A Mathematical Model for Simulating Photoacoustic Signal Generation Process in Biological Tissues

Abstract

Background: Biomedical photoacoustic imaging (PAI) is a hybrid imaging modality based on the laser-generated ultrasound waves due to the photoacoustic (PA) effect physical phenomenon that has been reported firstly by A. G. Bell in 1880. Numerical modeling-based simulation for the PA signal generation process in biological tissues helps researchers for decreasing error trials in-vitro and hence decreasing error rates for in-vivo experiments. Numerical modeling methods help in obtaining a rapid modeling procedure comparable to pure mathematics. However, if a proper simplified mathematical model can be founded before applying numerical modeling techniques, it will be a great advantage for the overall numerical model. Most scientific theories, equations, and assumptions, been proposed to mathematically model the complete PA signal generation and propagation process in biological tissues, are so complicated. Hence, the researchers, especially the beginners, will find a hard difficulty to explore and obtain a proper simplified mathematical model describing the process. That’s why this paper is introduced. Methods: In this paper we have tried to simplify understanding for the biomedical PA wave’s generation and propagation process, deducing a simplified mathematical model for the whole process. The proposed deduced model is based on three steps: a- pulsed laser irradiance, b- diffusion of light through biological tissue, and c- acoustic pressure wave generation and propagation from the target tissue to the ultrasound transducer surface. COMSOL Multiphysics, which is founded due to the finite element method (FEM) numerical modeling principle, has been utilized to validate the proposed deduced mathematical model on a simulated biological tissue including a tumor inside. Results and Conclusion: The time-dependent study been applied by COMSOL has assured that the proposed deduced mathematical model may be considered as a simplified, easy, and fast startup base for scientific researchers to numerically model and simulate biomedical PA signals’ generation and propagation process utilizing any proper software like COMSOL.