# A mathematical model to simulate the biological action of Infliximab on TNF-α in patients with Inflammatory Bowel Disease: the critical role of drug clearance

## TL;DR

This paper creates a mathematical model to understand how Infliximab, a drug for IBD, interacts with TNF-α and how drug clearance affects treatment outcomes.

## Contribution

The novel contribution is a low-dimensional mathematical model that integrates TNF-α dynamics, drug interactions, and variable clearance rates for personalized IBD treatment.

## Key findings

- The model shows that drug clearance significantly impacts treatment efficacy in IBD patients.
- Variable clearance rates linked to inflammation levels improve simulation accuracy of Infliximab therapy.
- The model supports personalized dosing strategies through therapeutic drug monitoring.

## Abstract

Inflammatory bowel disease (IBD), including Crohn s disease (CD) and ulcerative colitis (UC), is characterized by chronic intestinal inflammation driven by elevated tumor necrosis factor-alpha (TNF-\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}α). Infliximab, an anti-TNF-\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}α monoclonal antibody, is widely used in the treatment of inflammatory bowel disease but shows variable effectiveness due to interindividual pharmacokinetic diversity. We develop a low-dimensional mathematical model of ordinary differential equations to describe TNF-\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}α dynamics, its interactions with receptors and infliximab, and the influence of drug clearance on treatment outcomes in CD and UC. This model is combined with a pharmacokinetic framework that enables the estimation of the infliximab clearance coefficient, which can then be used to guide dosage adjustments in the treatment. The model balances biological realism with analytical tractability, enabling rigorous mathematical analysis and numerical simulations. The parameters are adapted for CD and UC. The study investigates how drug clearance influences treatment efficacy, initially using constant clearance values and later incorporating values that vary with the level of inflammation. Simulations are performed across a range of clearance rates and dosing regimens, providing detailed insights into infliximab and TNF-\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}α dynamics, as well as therapeutic drug monitoring parameters. Our results highlight the critical role of clearance and therapeutic drug monitoring in optimizing infliximab therapy. This approach offers valuable insights to support personalized treatment strategies in IBD.