Mathematical Diagnosis of Acute Myocardial Infarction and Failure Using Proportional Entropy
Keywords:
diagnosis, nonlinear systems, entropy, acute heart failureAbstract
Introduction: Physical and mathematical theories have allowed the development of new diagnostic methodologies of cardiac dynamics, as one based on the evaluation of entropy proportions to differentiate normality from cardiac disease, although its diagnostic capacity must be yet determined in specific critical scenarios as acute heart failure and acute myocardial infarction
Objective: To describe diagnostic evaluations of cardiac dynamics in patients diagnosed with acute myocardial infarction or acute heart failure.
Methods: A blind study was developed with 20 Holter registries; 5 normal, 8 with acute cardiac failure and 7 with acute myocardial infarction. Then, a method based on the proportions of the entropy of the numerical attractors was applied. The maximum and minimum values of the heart rate and the total number of beats per hour were taken for at least 18 hours, with which numerical attractors were generated, which measure the probability of consecutive heart rate pairs. An evaluation of all dynamics was made based on the entropy and its proportions. Finally, a comparison between the diagnostic precision of the mathematical method with respect to the conventional clinical diagnosis was performed.
Results: Normal cases were mathematically differentiated from the pathological ones through the evaluation of Holter registries for 18 hours, achieving values of sensitivity and specificity of 100% as well as a Kappa coefficient of 1, indicating a perfect diagnostic concordance between the mathematical method to diagnose the cardiac dynamics with respect to the clinical diagnosis.
Conclusions: The proportions of entropy allow to establish objective diagnoses of cardiac dynamics, mathematically differentiating normal dynamics from those with acute myocardial infarction and with acute cardiac failure.
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1. Calabrese JL. Ampliando las fronteras del reduccionismo. Deducción y sistemas no lineales. Psicoanálisis APdeBA. 1999;21(3):431-53.
2. Devaney R. A first course in chaotic dynamical systems theory and experiments. Reading Mass: Addison-Wesley; 1992.
3. Feynman R, Leighton R, Sands M. Leyes de Newton de la Dinámica. En: Feynman RP, Leighton RB, Sands M. Física. Vol. 3. Wilmington: Addison-Wesley Iberoamericana, S. A.; 1987. p. 1-14.
4. Feynman RP, Leighton RB, Sands M. Probabilidad. En: Física. Feynman RP, Leighton RB, Sands M. Física. Vol. 1. Wilmington: Addison-Wesley Iberoamericana, S. A.; 1998. p. 1-16.
5. Shore J. Relative Entropy, Probabilistic Inference and AI. Machine Intelligence and Pattern Recognition. 1986 [acceso: 22/01/2020]; 4:211-5. Disponible en: https://www.sciencedirect.com/science/article/pii/B9780444700582500206
6. Shannon CE. A Mathematical Theory of Communication. The Bell System Technical Journal. 1948;27:379-423.
7. Tolman R. Principles of statistical mechanics. New York: Dover Publications; 1979.
8. Mayer C, Bachler M, Hörtenhuber M, Stocker C, Holzinger A, Wassertheurer S. Selection of entropy-measure parameters for knowledge discovery in heart rate variability data. BMC Bioinformatics. 2014 [acceso: 22/01/2020]; 15(Suppl 6):S2. Disponible en: https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-15-S6-S2
9. Shaffer F, Ginsberg JP. An Overview of Heart Rate Variability Metrics and Norms. Front Public Health. 2017;5:258. PMCID: PMC5624990
10. Borchini R, Veronesi G, Bonzini M, Gianfagna F, Dashi O, Ferrario MM. Heart Rate Variability Frequency Domain Alterations among Healthy Nurses Exposed to Prolonged Work Stress. Int J Environ Res Public Health. 2018;15(1):113. PMCID: PMC5800212
11. O’Neal WT, Chen LY, Nazarian S, Soliman EZ. Reference Ranges for Short-Term Heart Rate Variability Measures in Individuals Free of Cardiovascular Disease: The Multi-Ethnic Study of Atherosclerosis (MESA). J Electrocardiol. 2016;49(5):686-90. PMCID: PMC5010946
12. Pincus SM. Assessing serial irregularity and its implications for health. Annals of the New York Academy of Sciences. 2001;954:245-67. Disponible en: https://nyaspubs.onlinelibrary.wiley.com/doi/abs/10.1111/j.1749-6632.2001.tb02755.x?sid=nlm%3Apubmed
13. Hornero R, Aboy M, Abasolo D, Mcnames J, Goldstein B. Interpretation of approximate entropy: analysis of intracranial pressure approximate entropy during acute intracranial hypertension. IEEE Trans Biomed Eng. 2005;52(10):1671-80. Disponible en: https://ieeexplore.ieee.org/document/1510851
14. Pincus SM. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci USA. 1991;88(6):2297-2301. PMCID: PMC51218
15. Arati AA, Inamdar AC. Heart Failure: Diagnosis, Management and Utilization. J Clin Med. 2016;5:62. PMCID: PMC4961993
16. Modin D, Madsen D, Biering T. Echo and heart failure: when do people need an echo, and when do they need natriuretic peptides? Echo Res Pract. 2018;R65-R79. Disponible en: https://erp.bioscientifica.com/view/journals/echo/5/2/ERP-18-0004.xml
17. Rodríguez J. Entropía Proporcional de los sistemas dinámicos cardiacos: Predicciones físicas y matemáticas de la dinámica cardiaca de aplicación clínica. Rev Colomb Cardiol. 2010 [acceso: 22/01/2020]; 17:115-29. Disponible en: https://www.sciencedirect.com/science/article/pii/S0120563310702291
18. Rodríguez J, Prieto S, Ramírez LJ. A novel heart rate attractor for the prediction of cardiovascular disease. Informatics in Medicine Unlocked. 2019 [acceso: 22/01/2020]; 15:100174. Disponible en: https://www.sciencedirect.com/science/article/pii/S235291481930005X
19. Rodríguez J, Prieto S, Bernal P, Izasa D, Salazar G, Correa C, et al. Entropía proporcional aplicada a la evolución de la dinámica cardiaca. Predicciones de aplicación clínica. En: Rodríguez LG, coord. La emergencia de los enfoques de la complejidad en América Latina: desafíos, contribuciones y compromisos para abordar los problemas complejos del siglo XXI. Vol I. Buenos Aires: Comunidad Editora Latinoamericana; 2015. p. 315-44.
20. Sangrador O, Arias M. Evaluación de la precisión de las pruebas diagnósticas (1). Variables discretas. Evid Pediatr. 2017 [acceso: 22/01/2020]; 13:28. Disponible en: https://evidenciasenpediatria.es/files/41-13048-RUTA/Fundamentos_MBE_28.pdf
21. Hassan SZ, Zhang H, Aziz W, Monfredi O, Abbas SA, Shah SA, et al. Inverse Correlation between Heart Rate Variability and Heart Rate Demonstrated by Linear and Nonlinear Analysis. PLoS One. 2016;11(6):e0157557. PMCID: PMC4919077
22. Rodríguez J. Dynamical systems applied to dynamic variables of patients from the Intensive Care Unit (ICU). Physical and mathematical Mortality predictions on ICU. Journal of Medicine and Medical Sciences. 2015 [acceso: 22/01/2020]; 6(8):102-8. Disponible en: https://www.interesjournals.org/articles/dynamical-systems-applied-to-dynamic-variables-of-patients-from-the-intensive-care-unit-icu-physical-and-mathematical-mo.pdf
23. Goldberger A, Amaral L, Hausdorff JM, Ivanov P, Peng Ch, Stanley HE. Fractal dynamics in physiology: alterations with disease and aging. PNAS 2002 [acceso: 22/01/2020]; 99:2466-72. Disponible en: https://www.pnas.org/content/99/suppl_1/2466
24. Sen J, McGill D. Fractal analysis of heart rate variability as a predictor of mortality: A systematic review and meta-analysis. Chaos. 2018 [acceso: 22/01/2020]; 28:072101. Disponible en: https://aip.scitation.org/doi/10.1063/1.5038818
25. 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 infarction. Circulation. 2000 [acceso: 22/01/2020]; 101:47-53. Disponible en: https://www.ahajournals.org/doi/10.1161/01.cir.101.1.47?url_ver=Z39.88-2003&rfr_id=ori%3Arid%3Acrossref.org&rfr_dat=cr_pub++0pubmed&
26. Sassi R, Cerutti S, Lombardi F, Malik M, Huikuri HV, Peng CK, et al. Advances in heart rate variability signal analysis: joint position statement by the e-Cardiology ESC Working Group and the European Heart Rhythm Association co-endorsed by the Asia Pacific Heart Rhythm Society. Europace. 2015;17:1341-53. PMID: 26177817
27. Rodríguez J, Prieto S, Correa C, Mendoza F, Weisz G, Soracipa M, et al. Physical mathematical evaluation of the cardiac dynamic applying the Zipf – Mandelbrot law. Journal of Modern of Physics. 2015 [acceso: 22/01/2020]; 6(13):1881-8. Disponible en: https://www.scirp.org/pdf/JMP_2015102911032237.pdf
28. Prieto S, Rodríguez J, Correa C, Soracipa Y. Diagnosis of cervical cells based on fractal and Euclidian geometrical measurements: Intrinsic Geometric Cellular Organization. BMC Medical Physics. 2014;14(2):1-9. PMCID: PMC4363990
29. Rodríguez J, Prieto S, Pérez C, Correa C, Soracipa M, Jattin J, et al. Predicción temporal de CD4+ en 80 pacientes con manejo antirretroviral a partir de valores de leucocitos. Infectio. 2020 [acceso: 22/01/2020]; 24:103-7. Disponible en: https://www.revistainfectio.org/index.php/infectio/article/view/841/937
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