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 oral potassium chloride tablets be taken?
AWith food and plenty of water, swallowed whole if slow-release
BCrushed and dissolved under the tongue
COn an empty stomach with only a small sip of water, then lie down
DLying down straight after the dose
2.PharmacologyHard
Why is glibenclamide (glyburide) generally avoided in older adults?
AIt is long-acting and can cause prolonged, severe hypoglycaemia
BIt causes severe weight loss and muscle wasting in older people
CIt is not absorbed in people over 65
DIt causes high blood glucose in older adults
3.Dosage calculationsMedium
A patient weighing 25 kg has a body surface area of 1.05 m². The prescription is 175 mg/m². Find the dose D in mg.
25 kgBSA = 1.05 m²175 mg/m²
D = mg
4.Dosage calculationsHard
The prescription is 2.08 mg. The ampoule contains 4000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
2.08 mg4000 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). An 86 kg patient is to be loaded intravenously with aminophylline to reach a theophylline level of 12 mg/L. The volume of distribution is 0.5 L/kg and the salt factor is S = 0.8. Find the loading dose LD of aminophylline in mg.
86 kgVd = 0.5 L/kgC = 12 mg/LS = 0.8
LD = mg
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). An 88-year-old man weighs 82 kg and has a serum creatinine of 2.6 mg/dL (230 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 atenolol dose is 100 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.9 of the drug is excreted unchanged by the kidneys. Using the Dettli dose fraction Q = 1 − fe·(1 − CrCl/normal CrCl), find the adjusted dose D. Round to the nearest whole number.
Answer: A · With food and plenty of water, swallowed whole if slow-release
Why this is the answer
Oral potassium can cause nausea and, if a tablet lodges, ulceration of the oesophagus or gut. Taking it with food and plenty of water and staying upright reduces this; levels are monitored.
Answer
A · With food and plenty of water, swallowed whole if slow-release
2.Pharmacology
Answer: A · It is long-acting and can cause prolonged, severe hypoglycaemia
Why this is the answer
Glibenclamide has a long action and active metabolites that accumulate when kidney function declines. Older adults are at high risk of prolonged hypoglycaemia, so shorter-acting agents or other drug classes are preferred.
Answer
A · It is long-acting and can cause prolonged, severe hypoglycaemia
3.Dosage calculations
Answer: D = 183.8 mg
Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).
Dose
D = 175·1.05 = 183.8 mg
Answer
D = 183.8 mg
4.Dosage calculations
Answer: V = 0.52 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
2.08 mg = 2080 mcg
Volume
V = 2080/4000 = 0.52 mL
Answer
V = 0.52 mL
5.Clinical pharmacokinetics
Answer: LD = 645 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 = 0.5·86 = 43 L
Amount of active drug needed
Vd·C = 43·12 = 516 mg
Loading dose
LD = 516/(0.8·1) = 645 mg
Answer
LD = 645 mg
In practice the dose is rounded to a convenient amount.
6.Clinical pharmacokinetics
Answer: D = 31 mg
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 − 88)·82/(72·2.6) = 22.78 mL/min
Dose fraction (Dettli)
Q = 1 − 0.9·(1 − 22.78/100) = 0.305
Adjusted dose
D = 0.305·100 = 30.5 ≈ 31 mg
Answer
D = 31 mg
In practice the dose is rounded to a convenient amount and checked against the product information.