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 with a fentanyl patch is given home-care advice. Which instruction is correct?
ACut the patch in half if the pain is mild
BAvoid heating pads, hot baths and saunas over or near the patch
CThrow used patches loose into the household bin with the packaging
DApply each new patch over the same skin area
2.PharmacologyHard
A patient with Parkinson's disease has nausea. Why should metoclopramide be avoided?
AIt inhibits the absorption of all oral drugs
BIt causes severe diarrhoea in Parkinson's disease
CIt blocks dopamine receptors in the brain and can worsen the parkinsonism
DIt increases dopamine levels in the brain too much and causes psychosis
3.Dosage calculationsMedium
A child weighing 24 kg is prescribed 2.5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
24 kg2.5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
A patient weighs 173.8 lb. The prescription is 0.5 mg/kg as a single dose, and the stock contains 10 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to one decimal place.
173.8 lb0.5 mg/kg10 mg/1 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A 74 kg patient is to be loaded with digoxin tablets to reach a level of 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.
74 kgVd = 7 L/kgC = 0.8 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion is started without a loading dose. The half-life in this patient is 10 h. How long t does it take to reach 95% of the steady-state level?
t½ = 10 h95% Css
t = h
3Solutions
1.Pharmacology
Answer: B · Avoid heating pads, hot baths and saunas over or near the patch
Why this is the answer
Heat increases fentanyl absorption and can cause overdose. Sites are rotated, patches are never cut, and used patches are folded sticky sides together and disposed of safely, away from children and pets.
Answer
B · Avoid heating pads, hot baths and saunas over or near the patch
2.Pharmacology
Answer: C · It blocks dopamine receptors in the brain and can worsen the parkinsonism
Why this is the answer
Metoclopramide crosses the blood–brain barrier and antagonises D2 receptors. In Parkinson's disease this worsens rigidity and bradykinesia, so antiemetics that do not block central dopamine receptors are preferred.
Answer
C · It blocks dopamine receptors in the brain and can worsen the parkinsonism
3.Dosage calculations
Answer: V = 2.4 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 = 2.5·24 = 60 mg
Volume
V = 60/25 = 2.4 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 2.4 mL
4.Dosage calculations
Answer: V = 4 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
173.8/2.2 = 79 kg
Dose
0.5·79 = 39.5 mg
Volume
V = (39.5/10)·1 = 3.95 ≈ 4 mL
Answer
V = 4 mL
5.Clinical pharmacokinetics
Answer: LD = 592 mcg
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 = 7·74 = 518 L
Amount of active drug needed
Vd·C = 518·0.8 = 414.4 mcg
Loading dose
LD = 414.4/(1·0.7) = 592 mcg
Answer
LD = 592 mcg
In practice the dose is rounded to a convenient amount.
6.Clinical pharmacokinetics
Answer: t = 43.22 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.
Rate constant
k = 0.693/10 = 0.06931 h⁻¹
Time to the given fraction of steady state
t = −ln(1 − 0.95)/0.06931 = 2.996/0.06931 = 43.22 h