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Publication · Medical Physics · D3-HIFU· September 2026

Beyond the skull density ratio: predicting how the skull shapes focused-ultrasound heating

A first result of D3-HIFU: skull descriptors predict thermal efficiency far better than SDR alone, and machine learning anticipates the temperature of each sonication.

Schematic of skull metrics: skull density ratio, skull thickness, diploe thickness and angle of incidence along an ultrasound beam converging on a deep brain target

Skull metrics computed along each ultrasound beam. NTUSlab illustration based on the paper.

📄 New in Medical Physics (open access). Below, the short story of what we did and why it matters.

Read the paper in Medical Physics ↗

The skull is the bottleneck

In MRgFUS, energy has to cross the skull to heat a deep target. Screening currently relies on a single number, the skull density ratio (SDR).

Patients with similar SDR can respond very differently, and energy escalation during the procedure still relies largely on experience.

What we did

We analysed 316 procedures (4,138 sonications), extracted skull properties beam by beam, and built two models tested on unseen procedures.

Key results: cohort of 316 procedures; SDR alone explains 48% of thermal efficiency variance versus 61% for a five-feature skull model; peak temperature predicted with 1.9 °C mean absolute error
Key numbers from the study. Pineda-Pardo et al., Medical Physics (2026).

What we found

SDR alone explained about half the variability; a five-feature skull model reached R² 0.61 (0.58 on an independent test set).

Subthalamotomies were less efficient than thalamotomies despite similar skulls: screening rules should not be transferred blindly between targets.

A machine-learning model predicted each sonication's peak temperature with a 1.9 °C mean error on unseen procedures.

Why it matters - and how it fits D3-HIFU

A continuous efficiency estimate instead of a yes/no cut-off, and objective choice of sonication parameters during treatment.

A first building block of the D3-HIFU decision-support platform; next, validation across the national network.

Thanks to all co-authors and to everyone who made this cohort possible.

Full paper and original figures in Medical Physics ↗

Source: Pineda-Pardo et al., Medical Physics 53(9), 2026. doi:10.1002/mp.70652.