# Numerical Modeling of Bowel Sound Propagation: Impact of Abdominal Tissue Properties
## 2 Theory and Model
### Transmission of Bowel Sounds
#### 2.2.2 Sound Propagation Models  
To simulate the propagation of bowel sounds within the abdominal cavity, obtaining anatomical data of the human abdomen is essential for determining its shape and size [23]. Given the clinical significance of the upper abdomen and its concentration of vital organs, we chose to focus our study on this region. However, we believe that the principles and methods employed in this study are equally applicable to other regions of the abdomen, providing a solid foundation for a more comprehensive understanding of bowel sound propagation. In order to model the propagation of bowel sounds within the abdominal cavity, we approximated the cavity as a semi-cylindrical structure in the coronal plane. This geometric representation not only streamlines the computational process but also maintains essential anatomical features, thereby aiding in the accurate simulation of sound wave propagation. The key dimensions of the abdominal cavity were determined based on average measurements of human anatomy, as shown in Figure 2a. The parameters \"a\",\"b\", and \"c\" denote the depth, length, and width of the peritoneal cavity, with respective measurements of 12.5 cm, 23 cm, and 25 cm [24]. Using this anatomical data, the thickness of each tissue layer within the abdominal cavity, including muscle, fat, and skin, was determined. For a typical human body, the muscle layer thickness is set at 12.50 mm, the fat layer thickness at 10.25 mm, and the skin layer thickness at 2.25 mm [25], as shown in Figure 2b. Additionally, as our model is a simulation, the values of parameters \"a\", \"b\", and \"c\", as well as the thickness of each tissue layer, can be adjusted to reflect individual anatomical variations. This customization allows the model to more accurately represent the specific characteristics of each person's abdominal cavity. By incorporating such flexibility, our model can be adapted to accommodate the anatomical differences among individuals, thereby enhancing its applicability and improving the precision of the simulations. In this model, the peritoneum's effect on sound propagation is assumed to be negligible, and the primary focus is on the influence of the fat and muscle layers, which significantly impact sound wave reflection, refraction, and attenuation. The composition and properties of these layers, such as their density, elasticity, and acoustic impedance, are essential for accurately predicting how sound waves behave as they travel through the abdominal cavity. This approach leads to a simplified yet effective representation of the abdominal cavity, as shown in Figure 2c, which incorporates the semi-cylindrical shape and multilayered structure of the tissue [26]. This modeling process establishes the geometric model of the abdominal cavity, which provides the necessary geometric foundation for the subsequent acoustic wave propagation simulation. Bowel sounds have low frequencies, relatively long wavelengths, and short propagation distances in the abdominal cavity. As a result, the effects of absorption and frequency-dependent attenuation are negligible within the simulated frequency range. Based on this assumption, sound propagation can be regarded as a linear process mainly affected by the density and elasticity of the medium, and the speed of sound is a key indicator of the elasticity of the medium [27]. Accurately modeling the propagation of bowel sounds within the abdominal cavity requires defining the sound speed and density for each tissue layer [28]. Acoustic impedance, defined as the product of the density (\(\rho\)) and the speed of sound (\(c\)) of a medium (\(Z=\rho\cdot c\)), is a physical quantity that describes the resistance encountered by sound waves as they pass through a medium. As shown in Table 1, which lists the acoustic properties of different tissues, fat has the lowest acoustic impedance, implying that sound  
Figure 2: Abdominal modeling process. (**a**) Abdominal anatomy in the standard anatomical position. (**b**) Tissue layers of the human abdomen.