Journal of Medicne and Medical Sciences (ISSN: 2141-9477) Vol. 4(9), pp. 370-381, September 2013. DOI: http:/dx.doi.org/10.14303/jmms.2013.080. Copyright © 2013 International Research Journals

 

Full Length Research Paper

Mathematical-physical prediction of cardiac dynamics using the proportional entropy of dynamic systems

Javier Rodríguez1*, Signed Prieto2, Darío Domínguez3, Martha Melo4, Fernán Mendoza5, Catalina Correa6, Yolanda Soracipa7, Laura Pinilla8, Juan Pardo9, Nathalia Ramírez10

*1MD, Insight Group Director. Special Internship in Physical and Mathematical Theories Applied to Medicine. School of Medicine – Universidad Militar Nueva Granada. Research Center, Clínica del Country.

2Insight Group Researcher, Universidad Militar Nueva Granada. Research Center, Clínica del Country.

3FRACUMNG Group Researcher. Mathematics Department, School of Basic Sciences, Universidad Militar Nueva Granada.

4FRACUMNG Group Researcher. Mathematics Department, School of Basic Sciences, Universidad Militar Nueva Granada.

5Cardiologist. Program of Cardiology Director, Fundación Clínica Abood Shaio. Teacher of the Universidad del Bosque.

6Psy. Insight Group Researcher, Universidad Militar Nueva Granada. Research Center, Clínica del Country.

7Lic. in Physics. Insight Group Researcher, Universidad Militar Nueva Granada. Research Center, Clínica del Country.

8 MD. Insight Group Researcher. Research Center, Clínica del Country.

9 MD. Hospital Universitario Mayor Mederi.

10 Insight Group Researcher. Research Center, Clínica del Country.

*Corresponding Author`s E-mail: grupoinsight2025@yahoo.es; Cel: 313 4057252.

Abstract

 

Heart dynamic characterized within the context of dynamical systems theory allows differentiating and predicting normal cardiac states, different levels of disease, as well as evolution towards disease. The purpose of this study is to apply a previously developed methodology to 450 electrocardiographic registers to establish its effectiveness and comparing it with clinical conventional diagnosis. The methodology was applied to 50 normal Holters and 400 Holters with different pathologies. After masking the diagnostic conclusions, the minimum and maximum heart rate and the total number of beats each hour  were used to construct an attractor for each Holter in a phase space, by means of which the probability, entropy and their proportions were evaluated in ordered pairs of heart rate. Measures were compared with the physical and mathematical parameters of normality and disease previously settled down. Diagnostic conclusions and dates from medical history of each Holter were unmasked, to calculate sensibility, specificity and coefficient Kappa respect to Gold-standard. This methodology allowed mathematically differentiating the normal, acute and chronic disease dynamics and the evolution among these states. Sensibility and specificity of 100% were obtained and Kappa coefficient was equal to 1, demonstrating its diagnostic utility.

Keywords: Chaotic attractor, Holter, phase space, entropy, probability, cardiac dynamics.