Open Access

ARTICLE

Physics-Informed Neural Networks for Osteosarcoma Tumor-Immune Dynamics

Pasquale De Luca^1,2,*, Livia Marcellino¹

1 Department of Science and Technology, Parthenope University of Naples, Naples, Italy
2 Department for the Promotion of Human Sciences and Quality of Life, University of Rome San Raffaele, Rome, Italy

* Corresponding Author: Pasquale De Luca. Email:

(This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)

Computer Modeling in Engineering & Sciences 2026, 147(3), 27 https://doi.org/10.32604/cmes.2026.082664

Received 20 March 2026; Accepted 02 May 2026; Issue published 30 June 2026

Abstract

Osteosarcoma is the most common primary malignant bone tumor in pediatric populations. This work presents an extended Physics-Informed Neural Network framework that incorporates interferon-gamma (IFN-γ) as a fifth biological variable, complementing previous four-variable formulations with an explicit cytokine-mediated macrophage activation pathway. The model couples five biological fields with mechanical tissue response through Biot’s poroelastic theory over a two-dimensional domain. Four distinct initial macrophage distributions were investigated. Numerical stability was achieved across all scenarios, with total loss values between 0.056 and 0.158 and mechanical residuals below 3.2×10−5. The boundary-concentrated configuration yielded the lowest biological loss. Predicted dynamics are biologically consistent, exhibiting initial immune-mediated suppression followed by progressive macrophage depletion. Comparison of the four scenarios suggests that spatial co-localization between macrophages and tumor boundaries enhances early immune-tumor contact via pressure-driven advection, while sustained immune engagement leads to measurable macrophage exhaustion. Temporal stiffness introduced by the rapid interferon-gamma decay was managed through curriculum learning and adaptive loss weighting.

---

Keywords

---