Application of the chaotic power law to the study of cardiac dynamics in patients with arrhythmias

Revista de la Facultad de Medicina

Cardona, Diana Margarita³  Pardo, Juan²  Prieto, Signed³  Victoria Rodríguez, Ligia³  Méndez, Laura³  Melo, Martha³  Correa, Catalina³  Rodríguez-Velásquez, Javier³  Domínguez, Darío³  Mendoza, Fernán¹ 

[1] Fundación Clínica Abood Shaio, Bogotá, Colombia;Hospital Universitario Mayor Mederi, Bogotá, Colombia;Universidad Militar Nueva Granada, Bogotá, Colombia

关键词: Fractals;    Nonlinear Dynamics;    Diagnosis;    Arrhythmias;    Cardiac;    (MeSH).;   

DOI  :  10.15446/revfacmed.v62n4.43444

学科分类：医学（综合）

来源: Universidad Nacional de Colombia * Facultad de Medicina

【 摘 要 】

Antecedentes. Se ha encontrado una ley exponencial para los sistemas dinámicos caóticos cardíacos que logra cuantificar las diferencias entre dinámicas cardíacas normales y aquellas con enfermedad aguda, así como la evolución entre estos estados. Objetivo. Confirmar la aplicabilidad clínica de la metodología desarrollada a partir de la ley matemática para la dinámica cardiaca en dinámicas con arritmia.Materiales y métodos. Se analizaron 60 holter, 10 correspondían a sujetos normales y 50 con diferentes tipos de arritmias. Para cada holter se construyó un atractor, se midió su dimensión fractal y ocupación espacial. Se aplicó la evaluación matemática para diferenciar dinámicas cardíacas normales de enfermas y en proceso de evolución. Se calculó la sensibilidad, especificidad y coeficiente Kappa. Resultados. La evaluación matemática diferenció los espacios de ocupación, normalidad, enfermedad aguda y evolución entre estos estados. Los valores de sensibilidad y especificidad fueron de 100% y el coeficiente Kappa fue de 1.Conclusiones. Se evidenció la aplicabilidad clínica de la metodología para casos con arritmias, siendo capaz de detectar cambios en la dinámica que no son clasificados como patológicos clínicamente. Palabras clave: Fractales; Dinámicas no Lineales; Diagnóstico; Arritmias Cardíacas (DeCS).Rodríguez-Velásquez J, Prieto S, Domínguez D, Correa C, Melo M, Pardo J, et al. Aplicación de la ley exponencial caótica al estudio de la dinámica cardiaca de pacientes con arritmias. Rev Fac Med. 2014;62(4):539-46. http://dx.doi.org/10.15446/revfacmed.v62n4.43444.Introduction From the temporary changes of the dynamic variables of a system, it is possible to determine its behavior. Predicting this behavior is the central problem of dynamical systems (1,2). In this theory, dynamical variables that are called attractors are put into graphic representations in the phase space (3). If they are completely irregular, they are chaotic attractors that can be studied with fractal geometry. Fractal geometry studies irregular objects of nature (4-6) rather than regular geometric objects that are studied by Euclidean geometry. There are several types of fractals. One of them, called the wild fractals, involves the super-positioning of its parts. To calculate its degree of irregularity —the fractal dimension— the box-counting method is generally used (7). This method allows us to observe the spatial distribution of a particular object in different scales through the use of overlapping grids of different sizes. According to the World Health Organization, cardiovascular diseases (CVD) represent 1.9% of yearly deaths in the Americas. CVDs are known as non-communicable diseases. Among these are included myocardial infarction and stroke. It is estimated that one in four people suffer from this disease category and that, by 2030, approximately 23.6 million people could die from this condition (8). One of the CVDs with the greatest incidence is arrhythmia (9), being associated with 50% of CVD deaths. According to medical literature, they can be divided into three categories: passive arrhythmias, automatic or ectopic arrhythmias, and re-entry arrhythmias (10).The most important diagnostic test for identifying significant —but of transitory, sudden, asymptomatic presentation— alterations in cardiac rhythm is the Holter test (11). This test allows for the visualization of the RR interval, with which interpretations regarding the variability of the heart rate (12), the appearance of non-mortal post-infarction arrhythmic events (13), and arrhythmias as a means of cardiovascular deterioration in the context of sepsis (14) can be made.A new interpretation of the concept of normality-disease has developed from the dynamical systems theory. In this new interpretation, an unhealthy dynamic would be either very regular or highly random (15-19) and a normal dynamic would be placed in between these two extremes. From this conception, measurements that seek to obtain better analyses of cardiac dynamics have been developed (20-23). However, it is still debatable which of these methods should be applied and under which conditions (24). In some cases, more than one study may be required to ascertain their applicability (25).The opportune diagnosis and treatment of arrhythmic cardiac conditions are of much relevance given their association with acute illnesses (26,26). The establishment of a measurement that allows for the quantification of the differences between arrhythmias that evolve into acute illnesses and arrhythmias that do not evolve into acute illnesses could help us to understand what type of intervention would be most appropriate. It could also help to give some patients priority care (28). New methodologies (29,30) have been developed from mathematical laws and theories that have allowed us to make objective quantifications and predictions regarding cardiac dynamics.An example of this is a methodology for the mathematical evaluation of the Holter test for which a power law (30) for chaotic cardiac dynamics was found. In this study, through the quantification of the occupancy space of attractors generated from the Holter values of the heart rates, normality was differentiated from acute illness and the evolution between these states.Based on the evaluation method found previously (30), this investigation sought to analyze cardiac dynamics associated with arrhythmias in order to test its evaluation capacity and its clinical applicability and as a diagnostic aid.Materials and me

【 授权许可】

Unknown