Gaussian representation of high-intensity focused ultrasound beams

Abstract

A method for fast numerical simulation of high-intensity focused ultrasound beams is derived. The method is based on the frequency-domain representation of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and assumes for each harmonic a Gaussian transverse pressure distribution at all distances from the transducer face. The beamwidths of the harmonics are constrained to vary inversely with the square root of the harmonic number, and as such this method may be viewed as an extension of a quasilinear approximation. The technique is capable of determining pressure or intensity fields of moderately nonlinear high-intensity focused ultrasound beams in water or biological tissue, usually requiring less than a minute of computer time on a modern workstation. Moreover, this method is particularly well suited to high-gain simulations since, unlike traditional finite-difference methods, it is not subject to resolution limitations in the transverse direction. Results are shown to be in reasonable agreement with numerical solutions of the full KZK equation in both tissue and water for moderately nonlinear beams.

Time-Domain Simulation of Ultrasound Propagation in a Tissue-Like Medium Based on the Resolution of the Nonlinear Acoustic Constitutive Relations

“…Simplifying assumptions have been needed in the past for modeling beam patterns from ultrasound transducers, as one-way parabolic approximations, most based on the Khokhlov-ZabolotskayaKuznetsov equation (KZK) [1][2][3][4][5][6][7][8] . To overcome the validity limitations of the parabolic approximations, i.e.…”

Simulation of the Thermal and Mechanical Effects of a Planar Rectangular High Intensity Ultrasound Transducer to Be Used for Destroying Atherosclerotic Plaque

“…The temperature vs. time history was obtained by solving the bio-heat equation proposed by Pennes (1948) numerically [29]. The explicit form of this equation is given by:…”

Temperature estimation of focused ultrasound exposures for stroke treatment

“…The power field was estimated using the KZK model [20]. The temperature vs time history was obtained by solving the bio-heat equation proposed by Pennes numerically [22].…”

“…Recently, experiments have demonstrated the ability of HIFU used for noninvasive procedures to dissolve thrombus [2, 3,[18][19][20]. Maxwell et al reported that histotripsy therapy using short, HIFU pulses can cause mechanical breakdown of targeted soft tissue by acoustic cavitation, which is guided by real-time ultrasound imaging [2,3].…”

“…A computer model [20] was used to estimate the temperature elevation, based on the transducer characteristics (frequency, diameter, degree of focusing), treatment protocol (pulse duration, duty factor, acoustical power), and the anatomical site (depth). A single element spherically focused transducer of 5 cm diameter, focusing at 10 cm and operating at either 0.5 MHz or 1 MHz was considered.…”