Pharmacokinetics · Short notes

Dosage Regimen Calculations: Short Notes & Cheat Sheet

Loading and maintenance doses, infusions, accumulation, dosing in renal impairment and obesity, salt factors and worked examples.

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Short notes

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Designing a dosage regimen

Vd sets the loading dose, clearance the maintenance dose and half-life the dosing interval.

Core equations

Loading dose = target concentration × Vd ÷ (F × S), where S is the salt factor.
Maintenance dose rate = target concentration × CL ÷ (F × S). For a dose every τ hours, dose = target concentration × CL × τ ÷ F.
IV infusion: steady-state concentration = infusion rate ÷ CL.
Accumulation factor for repeated doses = 1 ÷ (1 − e^(−kτ)); the shorter the interval relative to half-life, the more the drug accumulates.
Salt factors: aminophylline contains about 80% theophylline (S = 0.8); phenytoin sodium about 92% phenytoin (S = 0.92).

Worked examples

Loading dose: Vd 0.5 L/kg in a 70 kg patient is 35 L. For a target of 10 mg/L the loading dose is 10 × 35 = 350 mg (IV, F = 1).
Infusion: with CL 3 L/h and a target of 10 mg/L, the infusion rate is 10 × 3 = 30 mg/h.
Oral maintenance: CL 2 L/h, target 15 mg/L, F = 0.5, every 12 hours: dose = 15 × 2 × 12 ÷ 0.5 = 720 mg.
Units: mg/L equals µg/mL.

Special populations

Renal impairment: either reduce the dose and keep the interval, or keep the dose and lengthen the interval. A simple estimate: adjusted dose = normal dose × (patient's CrCl ÷ normal CrCl) for mainly renally cleared drugs.
Ideal body weight: men 50 kg + 2.3 kg per inch over 5 feet; women 45.5 kg + 2.3 kg per inch over 5 feet.
Adjusted body weight (e.g. aminoglycosides in obesity) = IBW + 0.4 × (actual weight − IBW).
Body surface area (Mosteller) = √(height in cm × weight in kg ÷ 3600).

Cheat sheet

High-yield facts in one place. Cover the right-hand column and test yourself.

Equations

Quantity	Equation
Loading dose	Cp × Vd ÷ (F × S)
Maintenance dose	Cp × CL × τ ÷ (F × S)
Infusion Css	Rate ÷ CL
Accumulation factor	1 ÷ (1 − e^(−kτ))
Cockcroft–Gault CrCl	(140 − age) × wt ÷ (72 × SCr) [× 0.85 female]
BSA (Mosteller)	√(height cm × weight kg ÷ 3600)

Salt factors

Product	S
Aminophylline → theophylline	≈ 0.8
Phenytoin sodium → phenytoin	≈ 0.92
Digoxin tablets (F)	≈ 0.7
Free acid / base	1.0

Memory aids

Load with Volume, Maintain with Clearance: Loading dose depends on Vd; maintenance dose depends on clearance.

Exam traps

Changing the maintenance dose does not change the time to steady state.
Clearance, not half-life, determines the maintenance dose rate.
Forgetting the salt factor overdoses or underdoses aminophylline and phenytoin.
Cockcroft–Gault uses weight in kg and creatinine in mg/dL.

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