Share This Article:

Physical Mathematical Evaluation of the Cardiac Dynamic Applying the Zipf-Mandelbrot Law

Full-Text HTML XML Download Download as PDF (Size:516KB) PP. 1881-1888
DOI: 10.4236/jmp.2015.613193    2,809 Downloads   3,215 Views   Citations

ABSTRACT

Introduction: The law of Zipf-Mandelbrot is a power law, which has been observed in natural languages. A mathematical diagnosis of fetal cardiac dynamics has been developed with this law. Objective: To develop a methodology for diagnostic aid to assess the degree of complexity of adult cardiac dynamics by Zipf-Mandelbrot law. Methodology: A mathematical induction was done for this; two groups of Holter recordings were selected: 11 with normal diagnosis and 11 with acute disease of each group, one Holter of each group was chosen for the induction, the law of Zipf-Mandelbrot was applied to evaluate the degree of complexity of each Holter, searching similarities or differences between the dynamics. A blind study was done with 20 Holters calculating sensitivity, specificity and the coefficient kappa. Results: The complexity grade of a normal cardiac dynamics varied between 0.9483 and 0.7046, and for an acute dynamic between 0.6707 and 0.4228. Conclusions: A new physical mathematical methodology for diagnostic aid was developed; it showed that the degree of complexity of normal cardiac dynamics was higher than those with acute disease, showing quantitatively how cardiac dynamics can evolve to acute state.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Rodríguez, J. , Prieto, S. , Correa, S. , Mendoza, F. , Weiz, G. , Soracipa, M. , Velásquez, N. , Pardo, J. , Martínez, M. and Barrios, F. (2015) Physical Mathematical Evaluation of the Cardiac Dynamic Applying the Zipf-Mandelbrot Law. Journal of Modern Physics, 6, 1881-1888. doi: 10.4236/jmp.2015.613193.

References

[1] Zipf, G. (1949) Human Behaviour and the Principle of Least Effort: An Introduction to Human Ecology. Addison-Wesley, Cambridge.
[2] Mandelbrot, B. (1972) Scaling and Power laws without Geometry. In: The Fractal Geometry of Nature, Freeman, San Francisco, 344-348.
[3] Mandelbrot, B. (2000) Hierarchical or Classification Trees, and the Dimension. In: Fractals: Form, Chance and Dimension, Tusquets, Barcelona, 161-166.
[4] Mandelbrot, B. (1954) Structure formelle des textes et comunication. World, 10, 1-27.
[5] Adamic, L. and Huberman, B. (2002) Zipf’s Law and the Internet. Glottometrics, 3, 143-150.
[6] Larsen-Freeman, D. (1997) Chaos/Complexity Science and Second Language Acquisition. Applied Linguistics, 18, 141-165.
http://dx.doi.org/10.1093/applin/18.2.141
[7] Mandelbrot, B. and Hudson, R. (2006) Fractals and Finance. Tusquets, Barcelona.
[8] Burgos, J. and Moreno-Tovar, P. (1996) Zipf-Scaling Behavior in the Immune System. Biosystems, 39, 227-232.
http://dx.doi.org/10.1016/0303-2647(96)01618-8
[9] Burgos, J. (1996) Fractal representation of the immune B cell repertoire. Biosystems, 39, 19-24.
http://dx.doi.org/10.1016/0303-2647(95)01574-4
[10] Rodríguez, J. (2005) Fractal Behavior of T Specify Repertory against Poa p9 Alergeno. Revista de la Facultad de Medicina, 53, 72-78.
[11] Rodríguez, J., Prieto, S., Ortiz, L., Bautista, A., Bernal, P. and Avilán, N. (2006) Zipf-Mandelbrot Law and Mathematical Approach in Fetal Cardiac Monitoring Diagnosis. Revista Facultad de Medicina—Universidad Nacional de Colombia, 54, 96-107.
[12] Rodríguez, J. (2006) Dynamical Systems Theory and ZIPF—Mandelbrot Law Applied to the Development of a Fetal Monitoring Diagnostic Methodology. Proceedings of the 18th FIGO World Congress of Gynecology and Obstetrics, Kuala Lumpur, 5-10 November 2006.
[13] Robledo, R. and Escobar, F.A. (2010) Chronic Non-Communicable Diseases in Colombia. Bulletin of the Health Observatory, 3, 1-9.
[14] Gallo, J., Farbiarz, J. and Alvarez, D. (1999) Spectral Analysis of Heart Rate Variability. IATREIA, 12, 61-71.
[15] Harris, P., Stein, P.K., Fung, G.L. and Drew, B.J. (2014) Heart Rate Variability Measured Early in Patients with Evolving Acute Coronary Syndrome and 1-Year Outcomes of Rehospitalization and Mortality. Journal of Vascular Health and Risk Management, 10, 451- 464.
http://dx.doi.org/10.2147/VHRM.S57524
[16] Rodríguez, J., Prieto, S., Correa, C., Bernal, P., Puerta, G., Vitery, S., et al. (2010) Theoretical Generalization of Normal and Sick Coronary Arteries with Fractal Dimensions and the Arterial Intrinsic Mathematical Harmony. BMC Medical Physics, 10, 1-6.
http://dx.doi.org/10.1186/1756-6649-10-1
[17] Rodríguez, J., Prieto, S., Correa, C., Bernal, P., álvarez, L., Forero, G., et al. (2012) Fractal Diagnosis of Left Heart Ventriculograms Fractal Geometry of Ventriculogram during Cardiac Dynamics. Revista Colombiana de Cardiología, 19, 18-24.
[18] Goldberger, A., Rigney, D.R. and West, B. (1990) Science in Pictures: Chaos and Fractals in Human Physiology. Scientific American, 262, 42-49.
http://dx.doi.org/10.1038/scientificamerican0290-42
[19] Goldberger, A.L. and West, B.J. (1987) Applications of Nonlinear Dynamics to Clinical Cardiology. Annals of the New York Academy of Sciences, 504, 195-213.
http://dx.doi.org/10.1111/j.1749-6632.1987.tb48733.x
[20] Goldberger, A.L., Rigney, D.R., Mietus, J., Antman, E.M. and Greenwald, S. (1988) Nonlinear Dynamics in Sudden Cardiac Death Syndrome: Heartrate Oscillations and Bifurcations. Experientia, 44, 983-987.
http://dx.doi.org/10.1007/BF01939894
[21] Pincus, S.M. (1991) Approximate Entropy as a Measure of System Complexity. Proceedings of the National Academy of Sciences of the United States of America, 88, 2297-2301.
http://dx.doi.org/10.1073/pnas.88.6.2297
[22] Richman, J.S. and Moorman, J.R. (2000) Physiological Time-Series Analysis Using Approximate Entropy and Sample Entropy. American Journal of Physiology—Heart and Circulatory Physiology, 278, H2039-H2049.
[23] Rodríguez, J., Correa, C., Ortiz, L., Prieto, S., Bernal, P. and Ayala, J. (2009) Evaluación matemática de la dinámica cardiaca con la teoría de la probabilidad. Revista Mexicana de Cardiología, 20, 183-189.
[24] Rodríguez, J. (2010) Proportional Entropy of the Cardiac Dynamic Systems. Physical and Mathematical Predictions of the Cardiac Dynamic for Clinical Application..Revista Colombiana de Cardiología, 17, 115-129.
[25] Rodríguez, J. (2011) Mathematical Law of Chaotic Cardiac Dynamic: Predictions of Clinic Application. Journal of Medicine and Medical Sciences, 2, 1050-1059.
[26] Rodríguez, J. (2012) Proportional Entropy Applied to the Evolution of Cardiac Dynamics. Predictions of Clinical Application. Comunidad del Pensamiento Complejo, Argentina.
[27] Rodríguez, J., Prieto, S., Correa, C., Bernal, P., Vitery, S., álvarez, L., Aristizabal, N. and Reynolds, J. (2012) Cardiac Diagnosis Based on Probability Applied to Patients with Pacemakers. Acta Médica Colombiana, 37, 183-191.
[28] Rodríguez, J., Narváez, R., Prieto, S., Correa, C., Bernal, P., Aguirre, G., Soracipa, Y. and Mora, J. (2013) The mathematical Law of Chaotic Dynamics Applied to Cardiac Arrhythmias. Journal of Medicine and Medical Sciences, 4, 291-300.
[29] Rodríguez, J., Prieto, S., Flórez, M., Alarcón, C., López, R., Aguirre, G., Morales, L., Lima, L. and Méndez, L. (2014) Physical-Mathematical Diagnosis of Cardiac Dynamic on Neonatal Sepsis: Predictions of Clinical Application.. Journal of Medicine and Medical Sciences, 5, 102-108.
[30] Rodríguez, J. (2012) New Physical and Mathematical Diagnosis of Fetal Monitoring: Clinical Application Prediction. Momento Revista de Física, 44, 49-65.
[31] Borgatta, L., Shrout, P.E. and Divon, M.Y. (1988) Reliability and Reproducibility of Nonstress Test Readings. American Journal of Obstetrics & Gynecology, 159, 554-558.
http://dx.doi.org/10.1016/S0002-9378(88)80006-1
[32] Cohen, J. (1960) A Coefficient of Agreement for Nominal Scales. Educational and Psychological Measurement, 20, 37-46.
http://dx.doi.org/10.1177/001316446002000104
[33] Ksela, J., Avbelj, V. and Kalisnik, J.M. (2015) Multifractality in Heartbeat Dynamics in Patients Undergoing Beating-Heart Myocardial Revascularization. Computers in Biology and Medicine, 60, 66-73.
http://dx.doi.org/10.1016/j.compbiomed.2015.02.012
[34] Chang, M.C., Peng, C.K. and Stanley, H.E. (2014) Emergence of Dynamical Complexity Related to Human Heart Rate Variability. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 90, Article ID: 062806.
http://dx.doi.org/10.1103/PhysRevE.90.062806
[35] Einstein, A. (1934) On the Method of Theoretical Physics. Philosophy of Science, 1, 163-169.
http://dx.doi.org/10.1086/286316
[36] Huikuri, H.V., Mökikallio, T., Peng, C.K., Goldberger, A.L., Hintze, U., Mogens Møller, M., et al. (2000) Fractal Correlation Properties of R-R Interval Dynamics and Mortality in Patients with Depressed Left Ventricular Function after an Acute Myocardial Infarction. Circulation, 101, 47-53.
http://dx.doi.org/10.1161/01.CIR.101.1.47
[37] Voss, A., Schulz, S., Schroeder, R., Baumert, M. and Caminal, P. (2009) Methods Derived from Nonlinear Dynamics for Analysing Heart Rate Variability. Philosophical Transactions of the Royal Society A, 367, 277-296.
http://dx.doi.org/10.1098/rsta.2008.0232
[38] Rodríguez, J. (2008) Binding to Class II HLA Theory: Probability, Combinatory and Entropy Applied to Peptide Sequences. Inmunología, 27, 151-166.
http://dx.doi.org/10.1016/S0213-9626(08)70064-7
[39] Rodríguez, J. (2010) A Method for Forecasting the Seasonal Dynamic of Malaria in the Municipalities of Colombia.. Revista Panamericana de Salud Pública, 27, 211-218.
[40] Rodríguez, J., Prieto, S., Correa, C., Forero, M., Pérez, C., Soracipa, Y., Mora, J., Rojas, N., Pineda, D. and López, F. (2013) Set Theory Applied to White Cell and Lymphocyte Counts: Prediction of CD4 T Lymphocytes in Patients with Human Immunodeficiency Virus/Aids. Inmunología, 32, 50-56.
http://dx.doi.org/10.1016/j.inmuno.2013.01.003
[41] Rodríguez, J., Prieto, S., Correa, C., Pérez, C., Mora, J., Bravo, J., Soracipa, Y. and álvarez, L. (2013) Predictions of CD4 Lymphocytes’ Count in HIV Patients from Complete Blood Count. BMC Medical Physics, 13, 3.
http://dx.doi.org/10.1186/1756-6649-13-3
[42] Rodríguez, J. (2011) New Diagnosis Aid Method with Fractal Geometry for Pre-Neoplasic Cervical Epithelial Cells.. Revista U.D.C.A Actualidad & Divulgación Científica, 14, 15-22.
[43] Prieto, S., Rodríguez, J., Correa, C. and Soracipa, Y. (2014) Diagnosis of Cervical Cells Based on Fractal and Euclidian Geometrical Measurements: Intrinsic Geometric Cellular Organization. BMC Medical Physics, 14, 1-9.
[44] Rodríguez, J., Prieto, S., Catalina, C., Dominguez, D., Cardona, D.M. and Melo, M. (2015) Geometrical Nuclear Diagnosis and Total Paths of Cervical Cell Evolution from Normality to Cancer. Journal of Cancer Research and Therapeutics, 11, 98-104.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.