# Dynamical modeling of TNF-α, IL-6, and IL-10 interactions in stroke-induced inflammation

## TL;DR

The paper develops a mathematical model to understand how cytokines like TNF-α, IL-6, and IL-10 interact during stroke-induced inflammation, offering insights into potential therapies.

## Contribution

The novel contribution is a systems biology model using ODEs to quantify cytokine dynamics and identify key regulatory thresholds in stroke inflammation.

## Key findings

- The model identifies a critical IL-10 suppression threshold (γT10≈0.06 hr⁻¹·nM⁻¹) that governs transitions between pro-inflammatory and resolution phases.
- Global sensitivity analysis shows that IL-10 production and TNF-α suppression are key control parameters in inflammation dynamics.
- Simulations suggest that augmenting IL-10 accelerates recovery, while inhibiting TNF-α may hinder long-term outcomes.

## Abstract

In acute stroke, dysregulated cytokine interactions drive secondary injury, yet bidirectional feedback mechanisms between pro-inflammatory mediators (TNF-α, IL-6) and the anti-inflammatory mediator IL-10 remain poorly quantified. We developed a systems biology model using nonlinear ordinary differential equations (ODEs) to resolve these dynamics, incorporating Nuclear Factor kappa-light-chain-enhancer of activated B cells (NF-κB)-mediated cross-activation, delayed IL-10 induction via a Hill function, and empirical parameterization from stroke data. Mathematical analysis revealed bistable inflammatory states via bifurcation theory, mechanistically explaining divergent inflammatory trajectory. Steady-state and stability analyses identified a critical IL-10 suppression threshold (γT10≈0.06 hr ⁻ ¹·nM ⁻ ¹) governing transitions between pro-inflammatory dominance and resolution phases. The model replicated experimentally observed cytokine dynamics, including TNF-α/IL-6 peaks (6–24 hours) and delayed IL-10 elevation (48 hours). Global sensitivity analysis highlighted IL-10 production (k10T) and TNF-α suppression (γT10) as key control parameters. Simulations predicted that IL-10 augmentation accelerates resolution, while TNF-α inhibition attenuates IL-10 induction, potentially compromising long-term recovery. By integrating dynamical systems theory with translational immunology, this model provides a mechanistic basis for optimizing immunomodulatory therapies in stroke and related inflammatory pathologies.