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Data-Driven Parameter Identification for Tumor Growth Models

Liu Liu, Yifei Wang, Qinyu Xu, Xiaoqian Xu

TL;DR

This work demonstrates a physics-informed neural network framework for data-driven parameter identification in tumor-growth models governed by nonlinear porous-medium PDEs. By embedding the governing dynamics into the loss and leveraging limited, noisy observations, the approach accurately recovers proliferation-rate parameters in synthetic scenarios and successfully infers parameters from real lab data, including cases with spatial variation and unknown initial density. Theoretical backing shows convergence of PINN solutions to classical PDE solutions, while empirical results establish robustness to noise and data scarcity. The method offers a practical pathway for parameter estimation and predictive modeling in cancer growth with potential for lab-to-clinic translation.

Abstract

Modeling tumor growth accurately is essential for understanding cancer progression and informing treatment strategies. To estimate the parameters in the tumor growth model described by a nonlinear PDE, we adopt Physics-Informed Neural Networks (PINNs), which show advantages especially when the observation data is scarce and contains noise. With the help of real-life lab data, we have demonstrated the potential of applying deep learning tools to address data-driven modeling for tumor growth in biology.

Data-Driven Parameter Identification for Tumor Growth Models

TL;DR

This work demonstrates a physics-informed neural network framework for data-driven parameter identification in tumor-growth models governed by nonlinear porous-medium PDEs. By embedding the governing dynamics into the loss and leveraging limited, noisy observations, the approach accurately recovers proliferation-rate parameters in synthetic scenarios and successfully infers parameters from real lab data, including cases with spatial variation and unknown initial density. Theoretical backing shows convergence of PINN solutions to classical PDE solutions, while empirical results establish robustness to noise and data scarcity. The method offers a practical pathway for parameter estimation and predictive modeling in cancer growth with potential for lab-to-clinic translation.

Abstract

Modeling tumor growth accurately is essential for understanding cancer progression and informing treatment strategies. To estimate the parameters in the tumor growth model described by a nonlinear PDE, we adopt Physics-Informed Neural Networks (PINNs), which show advantages especially when the observation data is scarce and contains noise. With the help of real-life lab data, we have demonstrated the potential of applying deep learning tools to address data-driven modeling for tumor growth in biology.

Paper Structure

This paper contains 20 sections, 4 theorems, 40 equations, 13 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Modeling of tumor growth
  3. Methods
  4. Analysis
  5. Classical theory of porous medium equations and universal approximation
  6. Loss function convergence
  7. PINN solution convergence
  8. Setup of PINNs and verification on sythetic data
  9. Recovering the proliferation rate from numerical tumor growth data
  10. PINNs setup
  11. Results
  12. Robustness to noisy data
  13. Prediction of proliferation rate based on observed data
  14. Observed data and problem setup
  15. Implementation details
  16. ...and 5 more sections

Key Result

Theorem 1

Suppose both $\rho_0$ and $f$ are smooth and positive, $\mathbf{g}\in C^{\infty}$ and bounded above, then pme admits a unique classical solution $\rho\in C^{2}(\overline{\Omega})\cap C^1([0,T])$. Moreover, we have the following comparison principle: Suppose $0<\epsilon<\rho_0<\frac{1}{\epsilon}$, th

Figures (13)

  • Figure 1: PINNs setup and framework
  • Figure 2: Predicted values of parameter $v$ by PINNs model (blue) compared with ground truth (red).
  • Figure 3: Relative errors for each value of $v$.
  • Figure 4: Relative errors between learning parameter and its target value.
  • Figure 5: Observed images of tumor growth in lab, in which the tumor growth profile is marked in red circle.
  • ...and 8 more figures

Theorems & Definitions (7)

  • Theorem 1
  • Theorem 2
  • Remark 1
  • Theorem 3
  • proof
  • Theorem 4
  • proof