Breast cancer is a prevalent form of cancer among women. It is associated with increased heat generation due to higher metabolism in the tumor and increased blood vessels resulting from angiogenesis. The thermal alterations result in a change in the breast surface temperature profile. Infrared imaging is an FDA-approved adjunctive to mammography, which employs the surface temperature alterations in detecting cancer. To apply infrared imaging in clinical settings, it is necessary to develop effective techniques to model the relation between the tumor characteristics and the breast surface temperatures. The present work describes the thermal modeling of breast cancer with physics-informed neural networks. Losses are assigned to random points in the domain based on the boundary conditions and governing equations that should be satisfied. The Adam optimizer in TensorFlow minimizes the losses to find the temperature field or thermal conductivity that satisfies the boundary conditions and the bioheat equation. Backpropagation computes the derivatives in the bioheat equation. Analyses of the three patient-specific cases show that the machine-learning model accurately reproduces the thermal behavior given by ansys-fluent simulation. Also, good agreement between the model prediction and the infrared images is observed. Moreover, the neural network accurately recovers the thermal conductivity within 6.5% relative error.

The present work demonstrates the use of customized Ansys-Fluent in performing 3D numerical simulations of nucleate boiling with a sharp interface and adaptive mesh refinement. The developed simulation approach is a reliable and effective tool to investigate 3D boiling phenomena by accurately capturing the thermal and fluid dynamic interfacial vapor-liquid interaction and reducing computational time. These methods account for 3D sharp interface and thermal conditions of saturation temperature refining the mesh around the bubble edge. User-Defined-Functions (UDFs) were developed to customize the software Ansys-Fluent to preserve the interface sharpness, maintain saturation temperature conditions, and perform effective adaptive mesh refinement in a localized region around the interface. Adaptive mesh refinement is accomplished by a UDF that identifies the cells near the contact line and the liquid-vapor interface and applies the adaptive mesh refinement algorithms only at the identified cells. Validating the approach considered spherical bubble growth with an observed acceptable difference between theoretical and simulation bubble growth rates of 10%. Bubble growth simulations with water reveal an influence region of 2.7 times the departure bubble diameter, and average heat transfer coefficient of 15000 W/m²-K. In addition, the results indicate a reduced computational time of 75 hours using adaptive mesh compared to uniform mesh.