# A figure of merit for transcranial ultrasound transmission based on coupled elastic-thermal analysis

## TL;DR

This paper introduces a new metric to evaluate how efficiently and safely ultrasound can pass through the skull for medical treatments.

## Contribution

A novel figure of merit (FOM) is introduced to assess transcranial ultrasound transmission efficiency and thermal safety.

## Key findings

- The FOM decreased significantly at incidence angles above 15° for 0.8 MHz, indicating reduced transmission and increased heating.
- The 2D microCT model was validated experimentally and provides a reliable framework for analyzing ultrasound transmission and heating effects.

## Abstract

Objective. To evaluate the efficiency of ultrasound transmission and its associated thermal effects on the skull, introducing a figure of merit (FOM) to assess the efficacy and safety of transcranial focused ultrasound (tFUS) at varying incidence angles and frequencies. Approach. A coupled elastic-thermal analysis was performed using a two-dimensional (2D) parallel solid plate skull model, validated through three-dimensional simulations. High-resolution micro-computed tomography (microCT) data from an ex vivo human skull sample was incorporated for realistic modeling. Simulations were conducted at frequencies of 0.8 MHz, 1 MHz, and 1.2 MHz to explore the impact of skull thickness, incidence angle, and absorption properties on ultrasound transmission and heating. The FOM was calculated for each scenario to provide an integrated measure of transmission efficiency and thermal safety. Experimental studies using the same ex vivo human skull validated the microCT-based simulation model. Main results. The FOM analysis demonstrated that at 0.8 MHz for an 8 mm thick skull, the FOM dropped by half for incidence angles above 15°, indicating reduced ultrasound transmission and heightened temperature rise at oblique angles. These findings suggest that dual-mode conversion at higher angles may not be suitable for tFUS applications, supporting the clinical preference for near-normal incidence. The validated 2D microCT model provides a reliable framework for studying the interplay between transmission and heating effects. Significance. This study provides an integrated framework for optimizing tFUS parameters by balancing transmission efficiency and thermal safety. The introduced FOM offers a novel metric to guide therapeutic applications, contributing to safer and more effective transcranial ultrasound treatments.