Mathematical modeling of the chest, its funnel-shaped deformation and thoracoplasty

Abstract


 The most common method of treating of the congenital funnel-shaped chest is thoracoplasty method by D. Nuss. During this surgery, a significant mechanical effect is created on the ribs, sternum, spinal column, which act instantly and continuously for a long time and create new biomechanical conditions for the «chest – rib – spine» system. Objective. To construct a functional model of the chest with a spinal column, which takes into account the movements in the costal-vertebral joints, it allows modeling the funnel-shaped deformation in conditions close to the reality, its operative correction, predicting the results and choosing the optimal parameters of thoracoplasty. Methods. Normal and funnel-shaped chest models based on the articular connection of the ribs to the spine were created using SolidWorks. The main calculations were made using the ANSYS program. To estimate the stress-strain state (SSS), stresses are selected by Mises. Results. The created dynamic mathematical model of the chest makes it possible to conduct a reliable analysis of the biomechanical interaction of the plate with the chest, to analyze the stress-strain state of the constructed models in the norm, with and without taking into account the movements in the costal-vertebral joints. In addition, it allows to simulate the operation by D. Nuss and to study the biomechanical changes in conditions close to reality, occurring in the «chest – rib – spine» system, to determine the areas of maximum loads and safety boundaries. Conclusions. The reproduction of articular ribs rotation in the dynamic model changes the picture of the SSS distribution. In the case of modeling the correction of funnel-shaped deformation of the chest by the method by D. Nuss, the largest zone of stress concentration was found on the outer posterior surface of the sixth pair of ribs. The most tense vertebrae were ThV– ThVI, but the maximum values did not exceed the permissible values. In the case of a lower plate conduction, the correction is achieved with better SSS values in the higher elements of the «chest – ribs – spine» system.