Pharmacokinetics
Introduced| English | Meaning |
|---|---|
| clearance/ˈklɪərəns/ | A longer half-life. |
| bioavailability | bioavailability |
| first-pass metabolism | first-pass metabolism |
| volume of distribution | volume of distribution |
| steady state/ˈstedi steɪt/ | steady state |
| loading dose | loading dose |
Why the fifth day feels different
- A patient takes one tablet a day of a drug whose half-life is 24 hours. Days 1 and 2 do little; by day 5 the effect is steady.
- The body sees concentration, not dose. Three numbers turn one into the other: volume, clearance and half-life.
Getting in: bioavailability
- Bioavailability 生物利用度 ($F$) is the fraction of a dose that reaches the circulation. An injection into a vein has $F$ = 1.
- A tablet is absorbed into the portal vein and passes the liver first. First-pass metabolism 首过代谢 can remove much of it before it reaches the body.
Put the journey of an oral drug in order.
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Absorption, distribution, metabolism and excretion (ADME).
Volume of distribution
- Volume of distribution 表观分布容积 ($V_d$) is the apparent volume the drug spreads into: dose ÷ plasma concentration.
- It is not a real space. About 3 L means the drug stays in plasma; 500 L means it is bound up in tissues, leaving little in the blood.
A drug has a volume of distribution of 500 L in a 70 kg adult. What does this tell you?
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Little drug stays in the blood, so the apparent volume is huge.
Clearance and half-life
- Clearance 清除率 ($CL$) is the volume of plasma cleared of drug per hour, mostly by the liver and kidneys.
- Half-life links the two: $t_{1/2} = 0.693 \times V_d / CL$. A bigger volume or a lower clearance means a longer half-life.
(Illustrative) $V_d$ = 70 L and $CL$ = 7 L/h. What is the half-life? Use 0.693.
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0.693 × 70 ÷ 7 = 6.93 h.
After a single dose, what percentage of the drug is left after 3 half-lives?
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100 → 50 → 25 → 12.5%.
Steady state and the loading dose
- With regular doses, the level climbs until intake equals removal: about 90% of steady state 稳态 after 3.3 half-lives, about 97% after 5.
- A loading dose 负荷剂量 fills the volume at once: $D_L = C_{target} \times V_d / F$. Clearance sets the maintenance dose; volume sets the loading dose.
With regular dosing, a drug is close to steady state after about 5 half-lives.
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About 97% of steady state after 5 half-lives.
Worked example: the three levers
- (Illustrative values, not a prescription) $V_d$ = 40 L, $CL$ = 5 L/h: $t_{1/2} = 0.693 \times 40 \div 5 = 5.5$ h.
- Liver disease halves clearance to 2.5 L/h: $t_{1/2}$ doubles to 11.1 h. The same dose now builds up to a level twice as high, and takes twice as long to get there.
Worked example: a loading dose
- (Illustrative) Target 10 mg/L, $V_d$ = 40 L, given into a vein ($F$ = 1): $D_L = 10 \times 40 \div 1 = 400$ mg.
- Given by mouth with $F$ = 0.5, the same target needs 400 ÷ 0.5 = 800 mg, because half is lost on the way.
(Illustrative) Target 4 mg/L, $V_d$ = 50 L, oral $F$ = 0.5. What loading dose is needed?
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4 × 50 ÷ 0.5 = 400 mg.
Three common slips
- Treating $V_d$ as a real volume. It is a ratio; 500 L is larger than the body.
- Equating half-life with how long the effect lasts. The effect depends on the level compared with the drug's working range.
- Expecting a loading dose to change the steady state. It only gets you there sooner; the maintenance dose sets the level.
Match each quantity to what it sets.
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Each lever controls a different part of the dosing plan.
Recap
- $F$ = fraction reaching the blood; first-pass metabolism lowers oral $F$.
- $t_{1/2} = 0.693\,V_d/CL$; steady state at about 4–5 half-lives (90% at 3.3, 97% at 5).
- Loading dose $= C_{target} V_d / F$; clearance sets the maintenance dose.