Locating multiple tumors by moving shape analysis.

Area of Science:

• Computational modeling
• Biomedical engineering
• Inverse problems

Background:

• Accurate tumor shape determination is crucial for effective cancer treatment planning.
• Non-invasive methods for characterizing subsurface abnormalities are highly sought after.
• Existing methods may lack precision in defining complex or irregular tumor geometries.

Purpose of the Study:

• To develop a computational methodology for determining the unknown shape of embedded tumors.
• To establish a link between surface temperature measurements and internal tumor geometry.
• To provide a framework for inverse problem-solving in bioheat transfer.

Main Methods:

• Defining a functional representing the mismatch between experimental and simulated temperature profiles.
• Modeling heat transfer in biological tissue with tumors using Pennes's bioheat transfer equation.
• Employing the Finite Element Method to approximate the solution and compute shape derivatives of the functional.
• Implementing an adaptive strategy to enhance the accuracy of the objective function.

Main Results:

• The proposed functional's minimum directly corresponds to the embedded tumor's true shape.
• The methodology was validated using numerical simulations, including cases with multiple connected tumors.
• The shape derivative computation using Finite Elements proved effective for inverse problem-solving.

Conclusions:

• The developed methodology offers a promising non-invasive approach for inferring tumor shapes from thermal data.
• This technique has the potential to improve diagnostic accuracy and treatment planning in oncology.
• Further research can explore real-world experimental validation and clinical applications.