Cluster analysis of cardiac data

The article includes the observation of the cluster analysis of medical
data on the example of the cardiac data. One of the main effective and commonly used Data Mining methods that applied to  the large amounts of information (for example, mathematical  economics) are clustering methods: the search for signs of similarity  between objects in the study of the subject area and the subsequent merger of objects into subsets (clusters) according to the established affinity. The main purpose of the investigation is to examine the  hypothesis of the possibility of diagnosing the patient health status,  as well as identifying his pathologies, using the analysis of  electrocardiogram (ECG) series and the allocation of similar clusters  based on the results of this analysis. However, the subject of  clustering techniques implementation to the ECG on the grounds of  similarity of forms have not previously been extensively investigated. In the model of the heart, which is used in this study,  the state of the heart is taken as a fixed oscillatory process of the  phenomenon of the FPU auto-return. But, on the other hand, since  the heart is an self-oscillating system and it has no need to start the  oscillations by obtaining the energy of “perturbation”, the concept of  FPU autoreturn is introduced in the study of the heart. The  mathematical modeling of the heart work by using a decomposition of the Fermi-Pasta-Ulam (FPU) was investigated. The formal description of the mathematical model of the heart as a system of connected cells myocytes is presented. This represents a  single oscillatory degree of freedom described by a  system of coupled nonlinear differential equations of the second  order equation of Van der Pol. Cluster analysis bases on the search  of similar clusters of Fourier spectrum which are received by FPU  recurrence. The current results that are obtained show that the  hypothesis is confirmed. In mathematical modeling of the FPU heart  modeling, which is based on the forms of Fourier spectra, were  identified. Subsets were identified, among which various subsets of  both forms of Fourier spectra with pathologies and forms of the  Fourier spectrum of healthy people were formed. From this study it  follows that the cluster analysis of the electrocardiogram may refer this ECG to any cluster and thereby diagnose the state of  cardiac health of the patient.

1. Motorina S.V., Kalinichenko A.N. Otsenka regulyarnosti v poryadke sledovaniya i dline kardiointervalov metodami matematicheskoy statistiki. Biomeditsinskaya radioeletronika. 2016. No. 8. P. 14–19. (In Russ.)

2. Dyuk V., Samoylenko A. Data Mining: uchebnyy kurs (+CD). Saint-Petersburg: Piter, 2001. 368 p. (In Russ.)

3. Natsional’nyy otkrytyy universitet Intuit. URL: https://www.intuit.ru/studies/courses/6/6/lecture/158. (Accessed: 11.01.2018). (In Russ.)

4. Motorina S.V., Kalinichenko A.N., Nemirko A.P. Vybor metoda klasterizatsii dlya algoritma vyyavleniya mertsatel’noy aritmii. Biotekhnosfera. 2015. No. 4 (40). P. 2– 5. (In Russ.)

5. Motorina S.V., Kalinichenko A.N. Otsenka regulyarnosti v poryadke sledovaniya i dline kardiointervalov metodami matematicheskoy statistiki. Biomeditsinskaya radioeletronika. 2016. No. 8. P. 14–19. (In Russ.)

6. Federal’nyy Zakon ot 29 iyulya 2017 goda No. 242-FZ “O vnesenii izmeneniy v otdel’nye zakonodatel’nye akty Rossiyskoy Federatsii po voprosam primeneniya informatsionnykh tekhnologiy v sfere okhrany zdorov’ya”. Sobranie zakonodatel’stva RF. 2017. No. 242-FZ. (In Russ.)

7. Motorina S.V., Kalinichenko A.N., Nemirko A.P. Vybor metoda klasterizatsii dlya algoritma vyyavleniya mertsatel’noy aritmii. Biotekhnosfera. 2015. No. 4 (40). P. 2– 5. (In Russ.)

8. 10 vedushchikh prichin smerti v mire. Vsemirnaya Organizatsiya Zdravookhraneniya. URL: http://www.who.int/mediacentre/factsheets/fs310/ru/. (Accessed: 13.11.2017). (In Russ.)

9. Federal’nyy Zakon ot 29 iyulya 2017 goda No. 242-FZ “O vnesenii izmeneniy v otdel’nye zakonodatel’nye akty Rossiyskoy Federatsii po voprosam primeneniya informatsionnykh tekhnologiy v sfere okhrany zdorov’ya”. Sobranie zakonodatel’stva RF. 2017. No. 242-FZ. (In Russ.)

10. Antonopoulos N., Gillam L. Cloud Computing: Principles, Systems and Applications. Springer Science & Business Media, 2010. 382 P. ISBN 978-1-84996-240-7.

11. 10 vedushchikh prichin smerti v mire. Vsemirnaya Organizatsiya Zdravookhraneniya. URL: http://www.who.int/mediacentre/factsheets/fs310/ru/. (Accessed: 13.11.2017). (In Russ.)

12. Matematicheskaya kardiologiya. Teoriya, klinicheskie rezul’taty, rekomendatsii, perspektivy.ed. V.A. Lishchuka, D.Sh. Gazizovoy. Moscow: OOO «PRINT PRO». 2015. 228 p. (In Russ.)

13. Antonopoulos N., Gillam L. Cloud Computing: Principles, Systems and Applications. Springer Science & Business Media, 2010. 382 P. ISBN 978-1-84996-240-7.

14. Novopashin M.A., Shmid A.V. D.SC. Berezin A.A. PhD, Forrester’s Concept in Modeling Heart Dynamics. IOSR Journal of Computer Engineering. May-Jun. 2017. Vol. 19. Issue 3, Ver. 2.

15. Matematicheskaya kardiologiya. Teoriya, klinicheskie rezul’taty, rekomendatsii, perspektivy.ed. V.A. Lishchuka, D.Sh. Gazizovoy. Moscow: OOO «PRINT PRO». 2015. 228 p. (In Russ.)

16. Berezin, A.A. Resonant interaction between the Fermi-Pasta-Ulam recurrences. Bulletin of the Lebedev Physics Institute. FIAN. 2004. No. 3. P. 13.

17. Novopashin M.A., Shmid A.V. D.SC. Berezin A.A. PhD, Forrester’s Concept in Modeling Heart Dynamics. IOSR Journal of Computer Engineering. May-Jun. 2017. Vol. 19. Issue 3, Ver. 2.

18. Wiener N. The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle. Arch. Del. Instit. De Cardiologia De Mexico. 1946. P. 205–265.

19. Berezin, A.A. Resonant interaction between the Fermi-Pasta-Ulam recurrences. Bulletin of the Lebedev Physics Institute. FIAN. 2004. No. 3. P. 13.

20. Van der Pol B, Van der Mark M. Le battement du coeur considere comme oscillation de relaxation et un model elecrtrique du coeur. L’Onde electrique. 1928. No. 7.

21. Wiener N. The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle. Arch. Del. Instit. De Cardiologia De Mexico. 1946. P. 205–265.

22. Forrester D. Mirovaya dinamika. Moscow: AST, 2006. P. 384. ISBN 5-17-019253-3.

23. Van der Pol B, Van der Mark M. Le battement du coeur considere comme oscillation de relaxation et un model elecrtrique du coeur. L’Onde electrique. 1928. No. 7.

24. Dzh.-O. Kim, Ch.U. M’yuller, U.R. Klekka et al. Faktornyy, diskriminantnyy i klasternyy analiz Moscow: Finansy i statistika, 1989. 215 P. (In Russ.)

25. Forrester D. Mirovaya dinamika. Moscow: AST, 2006. P. 384. ISBN 5-17-019253-3.

26. Fermi E., Pasta J., Ulam P. In: Collected Papers of E. Fermi. 1955. Vol. 2. 978 P.

27. Dzh.-O. Kim, Ch.U. M’yuller, U.R. Klekka et al. Faktornyy, diskriminantnyy i klasternyy analiz Moscow: Finansy i statistika, 1989. 215 P. (In Russ.)

28. Moyer, V. A. Screening for coronary heart disease with electrocardiography: U.S. Preventive Services Task Force recommendation statement. Annals of Internal Medicine. 2002. P. 157.

29. Fermi E., Pasta J., Ulam P. In: Collected Papers of E. Fermi. 1955. Vol. 2. 978 P.

30. Nygren A., Fiset C., Firek L., Clark J. W., Lindblad D. S., Clark R. B., Giles W. R. Mathematical model of an adult human atrial cell: The role of K+ currents in repolarization. Circ. Res. 1998. Vol. 82(1). P. 63–81

31. Moyer, V. A. Screening for coronary heart disease with electrocardiography: U.S. Preventive Services Task Force recommendation statement. Annals of Internal Medicine. 2002. P. 157.

32. Gray R. A., Pertsov A. M., Jalife J. Incomplete reen-try and epicardial breakthrough patterns during atrial ftbrillation in the sheep heart. Circulation 1996. Vol. 94. P. 2649–2661.

33. Nygren A., Fiset C., Firek L., Clark J. W., Lindblad D. S., Clark R. B., Giles W. R. Mathematical model of an adult human atrial cell: The role of K+ currents in repolarization. Circ. Res. 1998. Vol. 82(1). P. 63–81

34. Ellis W. S., Sippens Groenewegen A., Auslander D. M., Lesh M. D. The role of the crista terminalis in atrial flutter and fibrillation: A Computer Modelling Study. Annals Biomed Engineer. 2000. Vol. 28. P. 742–754.

35. Gray R. A., Pertsov A. M., Jalife J. Incomplete reen-try and epicardial breakthrough patterns during atrial ftbrillation in the sheep heart. Circulation 1996. Vol. 94. P. 2649–2661.

36. Cottle M., Hoover W., Kanwal S., Kohn M., Strome T., Treister N. W. Transforming Health Care Through Big Data, Institute for Health Technology Transformation, Washington DC, USA, 2013.

37. Ellis W. S., Sippens Groenewegen A., Auslander D. M., Lesh M. D. The role of the crista terminalis in atrial flutter and fibrillation: A Computer Modelling Study. Annals Biomed Engineer. 2000. Vol. 28. P. 742–754.

38. Ramirez R. J., Nattel S., Courtemanche M. Mathematical analysis of canine atrial action potentials: Rate, regional factors, and electrical remodeling. Am J Physiol. 2000. Vol. 279. P. 1767– 1785

39. Cottle M., Hoover W., Kanwal S., Kohn M., Strome T., Treister N. W. Transforming Health Care Through Big Data, Institute for Health Technology Transformation, Washington DC, USA, 2013.

40. Foster E., Gray R. A., Jalife J. Role of the pectinate muscle structure in atrial fibrillation: A Computer Study. Pacing Clin Electrophysiol. 1997. Vol. 20. 1134 P.

41. Ramirez R. J., Nattel S., Courtemanche M. Mathematical analysis of canine atrial action potentials: Rate, regional factors, and electrical remodeling. Am J Physiol. 2000. Vol. 279. P. 1767– 1785

42. Harrild D. M., Henriquez C. P. A computer model of normal conduction in the human atria. Circ Res 2000. Vol. 87(7). P. 25–36

43. Foster E., Gray R. A., Jalife J. Role of the pectinate muscle structure in atrial fibrillation: A Computer Study. Pacing Clin Electrophysiol. 1997. Vol. 20. 1134 P.

44. Nygren A., Giles W. R. Mathematical simulation of slowing in cardiac conduction velocity by elevated extracellular [K+] in a human atrial strand. Annals Biomed Engineer. 2000. Vol. 28. P. 951–957.

45. Harrild D. M., Henriquez C. P. A computer model of normal conduction in the human atria. Circ Res 2000. Vol. 87(7). P. 25–36

46. Friedman C., Shagina L., Lussier Y., Hripcsak G. Automated encoding of clinical documents based on natural language processing. Journal of the American Medical Informatics Association. 2004. Vol. 11. P. 392–402.

47. Nygren A., Giles W. R. Mathematical simulation of slowing in cardiac conduction velocity by elevated extracellular [K+] in a human atrial strand. Annals Biomed Engineer. 2000. Vol. 28. P. 951–957.

48. Fitz Hugh R. A. Impulses and physiological states in theoretical models of nerve membrane. Biophysics Journal. 1961. Vol. 1. P. 445–466.

49. Friedman C., Shagina L., Lussier Y., Hripcsak G. Automated encoding of clinical documents based on natural language processing. Journal of the American Medical Informatics Association. 2004. Vol. 11. P. 392–402.

50. Luo C-H., Rudy Y. A model of the ventricular cardiac action potential: Depolarization, repolarization, and their interaction. Circ. Res. 1991. Vol. 68(6). P. 1501– 1526.

51. Fitz Hugh R. A. Impulses and physiological states in theoretical models of nerve membrane. Biophysics Journal. 1961. Vol. 1. P. 445–466.

52. Van Wagoner D. R., Pond A. L., Lamorgese M., Rossie P. S., McCarthy P. M., Nerbonne J.M. Atrial L-type Ca2+ currents and human atrial ftbrillation. Circ. Res. 1999. Vol. 85 P. 428–436.

53. Luo C-H., Rudy Y. A model of the ventricular cardiac action potential: Depolarization, repolarization, and their interaction. Circ. Res. 1991. Vol. 68(6). P. 1501– 1526.

54. Hagar Y., Albers D., Pivovarov R., Chase H., Dukic V., Elhadad N. Survival analysis with electronic health record data: Experiments with chronic kidney disease. Statistical Analysis and Data Mining, ASA Data Sci. J. 2014. Vol. 7. P. 385–403.

55. Van Wagoner D. R., Pond A. L., Lamorgese M., Rossie P. S., McCarthy P. M., Nerbonne J.M. Atrial L-type Ca2+ currents and human atrial ftbrillation. Circ. Res. 1999. Vol. 85 P. 428–436.

56. Jain A. K., Murty M. N., Flynn P. J. Data clustering: A review ACM Computing Surveys. 1999. Vol. 31. P. 264–323.

57. Hagar Y., Albers D., Pivovarov R., Chase H., Dukic V., Elhadad N. Survival analysis with electronic health record data: Experiments with chronic kidney disease. Statistical Analysis and Data Mining, ASA Data Sci. J. 2014. Vol. 7. P. 385–403.

58. Jain A. K., Murty M. N., Flynn P. J. Data clustering: A review ACM Computing Surveys. 1999. Vol. 31. P. 264–323.