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
During an infusion of a vesicant chemotherapy drug, the patient reports burning, and the site is swollen. What should the nurse do first?
AIncrease the infusion rate to finish quickly
BStop the infusion, leave the cannula in and follow the protocol
CFlush the line with a large volume of saline
DRemove the cannula at once and massage the area firmly
2.PharmacologyHard
A woman with epilepsy who takes an antiepileptic drug plans to become pregnant. Which advice is standard?
AStop all antiepileptic drugs straight away as soon as she stops contraception
BNo change is needed, as antiepileptics carry no risk in pregnancy
CTake folic acid before conception and seek specialist review of her medication
DAvoid folic acid because it lowers drug levels
3.Dosage calculationsMedium
A child weighing 20 kg is prescribed 4 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
20 kg4 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
A child weighing 20 kg is prescribed 15 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give?
20 kg15 mg/kg120 mg/5 mL
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 35 mg/L at 1 h and 10.7 mg/L at 13 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 35 mg/L (1 h)C2 = 10.7 mg/L (13 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 93 kg patient on regular gentamicin doses is at steady state. The target is a peak of 7 mg/L and a trough of 1 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
93 kgVd = 0.3 L/kgCpeak = 7 mg/LCtrough = 1 mg/L
D = mg
3Solutions
1.Pharmacology
Answer: B · Stop the infusion, leave the cannula in and follow the protocol
Why this is the answer
Suspected extravasation of a vesicant is an emergency. The infusion is stopped, the cannula is left in so that drug can be aspirated, and the protocol, which may include an antidote and cold or warm packs, is followed.
Answer
B · Stop the infusion, leave the cannula in and follow the protocol
2.Pharmacology
Answer: C · Take folic acid before conception and seek specialist review of her medication
Why this is the answer
Folic acid before and in early pregnancy reduces the risk of neural tube defects. Medication should be reviewed before conception, but drugs should not be stopped suddenly because uncontrolled seizures are also dangerous.
Answer
C · Take folic acid before conception and seek specialist review of her medication
3.Dosage calculations
Answer: V = 1.6 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.
Dose from body weight
D = 4·20 = 80 mg
Volume
V = 80/50 = 1.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 1.6 mL
4.Dosage calculations
Answer: V = 12.5 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.
Dose from weight
15·20 = 300 mg
Volume
V = (300/120)·5 = 12.5 mL
Answer
V = 12.5 mL
5.Clinical pharmacokinetics
Answer: k = 0.09876 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(35/10.7)/12 = 1.185/12 = 0.09876 h⁻¹
Answer
k = 0.09876 h⁻¹
6.Clinical pharmacokinetics
Answer: D = 167.4 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.
Volume of distribution
Vd = 0.3·93 = 27.9 L
Dose
D = 27.9·(7 − 1) = 167.4 mg
Answer
D = 167.4 mg
In practice the dose is rounded to a convenient amount.