A mathematical model for simulating photoacoustic signal generation and propagation in biological tissues

Abstract

Photoacoustic (PA) medical imaging is a crossbred technique relying on light-induced ultrasonic waves due to the PA effect phenomenon recorded primarily in 1880 by A. G. Bell. Numerical simulation, also known as in-silico, studies assist scientists in minimizing incorrect PA experiments in both in-vitro and in-vivo. Numerical modeling techniques help to achieve a fast simulation process in contrast to pure mathematics alone. However, if a suitable facilitated mathematical model can be established prior to applying numerical modeling, it will be of great interest to the whole numeric model. Numerous mathematical equations, theorems, and propositions have been proposed to model the whole PA signal generation and propagation process in biological media. However, most of them are complicated and difficult to be understood by researchers, especially beginners. That’s why this paper was introduced. Our paper aims to simplify the understanding of the generation and propagation process of biomedical PA waves. We have developed a facilitated mathematical model for the entire process. The introduced developed mathematical model is based on three steps: (1) pulsed laser stimulation, (2) light diffusion, and (3) PA stress wave generation and propagation. The developed mathematical model has been implemented utilizing COMSOL Multiphysics, which relies on the finite element method (FEM) numerical modeling principle. The in-silico time-dependent study's results confirmed that the proposed mathematical model is a simple, efficient, accurate, and quick starting point for researchers to simulate biomedical PA signals' generation and propagation process utilizing any suitable software such as COMSOL multiphysics.