A Generalized Split-Step Angular Spectrum Method for Efficient Simulation of Wave Propagation in Heterogeneous Media

An efficient method for transcranial ultrasound focus correction based on the coupling of boundary integrals and finite elements

Transcranial focused ultrasound is a novel technique for the noninvasive treatment of brain diseases. The success of the treatment greatly depends on achieving precise and efficient intraoperative focus. However, compensating for aberrated ultrasound waves caused by the skull through numerical simulation-based phase corrections is a challenging task due to the significant computational burden involved in solving the acoustic wave equation. In this article, we propose a promising strategy using the coupling of the boundary integral equation method (BIEM) and the finite element method (FEM) to overcome the above limitation. Specifically, we adopt the BIEM to obtain the Robin-to-Dirichlet maps on the boundaries of the skull and then couple the maps to the FEM matrices via a dual interpolation technique, resulting in a computational domain including only the skull. Three simulation experiments were conducted to evaluate the effectiveness of the proposed method, including a convergence test and two skull-induced aberration corrections in 2D and 3D ultrasound. The results show that the method's convergence is guaranteed as the element size decreases, leading to a decrease in pressure error. The computation times for simulating a 500 kHz ultrasound field on a regular desktop computer were found to be 0.47 ± 0.01 s in the 2D case and 43.72 ± 1.49 s in the 3D case, provided that lower-upper decomposition (approximately 13 s in 2D and 2.5 h in 3D) was implemented in advance. We also demonstrated that more accurate transcranial focusing can be achieved by phase correction compared to the noncorrected results (with errors of 1.02 mm vs. 6.45 mm in 2D and 0.28 mm vs. 3.07 mm in 3D). The proposed strategy is valuable for enabling online ultrasound simulations during treatment, facilitating real-time adjustments and interventions.

Curved boundary integral method for electromagnetic fields

The angular spectrum method is a rigorous method to synthesize near and far-field electromagnetic beams from planar field distributions. However, this limitation of planar surfaces has restricted its applicability to beams with simple focal planes. We propose a curved boundary integral method (CBIM) to synthesize electromagnetic beams from arbitrary surfaces to address this limitation and expand the method's scope to synthesize beams from and between shaped objects. This study presents a detailed theoretical framework behind the CBIM and validates its effectiveness and accuracy with a comprehensive set of simulations. Additionally, we present mathematical proof to support our proposal. The proposed method satisfies Maxwell's equations and significantly benefits optical systems and inverse beam design. It allows for analyzing electromagnetic forward/backward propagation between optical elements using a single method. It is also valuable for optical force beam design and analysis.

Towards controlled drug delivery in brain tumors with microbubble-enhanced focused ultrasound

Brain tumors are particularly challenging malignancies, due to their location in a structurally and functionally distinct part of the human body - the central nervous system (CNS). The CNS is separated and protected by a unique system of brain and blood vessel cells which together prevent most bloodborne therapeutics from entering the brain tumor microenvironment (TME). Recently, great strides have been made through microbubble (MB) ultrasound contrast agents in conjunction with ultrasound energy to locally increase the permeability of brain vessels and modulate the brain TME. As we elaborate in this review, this physical method can effectively deliver a wide range of anticancer agents, including chemotherapeutics, antibodies, and nanoparticle drug conjugates across a range of preclinical brain tumors, including high grade glioma (glioblastoma), diffuse intrinsic pontine gliomas, and brain metastasis. Moreover, recent evidence suggests that this technology can promote the effective delivery of novel immunotherapeutic agents, including immune check-point inhibitors and chimeric antigen receptor T cells, among others. With early clinical studies demonstrating safety, and several Phase I/II trials testing the preclinical findings underway, this technology is making firm steps towards shaping the future treatments of primary and metastatic brain cancer. By elaborating on its key components, including ultrasound systems and MB technology, along with methods for closed-loop spatial and temporal control of MB activity, we highlight how this technology can be tuned to enable new, personalized treatment strategies for primary brain malignancies and brain metastases.