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 should a patient rinse the mouth after using an inhaled corticosteroid?
ATo prevent a fall in blood glucose
BTo reduce the risk of oral thrush (candidiasis) and hoarseness
CTo stop the drug being absorbed too quickly into the blood
DTo make the drug work faster in the lungs
2.PharmacologyHard
Why is vancomycin given by mouth, not intravenously, for Clostridioides difficile infection?
AIntravenous vancomycin causes C. difficile infection
BThe oral form is cheaper but has the same effect as IV
COral vancomycin is not absorbed, so it reaches high levels in the colon
DOral vancomycin is absorbed into the blood better than IV vancomycin
3.Dosage calculationsMedium
A patient weighs 22 kg and is prescribed 20 mg/kg as a single dose. Find the dose D in mg.
22 kg20 mg/kg
D = mg
4.Dosage calculationsHard
A patient weighs 198 lb. The prescription is 2 mg/kg as a single dose, and the stock contains 250 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?
198 lb2 mg/kg250 mg/5 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 220 mg of tobramycin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.
D = 220 mgC₀ = 9 mg/Lt½ = 2.5 h
CL = L/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 71-year-old man weighs 65 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 ciprofloxacin dose is 500 mg for a creatinine clearance of 100 mL/min, and a fraction fe = 0.6 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: B · To reduce the risk of oral thrush (candidiasis) and hoarseness
Why this is the answer
Steroid left in the mouth and throat suppresses local immunity and can cause candidiasis and a hoarse voice. Rinsing and spitting, and using a spacer, reduce this risk.
Answer
B · To reduce the risk of oral thrush (candidiasis) and hoarseness
2.Pharmacology
Answer: C · Oral vancomycin is not absorbed, so it reaches high levels in the colon
Why this is the answer
Oral vancomycin stays in the gut and acts directly on C. difficile in the colon. IV vancomycin is not excreted into the gut in useful amounts, so it does not treat this infection.
Answer
C · Oral vancomycin is not absorbed, so it reaches high levels in the colon
3.Dosage calculations
Answer: D = 440 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
20·22 = 440 mg
Answer
D = 440 mg
4.Dosage calculations
Answer: V = 3.6 mL
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.
Weight in kg
198/2.2 = 90 kg
Dose
2·90 = 180 mg
Volume
V = (180/250)·5 = 3.6 mL
Answer
V = 3.6 mL
5.Clinical pharmacokinetics
Answer: CL = 6.777 L/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.
Volume of distribution
Vd = 220/9 = 24.44 L
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Clearance
CL = 0.2773·24.44 = 6.777 L/h
Answer
CL = 6.777 L/h
6.Clinical pharmacokinetics
Answer: D = 269 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 − 71)·65/(72·2.7) = 23.07 mL/min
Dose fraction (Dettli)
Q = 1 − 0.6·(1 − 23.07/100) = 0.5384
Adjusted dose
D = 0.5384·500 = 269.2 ≈ 269 mg
Answer
D = 269 mg
In practice the dose is rounded to a convenient amount and checked against the product information.