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
A malnourished patient with alcohol dependence needs IV glucose. Which vitamin should be given before or with it?
AThiamine (vitamin B1)
BVitamin D
CVitamin C
DVitamin K (phytomenadione)
2.PharmacologyHard
A patient recently started on haloperidol develops high fever, "lead-pipe" muscle rigidity, confusion and a very high creatine kinase. What is the most likely diagnosis?
AAcute dystonia
BNeuroleptic malignant syndrome
CMalignant hyperthermia from anaesthesia
DSerotonin syndrome
3.Dosage calculationsMedium
A patient weighs 25 kg. The prescribed dose is 2 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
25 kg2 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
The prescription is 850 micrograms. The ampoule contains 1 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
850 mcg1 mg/mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). An 87 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.
87 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 42-year-old man weighs 62 kg and has a serum creatinine of 2 mg/dL (177 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.
Giving glucose without thiamine to a thiamine-deficient patient can trigger or worsen Wernicke's encephalopathy. Thiamine is therefore given before or alongside glucose.
Answer
A · Thiamine (vitamin B1)
2.Pharmacology
Answer: B · Neuroleptic malignant syndrome
Why this is the answer
Neuroleptic malignant syndrome follows dopamine antagonists and develops over days, with lead-pipe rigidity, fever and raised CK. Serotonin syndrome develops faster and features clonus and hyperreflexia.
Answer
B · Neuroleptic malignant syndrome
3.Dosage calculations
Answer: D = 25 mg
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Total per day
2·25 = 50 mg
Per dose
D = 50/2 = 25 mg
Answer
D = 25 mg
4.Dosage calculations
Answer: V = 0.85 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
1 mg/mL = 1000 mcg/mL
Volume
V = 850/1000 = 0.85 mL
Answer
V = 0.85 mL
5.Clinical pharmacokinetics
Answer: LD = 696 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 = 7·87 = 609 L
Amount of active drug needed
Vd·C = 609·0.8 = 487.2 mcg
Loading dose
LD = 487.2/(1·0.7) = 696 mcg
Answer
LD = 696 mcg
In practice the dose is rounded to a convenient amount.
6.Clinical pharmacokinetics
Answer: D = 48 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 − 42)·62/(72·2) = 42.19 mL/min
Dose fraction (Dettli)
Q = 1 − 0.9·(1 − 42.19/100) = 0.4798
Adjusted dose
D = 0.4798·100 = 47.98 ≈ 48 mg
Answer
D = 48 mg
In practice the dose is rounded to a convenient amount and checked against the product information.