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
Why are benzodiazepines used with great caution in older people?
AThey cause severe high blood pressure in older people
BThey raise the risk of confusion, falls and fractures
CThey cause permanent hearing loss in older people
DThey are not absorbed from the gut after age 65
2.PharmacologyHard
Which pair of adverse effects is characteristic of long-term amiodarone treatment?
AOtotoxicity and nephrotoxicity
BGum overgrowth and excess hair growth
CThyroid dysfunction and pulmonary fibrosis
DDry cough and angioedema
3.Dosage calculationsMedium
A child weighing 6 kg is prescribed 15 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
6 kg15 mg/kg10 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 1100 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?
1100 units5000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A 73 kg patient receives a theophylline infusion. The clearance is 0.035 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 10 mg/L?
73 kgCL = 0.035 L/kg/hCss = 10 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 50-year-old man weighs 77 kg and has a serum creatinine of 1.6 mg/dL (141 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 cefazolin dose is 1000 mg every 8 h for a creatinine clearance of 100 mL/min. Keeping the interval, the dose is reduced in proportion to the creatinine clearance. Find the adjusted dose D. Round to the nearest whole number.
Answer: B · They raise the risk of confusion, falls and fractures
Why this is the answer
Older people are more sensitive to benzodiazepines and often eliminate them more slowly. Sedation, unsteadiness and confusion raise the risk of falls and fractures.
Answer
B · They raise the risk of confusion, falls and fractures
2.Pharmacology
Answer: C · Thyroid dysfunction and pulmonary fibrosis
Why this is the answer
Amiodarone is iodine-rich and accumulates in tissues, causing hypo- or hyperthyroidism, pulmonary fibrosis, liver injury, photosensitivity and corneal deposits. The other pairs fit aminoglycosides, phenytoin and ACE inhibitors.
Answer
C · Thyroid dysfunction and pulmonary fibrosis
3.Dosage calculations
Answer: V = 9 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 = 15·6 = 90 mg
Volume
V = 90/10 = 9 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 9 mL
4.Dosage calculations
Answer: V = 0.22 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 = 1100/5000 = 0.22 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.22 mL
5.Clinical pharmacokinetics
Answer: R = 25.55 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
CL = 0.035·73 = 2.555 L/h
Infusion rate
R = 2.555·10 = 25.55 mg/h
Answer
R = 25.55 mg/h
6.Clinical pharmacokinetics
Answer: D = 602 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 − 50)·77/(72·1.6) = 60.16 mL/min
Adjusted dose
D = 1000·60.16/100 = 601.6 ≈ 602 mg
Answer
D = 602 mg
In practice the dose is rounded to a convenient amount and checked against the product information.