A Noninvasive and Dispersive Framework for Estimating Nonuniform Conductivity of Brain Tumor in Patient-Specific Head Models

Abstract

We propose a noninvasive and dispersive framework for estimating the spatially nonuniform conductivity of brain tumors using MR images. The method consists of two components: (i) voxel-wise assignment of tumor conductivity based on reference values fitted to the Cole–Cole model using empirical data from the literature and (ii) fine-tuning of a deep learning model pretrained on healthy participants A total of 67 cases, comprising both healthy participants and tumor patients and including 9,806 paired T1- and T2-weighted MR images, were used for training and evaluation. The proposed method successfully estimated patient-specific conductivity maps, exhibiting smooth spatial variations that reflected tissue characteristics, such as edema, necrosis, and rim-associated intensity gradients observed in T1- and T2-weighted MR images. At 10 kHz, case-wise mean conductivity values varied across patients, ranging from 0.132 to 0.512 S/m in the rim (defined as the region within 2 mm of the tumor boundary), from 0.132 to 0.608 S/m in the core (the area inside the rim), and from 0.141 to 0.542 S/m in the entire tumor. Electromagnetic simulations for transcranial magnetic stimulation in individualized head models showed substantial differences in intratumoral field distributions between uniform assignments and the proposed nonuniform maps. Furthermore, the proposed framework enables voxel-wise conductivity mapping across multiple frequencies (10 kHz, 1 MHz, and 100 MHz) by combining spatially resolved conductivity estimation with a physics-informed dispersive scaling model. This framework supports accurate whole-brain conductivity estimation by incorporating both individual anatomical structures and tumor-specific characteristics. Collectively, these results advance patient-specific EM modeling for tumor-bearing brains and lay the groundwork for subsequent validation in higher-frequency electromagnetic applications.