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
How should a patient take oral alendronate?
AWith milk at bedtime, then lying down straight away to aid absorption
BWith plain water on an empty stomach, staying upright for 30 minutes
CCrushed into yoghurt with calcium supplements
DWith breakfast and coffee to protect the stomach
2.PharmacologyHard
A patient with myasthenia gravis took extra pyridostigmine doses. She now has increasing weakness, heavy salivation, sweating, small pupils and diarrhoea. What is the most likely cause?
ACholinergic crisis from too much anticholinesterase drug
BAn allergic reaction to pyridostigmine
CA stroke unrelated to the medication
DMyasthenic crisis from too little anticholinesterase drug
3.Dosage calculationsMedium
A child weighing 20 kg is prescribed 7.5 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
20 kg7.5 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 1200 units of a drug that comes as 5000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
1200 units5000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A 100 kg patient is to be loaded with digoxin tablets to reach a level of 0.8 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.
100 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 125 mg/h with no loading dose. The patient's clearance is 5 L/h and the half-life is 8 h. What is the level C after 4 h?
R = 125 mg/hCL = 5 L/ht½ = 8 ht = 4 h
C = mg/L
3Solutions
1.Pharmacology
Answer: B · With plain water on an empty stomach, staying upright for 30 minutes
Why this is the answer
Alendronate is taken first thing in the morning with water only, before food or other drugs. Staying upright reduces the risk of oesophageal ulceration, and food or calcium blocks its absorption.
Answer
B · With plain water on an empty stomach, staying upright for 30 minutes
2.Pharmacology
Answer: A · Cholinergic crisis from too much anticholinesterase drug
Why this is the answer
Excess acetylcholine causes muscarinic signs (salivation, sweating, miosis, diarrhoea) and depolarising weakness. In myasthenic crisis, weakness occurs without these cholinergic signs; both can cause respiratory failure.
Answer
A · Cholinergic crisis from too much anticholinesterase drug
3.Dosage calculations
Answer: V = 3 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 = 7.5·20 = 150 mg
Volume
V = 150/50 = 3 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3 mL
4.Dosage calculations
Answer: V = 0.24 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 = 1200/5000 = 0.24 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.24 mL
5.Clinical pharmacokinetics
Answer: LD = 800 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 = 7·100 = 700 L
Amount of active drug needed
Vd·C = 700·0.8 = 560 mcg
Loading dose
LD = 560/(1·0.7) = 800 mcg
Answer
LD = 800 mcg
In practice the dose is rounded to a convenient amount.
6.Clinical pharmacokinetics
Answer: C = 7.322 mg/L
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.