contadores web
Skip to main navigation menu Skip to main content Skip to site footer
##common.pageHeaderLogo.altText##

Scientific and technological research article

Vol. 19 No. 2 (2017)

Adult dynamic heart evaluated by the proportions of entropy

DOI
https://doi.org/10.22267/rus.171902.87
Submitted
June 2, 2016
Published
2017-08-30

Abstract

Introduction: A new mathematical methodology of clinical application has been developed from the theory of dynamic systems, together with the theory of probability and the concept of entropy. Objective: To apply the methodology previously developed to evaluate the heart dynamics of adult through the probability and proportions of entropy of the attractor. Materials and methods: A blind study was developed taking as Gold Standard the conventional diagnosis issued by an expert with 480 Holter, 30 normal dynamics and 450 with different pathologies. For each Holter, a numerical attractor was generated by quantifying the probability of appearance of consecutive pairs of cardiac frequencies, subsequently evaluating entropy, S/K ratio and proportions for each dynamic for at least 18 hours. The values of sensitivity, specificity and Kappa coefficient were found. Results: The applied methodology allowed to differentiate quantitatively normality of disease, finding the values of the proportions in the established ranges. The sensitivity and specificity values were 100%, and Kappa coefficient was 1. Conclusion: It is possible to diagnose cardiac dynamics for at least 18 hours based on the probability distributions of the appearance of consecutive pairs of cardiac frequencies and their entropy.

References

  1. Devaney RL, Siegel PB, Mallinckrodt AJ, McKay S. A first course in chaotic dynamical systems: theory and experiment. Comput Phys. AIP Publishing; 1993;7(4):416–7.
  2. Peitgen H-O, Jürgens H, Saupe D. Strange attractors, the locus of chaos. In: Chaos and Fractals: New Frontiers of Science. New York: Springer-Verlag; 1992. p. 655–768.
  3. Calabrese JL. Ampliando las fronteras del reduccionismo. Deducción y Sist no lineales Psicoanálisis APdeBA. 1999;21(3):431–53.
  4. Feynman RP, Leighton RB, Sands M. Probability. In: Physics Vol 1: Mechanics, radiation, and heat. Wilmington: Addison-Wesley Iberoamericana; 1964. p. 1–11.
  5. Arrègle J. Procesos y tecnología de máquinas y motores térmicos. Valencia, España: Ed. Univ. Politéc. Valencia; 2002.
  6. Feynman RP, Leighton RB, Sands M. The Laws of Thermodynamics. In: Physics Vol 1: Mechanics, radiation, and heathysics. Wilmington: Addison-Wesley Iberoamericana; 1964. p. 1–13.
  7. Frodden E, Royo J. Entropía e información, Seminario Final del curso de Termodinámica, Depto. de Física, Facultad de Ciencias, Universidad de Chile, 2004.
  8. Shore JE. Relative entropy, probabilistic inference and AI. arXiv Prepr arXiv13043423. 2013;
  9. OMS. Centro de prensa. Enfermedades cardiovasculares [Internet]. [cited 2017 Jul 10]. Available from: http://www.who.int/mediacentre/factsheets/fs317/es/
  10. Mozaffarian D, Benjamin EJ, Go AS, Arnett DK, Blaha MJ, Cushman M, et al. Heart disease and stroke statistics-2015 update : A report from the American Heart Association. Vol. 131, Circulation. 2015. 29-39 p.
  11. 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(3):115–29.
  12. Rodríguez J, Prieto S, Correa C, Bautista J, Velasco A, Mendez L, et al. Mathematics physical assessment of cardiac dynamics based on theory of probability and proportions of entropy in the Intensive care Unit for patients with arrhythmia. In: International Conference on Medical Phyiscs. Birmingham, UK; 2015.
  13. Rodríguez J. Mathematical law of chaotic cardiac dynamics: Predictions for clinical application. J Med Med Sci. 2011;2(8):1050–9.
  14. Rodríguez-Velásquez J, Prieto @bullet Signed, Domínguez D, Correa @bullet Catalina, Melo M, Pardo J, et al. Application of the chaotic power law to the study of cardiac dynamics in patients with arrhythmias.
  15. Colombiana De A, Rodríguez J, Prieto S, Correa C, Oliveros H, Soracipa Y, et al. Diagnóstico físico-matemático de la dinámica cardiaca a partir de sistemas dinámicos y geometría fractal: disminución del tiempo de evaluación de la dinámica cardiaca de 21 a 16 horas. Acta Colomb Cuid Intensivo [Internet]. 2016;16(1):15–22. Available from: www.elsevier.es/acci
  16. Rodríguez Velásquez 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 [Internet]. 2015;6(8):209–20. Available from: http://www.interesjournals.org/JMMS
  17. Wu G-Q, Arzeno NM, Shen L-L, Tang D-K, Zheng D-A, Zhao N-Q, et al. Chaotic signatures of heart rate variability and its power spectrum in health, aging and heart failure. PLoS One. Public Library of Science; 2009;4(2):e4323.
  18. Braun C, Kowallik P, Freking A, Hadeler D, Kniffki K-D, Meesmann M. Demonstration of nonlinear components in heart rate variability of healthy persons. Am J Physiol Circ Physiol. Am Physiological Soc; 1998;275(5):H1577–84.
  19. Goldberger AL, Amaral LAN, Hausdorff JM, Ivanov PC, Peng C-K, Stanley HE. Fractal dynamics in physiology: Alterations with disease and aging. Proc Natl Acad Sci [Internet]. 2002;99(Supplement 1):2466–72. Available from: http://www.pnas.org/content/99/suppl_1/2466.short
  20. Huikuri H, Makikällo T, Peng C h., Goldberger A, Hintze U, Moller M. Fractal correlation Properties of R-R Interval Dynamics and Mortality in Patients with Depressed Left Ventricular Function After an Acute Miocardial Infarction. Circulation [Internet]. 2000;101. Available from: http://dx.doi.org/10.1161/01.CIR.101.1.47
  21. Perkiömäki JS, Mäkikallio TH, Huikuri H V. Fractal and Complexity Measures of Heart Rate Variability. Clin Exp Hypertens [Internet]. Taylor & Francis; 2005 Jan 1;27(2–3):149–58. Available from: http://dx.doi.org/10.1081/CEH-48742
  22. Voss A, Schulz S, Schroeder R, Baumert M, Caminal P. Methods derived from nonlinear dynamics for analysing heart rate variability. Philos Trans R Soc A Math Phys Eng Sci [Internet]. 2009 Jan 28;367(1887):277 LP-296. Available from: http://rsta.royalsocietypublishing.org/content/367/1887/277.abstract
  23. Rodríguez J, Prieto S, Domínguez D, Melo M, Mendoza F, Correa C, et al. Mathematical-physical prediction of cardiac dynamics using the proportional entropy of dynamic systems. J Med Med Sci [Internet]. 2013;4(9):370–81. Available from: http:/dx.doi.org/10.14303/jmms.2013.080
  24. Rodríguez J, Prieto S, Correa C, Soracipa Y, Mora J, Bernal P, et al. Predicciones de la entropía proporcional en la dinámica cardiaca. Rev Med. Universidad Militar Nueva Granada; 2015;23(2).
  25. Rodríguez J, Prieto S, Correa C, Soracipa Y, Aguirre G, Méndez L. Proportional entropy applied to the clinical diagnostic of cardiac dynamic: blind study with 600 holter. In: The 61st Annual Conference of the Israel Heart Society in association with The Israel Society of Cardiothoracic Surgery. Tel Aviv, Israel; 2014.
  26. Rodríguez J, Prieto S, Bernal P, Isaza D, Salazar G, Correa C, et al. Entropía proporcional aplicada a la evolución de la dinámica cardiaca. Predicciones de aplicación clínica. In: Rodríguez L, editor. La emergencia de los enfoques de la complejidad en América Latina Tomo I. Buenos Aires: Comunidad Editora Latinoamericana; 2016. p. 315–34.
  27. Matvéev AN. Física molecular. Moscú: MIR; 1987.
  28. Tolman R. Principles of statistical mechanics. 1st ed. New York: Dover Publications; 1979. 662 p.
  29. Al-Zaiti SS, Carey MG. The prevalence of clinical and electrocardiographic risk factors of cardiovascular death among on-duty professional firefighters. J Cardiovasc Nurs. NIH Public Access; 2015;30(5):440.
  30. Carey MG, Thevenin BJ-M. High resolution 12-lead electrocardiograms of on-duty professional firefighters: a pilot feasibility study. J Cardiovasc Nurs. NIH Public Access; 2009;24(4):261.
  31. Rodríguez-Velásquez J, Prieto-Bohórquez S, Flórez-Cárdenas M, Alarcón-Ávila C, López-Cruz R, Aguirre-Dávila G, et al. Cardiac dynamic systems in normal neonates: Neonate chaotic cardiac law. Rev Salud Uninorte. Fundación Universidad del Norte; 2014;30(3):361–70.
  32. Rodríguez J, Prieto S, Flórez M, Alarcón C, López R, Aguirrre G, et al. Physical-mathematical diagnosis of cardiac dynamic on neonatal sepsis: predictions of clinical application. J Med Med Sci. 2014;5(5):102–8.
  33. Rodríguez J, Prieto S, Correa C, Bernal P, Vitery S, Alvarez L, et al. Diagnóstico cardiaco basado en la probabilidad aplicado a pacientes con marcapasos. Acta Med Colomb. 2012;37(4):183–91.
  34. Rodríguez JO, Prieto SE, Correa C, Bernal PA, Puerta GE, Vitery S, et al. Theoretical generalization of normal and sick coronary arteries with fractal dimensions and the arterial intrinsic mathematical harmony. BMC Med Phys [Internet]. 2010;10:1–6. Available from: http://dx.doi.org/10.1186/1756-6649-10-1
  35. Rodríguez J, Prieto S, Correa C, Polo F, Soracipa Y, Blanco V, et al. Fractal and euclidean geometric generalization of normal and restenosed arteries. J Med Med Sci [Internet]. 2013;4(4):174–80. Available from: http://www.interesjournals.org/JMMS
  36. Prieto Bohórquez SE, Velásquez JOR, Correa Herrera SC, Soracipa Muñoz MY. Diagnosis of cervical cells based on fractal and Euclidian geometrical measurements: Intrinsic Geometric Cellular Organization. BMC Med Phys [Internet]. 2014;14(1):2. Available from: http://dx.doi.org/10.1186/1756-6649-14-2
  37. Rodríguez Velásquez J, Prieto Bohórquez S, Correa SC, Domínguez Cajeli D, Cardona Velásquez DM, Melo De Alonso M. Geometrical nuclear diagnosis and total paths of cervical cell evolution from normality to cancer. J Cancer Res Ther. 2015;11(1):98–104.
  38. Rodríguez Velásquez J, Prieto S, Correa C, Soracipa Y, Mora J, Forero M, et al. Generalización geométrica fractal de ventriculografías izquierdas normales y con disfunción leve. Acta Médica Colomb. Asociación Colombiana de Medicina Interna; 2014;39(2).
  39. Rodríguez J, Prieto S, Correa C, Mejía M, Ospino B, Munevar Á, et al. Simulación de trayectorias de alteración de estructuras eritrocitarias con base en la geometría fractal y euclidiana. Arch Med. Universidad de Manizales; 2014;14(2).
  40. Rodríguez JO, Prieto SE, Correa C, Pérez CE, Mora JT, Bravo J, et al. Predictions of CD4 lymphocytes’ count in HIV patients from complete blood count. BMC Med Phys. 2013;13:1.
  41. Rodríguez J, Prieto S, Melo M, Domínguez D, Correa C, Soracipa Y, et al. Predicción del número de linfocitos T CD4 en sangre periférica a partir de teoría de conjuntos y probabilidad en pacientes con VIH/SIDA. Inmunología. Elsevier; 2014;33(4):113–20.
  42. Rodríguez Velásquez J. Método para la predicción de la dinámica temporal de la malaria en los municipios de Colombia. Rev Panam Salud Publica. 2010;27(3):211–8.
  43. Rodríguez J. Teoría de unión al HLA clase II: teoría de probabilidad, combinatoria y entropía aplicadas a secuencias peptídicas. Inmunología. Elsevier; 2008;27(4):151–66.
  44. Moses LE. Statistical concepts fundamental to investigations. In: Bailar JCI, Hoaglin DC, editors. Medical Uses of Statistics. 3rd ed. Hoboken (Nueva Jersey): John Wiley & Sons; 2009. p. 5–26.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Most read articles by the same author(s)