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 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. More scientific theories, equations, and assumptions through the biomedical PA imaging research literature have been proposed trying to mathematically model the complete PA signal generation and propagation process in biological tissues. However, most of them have so complicated details. 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.