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 does neostigmine improve muscle strength in myasthenia gravis?
AIt inhibits acetylcholinesterase so more acetylcholine reaches the receptors
BIt increases the number of acetylcholine receptors at the neuromuscular junction
CIt blocks the autoantibodies against the receptor
DIt directly stimulates muscarinic receptors in muscle
2.PharmacologyHard
The volume of distribution of a drug is very large (for example 500 L in an adult). What does this suggest?
AThe drug is extensively taken up into tissues
BThe drug cannot be given intravenously
CThe drug is quickly excreted by the kidneys
DThe drug stays almost entirely in the plasma compartment
3.Dosage calculationsMedium
A child weighing 26 kg is prescribed 7.5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
26 kg7.5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
A patient is 153 cm tall and weighs 41 kg. The prescription is 50 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
153 cm41 kg50 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A patient has a lidocaine clearance of 550 mL/min. What infusion rate R in mg/min keeps the steady-state level at 2 mg/L?
CL = 550 mL/minCss = 2 mg/L
R = mg/min
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 73-year-old woman weighs 92 kg and has a serum creatinine of 2.5 mg/dL (221 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 digoxin dose is 250 mcg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.7 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 · It inhibits acetylcholinesterase so more acetylcholine reaches the receptors
Why this is the answer
Neostigmine inhibits acetylcholinesterase at the neuromuscular junction, so acetylcholine lasts longer and can activate the remaining nicotinic receptors more effectively.
Answer
A · It inhibits acetylcholinesterase so more acetylcholine reaches the receptors
2.Pharmacology
Answer: A · The drug is extensively taken up into tissues
Why this is the answer
A Vd far above total body water means the plasma concentration is low because most of the drug sits in tissues (for example fat or muscle), as with digoxin or amiodarone.
Answer
A · The drug is extensively taken up into tissues
3.Dosage calculations
Answer: V = 7.8 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 = 7.5·26 = 195 mg
Volume
V = 195/25 = 7.8 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 7.8 mL
4.Dosage calculations
Answer: D = 66 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).
Body surface area
BSA = √(153·41/3600) = √1.742 = 1.32 m²
Dose
D = 50·1.32 = 66 mg
Answer
D = 66 mg
5.Clinical pharmacokinetics
Answer: R = 1.1 mg/min
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/min
550 mL/min = 0.55 L/min
Infusion rate
R = 0.55·2 = 1.1 mg/min
Answer
R = 1.1 mg/min
6.Clinical pharmacokinetics
Answer: D = 126 mcg
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 − 73)·92/(72·2.5)·0.85 = 29.11 mL/min
Dose fraction (Dettli)
Q = 1 − 0.7·(1 − 29.11/100) = 0.5038
Adjusted dose
D = 0.5038·250 = 125.9 ≈ 126 mcg
Answer
D = 126 mcg
In practice the dose is rounded to a convenient amount and checked against the product information.