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Abstract <p>This study presents a highly nonlinear dual-phase lag (DPL) bioheat model for simulating heat transfer in spherical biological tissues subjected to a focused laser heat source. The formulation integrates temperature-dependent metabolic heat generation and blood perfusion with an external laser heat source, yielding a strongly coupled nonlinear system of governing equations. The numerical solution is obtained through a hybrid framework that combines the implicit finite difference method with Newton-Raphson iterations, ensuring robust and efficient convergence in the strongly nonlinear regime. Results reveal that accounting for strong nonlinearity produces substantially higher peak temperatures and significantly modified heat penetration profiles compared to the linear counterpart. These findings are further supported by numerical simulations, experimental measurements, an alternative finite element approach, and comparisons made with existing literature, underscoring the necessity of nonlinear modeling for the accurate forecasting of thermal response and further enhancement of the accuracy and safety of laser biotherapy.</p>

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Hybrid Numerical Analysis of a Nonlinear DPL Bioheat Model in Spherical Tissue with Experimental and FEM Validation

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • M. Khalid,
  • I. Abbas,
  • S. M. Sayed,
  • O. H. El-Kalaawy

摘要

Abstract

This study presents a highly nonlinear dual-phase lag (DPL) bioheat model for simulating heat transfer in spherical biological tissues subjected to a focused laser heat source. The formulation integrates temperature-dependent metabolic heat generation and blood perfusion with an external laser heat source, yielding a strongly coupled nonlinear system of governing equations. The numerical solution is obtained through a hybrid framework that combines the implicit finite difference method with Newton-Raphson iterations, ensuring robust and efficient convergence in the strongly nonlinear regime. Results reveal that accounting for strong nonlinearity produces substantially higher peak temperatures and significantly modified heat penetration profiles compared to the linear counterpart. These findings are further supported by numerical simulations, experimental measurements, an alternative finite element approach, and comparisons made with existing literature, underscoring the necessity of nonlinear modeling for the accurate forecasting of thermal response and further enhancement of the accuracy and safety of laser biotherapy.