# Pharmacokinetic Bolus vs Infusion Overlap Tutor

Overlay one-compartment IV bolus, intermittent short-infusion and continuous-infusion concentration curves at the same daily dose: accumulation ratio, steady-state Cmax/Cmin, AUC per interval, time to steady state, peak:trough fluctuation and loading doses.

> Canonical page: https://elysiatools.com/en/tools/pharmacokinetic-bolus-vs-infusion-overlap-tutor

- **Category:** Health

- **Keywords:** pharmacokinetics, bolus vs infusion, accumulation ratio, steady state, cmax cmin, loading dose, one compartment model, vancomycin kinetics

## Overview

A pharmacokinetics teaching tool for the classic one-compartment, first-order-elimination model.

Three regimens are overlaid on one chart at an identical daily dose: IV bolus every τ hours, the same dose as a short intermittent infusion of length T′, and a continuous infusion at rate D/τ. Curves are exact superposition sums, not stochastic simulations.

Derived quantities: k = CL/Vd, t½ = ln2/k, accumulation ratio R = 1/(1−e^(−kτ)), Cmax,ss and Cmin,ss for both bolus (Cmax = (D/Vd)·R, Cmin = Cmax·e^(−kτ)) and short infusion (Cmax = (Rin/CL)(1−e^(−kT′))/(1−e^(−kτ)), Cmin = Cmax·e^(−k(τ−T′))), Css = Rin/CL, AUC per interval = D/CL (identical for all arms), t90/t95 and doses to steady state, peak:trough ratio e^(kτ), and loading doses Css·Vd and D·R.

Drug presets for a 70 kg adult: vancomycin (Vd 0.7 L/kg, CL 0.06 L/h/kg), gentamicin (0.25 L/kg, 0.09 L/h/kg) and theophylline (0.5 L/kg, 0.035 L/h/kg), plus fully custom Vd/CL. Educational tool — not a dosing advisor.

## Inputs

- **Drug Preset (sets Vd and CL)** (select)
- **Volume of Distribution Vd (L)** (number): 49
- **Clearance CL (L/h)** (number): 4.2
- **Dose per Administration (mg)** (number): 1000
- **Dosing Interval τ (hours)** (number): 12
- **Short-Infusion Length T′ (hours)** (number): 1
- **Simulation Horizon (hours)** (number): 96

## When to use

- Comparing peak, trough, and steady-state concentration profiles between IV bolus, short infusion, and continuous infusion regimens.
- Teaching or studying core one-compartment pharmacokinetic principles, accumulation indices, and interval AUC equivalence.
- Evaluating the impact of dosing intervals and infusion durations on drug accumulation and peak-to-trough fluctuations.

## How it works

- Select a preconfigured drug profile (vancomycin, gentamicin, or theophylline) or enter custom volume of distribution (Vd) and clearance (CL) values.
- Define the regimen parameters including dose per administration, dosing interval (τ), short-infusion duration (T′), and total simulation horizon.
- The tool computes exact superposition sums to determine elimination rate (k), half-life (t½), accumulation ratio (R), steady-state Cmax/Cmin, and loading dose requirements.
- Review the interactive HTML report featuring overlaid concentration-time curves alongside comparative parameter tables and steady-state timelines.

## Use cases

- Visualizing how altering dosing intervals (τ) relative to half-life (t½) changes drug accumulation versus single-dose washout.
- Demonstrating why continuous infusion eliminates peak-to-trough fluctuations while maintaining the same average steady-state concentration (Css).
- Calculating theoretical loading doses required to immediately achieve targeted steady-state concentrations without waiting multiple half-lives.

## Frequently asked questions

### Why is the AUC per interval identical across all three regimens?

In linear one-compartment pharmacokinetics, interval AUC depends solely on total administered dose and clearance (AUC = Dose / CL), making total exposure equal when the daily dose is the same.

### How does the tool calculate the accumulation ratio (R)?

It uses the standard first-order equation R = 1 / (1 − e^(−kτ)), where k is the elimination rate constant (CL / Vd) and τ is the dosing interval.

### Are the concentration curves generated using stochastic simulations?

No. The curves are calculated using exact analytical superposition equations for one-compartment intravenous administration.

### What is the difference between bolus Cmax,ss and short-infusion Cmax,ss?

A bolus introduces the dose instantaneously, yielding Cmax,ss = (D / Vd) · R, while a short infusion accounts for drug elimination during infusion time T′, resulting in lower peak levels.

### Can this tool be used for clinical dosing recommendations?

No. This tool is designed strictly for educational and pharmacokinetic teaching purposes and should not be used as a clinical dosing advisor.

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