# Dosing Interval Designer (Peak/Trough Ratio) Design the dosing interval τ from the steady-state peak/trough concentration ratio. For one-compartment linear kinetics at steady state, the peak-to-trough ratio over one interval is P = Cmax,ss / Cmin,ss = e^(kτ) where k = ln2 / t½. Mode A: given a target peak/trough ratio, solve for the dosing interval τ = ln(P) · t½ / ln2. Mode B: given a chosen interval τ, compute the resulting peak/trough ratio P = e^(kτ). Note: P reflects fluctuation WITHIN one interval and is NOT the accumulation index (R = 1/(1-e^(-kτ))). Valid only for linear one-compartment kinetics, steady state, fixed dose and interval. Not medical advice. > Canonical page: https://elysiatools.com/en/tools/dosing-interval-designer - **Category:** Health - **Keywords:** dosing interval, peak trough ratio, Cmax, Cmin, fluctuation, tau, half-life, steady state, one-compartment, pharmacokinetics, pk, drug, medicine ## Overview Dosing Interval Designer calculates the dosing interval from a target steady-state peak/trough ratio or calculates the resulting ratio from a chosen interval. It uses linear one-compartment kinetics at steady state with a fixed dose and interval, and is not medical advice. ## Inputs - **Calculation Mode** (select) - **Half-life t½ (h)** (number): Elimination half-life. Must be positive. - **Peak/trough ratio Cmax/Cmin** (number): Target peak/trough ratio. Required in mode A. Must be >1 (peak exceeds trough). - **Dosing interval τ (h)** (number): Chosen dosing interval. Required in mode B. Must be positive. - **Decimal Places** (number) ## When to use - Estimate the dosing interval needed for a target peak/trough concentration ratio. - Calculate within-interval fluctuation for a proposed dosing interval. - Check pharmacokinetic assumptions using a known elimination half-life. ## How it works - Enter the elimination half-life in hours. - Choose From peak/trough ratio → τ or From τ → peak/trough ratio. - Enter either the target ratio or dosing interval, depending on the selected mode. - The tool calculates the result using k = ln2 / t½ and returns JSON with the interval, ratio, elimination rate constant, method, and model details. ## Use cases - Pharmacokinetic modeling of steady-state concentration fluctuation. - Comparing proposed dosing intervals using a known half-life. - Teaching or checking the relationship between half-life, interval, and peak/trough ratio. ## Frequently asked questions ### What does this tool calculate? It calculates a dosing interval from a target peak/trough ratio or calculates the peak/trough ratio from a chosen interval. ### What is the peak/trough ratio? It is the steady-state concentration ratio Cmax,ss/Cmin,ss across one dosing interval. ### What inputs are required? A positive half-life is always required. Mode A requires a ratio greater than 1, while Mode B requires a positive dosing interval. ### Is the peak/trough ratio the accumulation index? No. It describes fluctuation within one interval and is not the accumulation index. ### Does this provide medical advice? No. The calculation is for pharmacokinetic modeling and should not be used as medical advice. ## Related tools - [A-a Gradient (Alveolar-Arterial O₂)](https://elysiatools.com/en/tools/a-a-gradient-calculator): Calculate the alveolar-arterial O₂ gradient to distinguish hypoxemia causes. PAO₂ = FiO₂×(P_atm−47) − PaCO₂/0.8; A-a = PAO₂ − PaO₂. Normal ≈ (Age+10)/4. Elevated → V/Q mismatch, shunt, diffusion impairment. 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