基于时间分数阶、静态记忆、傅里叶伪谱方法的功率律超声吸收建模
医学物理
2025-06-06 v2
摘要
我们描述并实现了一种用于模拟组织中超声频率相关功率律吸收的数值方法，其损耗形式为分数时间导数。所采用的（卡普图）分数时间导数需要完整的历史信息，这包含在迭代过程中。 resulting numerical method requires a fixed (static) memory cost irrespective of the number of time steps. The spatial domain is treated by the Fourier spectral method. Numerically comparisons are made against a model for the same power-law absorption with loss described by the fractional-Laplacian operator. One advantage of the fractional time derivative over the fractional-Laplacian operator is the local treatment of the power-law, allowing for a spatially varying frequency power-law.
引用
@article{arxiv.2408.02541,
title = {Modelling power-law ultrasound absorption using a time-fractional, static memory, Fourier pseudo-spectral method},
author = {Matthew. J. King and Timon. S. Gutleb and B. E. Treeby and B. T. Cox},
journal= {arXiv preprint arXiv:2408.02541},
year = {2025}
}