Modified Pennes bioheat equation with heterogeneous blood perfusion: A newer perspective

The Pennes bioheat equation is a widely used mathematical model for predicting temperature distribution in biological tissues. However, it assumes homogeneous blood perfusion throughout the tissue, which may not accurately represent the complex perfusion patterns observed in tumors. In this study, we propose modification to traditional Pennes bioheat equation that incorporates the effects of perfusion heterogeneity by introducing a spatially varying perfusion term, represented by a perfusion coefficient, ωb(x,y,z) to account for local variations in blood flow at each spatial location within the biological tissue. Therefore, heterogeneous blood perfusion at each tumor tissue voxel location relax the uniform blood perfusion assumption. By incorporating these modifications, the model allows for a more realistic representation of the heat exchange between the biological tissue and blood flow, by predicting the non-uniform temperature distribution particularly in tumors with irregular blood vessel growth and organization, thereby facilitating treatment planning and optimization of thermal therapies, and leading to more effective therapeutic outcomes. The spatially varying perfusion coefficient can be obtained through advanced imaging techniques such as dynamic contrast-enhanced MRI or Doppler ultrasound enabling the assessment of perfusion heterogeneity in biological tissues. In conclusion, the modified Pennes bioheat equation offers a valuable tool for understanding the intricate relationship between with heterogeneous blood perfusion and temperature distribution in biological tissues, providing important insights to the thermal response of tumors and guiding the development of improved therapeutic strategies in optimizing cancer treatments.