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
Which teaching about antiepileptic drugs is most important?
AAlcohol has no effect on seizure control
BStop the drug when you have had no seizures for one whole week
CDo not stop the drug suddenly, as this can trigger severe seizures
DTake a double dose if you feel a seizure coming
2.PharmacologyHard
Which finding most favours serotonin syndrome over neuroleptic malignant syndrome?
ARecent start of an antipsychotic drug
BSlow onset over days with lead-pipe rigidity
CA very high creatine kinase
DRapid onset with hyperreflexia and clonus
3.Dosage calculationsMedium
A patient weighs 18 kg and is prescribed 15 mg/kg as a single dose. Find the dose D in mg.
18 kg15 mg/kg
D = mg
4.Dosage calculationsHard
A child weighing 12 kg is prescribed 5 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?
12 kg5 mg/kg250 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A 67 kg patient is to be loaded with digoxin tablets to reach a level of 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.
67 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 55-year-old man weighs 51 kg and has a serum creatinine of 1.4 mg/dL (124 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 tobramycin regimen is 120 mg every 8 h for a creatinine clearance of 120 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.
Answer: C · Do not stop the drug suddenly, as this can trigger severe seizures
Why this is the answer
Abrupt withdrawal of antiepileptic drugs can cause rebound seizures and even status epilepticus. Any change is made gradually under medical supervision.
Answer
C · Do not stop the drug suddenly, as this can trigger severe seizures
2.Pharmacology
Answer: D · Rapid onset with hyperreflexia and clonus
Why this is the answer
Serotonin syndrome develops within hours of a serotonergic drug and causes clonus, hyperreflexia, agitation, dilated pupils and diarrhoea. NMS develops over days after a dopamine antagonist, with lead-pipe rigidity and slow reflexes.
Answer
D · Rapid onset with hyperreflexia and clonus
3.Dosage calculations
Answer: D = 270 mg
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
15·18 = 270 mg
Answer
D = 270 mg
4.Dosage calculations
Answer: V = 1.2 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
5·12 = 60 mg
Volume
V = (60/250)·5 = 1.2 mL
Answer
V = 1.2 mL
5.Clinical pharmacokinetics
Answer: LD = 670 mcg
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.
Volume of distribution
Vd = 7·67 = 469 L
Amount of active drug needed
Vd·C = 469·1 = 469 mcg
Loading dose
LD = 469/(1·0.7) = 670 mcg
Answer
LD = 670 mcg
In practice the dose is rounded to a convenient amount.
6.Clinical pharmacokinetics
Answer: τ = 22.3 h
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 − 55)·51/(72·1.4) = 43.01 mL/min
New interval
τ = 8·120/43.01 = 22.32 ≈ 22.3 h
Answer
τ = 22.3 h
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.