Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
Check the result: levels fall by half every half-life, and steady state takes about five half-lives.
2Practice problems
1.PharmacologyMedium
When should a patient take a once-daily proton pump inhibitor such as omeprazole?
AAbout 30–60 minutes before the first meal of the day
BWith a glass of milk at bedtime, when acid output is highest
CStraight after a large evening meal
DOnly when heartburn is severe
2.PharmacologyHard
A patient with severe liver cirrhosis needs a benzodiazepine for alcohol withdrawal. Why is lorazepam often chosen instead of diazepam?
ALorazepam is cleared by simple conjugation and has no active metabolites
BLorazepam does not cause sedation in liver disease
CLorazepam is a stronger anticonvulsant than all other benzodiazepines
DLorazepam is excreted unchanged in the urine without any metabolism
3.Dosage calculationsMedium
A child weighing 16 kg is prescribed 15 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
16 kg15 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
A child weighing 18 kg is prescribed 20 mg/kg per dose of an oral suspension that contains 100 mg in 5 mL. What volume V do you give?
18 kg20 mg/kg100 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 7 mg/L at 1 h and 2.8 mg/L at 5 h. Assume first-order elimination. Find the half-life t½.
C1 = 7 mg/L (1 h)C2 = 2.8 mg/L (5 h)
t½ = h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 61-year-old woman weighs 94 kg and has a serum creatinine of 2.8 mg/dL (248 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual digoxin dose is 250 mcg for a creatinine clearance of 120 mL/min, and a fraction fe = 0.7 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.
Answer: A · About 30–60 minutes before the first meal of the day
Why this is the answer
Proton pump inhibitors block pumps that are active, so they work best when taken before breakfast. Food then activates the pumps when the drug level is high.
Answer
A · About 30–60 minutes before the first meal of the day
2.Pharmacology
Answer: A · Lorazepam is cleared by simple conjugation and has no active metabolites
Why this is the answer
Diazepam is metabolised by CYP enzymes into long-acting active metabolites, which accumulate in liver failure. Lorazepam, oxazepam and temazepam are glucuronidated, a process better preserved in liver disease.
Answer
A · Lorazepam is cleared by simple conjugation and has no active metabolites
3.Dosage calculations
Answer: V = 9.6 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
Dose from body weight
D = 15·16 = 240 mg
Volume
V = 240/25 = 9.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 9.6 mL
4.Dosage calculations
Answer: V = 18 mL
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Dose from weight
20·18 = 360 mg
Volume
V = (360/100)·5 = 18 mL
Answer
V = 18 mL
5.Clinical pharmacokinetics
Answer: t½ = 3.026 h
Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Elimination rate constant
k = ln(7/2.8)/4 = 0.9163/4 = 0.2291 h⁻¹
Half-life
t½ = 0.693/0.2291 = 3.026 h
Answer
t½ = 3.026 h
6.Clinical pharmacokinetics
Answer: D = 121 mcg
Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Creatinine clearance (Cockcroft–Gault)
CrCl = (140 − 61)·94/(72·2.8)·0.85 = 31.31 mL/min
Dose fraction (Dettli)
Q = 1 − 0.7·(1 − 31.31/120) = 0.4826
Adjusted dose
D = 0.4826·250 = 120.7 ≈ 121 mcg
Answer
D = 121 mcg
In practice the dose is rounded to a convenient amount and checked against the product information.