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 patient has oral mucositis after chemotherapy. Which advice is appropriate?
ABrush hard with a firm toothbrush to remove debris
BEat spicy and acidic foods to stimulate healing
CUse an alcohol-based mouthwash several times a day to kill germs
DUse a soft toothbrush and rinse with saline or a bland mouthwash
2.PharmacologyHard
Why can beta blockers mask the warning signs of hypoglycaemia in people with diabetes?
AThey cause hyperthermia that hides sweating
BThey raise blood glucose so that hypoglycaemia cannot occur at all
CThey blunt adrenergic symptoms such as tremor and palpitations
DThey block insulin release completely
3.Dosage calculationsMedium
A patient weighs 15 kg and is prescribed 25 mg/kg as a single dose. Find the dose D in mg.
15 kg25 mg/kg
D = mg
4.Dosage calculationsHard
The prescription is 0.19 mg. The ampoule contains 1000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
0.19 mg1000 mcg/mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A 58 kg patient is to receive an aminophylline infusion (salt factor S = 0.8: 80% of aminophylline is theophylline). The theophylline clearance is 0.04 L/kg/h. What aminophylline infusion rate R in mg/h gives a steady-state theophylline level of 12 mg/L?
58 kgCL = 0.04 L/kg/hCss = 12 mg/LS = 0.8
R = mg/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 55-year-old man weighs 78 kg and has a serum creatinine of 2.7 mg/dL (239 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 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: D · Use a soft toothbrush and rinse with saline or a bland mouthwash
Why this is the answer
Chemotherapy damages rapidly dividing mucosal cells. Gentle oral care, saline rinses and avoiding alcohol, spicy and acidic foods reduce pain and infection risk.
Answer
D · Use a soft toothbrush and rinse with saline or a bland mouthwash
2.Pharmacology
Answer: C · They blunt adrenergic symptoms such as tremor and palpitations
Why this is the answer
Tremor, palpitations and anxiety in hypoglycaemia are adrenaline-driven; beta blockade dampens them, so patients may notice low glucose later. Sweating is cholinergic and often persists.
Answer
C · They blunt adrenergic symptoms such as tremor and palpitations
3.Dosage calculations
Answer: D = 375 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.
Dose
25·15 = 375 mg
Answer
D = 375 mg
4.Dosage calculations
Answer: V = 0.19 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
0.19 mg = 190 mcg
Volume
V = 190/1000 = 0.19 mL
Answer
V = 0.19 mL
5.Clinical pharmacokinetics
Answer: R = 34.8 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 = 0.04·58 = 2.32 L/h
Infusion rate
R = CL·Css/S = 2.32·12/0.8 = 34.8 mg/h
Answer
R = 34.8 mg/h
6.Clinical pharmacokinetics
Answer: D = 341 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 − 55)·78/(72·2.7) = 34.1 mL/min
Adjusted dose
D = 1000·34.1/100 = 341 mg
Answer
D = 341 mg
In practice the dose is rounded to a convenient amount and checked against the product information.