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This paper introduces Trident, a ray tracing method to calculate the spatial heat production during HIFU, handling both longitudinal and shear waves in isotropic solids. Trident is especially advantageous for setups with complex geometries where other numerical methods prove computationally prohibitive. It outperforms current state-of-the-art ray tracing techniques by being at least 20 times faster without sacrificing accuracy. Conversely, when given the same running time, it can achieve 2 orders of magnitude higher accuracy. The improvement is due to the specially developed approach that captures the intensity decrease due to geometrical spreading in an efficient way. Trident was validated against a known reference method and temperature measurements on bovine cortical bone during HIFU sonication. Results indicate a good agreement with experimental temperature measurements. In highly attenuating solid cortical bone, the Trident method was able to model temperature increases within 3\u2009K of peak temperatures measured by optical probes.<\/jats:p>","DOI":"10.1121\/10.0036452","type":"journal-article","created":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T12:15:00Z","timestamp":1744978500000},"page":"3005-3016","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Trident: Three-dimensional ray tracing for modeling high intensity focused ultrasound ablation"],"prefix":"10.1121","volume":"157","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2621-8046","authenticated-orcid":false,"given":"Boris J. 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