Fractal and Spectral Dimensions as Determinants of Thermal Ablation Outcomes in Cancer Tissues

TL;DR

This study introduces a fractal-fractional bio-heat model to better understand how tissue architecture influences thermal ablation outcomes in cancer, emphasizing the role of spectral dimension and topology in treatment variability.

Contribution

The paper develops a novel fractal-fractional bio-heat model incorporating tissue heterogeneity and memory effects to predict ablation efficacy based on tissue structure.

Findings

Spectral dimension significantly influences coagulation zone expansion.

Fractal geometry and connectivity affect heat transfer and ablation success.

Model reproduces clinical differences between primary and metastatic tumors.

Abstract

Clinical thermal ablation outcomes display significant variability that classical bio-heat models cannot fully explain. One reason may lie in the fractal architecture of biological tissues, which has been identified as a robust biomarker directly correlated with cancer grades. This structural heterogeneity, together with memory effects (e.g., thermotolerance), causes heat transfer in living tissues to differ from Fourier diffusion, resulting in anomalous biological transport. In this work, we implemented a realistic fractal-fractional bio-heat model, with non-linear perfusion and PI-controlled power delivery, to quantify the role of tissue fractality in ablation outcomes. Our results reveal that the expansion of coagulation zones is jointly controlled by fractal geometry and its associated topological connectivity. These findings highlight spectral dimension as a key driver of clinical variability, successfully reproducing the reduced ablative efficacy in liver metastases compared to primary carcinomas, and provide evidence for topologically informed treatment strategies for the thermal ablation of malignant neoplasms.