On the Born series methods for solving inhomogeneous Helmholtz equation in biomedical photoacoustics

Ujjal Mandal; Jagpreet Singh; Ratan K. Saha

doi:10.1117/12.2670935

11 August 2023 On the Born series methods for solving inhomogeneous Helmholtz equation in biomedical photoacoustics

Ujjal Mandal, Jagpreet Singh, Ratan K. Saha

Proceedings Volume 12631, Opto-Acoustic Methods and Applications in Biophotonics VI; 126310W (2023) https://doi.org/10.1117/12.2670935
Event: European Conferences on Biomedical Optics, 2023, Munich, Germany

Abstract

The Born series methods, namely, Traditional Born Series (TBS) and Convergent Born Series (CBS), have been recently implemented to numerically solve the time-independent Photoacoustic (PA) wave equation for an acoustically inhomogeneous source. The TBS algorithm diverges when the sound-speed mismatch is ⪆20%, however, the CBS technique provides faithful result even beyond this limit. These protocols are iterative in nature and computationally expensive. Currently, MATLAB-based implementations are available to study PA emission from a single source mimicking a cell. However, efficient numerical implementation strategy is further needed particularly to calculate PA field from a tissue. Therefore, to develop insights, uniprocessor-based C codes were realized for these schemes. The PA field (in 2D) was computed at a distance 35 μm from a source (a light absorbing disc of radius 7.5 μm) over a frequency range from 7.32 to 512 MHz with a resolution of 7.32 MHz. The sound-speed within the source region was varied from vs = 1200, 1500 and 1800 m/s, but the same quantity for the ambient medium was fixed to v_f = 1500 m/s. The C program was found to be at least ten times slower than the corresponding MATLAB program. It may be because MATLAB inherently implements parallel computing while evaluating the forward and backward Fast Fourier Transforms (FFTs) associated with the Born series approaches. Multiprocessor-based FFTs and parallel nested loops are being incorporated into the C program for enhancement of its execution speed.

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Ujjal Mandal, Jagpreet Singh, and Ratan K. Saha "On the Born series methods for solving inhomogeneous Helmholtz equation in biomedical photoacoustics", Proc. SPIE 12631, Opto-Acoustic Methods and Applications in Biophotonics VI, 126310W (11 August 2023); https://doi.org/10.1117/12.2670935

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KEYWORDS

Inhomogeneities

Photoacoustic spectroscopy

Biomedical optics

MATLAB

Fourier transforms

Parallel computing

Tissues

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