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?
AStop the drug when you have had no seizures for one whole week
BAlcohol has no effect on seizure control
CTake a double dose if you feel a seizure coming
DDo not stop the drug suddenly, as this can trigger severe seizures
2.PharmacologyHard
A patient receiving a phenylephrine infusion has a rise in blood pressure and a fall in heart rate. What is the best explanation?
APhenylephrine directly blocks beta-1 receptors in the heart's conduction system
BAlpha-1 vasoconstriction raises blood pressure and causes reflex bradycardia
CThe fall in heart rate shows phenylephrine toxicity of the AV node
DPhenylephrine stimulates muscarinic receptors
3.Dosage calculationsMedium
A dose of 40 mg is needed from a 1% (w/v) solution. What volume V contains this dose?
40 mg1% w/v
V = mL
4.Dosage calculationsHard
The prescription is 0.27 mg. The ampoule contains 1000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
0.27 mg1000 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 9 mg/L at 1 h and 4.5 mg/L at 3 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 9 mg/L (1 h)C2 = 4.5 mg/L (3 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 86-year-old man weighs 85 kg and has a serum creatinine of 2 mg/dL (177 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: D · 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
D · Do not stop the drug suddenly, as this can trigger severe seizures
2.Pharmacology
Answer: B · Alpha-1 vasoconstriction raises blood pressure and causes reflex bradycardia
Why this is the answer
Phenylephrine is a pure alpha-1 agonist with little direct cardiac action. The higher blood pressure activates baroreceptors, which increase vagal tone and slow the heart.
Answer
B · Alpha-1 vasoconstriction raises blood pressure and causes reflex bradycardia
3.Dosage calculations
Answer: V = 4 mL
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Concentration
1% = 10 mg/mL
Volume
V = 40/10 = 4 mL
Answer
V = 4 mL
4.Dosage calculations
Answer: V = 0.27 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.
Same units
0.27 mg = 270 mcg
Volume
V = 270/1000 = 0.27 mL
Answer
V = 0.27 mL
5.Clinical pharmacokinetics
Answer: k = 0.3466 h⁻¹
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(9/4.5)/2 = 0.6931/2 = 0.3466 h⁻¹
Answer
k = 0.3466 h⁻¹
6.Clinical pharmacokinetics
Answer: τ = 30.1 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 − 86)·85/(72·2) = 31.88 mL/min
New interval
τ = 8·120/31.88 = 30.12 ≈ 30.1 h
Answer
τ = 30.1 h
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.