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Product 05 — Prototype

Kirchhoff PK
Circuit-Law Clearance Modeling

A visual modeling tool that applies Kirchhoff's Circuit Laws — KCL for parallel and KVL for series — to derive model-independent pharmacokinetic clearance equations. Build hepatic, renal, and Michaelis-Menten kinetic networks as if they were electrical circuits, and see where the standard differential-equation derivations break down.

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Why circuit laws?

Clearance in pharmacokinetics has been derived from differential equations for decades. That gives the right answer in simple cases (well-stirred liver) and the wrong answer in many real-world settings — slow alternate-route absorption, controlled-release formulations, and hepatic clearance with clinically relevant basolateral transporters.

Standard (differential equation)
CL_AR = CL_iv

Implicitly assumes input is infinitely fast. When it isn't, AUC is over-predicted and apparent F can exceed 100%.

Kirchhoff-corrected
1/CL_AR = 1/CL_site + 1/CL_iv

Series resistors in an electrical circuit. Same rule, same answer — always correct, regardless of mechanism.

What it does

Visual Compartment Network

Drag-and-drop liver, kidney, gut, injection site, systemic, peripheral, and custom compartments onto an infinite canvas. Connect them with series or parallel edges.

Kirchhoff-Corrected Equations

Standard textbook equations for alternate-route clearance and hepatic transporters are wrong. Kirchhoff's circuit laws (KCL parallel, KVL series) give the correct, model-independent answers.

Live Concentration-Time Curves

Edit any parameter and watch the C-t curve update instantly. Compare the Kirchhoff prediction against the standard model to see when (and how much) the standard model is wrong.

Five Pre-Built Scenarios

IV bolus, oral dose with first-pass extraction, SC slow release (the F > 100% case), high-clearance CR design, and OATP-substrate hepatic clearance.

Source papers

This product implements the equations from the Benet-lab series of papers on applying Kirchhoff's Laws to pharmacokinetics.

  • Pachter et al., Pharmacol. Ther. 239 (2022) 108278
    Foundational paper applying Kirchhoff's Laws to PK clearance
  • Benet & Sodhi, AAPS J. 25 (2023) 38
    Model-independent equation for alternate-route clearance
  • Wakuda et al., AAPS J. 26 (2024) 22
    F > 100% paradox resolved by Kirchhoff correction