How to Cite
Rodríguez-Velásquez, J. O., Gilraldo-Cardona, J. F., Barrios-Arroyave, F. A., Prieto-Bohórquez, S. E., Correa-Herrera, S. C., & Soracipa-Muñoz, M. Y. (2019). Exponential law of chaotic cardiac dynamics applied to 18 hours. Salud UIS, 51(2), 148–155. https://doi.org/10.18273/revsal.v51n2-2019007
Abstract
Introduction: The application of an exponential law for chaotic dynamic cardiac systems has been reduced to 18 hours for Holter analysis, quantifying normal and pathological cardiac dynamics, as well as the evolution between these states. Methodology: 80 electrocardiographic records were analyzed, 15 with normal dynamics and 65 with different pathologies. A chaotic attractor was constructed for each cardiac dynamic based on the simulation of the cardiac frequency sequence for 18 hours, after the fractal dimension of each attractor and its spatial occupation were found. The differentiating parameters of the chaotic exponential law were applied differentiating normal cardiac dynamics from those pathological, finally the sensitivity, specificity and Kappa coefficient were calculated. Results: The normal dynamics presented occupancy spaces above 200 in the Kp grid, and for the Kg grid above 67. In the cases of acute disease, the values in the Kp and Kg grids were below 73 and 22 respectively. The values of sensitivity and specificity were 100% and the Kappa coefficient was 1. Conclusion: The application of the exponential law for 18 hours showed that it was possible to characterize mathematically the cardiac dynamics, allowing reducing the time of evaluation.
References
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24. Bikou O, Delides A, Drougou A, Nonni A, Patsouris E, Pavlakis K. Fractal dimension as a diagnostic tool of complex endometrial hyperplasia and welldifferentiated endometrioid carcinoma. In Vivo. 2016; 30(5): 681-690.
25. Zatloukal Z. Granulometry and fractal dimensions. Ceska Slov Farm. 2003; 52(5): 244-247.
26. Saidov T, Heneweer C, Kuenen M, von Broich, Wijkstra H, Rosette J, et al. Fractal dimension of tumor microvasculature by DCE-US: preliminary study in mice. Ultrasound Med
Biol. 2016; 42(12): 2852-2863. doi: 10.1016/j.ultrasmedbio.2016.08.001.
27. Verma G, Luciani ML, Palombo A, Metaxa L, Panzironi G, Pediconi F, et al. Microcalcification morphological descriptors and parenchyma fractal dimension hierarchically interact in breast cancer: a diagnostic perspective. Comput Biol Med. 2018; 93: 16. doi: 10.1016/j.compbiomed.2017.12.004.
28. Rodríguez J, Prieto S, Correa C, Bernal P, Puerta G, Vitery S, et al. Theoretical generalization of normal and sick coronary arteries with fractal dimensions and the arterial intrinsic mathematical harmony. BMC Medical Physics. 2010; 10:1-6. doi: 10.1186/1756-6649-10-1.
29. Rodríguez J, Prieto S, Correa C, Posso H, Bernal P, Puerta G, et al. Generalización fractal de células preneoplásicas y cancerígenas del epitelio escamoso cervical. Una Nueva metodología de aplicación clínica. Rev Fac Med. 2010; 18(2):173-181.
30. Rodríguez J, Correa C, Melo M, Domínguez D, Prieto S, Cardona DM, et al. Chaotic cardiac law: Developing predictions of clinical application. J Med Med Sci. 2013;4(2): 79-84.
31. Rodríguez J, Narváez R, Prieto S, Correa C, Bernal P, Aguirre G, Soracipa Y, Mora J. The mathematical law of chaotic dynamics applied to cardiac arrhythmias. J. Med. Med. Sci. 2013; 4(7): 291-300.
32. Gao J, Hu J, Liu F, Cao Y. Multiscale entropy analysis of biological signals: a fundamental biscaling law. Front. Comput. Neurosci. 2015; 9:64. doi: 10.3389/fncom.2015.00064.
33. Nogueira ML, Garner DM, Osório E, de Abreu LC, Valenti VE. Globally chaotic analysis of Heart Rate Variability during acute auditory stimulus by heavy metal music. Medical Express. 2015;2(5): 1-7. doi: 10.5935/MedicalExpress.2015.05.04.
34. Krogh T, Christini DJ. Nonlinear dynamics in cardiology. Annu Rev Biomed Eng. 2012; 14: 179-203. doi: 10.1146/annurev-bioeng-071811-150106.
35. Huikuri HV, Mäkikallio TH, Peng Ch, Goldberger AL, Hintze U, Moller M. Fractal correlation properties of R-R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infartion. Circulation. 2000; 101: 47-53.
36. Porta A, Guzzetti S, Montano N, Furlan R, Pagani M, Malliani A. et al. Entropy, entropy rate and pattern classification as tools to typify complexity in short heart period variability series. IEEE Trans. Biomed Eng. 2001; 48: 1282-1291.
37. Guzzetti S, Borroni E, Garbelli PE, Ceriani E, Della P, Montano N, et al. Symbolic dynamics of heart rate variability: a probe to investigate cardiac autonomic
modulation. Circulation. 2005; 112: 465-470. doi: 10.1161/CIRCULATIONAHA.104.518449.
38. Maestri R, Pinna GD, Accardo A, Allegrini P, Balocchi R, D’Addio G, et al. Nonlinear indices of heart rate variability in chronic heart failure patients: redundancy and comparative clinical value. J Cardiovasc Electrophysiol. 2017; 18: 425-433. doi: 10.1111/j.1540-8167.2007.00728.x.
39. Voss A, Schulz S, Schroeder R, Baumert M, Caminal P. Methods derived from nonlinear dynamics for analysing heart rate variability. Philos Trans A Math Phys Eng Sci. 2009; 367: 277-96. doi: 10.1098/rsta.2008.0232.
40. Perkiömäki J, Mäkikallio TH, Huikuri HV. Fractal and complexity measures of Heart Rate Variability. Clin Exp Hypertens. 2005; 2:149-158. doi: 10.1081/CEH-48742.
41. Rodríguez J, Correa C, Prieto S, Valencia LE, Barrios FA. Evaluación de la dinámica cardiaca a partir de la ley caótica exponencial: reducción a 16 horas. Arch Medicina. 2017; 13(2):3. doi: 10.3823/1343.
42. Rodríguez J. Método para la predicción de la dinámica temporal de la malaria en los municipios de Colombia. Rev Panam Salud Pública 2010; 27(3): 211-218.
43. Rodríguez J, Prieto S, Correa C, Melo M, Dominguez D, Olarte N, et al. Prediction of CD4+ Cells counts in HIV/AIDS Patients based on sets and probability theories. Current HIV Research. 2018;16(6). doi: 10.2174/1570162X17666190306125819.
44. Rodríguez J. Teoría de unión al HLA clase II teorías de Probabilidad Combinatoria y Entropía aplicadas a secuencias peptídicas. Inmunología 2008; 27(4): 151-66. doi: 10.1016/S0213-9626(08)70064-7.
45. Rodríguez J. Entropía proporcional de los sistemas dinámicos cardiacos: predicciones físicas y matemáticas de la dinámica cardiaca de aplicación clínica. Rev Colomb Cardiol 2010; 17: 115-129. doi: 10.1016/S0120-5633(10)70229-1.
46. Rodríguez J. Dynamical systems applied to dynamic variables of patients from the intensive care unit (ICU): Physical and mathematical mortality predictions on ICU. J Med Med Sci. 2015; 6(8): 209-220.
2. Peitgen H, Jürgens H, Saupe D. Strange attractors, the locus of chaos. En: Chaos and Fractals: New Frontiers of Science. Springer-Verlag. NY. 1992; pp. 655-768. doi: 10.1007/b97624.
3. Calabrese JL. Ampliando las fronteras del reduccionismo. Deducción y sistemas no lineales. Psicoanálisis ApdeBA. 1999; 21(3): 431-453.
4. Mandelbrot B. Cambios de escala y leyes potenciales sin geometría. En: The fractal geometry of nature. Freeman Ed. San Francisco, 1972: pp. 477-487. doi:
10.1119/1.13295.
5. Mandelbrot B. Árboles jerárquicos o de clasificación, y la dimensión. En: Los Objetos Fractales. Tusquets Eds S.A. Barcelona. 2000; 161-166.
6. Mandelbrot B. How Long Is the Coast of Britain? statistical self-similarity and fractional dimension. Science. 1967; 156: 636-638. doi: 10.1126/science.156.3775.636.
7. Peitgen H, Jürgens H, Saupe D. The Box-Counting Dimension En: Chaos and Chaos and Fractals: New Frontiers of Science. Springer-Verlag. N.Y. 1992. doi: 10.1007/b97624
8. World Health Organization. Noncommunicable diseases. World Health Organization; 2018.
9. Mozaffarian D, Benjamin E, Go AS, Arnett DK, Blaha MJ, Cushman M, et al. Heart Disease and Stroke Statistics-2015 Update. A report from the American heart association. Circulation. 2015; 131: e29-e322. doi: 10.1161/CIR.0000000000000152.
10. Steinberg JS, Varma N, Cygankiewicz I, Aziz P, Balsam P, Baranchuk A, et al. 2017 ISHNEHRS expert consensus statement on ambulatory ECG and external cardiacmonitoring/telemetry. Heart Rhythm. 2017; 14: e55-e96. doi: 10.1016/j.hrthm.2017.03.038.
11. Barron H, Viskin S. Autonomic markers and prediction of cardiac death after myocardial infarction. Lancet. 1998; 351: 461-462. doi: 10.1016/S0140-6736(05)78676-1.
12. Hilldebrand S, Gast KB, de Mutsert R, Swenne CA, Jukema JW, Middeldorp, et al. Heart rate variability and first cardiovascular event in populations without known cardiovascular disease: meta-analysis and dose–response meta-regression. EP Europace. 2013; 15(5): 742-749. DOI: 10.1093/europace/eus341.
13. Lui G, Wang L, Wang Q, Zhou G, Wang Y, Jiang Q. A New approach to detect congestive heart failure using short-term heart rate variability measures. PLoS One. 2014; 9(4): e93399. doi: 10.1371/journal.pone.0093399.
14. Wolf M, Varigos G, Hunt D, Sluman J. Sinus arrhythmia in acute myocardial infarction. Med J Aus. 1978; 2: 52-53. doi: 10.5694/j.1326-5377.1925.tb11693.x.
15. Goldberger A, Amaral L, Hausdorff JM, Ivanov P, Peng Ch, Stanley HE. Fractal dynamics in physiology: alterations with disease and aging. PNAS. 2002; 99: 2466-2472. doi: 10.1073/pnas.012579499.
16. Higgins JP. Nonlinear systems in medicine. Yale J Biol Med. 2002; 75: 247-260.
17. Costa M, Goldberger AL, Peng CK. Multiscale entropy analysis of complex physiologic Time Series. Phys Rev Lett. 2002; 89(6): 0681021-0681024. doi: 10.1103/PhysRevLett.89.068102.
18. Wu GQ, Arzeno NM, Shen LL, Tang DK, ZhengDA, Zhao NQ, et al. Chaotic signatures of heart rate variability and its power spectrum in health, aging and heart failure. PLoS ONE. 2009; e4323. doi: 10.1371/journal.pone.0004323.
19. Braun C, Kowallik P, Freking A, Hadeler D, Kniffki K, Meesmann M. Demonstration of nonlinear components in heart rate variability of healthy persons. Am J Physiol. 1998; 275: H1577-H1584. doi: 10.1152/ajpheart.1998.275.5.H1577.
20. Rodríguez J. Mathematical law of chaotic cardiac dynamic: Predictions of clinic application. J Med Med Sci. 2011; 2(8): 1050-1059.
21. Huikuri HV, Mäkikallio TH, Peng Ch, Goldberger AL, Hintze U, Moller M. Fractal correlation properties of R-R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infartion. Circulation. 2000; 101: 47-53. doi: 10.1161/01.CIR.101.1.47.
22. Barwad A, Dey P. Multifractal spectrum differentiation of well-differentiated adenocarcinoma from complex atypical hyperplasia of the uterus. Anal Quant Cytol Histol. 2012; 34(2):
105-108.
23. Moreno PA, Vélez PE, Martínez E, Garreta LE, Díaz N, Amador S, et al. The human genome: a multifractal analysis. BMC Genomics. 2011; 12: 506. doi: 10.1186/1471-2164-12-506.
24. Bikou O, Delides A, Drougou A, Nonni A, Patsouris E, Pavlakis K. Fractal dimension as a diagnostic tool of complex endometrial hyperplasia and welldifferentiated endometrioid carcinoma. In Vivo. 2016; 30(5): 681-690.
25. Zatloukal Z. Granulometry and fractal dimensions. Ceska Slov Farm. 2003; 52(5): 244-247.
26. Saidov T, Heneweer C, Kuenen M, von Broich, Wijkstra H, Rosette J, et al. Fractal dimension of tumor microvasculature by DCE-US: preliminary study in mice. Ultrasound Med
Biol. 2016; 42(12): 2852-2863. doi: 10.1016/j.ultrasmedbio.2016.08.001.
27. Verma G, Luciani ML, Palombo A, Metaxa L, Panzironi G, Pediconi F, et al. Microcalcification morphological descriptors and parenchyma fractal dimension hierarchically interact in breast cancer: a diagnostic perspective. Comput Biol Med. 2018; 93: 16. doi: 10.1016/j.compbiomed.2017.12.004.
28. Rodríguez J, Prieto S, Correa C, Bernal P, Puerta G, Vitery S, et al. Theoretical generalization of normal and sick coronary arteries with fractal dimensions and the arterial intrinsic mathematical harmony. BMC Medical Physics. 2010; 10:1-6. doi: 10.1186/1756-6649-10-1.
29. Rodríguez J, Prieto S, Correa C, Posso H, Bernal P, Puerta G, et al. Generalización fractal de células preneoplásicas y cancerígenas del epitelio escamoso cervical. Una Nueva metodología de aplicación clínica. Rev Fac Med. 2010; 18(2):173-181.
30. Rodríguez J, Correa C, Melo M, Domínguez D, Prieto S, Cardona DM, et al. Chaotic cardiac law: Developing predictions of clinical application. J Med Med Sci. 2013;4(2): 79-84.
31. Rodríguez J, Narváez R, Prieto S, Correa C, Bernal P, Aguirre G, Soracipa Y, Mora J. The mathematical law of chaotic dynamics applied to cardiac arrhythmias. J. Med. Med. Sci. 2013; 4(7): 291-300.
32. Gao J, Hu J, Liu F, Cao Y. Multiscale entropy analysis of biological signals: a fundamental biscaling law. Front. Comput. Neurosci. 2015; 9:64. doi: 10.3389/fncom.2015.00064.
33. Nogueira ML, Garner DM, Osório E, de Abreu LC, Valenti VE. Globally chaotic analysis of Heart Rate Variability during acute auditory stimulus by heavy metal music. Medical Express. 2015;2(5): 1-7. doi: 10.5935/MedicalExpress.2015.05.04.
34. Krogh T, Christini DJ. Nonlinear dynamics in cardiology. Annu Rev Biomed Eng. 2012; 14: 179-203. doi: 10.1146/annurev-bioeng-071811-150106.
35. Huikuri HV, Mäkikallio TH, Peng Ch, Goldberger AL, Hintze U, Moller M. Fractal correlation properties of R-R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infartion. Circulation. 2000; 101: 47-53.
36. Porta A, Guzzetti S, Montano N, Furlan R, Pagani M, Malliani A. et al. Entropy, entropy rate and pattern classification as tools to typify complexity in short heart period variability series. IEEE Trans. Biomed Eng. 2001; 48: 1282-1291.
37. Guzzetti S, Borroni E, Garbelli PE, Ceriani E, Della P, Montano N, et al. Symbolic dynamics of heart rate variability: a probe to investigate cardiac autonomic
modulation. Circulation. 2005; 112: 465-470. doi: 10.1161/CIRCULATIONAHA.104.518449.
38. Maestri R, Pinna GD, Accardo A, Allegrini P, Balocchi R, D’Addio G, et al. Nonlinear indices of heart rate variability in chronic heart failure patients: redundancy and comparative clinical value. J Cardiovasc Electrophysiol. 2017; 18: 425-433. doi: 10.1111/j.1540-8167.2007.00728.x.
39. Voss A, Schulz S, Schroeder R, Baumert M, Caminal P. Methods derived from nonlinear dynamics for analysing heart rate variability. Philos Trans A Math Phys Eng Sci. 2009; 367: 277-96. doi: 10.1098/rsta.2008.0232.
40. Perkiömäki J, Mäkikallio TH, Huikuri HV. Fractal and complexity measures of Heart Rate Variability. Clin Exp Hypertens. 2005; 2:149-158. doi: 10.1081/CEH-48742.
41. Rodríguez J, Correa C, Prieto S, Valencia LE, Barrios FA. Evaluación de la dinámica cardiaca a partir de la ley caótica exponencial: reducción a 16 horas. Arch Medicina. 2017; 13(2):3. doi: 10.3823/1343.
42. Rodríguez J. Método para la predicción de la dinámica temporal de la malaria en los municipios de Colombia. Rev Panam Salud Pública 2010; 27(3): 211-218.
43. Rodríguez J, Prieto S, Correa C, Melo M, Dominguez D, Olarte N, et al. Prediction of CD4+ Cells counts in HIV/AIDS Patients based on sets and probability theories. Current HIV Research. 2018;16(6). doi: 10.2174/1570162X17666190306125819.
44. Rodríguez J. Teoría de unión al HLA clase II teorías de Probabilidad Combinatoria y Entropía aplicadas a secuencias peptídicas. Inmunología 2008; 27(4): 151-66. doi: 10.1016/S0213-9626(08)70064-7.
45. Rodríguez J. Entropía proporcional de los sistemas dinámicos cardiacos: predicciones físicas y matemáticas de la dinámica cardiaca de aplicación clínica. Rev Colomb Cardiol 2010; 17: 115-129. doi: 10.1016/S0120-5633(10)70229-1.
46. Rodríguez J. Dynamical systems applied to dynamic variables of patients from the intensive care unit (ICU): Physical and mathematical mortality predictions on ICU. J Med Med Sci. 2015; 6(8): 209-220.
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