes — Lecture 4, Drug clearance · Section 3, renal drug clearance and interpretation against GFR
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About this course and its sources
Bilingual lessons organised from the supplied BMS 123 General Pharmacology II lecture notes (Principles of Pharmacokinetics and Principles of Pharmacodynamics). Diagrams are original educational schematics; pharmacology, nursing and French-language review are pending.