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 receiving chemotherapy has a very low neutrophil count and is going home. Which teaching is most important?
ATake paracetamol regularly so that fevers do not show
BEat plenty of raw shellfish to boost protein
CReport a temperature of 38 °C (100.4 °F) or higher straight away
DExercise in crowded gyms to build strength
2.PharmacologyHard
Why can beta blockers mask the warning signs of hypoglycaemia in people with diabetes?
AThey raise blood glucose so that hypoglycaemia cannot occur at all
BThey blunt adrenergic symptoms such as tremor and palpitations
CThey block insulin release completely
DThey cause hyperthermia that hides sweating
3.Dosage calculationsMedium
A child weighing 40 kg is prescribed 2 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?
40 kg2 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
A patient is 166 cm tall and weighs 81 kg. The prescription is 75 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
166 cm81 kg75 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 100 mg of tobramycin. The level back-extrapolated to time zero is 6 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.
D = 100 mgC₀ = 6 mg/Lt½ = 2.5 h
CL = L/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 50 kg patient takes oral aminophylline (S = 0.8, F = 1) every 8 h. The theophylline clearance is 0.035 L/kg/h. What dose D in mg gives an average steady-state level of 12 mg/L?
Answer: C · Report a temperature of 38 °C (100.4 °F) or higher straight away
Why this is the answer
Neutropenic patients may have few signs of infection other than fever, and sepsis can develop quickly. A fever needs urgent assessment; good hand hygiene and avoiding sick contacts are also taught.
Answer
C · Report a temperature of 38 °C (100.4 °F) or higher straight away
2.Pharmacology
Answer: B · They blunt adrenergic symptoms such as tremor and palpitations
Why this is the answer
Tremor, palpitations and anxiety in hypoglycaemia are adrenaline-driven; beta blockade dampens them, so patients may notice low glucose later. Sweating is cholinergic and often persists.
Answer
B · They blunt adrenergic symptoms such as tremor and palpitations
3.Dosage calculations
Answer: V = 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 = 2·40 = 80 mg
Volume
V = 80/20 = 4 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 4 mL
4.Dosage calculations
Answer: D = 144.9 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).
Body surface area
BSA = √(166·81/3600) = √3.735 = 1.933 m²
Dose
D = 75·1.933 = 144.9 mg
Answer
D = 144.9 mg
5.Clinical pharmacokinetics
Answer: CL = 4.621 L/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.
Volume of distribution
Vd = 100/6 = 16.67 L
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Clearance
CL = 0.2773·16.67 = 4.621 L/h
Answer
CL = 4.621 L/h
6.Clinical pharmacokinetics
Answer: D = 210 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.
Clearance
CL = 0.035·50 = 1.75 L/h
Dose
D = Css,avg·CL·τ/(S·F) = 12·1.75·8/(0.8·1) = 210 mg