DIFFERENTIATING CHAOTIC AND REGULAR TIME SERIES FOR IDENTIFICATION OF ARTERIOVENOUS FISTULA STATE

The article proposes a method for the automatic classification of time series responding to normally and pathologically functioning arteriovenous fistula in patients during hemodialysis. The method is based on the hypothesis that a normally functioning fistula blood flow is laminar, and a pathologically functioning one is turbulent, as well as on its analogy to the mathematical problem on differentiation of regular and chaotic time series. Two methods were applied to solve the problem. The first method involved finding the series position in the entropy-complexity plane. Following that, the specified position was compared with the identified clusters of values of a time series set. Proposed by the authors, the second method involved constructing an object-attribute graph within the framework of the theory of formal concepts analysis. Both methods proved to be effective in determining the fistula state, with the second method being more efficient for detecting thrombosed fistulas.

1. Chan L., Chaudhary K., Saha A. et al. AKI in Hospitalized Patients with COVID-19 // J Am Soc Nephrol. 2021. Vol. 32, Is. 1. P. 151-160.

2. Hill N. R., Fatoba S. T., Oke J. L. et al. Global Prevalence of Chronic Kidney Disease // PLoS One. 2016. Vol. 11, Is. 7. P. 1-18.

3. Liyanage T., Ninomiya T., Jha V. et al. Worldwide Access to Treatment for End-Stage Kidney Disease: A Systematic Review // The Lancet. 2015. Vol. 385, Is. 9981. P. 1975-1982.

4. Burkhart H. M., Cikrit D. F. Arteriovenous Fistulae for Hemodialysis // Semin Vasc Surg. 1997. Vol. 10, Is. 3. P. 162‒165.

5. Hasuike Y., Kakita N., Aichi M. et al. Imbalance of Coagulation and Fibrinolysis Can Predict Vascular Access Failure in Patients on Hemodialysis after Vascular Access Intervention // J Vasc Surg. 2019. Vol. 69, Is. 1. P. 174‒180.e2.

6. Ravani P., Quinn R., Oliver M. et al. Examining the Association between Hemodialysis Access Type and Mortality: The Role of Access Complications // Clin J Am Soc Nephrol. 2017. Vol. 12, Is. 6. P. 955-964.

7. Salman L., Beathard G. Interventional Nephrology: Physical Examination as a Tool for Surveillance for the Hemodialysis Arteriovenous Access // Clin J Am Soc Nephrol. 2013. Vol. 8, Is. 7. P. 1220-1227.

8. Sato T. New Diagnostic Method According to the Acoustic Analysis of the Shunt Blood Vessel Noise // Jpn Soc Dial Ther J. 2005. Vol. 2. P. 332-341.

9. Kokorozashi N. Analysis of the Shunt Sound Frequency Characteristic Changes Associated with Shunt Stenosis // Jpn Soc Dial Ther J. 2010. Vol. 3. P. 287-295.

10. Todo A., Kadonaka T., Yoshioka M., Ueno A., Mitani M., Katsurao H. Frequency Analysis of Shunt Sounds in the Arteriovenous Fistula on Hemodialysis Patients // Proceedings of the 6th International Conference on Soft Computing and Intelligent Systems, and the 13th International Symposium on Advanced Intelligence Systems. 2012. P. 1113‒1118.

11. Remuzzi A., Ene-Iordache B. Novel Paradigms for Dialysis Vascular Access: Upstream Hemodynamics and Vascular Remodeling in Dialysis Access Stenosis // Clin J Am Soc Nephrol. 2013. Vol. 8, Is. 12. P. 2186-2193.

12. Brahmbhatt A., Remuzzi A., Franzoni M., Misra S. The Molecular Mechanisms of Hemodialysis Vascular Access Failure // Kidney Int. 2016. Vol. 89, Is. 2. P. 303-316.

13. Badero O. J., Salifu M. O., Wasse H., Work J. Frequency of Swing-Segment Stenosis in Referred Dialysis Patients with Angiographically Documented Lesions // Am J Kidney Dis. 2008. Vol. 51, Is. 1. P. 93-98.

14. Lee T., Barker J., Allon M. Needle Infiltration of Arteriovenous Fistulae in Hemodialysis: Risk Factors and Consequences // Am J Kidney Dis. 2006. Vol. 47, Is. 6. P. 1020-1026.

15. Raghavan U. N., Albert R., Kumara S. Near Linear Time Algorithm to Detect Community Structures in Large-Scale Networks // Phys Rev E. 2007. Vol. 76, Is. 3, Pt. 2. P. 036106.

16. Buzmakov A., Egho E., Jay N., Kuznetsov S. O., Napoli A., Raïssi C. On Mining Complex Sequential Data by Means of FCA and Pattern Structures // Int J Gen Syst. 2015. Vol. 45, Is. 2. P. 135‒159.

17. EA-56137. Регистр данных о состоянии сосудистого доступа у больных, находящихся на гемодиализе : заявка на регистрацию базы данных от 25.11.2021. URL: https://rospatent.gov.ru/ru/state services

18. EA-56151. Мобильное приложение сбора, обработки и хранения данных в регистре с целью классификации состояния сосудистого доступа для гемодиализа: программа для ЭВМ : заявка на регистрацию от 08.02.2022. URL: https://rospatent. gov.ru/ru/stateservices

19. Rosso O. A., Carpi L. C., Saco P. M., Ravetti M. G., Plastino A., Larrondo H. A. Causality and the Entropy-Complexity Plane: Robustness and Missing Ordinal Patterns // Physica A: Statistical Mechanics and its Applications. 2012. Vol. 391, Is. 1‒2. P. 42‒55.

20. Bandt C., Pompe B. Permutation Entropy: A Natural Complexity Measure for Time Series // Phys Rev Lett. 2002. Vol. 88, Is. 17. P. 174102. https://doi.org/10.1103/ PhysRevLett.88.174102.

21. Aggarwal C. C., Reddy C. K. Data Clustering: Algorithms and Applications. 1st ed. Chapman and Hall/CRC, 2014.

22. Wishart D. Numerical Classification Methods for Deriving Natural Classes // Nature. 1969. Vol. 221. P. 97-98.

23. Thrun M. C., Ultsch A. Using Projection-Based Clustering to Find Distance- and Density-Based Clusters in High-Dimensional Data // J Classif. 2020. Vol. 38. P. 280-312.

24. Лапко А. В., Ченцов С. В. Непараметрические системы обработки информации. М. : Наука, 2000. 350 с.

25. Gromov V. A., Borisenko E. A. Predictive Clustering on Non-Successive Observations for Multi-Step Ahead Chaotic Time Series Prediction // Neural Computing and Appl. 2015. Vol. 26. P. 1827-1838.