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Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Accelerating frequency-domain numerical methods for weakly nonlinear focused ultrasound using nested meshes.

Samuel P Groth1, Pierre Gélat2, Seyyed R Haqshenas2

  • 1Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom.

The Journal of the Acoustical Society of America
|August 3, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces nested meshing for simulating focused ultrasound (FUS) therapies. This method significantly reduces computational demands by using harmonic-specific meshes, improving efficiency for FUS treatment planning.

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Area of Science:

  • Acoustics and Ultrasound Physics
  • Computational Physics
  • Medical Imaging and Therapy

Background:

  • Numerical simulation of nonlinear ultrasound is crucial for focused ultrasound (FUS) therapies.
  • High computational costs arise from large domains and harmonic generation in FUS simulations.
  • Current uniform meshing is inefficient, requiring fine resolution for all harmonics.

Purpose of the Study:

  • To develop a more computationally efficient numerical strategy for simulating weakly nonlinear ultrasound.
  • To reduce memory consumption and computation time in focused ultrasound simulations.
  • To enable accurate modeling of harmonic generation in FUS treatment planning.

Main Methods:

  • Proposes a nested meshing strategy where each harmonic is simulated on a separate, resolution-optimized mesh.
  • Employs a fast volume potential approach for rapid computation of harmonics via integral evaluation.
  • Utilizes the midpoint rule and Fast Fourier Transforms (FFT) for efficient numerical integration.

Main Results:

  • Nested meshing achieves at least an order of magnitude reduction in memory and computation time.
  • Demonstrates the feasibility of nested meshing due to the localized nature of higher harmonics.
  • Validates the approach through numerical experiments for FUS transducers in homogeneous media.

Conclusions:

  • Nested meshing offers a significant computational advantage for nonlinear ultrasound simulations.
  • The proposed method enhances the efficiency of FUS treatment planning simulations.
  • The approach is generalizable to inhomogeneous acoustic propagation domains.