MATHEMATICAL MODELING OF DYNAMICS OF POST-RESECTION LIVER REGENERATION BY NONLINEAR APPROXIMATION

A mathematical model of the dynamics of liver mass after its partial anatomical resection in a volume of 67% of the initial mass in a rat experiment using the method of G. Higgins and R. Anderson was proposed, constructed through an approximation to the square root equation by the least squares method. The accuracy of the model is confirmed by low mean approximation errors: 14.6% and 9.6% for simple resection and for resection with intraoperative microtraumatic application to the liver parenchyma, respectively. The proposed model has potential applications as a standard for evaluating liver regeneration after resections in the clinic. A universal evaluation criterion of the intensity of the regenerative process is proposed - the regeneration factor.

1. Improvement in perioperative outcome after hepatic resection: analysis of 1,803 consecutive cases over the past decade / W.R. Jarnagin, M. Gonen, Y. Fong [et al.] // Ann. Surg. — 2002. — № 236. — Р. 397­406.

2. One thousand fifty­six hepatectomies without mortality in 8 years / H. Imamura, Y. Seyama, N. Kokudo [et al.] // Arch. Surg. — 2003. — № 138. — Р. 1198­1206.

3. The «50–50 criteria» on postoperative day 5: an accurate predictor of liver failure and death after hepatectomy / S. Balzan, J. Belghiti, O. Farges [et al.] // Ann. Surg. — 2005. — № 242. — Р. 824­828.

4. The value of residual liver volume as a predictor ofhepatic dysfunction and infection after major liver resection / M.J. Schindl, D.N. Redhead, K.C. Fearon [et al.] // Gut. — 2005. — Vol. 54. — P. 289­296.

5. Posthepatectomy liver failure: a definition and grading by the International Study Group of Liver Surgery (ISGLS) / N.N. Rahbari, O.J. Garden, R. Padbury [et al.] // Surgery. — 2011. — Vol. 149. — P. 713­724.

6. Seven hundred forty­seven hepatectomies in the 1990s: an update to evaluate the actual risk of liver resection / J. Belghiti, K. Hiramatsu, S. Benoist [et al.] // J. Am. Coll. Surg. — 2000. — Vol. 191. — P. 38­46.

7. Liver resection: 10­year experience from a single institution / J.C. Coelho, C.M. Claus, T.N. Machuca [et al.] // Arq. Gastroenterol. — 2004. — Vol. 41. — P. 229­233.

8. National trends in the use and outcomes of hepatic resection / J.B. Dimick, R.M. Wainess, J.A. Cowan [et al.] // J. Am. Coll. Surg. — 2004. — Vol. 199. — P. 31­38.

9. Risk factors for postoperative complications after liver resection / Н.С. Sun, L.X. Qin, L. Wang [et al.] // Hepatobiliary Pancreat. Dis. Int. — 2005. — Vol. 4. — P. 370­374.

10. Resective surgery for liver tumor: a multivariate analysis of causes and risk factors linked to postoperative complications / Е. Benzoni, D. Lorenzin, U. Baccarani [et al.] // Hepatobiliary Pancreat. Dis. Int. — 2006. — Vol. 5. — P. 526­533.

11. Prospective validation of the ‘fifty­fifty’ criteria as an early and accurate predictor of death after liver resection in intensive care unit patients / С. Paugam­Burtz, S. Janny, D. Delefosse [et al.] // Ann. Surg. — 2009. — Vol. 249. — P. 124­128.

12. Liver failure after partial hepatic resection: definition, pathophysiology, risk factors and treatment / M.A.J. Van Den Broek [et al.] // Liver International. – 2008. – Т. 28. – №. 6. – С. 767-780.

13. Пострезекционная печеночная недостаточность: современные проблемы определения, эпидемиологии, патогенеза, оценки факторов риска, профилактики и лечения / В. А. Вишневский [и др.] // Украинский журнал хирургии. – 2013. – Т. 22. – №. 3. – С. 172-182.

14. Lyzikov A.N. Мechanisms of liver regeneration in normal and pathologic conditions / A.N. Lyzikov. Skuratov. B.B. Osipov // Problemy zdorovia i ekologii. – 2015. – № 1 (43). – S. 4-9.

15. Apte U.M. Liver Regeneration: Basic Mechanisms, Relevant Models and Clinical Applications / U.M. Apte. – Academic Press, 2015. – 309 c.

16. Kiseleva E.A. Post-resection liver regeneration / E.A. Kiseleva. L.N. Tsvetikova. A.A. Andreyev // Vestnik Voronezhskogo instituta vysokikh tekhnologiy. – 2016. – № 2 (17). – S. 8-12.

17. Michalopoulos G.K. Principles of liver regeneration and growth homeostasis / G.K. Michalopoulos // Comprehensive Physiology. – 2013. – № 3. – C. 485-513.

18. Higgins G.M. Experimental pathology of the liver / G.M. Higgins // Arch. Pathol. – 1931. – Т. 12. – С. 186-202.

19. Liver regeneration and surgical outcome in donors of right‐lobe liver grafts / E. A. Pomfret [et al.] // Transplantation. – 2003. – Т. 76. – №. 1. – С. 5-10.

20. Improvement in perioperative outcome after hepatic resection: analysis of 1,803 consecutive cases over the past decade / W.R. Jarnagin [et al.] // Annals of surgery. – 2002. – Т. 236. – №. 4. – С. 397-407.

21. Seven hundred forty-seven hepatectomies in the 1990s: an update to evaluate the actual risk of liver resection / J. Belghiti [et al.] // Journal of the American College of Surgeons. – 2000. – Т. 191. – №. 1. – С. 38-46.

22. Evaluation of long-term survival after hepatic resection for metastatic colorectal cancer: a multifactorial model of 929 patients / M. Rees [et al.] // Annals of surgery. – 2008. – Т. 247. – №. 1. – С. 125-135.

23. Preoperative prognostic score for predicting survival after hepatic resection for colorectal liver metastases / H.Z. Malik [et al.] // Annals of surgery. – 2007. – Т. 246. – №. 5. – С. 806-814.