Multi-frequency characterization of the speed of sound and attenuation coefficient for longitudinal transmission of freshly excised human skulls

• Published in: Physics in medicine & biology 2011-01, Vol.56 (1), p.219-250
• Main Authors: Pichardo, Samuel, Sin, Vivian W, Hynynen, Kullervo
• Format: Article
• Language: English
• Subjects: Biomechanical Phenomena; Computer Simulation; Humans; Imaging, Three-Dimensional; Models, Biological; Skull - diagnostic imaging; Skull - physiology; Tomography, X-Ray Computed - methods; Ultrasonics - methods; Ultrasonography
• ISSN: 0031-9155; 1361-6560
• DOI: 10.1088/0031-9155/56/1/014

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 a