A waveform diversity method for optimizing 3-d power depositions generated by ultrasound phased arrays

An Optimized Control Approach for HIFU Tissue Ablation Using PDE Constrained Optimization Method

High-intensity focused ultrasound (HIFU) is a widely used technique capable of providing noninvasive heating and ablation for a wide range of applications. However, the major challenges lie in the determination of the position and the amount of heat deposition over a target area. In order to assure that the thermal area is confined to tumor locations, an optimization method should be employed. Sequential quadratic programming and steepest gradient method with closed-form solution have been previously used to solve this kind of problem. However, these methods are complex and computationally inefficient. The goal of this article is to solve and control the solution of inverse problems with partial differential equation (PDE) constraints. Therefore, a distinguishing challenge of this technique is the handling of large numbers of optimization variables in combination with the complexities of discretized PDEs. In our method, the objective function is formulated as the square difference between the actual thermal dose and the desired one. At each iteration of the optimization procedure, we need to develop and solve the variation problem, the adjoint problem, and the gradient of the objective function. The analytical formula for the gradient is derived and calculated based on the solution of the adjoint problem. Several factors have been taken into consideration to demonstrate the robustness and efficiency of the proposed algorithm. The simulation results for all cases indicate the robustness and the computational efficiency of our proposed method compared to the steepest gradient descent method with the closed-form solution.

Robust Waveform Design of Ultrasound Arrays for Medical Imaging

Sound speed is an effective parameter in designing an optimal beamformer. In conventional ultrasound imaging systems, the beamformer is designed assuming a fixed value of speed, whereas the speed in a tissue is not known precisely and also may fluctuate by a great value. The errors in estimating sound speed may lead to a severe degradation in the reconstructed image, as mainlobe width and sidelobe level of the beampattern are sensitive to the speed variations. In this paper, we consider the design of a transmit beamformer, which is robust to the speed variations. The problem is formulated as a convex optimization problem versus the covariance matrix of the excitation waveforms to obtain a beampattern with predefined mainlobe width and a minimum sidelobe level for all possible variations of speed. Then, by eigen-analysis of the obtained covariance matrix, a set of nonidentical single-carrier short-pulses for the excitation waveforms were designed. Various simulations indicate that the proposed method can yield a robust beampattern whose mainlobe width and sidelobe level almost remain constant by 10% speed variations. In contrast, the beampatterns obtained by nonrobust methods suffer extensive changes.

Numerical Modeling of Ultrasound Propagation in Weakly Heterogeneous Media Using a Mixed-Domain Method

A mixed-domain method (MDM) is presented in this paper for modeling one-way linear/nonlinear wave propagation in biological tissue with arbitrary heterogeneities, in which sound speed, density, attenuation coefficients, and nonlinear coefficients are all spatial varying functions. The present method is based on solving an integral equation derived from a Westervelt-like equation. One-dimensional problems are first studied to verify the MDM and to reveal its limitations. It is shown that this method is accurate for cases with small variation of sound speed. A 2-D case is further studied with focused ultrasound beams to validate the application of the method in the medical field. Results from the MATLAB toolbox k-Wave are used as the benchmark. Normalized root-mean-square (rms) error estimated at the focus of the transducer is 0.0133 when the coarsest mesh (1/3 of the wavelength) is used in the MDM. Fundamental and second-harmonic fields throughout the considered computational domains are compared and good agreement is observed. Overall, this paper demonstrates that the MDM is a computationally efficient and accurate method when used to model wave propagation in biological tissue with relatively weak heterogeneities.

Beamforming for hyperthermia treatment by training a weighted network of an ultrasonic array

We propose a beamforming algorithm based on waveform diversity for hyperthermia treatment of breast cancer using an ultrasonic array. The introduced array has a structure with a network connecting the feeding nodes and the array elements, and the objective of the algorithm is to train the weight matrix of the network to minimize the difference between the generated beam pattern and the ideal one. The training procedure of the algorithm, which is inspired by the idea of machine learning, comprises three parts: forward calculation, comparison, and backward calculation. The forward calculation maps the weight matrix to the beam pattern, and in the comparison step, the generated beam pattern is modified based on the error, and finally, the backward calculation maps the modified beam pattern to a refined weight matrix which performs better than the original one. An optimal weight matrix is obtained by iterative training. The effectiveness of the algorithm is demonstrated by using numerical simulations.

Modeling of wave propagation for medical ultrasound: a review

Numerical modeling of medical ultrasound has advanced tremendously in the past two decades. This opens up a great number of opportunities for medical ultrasound and associated technologies. Numerous new governing equations and algorithms have emerged and been applied to studying various medical ultrasound applications, including ultrasound imaging, photo-acoustic imaging, and therapeutic ultrasound. In addition, thanks to the rapid development of computers, modeling acoustic wave propagation in three-dimensional, large-scale domains has become a reality. This article will provide an indepth literature and technical review of recent progress on numerical modeling of medical ultrasound. Future challenges will also be discussed.

Improving conformal tumour heating by adaptively removing control points from waveform diversity beamforming calculations: a simulation study

Waveform diversity is a phased array beamforming strategy that determines an optimal sequence of excitation signals to maximise power at specified tumour control points while simultaneously minimising power delivered to sensitive normal tissues. Waveform diversity is combined with mode scanning, a deterministic excitation signal synthesis algorithm, and an adaptive control point removal algorithm in an effort to achieve higher, more uniform tumour temperatures. Simulations were evaluated for a 1444 element spherical section ultrasound phased array that delivers therapeutic heat to a 3 cm spherical tumour model located 12 cm from the array. By selectively deleting tumour control points, the tumour volume heated above 42°C increased from 2.28 cm3 to 11.22 cm3. At the expense of a slight increase in the normal tissue volume heated above the target temperature of 42°C, the size of the tumour volume heated above 42°C after tumour points were deleted was almost five times larger than the size of the original heated tumour volume. Several other configurations were also simulated, and the largest heated tumour volumes, subject to a 43°C peak temperature constraint, were achieved when the tumour control points were located along the back edge of the tumour and laterally around the tumour periphery. The simulated power depositions obtained from the results of the adaptive control point removal algorithm, when optimised for waveform diversity combined with mode scanning, consistently increased the penetration depth and the size of the heated tumour volume while increasing the heated normal tissue volume by a small amount.