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

<i>Objective.</i>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.<i>Approach.</i>We propose a multi-layer analytical framework that incorporates four key factors-skull thickness, skull density ratio, 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<i>ex-vivo</i>human skulls across 100 kHz to 1000 kHz frequency range.<i>Main Results.</i>Median prediction deviations for peak pressure insertion loss were +1.1 dB (interquartile range (IQR): +0.2 dB to +2.2 dB) relative to measurement and -1.7 dB (IQR: -2.7 dB to -0.7 dB) relative to simulation. The relative median percentage errors were +30.1% (IQR: +9.5% to +35.6%) and -20.3% (IQR: -31.7% to -10.1%), respectively. Median spearman correlation and cosine similarity values reached 0.92 (IQR: 0.86-0.98,<i>p</i>< 0.001) and 0.73 (IQR: 0.49-0.82), respectively. Uncertainty analysis showed that varying transducer-skull spacing resulted in a median absolute percentage uncertainty of 18.1% (IQR: 17.2% to 21.3%).<i>Significance.</i>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.