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 is a spacer recommended with a metered-dose inhaler?
AIt turns the inhaler into a nebuliser
BIt doubles the dose of drug released by each puff of the inhaler
CIt removes the need to shake the inhaler
DMore drug reaches the lungs and less stays in the mouth
2.PharmacologyHard
Why is pyridoxine (vitamin B6) often given together with isoniazid for tuberculosis?
ATo increase the absorption of isoniazid
BTo prevent peripheral neuropathy
CTo reduce bacterial resistance
DTo prevent liver damage from isoniazid
3.Dosage calculationsMedium
A child weighing 38 kg is prescribed 4 mg/kg of a drug. The stock solution contains 40 mg/mL. Draw up the dose: what volume V do you give?
38 kg4 mg/kg40 mg/mL
V = mL
4.Dosage calculationsHard
The prescription is 490 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
490 units1000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). An 85 kg patient is to be loaded with digoxin tablets to reach a level of 1 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.
85 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 60-year-old man weighs 77 kg and has a serum creatinine of 1.9 mg/dL (168 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 levetiracetam dose is 1000 mg every 12 h for a creatinine clearance of 120 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: D · More drug reaches the lungs and less stays in the mouth
Why this is the answer
A spacer holds the aerosol so it can be inhaled slowly, without precise coordination. This improves lung delivery and reduces mouth side effects such as thrush from inhaled steroids.
Answer
D · More drug reaches the lungs and less stays in the mouth
2.Pharmacology
Answer: B · To prevent peripheral neuropathy
Why this is the answer
Isoniazid causes pyridoxine deficiency, which can lead to peripheral neuropathy. The risk is greater in slow acetylators, malnourished patients and people with diabetes or alcohol dependence.
Answer
B · To prevent peripheral neuropathy
3.Dosage calculations
Answer: V = 3.8 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 = 4·38 = 152 mg
Volume
V = 152/40 = 3.8 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3.8 mL
4.Dosage calculations
Answer: V = 0.49 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 = 490/1000 = 0.49 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.49 mL
5.Clinical pharmacokinetics
Answer: LD = 850 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 = 7·85 = 595 L
Amount of active drug needed
Vd·C = 595·1 = 595 mcg
Loading dose
LD = 595/(1·0.7) = 850 mcg
Answer
LD = 850 mcg
In practice the dose is rounded to a convenient amount.
6.Clinical pharmacokinetics
Answer: D = 375 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 − 60)·77/(72·1.9) = 45.03 mL/min
Adjusted dose
D = 1000·45.03/120 = 375.2 ≈ 375 mg
Answer
D = 375 mg
In practice the dose is rounded to a convenient amount and checked against the product information.