Multi-frequency characterization of the speed of sound and attenuation coefficient for longitudinal transmission of freshly excised human skulls
Bibliographic record
Abstract
For medical applications of ultrasound inside the brain, it is necessary to understand the relationship between the apparent density of skull bone and its corresponding speed of sound and attenuation coefficient. Although there have been previous studies exploring this phenomenon, there is still a need to extend the measurements to cover more of the clinically relevant frequency range. The results of measurements of the longitudinal speed of sound and attenuation coefficient are presented for specimens of human calvaria. The study was performed for the frequencies of 0.27, 0.836, 1.402, 1.965 and 2.525 MHz. Specimens were obtained from fresh cadavers through a protocol with the Division of Anatomy of the University of Toronto. The protocol was approved by the Research Ethics Board of Sunnybrook Health Sciences Centre. The specimens were mounted in polycarbonate supports that were marked for stereoscopic positioning. Computer tomography (CT) scans of the skulls mounted on their supports were performed, and a three-dimensional skull surface was reconstructed. This surface was used to guide a positioning system to ensure the normal sound incidence of an acoustic signal. This signal was produced by a focused device with a diameter of 5 cm and a focal length of 10 cm. Measurements of delay in time of flight were carried out using a needle hydrophone. Measurements of effective transmitted energy were carried out using a radiation force method with a 10 µg resolution scale. Preliminary functions of speed of sound and attenuation coefficient, both of which are related to apparent density, were established using a multi-layer propagation model that takes into account speed of sound, density and thickness of the layer. An optimization process was executed from a large set of random functions and the best functions were chosen for those ones that closest reproduced the experimental observations. The final functions were obtained after a second pass of the optimization process was executed, but this time using a finite-difference time-difference solution of the Westervelt equation, which is more precise than the multi-layer model but much more time consuming for computation. For six of seven specimens, measurements were carried out on five locations on the calvaria, and for the other specimen three measurements were made. In total, measurements were carried out on 33 locations. Results indicated the presence of dispersion effects and that these effects are different according to the type of bone in the skull (cortical and trabecular). Additionally, both the speed of sound and attenuation showed dependence on the skull density that varied with the frequency. Using the optimal functions and the information of density from the CT scans, the average values (±s.d.) of the speed of sound for cortical bone were estimated to be 2384(± 130), 2471(± 90), 2504(± 120), 2327(± 90) and 2053(± 40) m s(-1) for the frequencies of 270, 836, 1402, 1965 and 2526 kHz, respectively. For trabecular bone, and in the same order of frequency values, the speeds of sound were 2140(± 130), 2300(± 100), 2219(± 200), 2133(± 130) and 1937(± 40) m s(-1), respectively. The average values of the attenuation coefficient for cortical bone were 33(± 9), 240(± 9) and 307(± 30) Np m(-1) for the frequencies of 270, 836, and 1402, respectively. For trabecular bone, and in the same order of frequency values, the average values of the attenuation coefficient were 34(± 13), 216(± 16) and 375(± 30) Np m(-1), respectively. For frequencies of 1.965 and 2.525 MHz, no measurable radiation force was detected with the setup used.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".