Mathematical modeling to predict the migration of foreign bodies of gunshot origin

Abstract

Background. The purpose is to demonstrate the possibilities of mathematical methods when studying the migration of foreign bodies of gunshot origin. Materials and methods. Eighty-two cases of gunshot shrapnel blind wounds of different localization over a certain period were analyzed, where there was migration of a foreign body in different ways. All the wounded were male, the average age was 43.2 ± 4.1 years. According to the type of migration of foreign bodies of gunshot origin, we distinguish the following directions: respiratory tract, gastrointestinal tract, vascular bed (main veins and arteries, heart), urogenital tract, in cavities (pleural, abdominal, pericardial, joint), in soft tissues during suppuration, when the source is a foreign body that moves along the flow of pus. When calculating the migration distance, the average anatomical dimensions of the organs were used. The size and weight of foreign bodies that migrated as a result of a gunshot wound were determined. To calculate the main indicators, the following data were taken into account: time of detection of a foreign body after injury (minutes), distance of migration at the time of detection of a foreign body (cm), time of estimated end of migration (removal of a foreign body) (minutes, months), distance that a foreign body can make (cm), number of cases of migration. Mathematical calculations are based on Newton’s equation of motion. According to the results of mathematical calculations, the following data were obtained: the average speed of migration by the direction of migration, the calculation of the root mean square error for the speed, the interval of finding the average speed, the calculated distance that the foreign body will make. Results. According to the size of foreign bodies of gunshot origin, which migrated, the distribution was as follows: up to 5 mm in the largest dimension — 18 (19.8 %), from 5.1 to 8 mm — 73 (80.2 %) cases. The average weight of removed foreign bodies that migrated was 4.2 ± 0.4 grams. The number of detected foreign bodies that migrated was 91, of which 90 were removed and one was not removed. Single foreign bodies accounted for 79 (96.3 %), multiple — 3 (3.7 %) cases. An expected time during which a foreign body can cover the average possible distance was estimated: based on the results, the average speed of movement of a foreign body of gunshot origin on different parts of the human body was calculated, taking into account the time of wound detection; the average time of the approximate end of migration (removal of the foreign body) and the average distance that the foreign body can make are evaluated; it is calculated in what expected time a body can cover the average possible distance of migration at an average speed. Conclusions. The average speed of migration by the direction of migration and the calculated distance that the foreign body will make allows you to predict the location of the foreign body by the direction of migration, which affects operative access and the scope of surgical intervention. All foreign bodies of gunshot origin that migrated were small or medium and weighed up to 5 grams. Features of the anatomical structure and function of organs by the direction of migration affect the prediction of the location of the foreign body.

Keywords

• foreign bodies
• gunshot wound
• migration
• prognosis
• mathematical modeling