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Purpose <p>This study presents a preliminary application of Physics-Informed Neural Networks (PINNs) for computing breast temperature distributions using a simplified three-dimensional geometry. The results were validated against experimental data reported by Gautherie (1980) and numerical results from Das and Mishra (2015). A standard (vanilla) PINN architecture was employed.</p> Methods <p>The mathematical model adopted was the Bioheat Transfer Equation (BHTE), also known as Pennes’ equation, which was solved using a standard PINN implementation. A simplified three-dimensional geometry was considered, in which the tumor was modeled as a sphere. Boundary conditions of the first and third kinds were applied.</p> Results <p>The PINN successfully reproduces the overall thermal trend across the domain and captures the localized temperature elevation associated with the presence of a tumor. Acceptable levels of error were observed when the computed temperatures were compared with experimental and numerical data reported in two independent studies, Gautherie (1980) and Das and Mishra (2015).</p> Conclusion <p>PINNs provide a flexible framework for incorporating physical laws and heterogeneous tissue properties, enabling meaningful comparisons with classical thermographic datasets and established numerical simulations. In addition, they show potential for patient-specific parameter estimation. Further improvements may be achieved by combining the PINN architecture with other neural network approaches.</p>

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A first approach to breast temperature profile calculations using physics informed neural network including validation against experimental and numerical data

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月24日

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  • Elenilton Xavier de Vasconcelos Filho,
  • Luciete Alves Bezerra,
  • Rita de Cássia Fernandes de Lima

摘要

Purpose

This study presents a preliminary application of Physics-Informed Neural Networks (PINNs) for computing breast temperature distributions using a simplified three-dimensional geometry. The results were validated against experimental data reported by Gautherie (1980) and numerical results from Das and Mishra (2015). A standard (vanilla) PINN architecture was employed.

Methods

The mathematical model adopted was the Bioheat Transfer Equation (BHTE), also known as Pennes’ equation, which was solved using a standard PINN implementation. A simplified three-dimensional geometry was considered, in which the tumor was modeled as a sphere. Boundary conditions of the first and third kinds were applied.

Results

The PINN successfully reproduces the overall thermal trend across the domain and captures the localized temperature elevation associated with the presence of a tumor. Acceptable levels of error were observed when the computed temperatures were compared with experimental and numerical data reported in two independent studies, Gautherie (1980) and Das and Mishra (2015).

Conclusion

PINNs provide a flexible framework for incorporating physical laws and heterogeneous tissue properties, enabling meaningful comparisons with classical thermographic datasets and established numerical simulations. In addition, they show potential for patient-specific parameter estimation. Further improvements may be achieved by combining the PINN architecture with other neural network approaches.