Abstract
Finite-difference time domain (FDTD) techniques are widely used to model the propagation of viscoelastic waves through complex and heterogeneous structures. However, in the specific case of media mixing liquid and solid, attempts to model continuous media onto a Cartesian grid produces errors when the liquid-solid interface between different media do not align precisely with the Cartesian grid. The increase in spatial resolution required to eliminate this grid staircasing effect can be computationally prohibitive. Here, a modification to the Virieux staggered-grid FDTD scheme called the superposition method is presented. This method is intended to reduce this staircasing effect while keeping a manageable computational time. The method was validated by comparing low-spatial-resolution simulations against simulations with sufficiently high resolution to provide reasonably accurate results at any incident angle. The comparison of the root-mean-square of the stress amplitude maps showed that the amplitude of artifactual waves could be reduced by several orders of magnitude when compared to the Virieux staggered-grid FDTD method and that the superposition method helped to significantly reduce the staircasing effect in FDTD simulations.
Highlights
IntroductionFinite-difference time domain (FDTD) methods have been used extensively to model the propagation of ultrasound in heterogeneous media. The use of FDTD simulations has been validated for planning transcranial ultrasound treatments, which is an emerging modality for treatment of brain disorders including thalamotomy for treatment of essential tremor and chronic neuropathic pain, and thermal ablation of brain tumours. Applying transcranial focused ultrasound presents several challenges due to the presence of the skull, which is a problematic biological tissue to focus through due to its strong acoustic mismatch with water, conversion between compressive and transverse waves, scattering, and attenuative properties, which gives rise to phase aberrations, standing waves, and undesired tissue heating.6–9A source of error in FDTD solutions of the viscoelastic wave equation arises when the liquid-solid interface does not align with the Cartesian grid. This staircase effect was first described by Fornberg. Staircasing refers to the spatial approximation required to define continuous geometries onto a discrete Cartesian grid in two and three dimensions
The use of Finite-difference time domain (FDTD) simulations has been validated for planning transcranial ultrasound treatments,2 which is an emerging modality for treatment of brain disorders including thalamotomy for treatment of essential tremor3 and chronic neuropathic pain,4 and thermal ablation of brain tumours
A source of error in FDTD solutions of the viscoelastic wave equation arises when the liquid-solid interface does not align with the Cartesian grid
Summary
Finite-difference time domain (FDTD) methods have been used extensively to model the propagation of ultrasound in heterogeneous media. The use of FDTD simulations has been validated for planning transcranial ultrasound treatments, which is an emerging modality for treatment of brain disorders including thalamotomy for treatment of essential tremor and chronic neuropathic pain, and thermal ablation of brain tumours. Applying transcranial focused ultrasound presents several challenges due to the presence of the skull, which is a problematic biological tissue to focus through due to its strong acoustic mismatch with water, conversion between compressive and transverse waves, scattering, and attenuative properties, which gives rise to phase aberrations, standing waves, and undesired tissue heating.6–9A source of error in FDTD solutions of the viscoelastic wave equation arises when the liquid-solid interface does not align with the Cartesian grid. This staircase effect was first described by Fornberg. Staircasing refers to the spatial approximation required to define continuous geometries onto a discrete Cartesian grid in two and three dimensions Finite-difference time domain (FDTD) methods have been used extensively to model the propagation of ultrasound in heterogeneous media.. The use of FDTD simulations has been validated for planning transcranial ultrasound treatments, which is an emerging modality for treatment of brain disorders including thalamotomy for treatment of essential tremor and chronic neuropathic pain, and thermal ablation of brain tumours.. A source of error in FDTD solutions of the viscoelastic wave equation arises when the liquid-solid interface does not align with the Cartesian grid.. A source of error in FDTD solutions of the viscoelastic wave equation arises when the liquid-solid interface does not align with the Cartesian grid.16 This staircase effect was first described by Fornberg..
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