Investigating glucose-lactate metabolism in glioblastoma multiforme via universal physics-informed neural networks

Shadi Vandvajdi; Yuannong Mao; Mahla Poudineh; Mohammad Kohandel; Shadi Vandvajdi; Yuannong Mao; Mahla Poudineh; Mohammad Kohandel

doi:10.3934/mbe.2025091

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 9: 2486-2505. doi: 10.3934/mbe.2025091

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Investigating glucose-lactate metabolism in glioblastoma multiforme via universal physics-informed neural networks

1.
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
2.
Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

Received: 08 May 2025 Revised: 02 July 2025 Accepted: 08 July 2025 Published: 28 July 2025

Understanding the metabolic adaptations of cancer cells is crucial for uncovering potential therapeutic targets and improving treatment strategies. In this study, we present a hybrid modeling framework that combines Physics-Informed Neural Networks (PINNs) and Universal PINNs (UPINNs) to investigate glucose-lactate metabolism in glioblastoma cell lines. We first employed PINNs to infer critical model parameters governing glucose uptake and phenotypic switching in tumor cells, demonstrating high accuracy using synthetic data. We then extended this framework using UPINNs to uncover hidden metabolic dynamics that could not be explicitly modeled, introducing a latent variable $ W $ to represent unknown functional behavior in glycolytic processes. Our approach was validated for both synthetic and experimental datasets for two glioblastoma cell lines (LN18 and LN229) with distinct metabolic phenotypes. The UPINN framework not only captured cell-type-specific behaviors but also remained robust in the presence of moderate experimental noise. Furthermore, we explored the sensitivity of the model to the trade-off between data fidelity and mechanistic constraints, showing that the choice of loss term weighting significantly impacts predictive performance. While our application centered on cancer metabolism, the proposed method was general and applicable to a wide range of systems described by differential equations, including problems in biology, engineering, and physical sciences. This work demonstrates the potential of UPINNs as a powerful and interpretable tool for data-driven discovery in partially observed dynamical systems.
- universal physics-informed neural networks,
- deep learning,
- glioblastoma multiforme,
- glucose-lactate metabolism
Citation: Shadi Vandvajdi, Yuannong Mao, Mahla Poudineh, Mohammad Kohandel. Investigating glucose-lactate metabolism in glioblastoma multiforme via universal physics-informed neural networks[J]. Mathematical Biosciences and Engineering, 2025, 22(9): 2486-2505. doi: 10.3934/mbe.2025091

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Abstract

Understanding the metabolic adaptations of cancer cells is crucial for uncovering potential therapeutic targets and improving treatment strategies. In this study, we present a hybrid modeling framework that combines Physics-Informed Neural Networks (PINNs) and Universal PINNs (UPINNs) to investigate glucose-lactate metabolism in glioblastoma cell lines. We first employed PINNs to infer critical model parameters governing glucose uptake and phenotypic switching in tumor cells, demonstrating high accuracy using synthetic data. We then extended this framework using UPINNs to uncover hidden metabolic dynamics that could not be explicitly modeled, introducing a latent variable $ W $ to represent unknown functional behavior in glycolytic processes. Our approach was validated for both synthetic and experimental datasets for two glioblastoma cell lines (LN18 and LN229) with distinct metabolic phenotypes. The UPINN framework not only captured cell-type-specific behaviors but also remained robust in the presence of moderate experimental noise. Furthermore, we explored the sensitivity of the model to the trade-off between data fidelity and mechanistic constraints, showing that the choice of loss term weighting significantly impacts predictive performance. While our application centered on cancer metabolism, the proposed method was general and applicable to a wide range of systems described by differential equations, including problems in biology, engineering, and physical sciences. This work demonstrates the potential of UPINNs as a powerful and interpretable tool for data-driven discovery in partially observed dynamical systems.

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