A frequency-dependent and nonlinear, time-explicit five-layer human head numerical model for realistic estimation of focused acoustic transmission through the human skull for noninvasive high-intensity and high-frequency transcranial ultrasound stimulation: An application to neurological and psychiatric disorders

Abstract

Transcranial focused ultrasound is a promising noninvasive technique for neuromodulation in neurological and psychiatric disorders, but accurate prediction of acoustic transmission through the skull remains a major challenge. In this study, we present a five-layer numerical human head model that integrates frequency-dependent acoustic parameters with nonlinear time-explicit dynamics to realistically capture ultrasound propagation. The model explicitly represents skin, trabecular bone, cortical bone, and brain, each assigned experimentally derived acoustic properties across a clinically relevant frequency range (0.5–5 MHz). Numerical simulations were performed in the frequency domain and time-explicit to quantify sound transmission loss and focal depth under high-intensity and high-frequency stimulation. The results show the effect of frequency, radius of curvature, and skull thickness on maximum pressure ratio, focal depth, and focus zone inside the brain tissue. Findings indicate that skull geometry, particularly radius of curvature and thickness, strongly influences the focal zone, with thinner skull regions allowing deeper penetration and reduced transmission loss. Comparison of the frequency-domain model with the time-explicit model demonstrated broadly similar trends; however, the frequency-domain approach consistently underestimated transmission loss and was unable to capture nonlinear effects such as frequency harmonics. These findings highlight the importance of nonlinear, time-explicit modeling for accurate transcranial ultrasound planning and suggest that the proposed framework provides a robust tool for optimizing stimulation parameters and identifying ideal target zones, supporting the development of safer and more effective neuromodulation strategies.