A viscoelastic model for the prediction of transcranial ultrasound propagation: application for the estimation of shear acoustic properties in the human skull

Abstract

A better understanding of ultrasound transmission through human skull is fundamental to develop optimal imaging and therapeutic applications. In this study, we present global attenuation values and functions that correlate apparent density calculated from computed tomography (CT) scans to shear speed of sound. For this purpose, we used a model for sound propagation based on the viscoelastic wave equation (VWE) assuming isotropic conditions. The model was validated using a series of measurements with plates of different plastic materials and angles of incidence of 0°, 15° and 50°. The optimal functions for transcranial ultrasound propagation were established using the VWE, scan measurements of transcranial propagation with an angle of incidence of 40° and a genetic optimization algorithm. Ten (10) locations over three (3) skulls were used for ultrasound frequencies of 270 kHz and 836 kHz. Results with plastic materials demonstrated that the viscoelastic modeling predicted both longitudinal and shear propagation with an average (± s.d.) error of 9(±7)% of the wavelength in the predicted delay and an error of 6.7(±5)% in the estimation of transmitted power. Using the new optimal functions of speed of sound and global attenuation for the human skull, the proposed model predicted the transcranial ultrasound transmission for a frequency of 270 kHz with an expected error in the predicted delay of 5(±2.7)% of the wavelength. The sound propagation model predicted accurately sound propagation regardless either shear or longitudinal sound transmission dominated. For 836 kHz, the model predicted accurately in average with an error in the predicted delay of 17(±16)% of the wavelength. Results indicated the high importance of the specificity of the information at a voxel level to better understand ultrasound transmission through the skull. These results and new model will be very valuable tools for the future development of transcranial applications of ultrasound therapy and imaging.

Ray Theory-Based Transcranial Phase Correction for Intracranial Imaging: A Phantom Study

“…Its basic acoustic parameters, i.e., longitudinal and shear velocity and attenuation, were respectively measured as c l = 2462m/s, c s = 1129m/s and α = 4dB/MHz/cm by using the ultrasound transmission method [35]. The longitudinal velocity of the material was close to that of the cranial bones, and the material was thus suitable for phantom construction of cranial bones [36]. The X-ray CT image of the cranial bones was extended in the vertical direction and printed using a photopolymer 3D printer to prepare the cranial bone phantom.…”

Numerical Evaluation of the Influence of Skull Heterogeneity on Transcranial Ultrasonic Focusing

“…In transcranial ultrasonic investigations, the assumption that the skull's elastic properties vary along with Hounsfield unit in CTimages has been verified experimentally for transcranial focusing (Top et al, 2016;Pichardo et al, 2017). Under that hypothesis, the elastic properties of the computational region, such as density, wave velocity, and attenuation, can be acquired with the following equations (Pichardo et al, 2011(Pichardo et al, , 2017Top et al, 2016):…”

“…In addition, c L is the longitudinal wave speed matrix, with c w = 1500m/s as the sound speed in water and c b = 2900m/s as the maximum longitudinal wave speed in the skull. The shear wave speed is approximated as c s = 7c l /11 in the skull (Pichardo et al, 2017). The term λ is the frequency-dependent longitudinal wave attenuation matrix, with λ min = 12Npm −1 as the minimum attenuation coefficient and λ max = 460Npm −1 as the maximum attenuation coefficient (Pichardo et al, 2011).…”

“…However, three-dimensional acoustic full-wave simulations are limited by excessive time consumption and memory requirements (Pichardo et al, 2017). Recently, ray tracing (RT) has been implemented in long-bone structure imaging (Renaud et al, 2018) and phase compensation for B-mode image reconstruction (Szostek and Piórkowski, 2016).…”

Development of custom RF coils for use in a small animal platform for magnetic resonance-guided focused ultrasound hyperthermia compatible with a clinical MRI scanner

“…Matching of the transducer to 50 X was achieved using an LC network. The acoustic beam for the transducer was simulated through the 2D implementation of the staggered-grid finitedifference time-domain (FDTD) viscoelastic model [24,25]. The model was implemented using fourth order in space and second order in time derivative operators to minimize the effects of numerical dispersion [26][27][28].…”