Session: 07-08-04: Computational Modeling in Biomedical Applications

Paper Number: 191627

A Lumped Modification of the Pennes Bioheat Equation for Thermal Therapy 

Magnetic Thermal Therapy (MTT) is a minimally invasive heating modality with strong potential for treating deep-seated tumors. Treatment planning for MTT is commonly performed using the Pennes bioheat equation because of its simplicity and computational efficiency. However, the Pennes model treats blood perfusion as an empirical convective heat-sink term, does not explicitly conserve energy, and effectively assumes blood behaves as an infinite heat-capacity sink. These assumptions are often acceptable in thermal therapies with modest power deposition (~3-5 [W]), but those assumptions need to be considered for MTT, where Joule heating from induced eddy currents can make blood-temperature rise non-negligible. In contrast, generic bioheat transfer models account for blood thermal storage through coupled tissue-blood energy equations, but their computational cost limits their practicality for treatment planning and repeated simulations.

In this study, we propose an energy-conserving extension of the Pennes bioheat equation for MTT by introducing a lumped correction term that captures finite blood heat capacity while retaining the efficiency of a single-equation model. The framework was implemented by adapting a previously reported human-scale MTT computational model and incorporating both nanoparticle-mediated heating and Joule heating. A worst-case analysis was performed for , where denotes the efficiency of heat transfer to blood, or equivalently, the ratio of heat that increases blood temperature to the energy otherwise carried away through the perfusion heat-sink term. Temperature predictions from the proposed Pennes+lumped formulation were compared against the conventional Pennes model to evaluate the influence of blood thermal storage on predicted thermal response.

The results show that the proposed model predicts a measurable rise in blood temperature in the worst-case scenario, with blood temperature increasing by approximately 5 [°C] over the heating period. This behavior is not captured by the conventional Pennes model, which assumes blood remains an ideal heat sink. The added lumped term therefore changes the effective heat-removal behavior and yields a more physically consistent prediction under conditions where eddy-current heating is significant. At the same time, the model avoids the computational burden associated with solving fully coupled generic bioheat equations. These findings suggest that a lumped energy-conserving correction may provide a practical middle ground between the simplicity of Pennes and the fidelity of generic bioheat models for MTT planning.

Overall, this work presents a computationally efficient modification to the classical Pennes formulation for MTT applications where blood heating cannot be ignored. The proposed approach preserves the convenience of standard treatment-planning workflows while improving physical realism in the presence of Joule heating. Future work will evaluate a range of  values, compare the proposed formulation directly against generic bioheat transfer equations, and correlate the terms in the generic bioheat model with the lumped correction to identify the corresponding effective under different heating and perfusion conditions.

Presenting Author: Anilchandra Attaluri Penn State Harrisburg

Presenting Author Biography: Anilchandra Attaluri received the Ph.D. degree in mechanical engineering with a focus on bio-transport and imaging from the University of Maryland at Baltimore County, Baltimore, MD, USA, in 2012. He received post-doctoral training in magnetic hyperthermia from the Department of Radiation Oncology & Molecular Radiation Sciences, The Johns Hopkins University School of Medicine, Baltimore. Focusing on experimental, preclinical, and finite element analysis, his work resulted in novel applicators and pioneering data for improving magnetic nanoparticle hyperthermia. In 2017, he joined the School of Science, Engineering, and Technology, Pennsylvania State University, Harrisburg, PA, USA, at which he now serves as an Associate Professor of mechanical engineering. His research interests include the field of theranostic technologies and systems with an emphasis on devices and image-based modelling. He teaches courses on capstone design, engineering simulations, and computational techniques for biomedical applications.

Authors:

Shreeniket Pawar Penn State Harrisburg
Anilchandra Attaluri Penn State Harrisburg