Simulation of the Second-Harmonic Ultrasound Field in Heterogeneous Soft Tissue Using a Mixed-Domain Method

Characterization of weakly nonlinear effects in relationship to transducer parameters in focused ultrasound therapy

BACKGROUND

Focused ultrasound therapy has been widely used for the treatment of various diseases, employing different types of transducers. The focused ultrasound pressure fields inevitably exhibit nonlinear effects, which can influence the ablation region. However, the nonlinear effects exhibit noticeable variations across different applications. The characterization of the nonlinear pressure fields of ultrasound is important for the effective implementation of focused ultrasound therapy.

PURPOSE

The traditional angular spectrum method (ASM) was extended to accurately and efficiently simulate the propagation of weakly nonlinear ultrasound in heterogeneous mediums of clinical model. The nonlinear effects were further analyzed in relationship to the transducer parameters that are different in various applications.

METHODS

The pressure fields were simulated using the extended ASM, incorporating calculations for phase aberration in the frequency domain and magnitude compensation in the spatial domain to account for heterogeneous acoustic impedance mismatch. Validation was performed by comparison to k-Wave simulation results using two simplified clinical models, an abdominal soft tissue and a transcranial skull model. The nonlinear effects were then analyzed in relation to the transducer parameters of f-number and effective source area based on the same acoustic output power. The analysis of nonlinear effects was conducted under both homogeneous medium and the clinical models.

RESULTS

The simulation results demonstrated a maximum error of 3.93% in the calculated harmonic pressure of the abdominal model, and a maximum error of 4.89% within the transcranial model when comparing the extended ASM simulation results to those obtained from k-Wave simulations. The characterization of the nonlinear effects reveals a strong correlation with the transducer parameters. Specifically, the results indicate that the nonlinear effects intensify with an increase in the effective source area and f-number, under the same acoustic output power of the transducer. However, the clinical model also showed an influence on the nonlinear effects in relation to the f-number.

CONCLUSION

The extended ASM was demonstrated as an accurate and efficient simulation tool, and the simulation results provide a reference for evaluating the intensity of nonlinear effects in various transducer designs.

A rapid element pressure field simulation method for transcranial phase correction in focused ultrasound therapy

Transcranial focused ultrasound ablation has emerged as a promising technique for treating neurological disorders. The clinical system exclusively employed the ray tracing method to compute phase aberrations induced by the human skull, taking into account computational time constraints. However, this method compromises slightly on accuracy compared to simulation-based methods. This study evaluates a fast simulation method that simulates the time-harmonic pressure field within the region of interest for effective phase correction. Experimental validation was carried out using a 512-element, 670 kHz hemispherical transducer for fourex vivoskulls. The ray tracing method achieved a restoration ratio of 64.81% ± 4.33% of acoustic intensity normalized to hydrophone measurements. In comparison, the rapid simulation method demonstrated improved results with a restoration ratio of 73.10% ± 7.46%, albeit slightly lower than the full-wave simulation which achieved a restoration ratio of 75.87% ± 5.40%. The rapid simulation methods exhibited computational times that were less than five minutes for parallel computation with 8 threads. The incident angle was calculated, and a maximum difference of 6.8 degrees was found when the fixed position of the skull was changed. Meanwhile, the restoration ratio of acoustic intensity was validated to be above 70% for different target positions away from the geometrical focus of the transducer. The favorable balance between time consumption and correction accuracy makes this method valuable for clinical treatment applications.

mSOUND: An Open Source Toolbox for Modeling Acoustic Wave Propagation in Heterogeneous Media

mSOUND is an open-source toolbox written in MATLAB. This toolbox is intended for modeling linear/ nonlinear acoustic wave propagation in media (primarily biological tissues) with arbitrary heterogeneities, in which, the speed of sound, density, attenuation coefficient, power-law exponent, and nonlinear coefficient are all spatially varying functions. The computational model is an iterative one-way model based on a mixed domain method. In this article, a general guideline is given along with three representative examples to illustrate how to set up simulations using mSOUND. The first example uses the transient mixed-domain method (TMDM) forward projection to compute the transient acoustic field for a given source defined on a plane. The second example uses the frequency-specific mixed-domain method (FSMDM) forward projection to rapidly obtain the pressure distribution directly at the frequencies of interest, assuming linear or weakly nonlinear wave propagation. The third example demonstrates how to use TMDM backward projection to reconstruct the initial acoustic pressure field to facilitate photoacoustic tomography (PAT). mSOUND (https://m-sound.github.io/mSOUND/home) is designed to be complementary to existing ultrasound modeling toolboxes and is expected to be useful for a wide range of applications in medical ultrasound including treatment planning, PAT, transducer design, and characterization.

A modified mixed domain method for modeling acoustic wave propagation in strongly heterogeneous media

In this paper, phase correction and amplitude compensation are introduced to a previously developed mixed domain method (MDM), which is only accurate for modeling wave propagation in weakly heterogeneous media. Multiple reflections are also incorporated with the one-way model to improve the accuracy. The resulting model is denoted as the modified mixed domain method (MMDM) and is numerically evaluated for its accuracy and efficiency using four distinct cases. It is found that the MMDM is significantly more accurate than the MDM for strongly heterogeneous media, especially when the phase aberrating layer is approximately perpendicular to the acoustic beam. Additionally, a convergence study suggests that the second-order reflection could be sufficient for cases involving high contrast inhomogeneities and large loss values (e.g., skulls). The method developed in this work could facilitate therapeutic ultrasound for treating brain-related diseases and disorders.