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
A parent will give a liquid medicine to a child at home. Which advice is safest?
AUse the oral syringe or measuring cup supplied with it
BMix the dose into a full bottle of milk
CUse any kitchen teaspoon
DEstimate the dose by pouring the liquid into a small cup
2.PharmacologyHard
A patient who uses insulin is taught sick-day rules. Which statement shows a need for further teaching?
A"I will seek help if I keep vomiting or have ketones."
B"I will check my blood glucose and ketones more often while I am ill."
C"I will keep drinking fluids, even if I cannot eat much."
D"If I am ill and not eating, I will stop my insulin completely."
3.Dosage calculationsMedium
A child weighing 33 kg is prescribed 2 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
33 kg2 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 8600 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?
8600 units10000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A 59 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 15 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.
59 kgVd = 0.7 L/kgC = 15 mg/LS = 0.92
LD = mg
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's gentamicin half-life is 3 h. The target is a peak of 8 mg/L and a trough of 1 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 = 1 mg/L
τ = h
3Solutions
1.Pharmacology
Answer: A · Use the oral syringe or measuring cup supplied with it
Why this is the answer
Kitchen spoons are inaccurate and can cause under- or overdosing. Oral syringes in millilitres are the most accurate, and mixing doses into a whole bottle risks the child not getting the full dose.
Answer
A · Use the oral syringe or measuring cup supplied with it
2.Pharmacology
Answer: D · "If I am ill and not eating, I will stop my insulin completely."
Why this is the answer
Stress hormones during illness often raise glucose, so basal insulin is usually continued and doses may need adjusting. Stopping insulin in type 1 diabetes can lead to ketoacidosis.
Answer
D · "If I am ill and not eating, I will stop my insulin completely."
3.Dosage calculations
Answer: V = 6.6 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 = 2·33 = 66 mg
Volume
V = 66/10 = 6.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 6.6 mL
4.Dosage calculations
Answer: V = 0.86 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 = 8600/10000 = 0.86 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.86 mL
5.Clinical pharmacokinetics
Answer: LD = 673.4 mg
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 = 0.7·59 = 41.3 L
Amount of active drug needed
Vd·C = 41.3·15 = 619.5 mg
Loading dose
LD = 619.5/(0.92·1) = 673.4 mg
Answer
LD = 673.4 mg
In practice the dose is rounded to a convenient amount.
6.Clinical pharmacokinetics
Answer: τ = 9 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(8/1)/0.231 = 2.079/0.231 = 9 h
Answer
τ = 9 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.