A hybrid implicit-explicit finite element framework for real-time bioheat transfer simulation in deformable...

Real-time simulation of bioheat transfer in deformable tissues is essential for realistic surgical training, yet it remains challenging due to stringent requirements for numerical stability and computational efficiency. To overcome these limitations, we propose a unified finite element framework that seamlessly integrates implicit and explicit schemes, enabling real-time updates of tissue deformation while maintaining computationally efficient thermal simulations.

This paper proposes a novel hybrid finite element framework that employs an optimization-based implicit time integration scheme for tissue mechanics, ensuring numerical stability even under large deformations, while utilizing an explicit time-integration scheme for the Pennes bioheat transfer model to achieve computationally efficient thermal simulations. Additionally, the framework integrates a physiological motion model to reproduce realistic tissue dynamics, enhancing the fidelity of surgical simulation.

Validation against commercial software Abaqus and COMSOL under pure conduction, blood perfusion, and motion scenarios demonstrates excellent accuracy, with maximum normalized relative error below 0.4%, RMSE below 0.009 °C, and RL²NE below 0.0015 across all scenarios. GPU-accelerated thermal computation achieved single-step execution times below 50μs for meshes up to 50,000 elements. Real-time performance was confirmed on consumer-grade hardware in liver ablation simulations, highlighting the framework's suitability for interactive surgical training applications.

The hybrid implicit-explicit strategy effectively balances numerical stability with computational efficiency in coupled thermo-mechanical simulations. The demonstrated accuracy and real-time performance highlight the framework's potential for interactive surgical training applications, particularly in thermal ablation therapy.