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 is starting lamotrigine. Which adverse effect should the patient report at once?
AMild headache on the first day
BA brief change in taste
CSlight tiredness in the afternoon
DAny new skin rash
2.PharmacologyHard
A patient on warfarin also takes ginkgo and high-dose garlic supplements and is having minor surgery next week. What should the nurse do?
AAdvise stopping warfarin without telling anyone
BAdvise taking extra supplements to improve healing
CIgnore the supplements, as natural products are safe with warfarin
DTell the surgical team, as the supplements can increase bleeding
3.Dosage calculationsMedium
An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.3 mg IM for anaphylaxis. What volume V do you draw up?
1:10000.3 mg
V = mL
4.Dosage calculationsHard
A patient weighs 24.2 lb. The prescription is 0.5 mg/kg as a single dose, and the stock contains 125 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?
24.2 lb0.5 mg/kg125 mg/5 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). After an IV dose of tobramycin, the level is 10 mg/L at 1 h and 1.3 mg/L at 7 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 10 mg/L (1 h)C2 = 1.3 mg/L (7 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 45-year-old woman weighs 58 kg and has a serum creatinine of 3.2 mg/dL (283 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 120 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.
Lamotrigine can cause serious skin reactions such as Stevens–Johnson syndrome. The dose is increased slowly, especially with valproate, and any rash must be assessed promptly.
Answer
D · Any new skin rash
2.Pharmacology
Answer: D · Tell the surgical team, as the supplements can increase bleeding
Why this is the answer
Ginkgo and garlic may impair platelet function and add to warfarin's bleeding risk. The team needs a full list of supplements so it can plan, and the patient should not change warfarin without advice.
Answer
D · Tell the surgical team, as the supplements can increase bleeding
3.Dosage calculations
Answer: V = 0.3 mL
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Concentration
1:1000 = 1 g/1000 mL = 1 mg/mL
Volume
V = 0.3/1 = 0.3 mL
Answer
V = 0.3 mL
US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.
4.Dosage calculations
Answer: V = 0.22 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
24.2/2.2 = 11 kg
Dose
0.5·11 = 5.5 mg
Volume
V = (5.5/125)·5 = 0.22 mL
Answer
V = 0.22 mL
5.Clinical pharmacokinetics
Answer: k = 0.34 h⁻¹
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.
Elimination rate constant
k = ln(10/1.3)/6 = 2.04/6 = 0.34 h⁻¹
Answer
k = 0.34 h⁻¹
6.Clinical pharmacokinetics
Answer: D = 251 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 − 45)·58/(72·3.2)·0.85 = 20.33 mL/min
Dose fraction (Dettli)
Q = 1 − 0.6·(1 − 20.33/120) = 0.5016
Adjusted dose
D = 0.5016·500 = 250.8 ≈ 251 mg
Answer
D = 251 mg
In practice the dose is rounded to a convenient amount and checked against the product information.