Mathematical calculation and coefficient value of chest shape recovery for planning thoracoplasty of pectus excavatum




chest, pectus excavatum, thoracoplasty, mathematical modeling


Background. Pectus excavatum is characterized by retraction of the sternum and anterior ribs of different depth and width. The formation, its prediction, calculation of chest deformity, and their study when planning thoracoplasty using the Nuss procedure for this pathology is an important problem of orthopedics and thoracic surgery. The purpose of the work was to calculate the coefficient of restoration of the chest shape by the ratio of the pectus excavatum depth and the chest size in the frontal plane before and after mathematical modeling of thoracoplasty using the Nuss procedure. Methods. To assess displacement of ribs depen-ding on depth deformity of chest h, two models were built. The first model is a flat frame on supports, the elements of which consist of cartilaginous parts of ribs and sternum. For this model, the dependence of the force F was determined, which is necessary to correct the depth of chest deformity. The second model is a curved bar that simulates a rib, to one of the ends of which a support load is applied, calculated during the analysis of the first model. For this model, the displacement of the plate fixation point under the action of a given force was determined. To obtain more accurate results, a finite element study was performed on a chest model. Results. The correction of pectus excavatum depth without fixing plate to ribs was simulated. The displacements of rib sections in the place of plate fixation at different depths of pectus excavatum was assessed: h = 2 cm, h = 3 cm, h = 4 cm, h = 5 cm. The analysis of calculation results showed that after correction of the depth of chest deformity, its size in the frontal plane decreases. So, at the maximum deformation depth h = 5 cm, the deviation of the rib sections at the plate fixation point occurred by 2.4 cm. Conclusions. The relationship between the pectus excavatum depth and chest size in the frontal plane was established when modeling the newly formed chest form during for Nuss procedure. The coefficient of restoring the chest shape was mathematically calculated, which is 2 (2∆ = h), where h is the depth of pectus excavatum. The practical significance of the coefficient is that when planning thoracoplasty and shaping plate, the distance between its lateral ends, which corresponds to the chest shape and adjoin ribs, must be reduced by ½ h (where h is the depth of pectus excavatum) before correcting the pectus excavatum full adherence to the ribs in the postoperative period.


Nuss D., Obermeyer R.J., Kelly R.E. Nuss bar procedure: past, present and future. Ann. Cardiothorac. Surg. 2016 Sep. 5(5). Р. 422-433. doi: 10.21037/acs.2016.08.05.

Park H.J., Jeong J.Y., Jo W.M., Shin J.S., Lee I.S., Kim K.T., Choi Y.H. Minimally invasive repair of pectus excavatum: a novel morphology-tailored, patient-specific approach. J. Thorac. Cardiovasc. Surg. 2010 Feb. 139(2). Р. 379-386. doi: 10.1016/j.jtcvs.2009.09.003.

Гаврюшин С.С., Кузьмичев В.А., Грибов Д.А. Биомеханическое моделирование хирургического лечения воронко-образной деформации грудной клетки. Российский журнал биомеханики. 2014. Т. 18. № 1. С. 36-47.

Улещенко Д.В., Сташкевич А.Т., Шевчук А.В. Оптимізація діагностики різних варіантів лійкоподібної деформації грудної клітки. Проблеми травматології та остеосинтезу. 2019. 3(17). С. 41-56.

Chang P.Y., Hsu Z.Y., Chen D.P., Lai J.Y., Wang C.J. Preliminary analysis of the forces on the thoracic cage of patients with pectus excavatum after the Nuss procedure. Clin. Biomech. (Bristol, Avon). 2008 Aug. 23(7). Р. 881-885. doi: 10.1016/j.clinbiomech.2008.02.010. Epub 2008, Apr 1. PMID: 18381225.

Nagasao T., Miyamoto J., Tamaki T., Ichihara K., Jiang H., Taguchi T., Yozu R., Nakajima T. Stress distribution on the thorax after the Nuss procedure for pectus excavatum results in different patterns between adult and child patients. J. Thorac. Cardiovasc. Surg. 2007 Dec. 134(6). Р. 1502-1507. doi: 10.1016/j.jtcvs.2007.08.013. PMID: 18023673.

Wang H., Yang J., Liu W., Xia H. Finite Element Analysis-Aided Design of Customized Nuss Bar in Pectus Excavatum Surgery. Ann. Thorac. Surg. 2018 Sep. 106(3). Р. 938-939. doi: 10.1016/j.athoracsur.2018.01.086.

Xie L., Cai S., Xie L., Chen G., Zhou H. Development of a computer-aided design and finite-element analysis combined method for customized Nuss bar in pectus excavatum surgery. Sci. Rep. 2017, Jun 14. 7(1). 3543. doi: 10.1038/s41598-017-03622-y.

Lin K.H., Huang Y.J., Hsu H.H., Lee S.C. et al. The Role of Three-Dimensional Printing in the Nuss Procedure: Three-Dimensional Printed Model-Assisted Nuss Procedure. Ann. Thorac. Surg. 2018 Feb. 105(2). Р. 413-417. doi: 10.1016/j.athoracsur.2017.09.031. Epub 2017, Dec 15. PMID: 29254650.

Huang Y.J., Lin K.H., Chen Y.Y., Wu T.H. et al. Feasibility and Clinical Effectiveness of Three-Dimensional Printed Model-Assisted Nuss Procedure. Ann. Thorac. Surg. 2019 Apr. 107(4). Р. 1089-1096. doi: 10.1016/j.athoracsur.2018.09.021.

Awrejcewicz J., Luczak B. Dynamics of human thorax with Lorenz pectus bar. XXII symposium — vibrations in physical systems. Poznań-Będlewo, 2006. Р. 59-64.

Bone mechanics handbook. Ed. by Stephen C. Cowin. March 15 2001 by CRC Press Reference. 980 p.

Межецкий Г.Д., Загребин Г.Г., Решетник Н.Н. Сопротивление материалов: Учебник. Под общ. ред. Г.Д. Межецкого, Г.Г. Загребина. 5-е изд. Москва, 2016. 432 с

Zienkiewicz O.C., Taylor R.L. The Finite Element Method for Solid and Structural Mechanics. 6th ed. Butterworth-Heinemann, 2005. 736 p.





Original Researches