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
Which assessment is most important before giving a dose of IV morphine?
APupil size and hearing
BBlood glucose and temperature, checked before each dose
CRespiratory rate and level of sedation
DBowel sounds and urine colour
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?
AIgnore the supplements, as natural products are safe with warfarin
BAdvise taking extra supplements to improve healing
CAdvise stopping warfarin without telling anyone
DTell the surgical team, as the supplements can increase bleeding
3.Dosage calculationsMedium
A patient weighs 60 kg. The prescribed dose is 25 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?
60 kg25 mg/kg/day4× per day
D = mg
4.Dosage calculationsHard
A patient weighs 165 lb. The prescription is 0.5 mg/kg as a single dose, and the stock contains 100 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to two decimal places.
165 lb0.5 mg/kg100 mg/1 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 30 mg/L at 2 h and 11.9 mg/L at 18 h. Assume first-order elimination. Find the half-life t½.
C1 = 30 mg/L (2 h)C2 = 11.9 mg/L (18 h)
t½ = h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 46-year-old man weighs 91 kg and has a serum creatinine of 2.1 mg/dL (186 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 vancomycin regimen is 1000 mg every 12 h for a creatinine clearance of 120 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.
Answer: C · Respiratory rate and level of sedation
Why this is the answer
Opioids can cause respiratory depression, which is usually preceded by increasing sedation. Both are checked before and after each dose.
Answer
C · Respiratory rate and level of sedation
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: 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.
Total per day
25·60 = 1500 mg
Per dose
D = 1500/4 = 375 mg
Answer
D = 375 mg
4.Dosage calculations
Answer: V = 0.38 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
165/2.2 = 75 kg
Dose
0.5·75 = 37.5 mg
Volume
V = (37.5/100)·1 = 0.375 ≈ 0.38 mL
Answer
V = 0.38 mL
5.Clinical pharmacokinetics
Answer: t½ = 11.99 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.
Elimination rate constant
k = ln(30/11.9)/16 = 0.9247/16 = 0.05779 h⁻¹
Half-life
t½ = 0.693/0.05779 = 11.99 h
Answer
t½ = 11.99 h
6.Clinical pharmacokinetics
Answer: τ = 25.5 h
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 − 46)·91/(72·2.1) = 56.57 mL/min
New interval
τ = 12·120/56.57 = 25.45 ≈ 25.5 h
Answer
τ = 25.5 h
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.