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
Typical antipsychotics such as haloperidol work mainly by blocking:
AGABA-A receptors
BSerotonin reuptake
CDopamine D2 receptors
DAcetylcholinesterase
2.PharmacologyHard
Why are oral liquid medicines drawn up in dedicated oral or enteral syringes that do not fit IV connectors?
ATo keep the medicine sterile for injection
BBecause IV syringes cannot hold liquids
CTo prevent oral liquids being given intravenously by mistake
DTo make the oral dose more accurate than a dose given through an IV syringe
3.Dosage calculationsMedium
A patient weighing 20 kg has a body surface area of 0.95 m². The prescription is 100 mg/m². Find the dose D in mg.
20 kgBSA = 0.95 m²100 mg/m²
D = mg
4.Dosage calculationsHard
A patient weighs 134.2 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? Round to one decimal place.
134.2 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 8 mg/L at 2 h and 1.3 mg/L at 10 h. Assume first-order elimination. Find the half-life t½.
C1 = 8 mg/L (2 h)C2 = 1.3 mg/L (10 h)
t½ = h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 68-year-old man weighs 74 kg and has a serum creatinine of 2.3 mg/dL (203 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.
Haloperidol blocks D2 receptors in the mesolimbic pathway, reducing positive symptoms. Blocking D2 in other pathways causes extrapyramidal effects and raised prolactin.
Answer
C · Dopamine D2 receptors
2.Pharmacology
Answer: C · To prevent oral liquids being given intravenously by mistake
Why this is the answer
Wrong-route errors, such as giving an oral liquid IV, can be fatal. Syringes with connectors that cannot fit IV lines make this error physically difficult.
Answer
C · To prevent oral liquids being given intravenously by mistake
3.Dosage calculations
Answer: D = 95 mg
Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).
Dose
D = 100·0.95 = 95 mg
Answer
D = 95 mg
4.Dosage calculations
Answer: V = 1.2 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
134.2/2.2 = 61 kg
Dose
0.5·61 = 30.5 mg
Volume
V = (30.5/125)·5 = 1.22 ≈ 1.2 mL
Answer
V = 1.2 mL
5.Clinical pharmacokinetics
Answer: t½ = 3.052 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(8/1.3)/8 = 1.817/8 = 0.2271 h⁻¹
Half-life
t½ = 0.693/0.2271 = 3.052 h
Answer
t½ = 3.052 h
6.Clinical pharmacokinetics
Answer: τ = 44.8 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 − 68)·74/(72·2.3) = 32.17 mL/min
New interval
τ = 12·120/32.17 = 44.76 ≈ 44.8 h
Answer
τ = 44.8 h
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.