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 assessment is most important before giving a dose of IV morphine?
ABlood glucose and temperature, checked before each dose
BPupil size and hearing
CBowel sounds and urine colour
DRespiratory rate and level of sedation
2.PharmacologyHard
A patient on digoxin and furosemide develops nausea, visual disturbances and an irregular pulse. Which electrolyte disturbance most likely made digoxin toxicity more likely?
AHypokalaemia
BHypernatraemia
CHypocalcaemia
DHyperkalaemia
3.Dosage calculationsMedium
A child weighing 13 kg is prescribed 20 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
13 kg20 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 6400 units of a drug that comes as 10000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
6400 units10000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 60 mL/min. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?
CL = 60 mL/minCss = 25 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's tobramycin half-life is 3 h. The target is a peak of 8 mg/L and a trough of 0.5 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.
t½ = 3 hCpeak = 8 mg/LCtrough = 0.5 mg/L
τ = h
3Solutions
1.Pharmacology
Answer: D · Respiratory rate and level of sedation
Why this is the answer
Opioids can cause respiratory depression, which is usually preceded by increasing sedation. Both are checked before and after each dose.
Answer
D · Respiratory rate and level of sedation
2.Pharmacology
Answer: A · Hypokalaemia
Why this is the answer
Digoxin binds the Na⁺/K⁺-ATPase at the same site as potassium. Low potassium, often caused by loop or thiazide diuretics, increases digoxin binding and toxicity.
Answer
A · Hypokalaemia
3.Dosage calculations
Answer: V = 5.2 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 = 20·13 = 260 mg
Volume
V = 260/50 = 5.2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 5.2 mL
4.Dosage calculations
Answer: V = 0.64 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.
Volume
V = 6400/10000 = 0.64 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.64 mL
5.Clinical pharmacokinetics
Answer: R = 90 mg/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.
Clearance in L/h
60·60/1000 = 3.6 L/h
Infusion rate
R = 3.6·25 = 90 mg/h
Answer
R = 90 mg/h
6.Clinical pharmacokinetics
Answer: τ = 12 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.
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Dosing interval
τ = ln(8/0.5)/0.231 = 2.773/0.231 = 12 h
Answer
τ = 12 h
In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.