A multi-layer transcranial focused ultrasound model for neuromodulation procedure planning and insertion loss estimation

Objective Transcranial focused ultrasound (tFUS) for neuromodulation has attracted increasing attention, yet accurate pre-procedural planning and dose estimation is constrained by oversimplified skull representations and by the neglect of transducer-skull spacing induced wave interactions. This study aims to develop and validate a computationally efficient, CT-informed analytical framework for predicting frequency-dependent insertion loss. Approach We propose a multi-layer analytical framework that incorporates four key factors - skull thickness, skull density ratio (SDR), ultrasound insertion angle, and the transducer physical geometry and spacing from the skull – to predict frequency-dependent pressure insertion loss. Model accuracy was evaluated against k-Wave simulations and hydrophone measurements in 20 ex-vivo human skulls across 100 kHz to 1000 kHz frequency range. Main results Median root-mean-squared errors (RMSE) for peak pressure insertion loss were +1.1 dB relative to measurement and -1.7 dB relative to simulation. The relative median RMSE in percentage are: +30.1% and -20.3%, respectively. Median spearman correlation and cosine similarity values reached 0.92 (p<0.001) and 0.73, respectively. Uncertainty analysis showed that varying transducer-skull spacing altered predicted pressure insertion loss by -2.0 dB to +1.4 dB, with a median absolute percentage uncertainty of 18.1%. These results demonstrated that the proposed analytical model attains near-measurement accuracy while remaining computationally lightweight. Significance The balance of accuracy and efficiency of the proposed CT-informed multi-layer model makes it a practical tool for transducer positioning, frequency selection, and dose control in tFUS neuromodulation, with potential to improve reproducibility and safety in clinical applications.