MRI-based estimation of physiologically consistent head conductivity and its impact on depth-dependent electric field...

Objective. Accurate estimation of spatially heterogeneous conductivity distributions is essential for reliable electric field modeling in non-invasive brain stimulation. Existing deep learning-based approaches tend to produce conductivity distributions converging toward uniform values, failing to capture physiologically plausible intra-tissue variability or MRI-conductivity relationships. This limitation restricts the ability to resolve depth-dependent electric field characteristics that are relevant for understanding the mechanisms of neural activation. Here, we propose a novel framework for estimating physiologically consistent head conductivity distributions from T1- and T2-weighted MRI.Approach. The framework incorporates a statistical-rank constraint-based loss function incorporating three components: a statistical loss enforcing consistency with reference conductivity statistics, a rank loss that preserves MRI intensity-conductivity ordering, and a smoothness loss suppressing unrealistic spatial variations. The rank constraint is motivated by the physiological relationship between MRI signal intensity and tissue water content, which is linked to ionic conductivity. The framework was evaluated using 35 subjects from the IXI dataset, with external validation on 11 independent subjects acquired under different imaging conditions.Main results. The proposed method improved intra-tissue conductivity variability toward reference values and increased the Spearman correlation between conductivity and MRI intensity by up to ∼0.8 across tissues, compared to existing methods. Ablation analysis confirmed the contribution of each loss component. Electric field simulations revealed a peak at approximately 0.5 mm within gray matter and systematically smoother depth-dependent field gradients, indicating reduced artificial discontinuities at tissue boundaries, with consistent results in the external dataset.Significance. The proposed framework provides a unified pipeline from MRI-based conductivity estimation to electric field simulation without requiring voxel-wise ground truth. Physiologically consistent conductivity distributions produce quantitatively distinct and mechanistically interpretable depth-dependent electric field profiles in transcranial magnetic stimulation, supporting improved understanding of cortical activation. The implementation of the proposed method is available from the corresponding author upon reasonable request.