Mathematical modeling of foreign bodies with different density in biological and non-biological models in the experiment

Abstract

Background. Modeling allows investigating both existing and predicted processes and is widely used in basic science and in many industries. The aim is to develop a mathematical model for determining the size of the foreign bodies (FB) and their radiographic density in non-biological and biological models to improve the results of diagnosis for gunshot ricochet wounds. Materials and methods. In the biological non-living model (a piece of pork) and non-biological models (polystyrene, foam rubber), we place the FB made of paper, leather, rubber, plastic, and lithium-ion batteries. The number of the FB is 9 of each type. Number of models is 3 each: pork, polystyrene, foam rubber. We measure the dimensions of the FB and models with a metric ruler. For each model, we select the FB, which we label with the study number. We immerse the FB to the same depth using a Billroth general surgical medium hemostatic clamp in the following sequence: paper, leather, rubber, plastic, and lithium-ion battery. Multislice computed tomography (MSCT) of the models is performed on the Revolution EVO (2021) apparatus with measurement of the sizes and radiographic density of the FB and models. Radiographic density was measured in conventional units on the Hounsfield scale. For each study group, the ratio of the actual sizes of the removed FB and according to MSCT data was determined in the MathCad 15 computer math software, depending on the radiological density of the FB and the model. Results. According to MSCT data, the radiographic density of the models on the Hounsfield scale is as follows: polystyrene — –990.0 ± 0.3 units; foam rubber — –985.0 ± 0.2 units; pork — 62.0 ± 0.3 units; radiographic density of the foreign bodies: paper — –743.0 ± 10.3 units, leather — –258.0 ± 14.2 units, rubber — –12.0 ± 2.6 units, plastic — 183.0 ± 14.6 units, lithium-ion batteries — 3071 units. Visualization of paper in non-biological and biological models and leather in non-biological models is problematic due to the similar radiographic density of the models and the inability to measure the dimensions. When the FB (rubber, plastic, battery) is immersed in polystyrene, the coefficient of length (CL) is 1.0612, the coefficient of width (CW) is 1.928; in foam rubber: CL is 0.9926, CW is 1.9641; in pork: CL is 0.8394, CW is 1.534. Comparing the average coefficients of the ratio (CL and CW), we find that the coefficient in a biological model is closest to 1. This means that the FB from rubber, plastic, and batteries are best detected in pork. Conclusions. The actual dimensions of the FB placed in biological and non-biological models differ from those obtained by MSCT. Data correction is performed through calculated coefficients for length and width. The radiographic density of the model affects the radial visualization of the FB. The use of mathematical modeling in determining the sizes and radiographic density allows reducing the measurement error and determine the structure of the FB.

Keywords

• mathematical modeling
• foreign bodies
• biological model
• non-biological model
• experiment