Ley matemática exponencial aplicada a la evaluación de la dinámica cardiaca en 18 horas
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Fecha
2018
Autores
Correa Herrera, Catalina
Rodríguez Velásquez, Javier
Prieto Bohorquez, Signed Esperanza
Urina, Miguel
Rodríguez, Dharma
Echeverri-Ocampo, Isabel
Meléndez-Pertuz, Farid
Oyaga, Rafael
Guzmán, Esmeralda
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ECIMED
Resumen
Antecedentes: la teoría de los sistemas dinámicos estudia la evolución de los sistemas.
Mediante esta teoría y la geometría fractal se desarrolló una ley matemática de ayuda
diagnóstica a los sistemas dinámicos cardiacos, que permite diferenciar entre normalidad
y enfermedad, y la evolución entre los dos estados.
Objetivo: confirmar la capacidad diagnóstica de la ley matemática exponencial
desarrollada inicialmente para dinámicas cardiacas en 21 horas, para dinámicas evaluadas
en 18 horas.
Método: se tomaron 400 registros electrocardiográficos, 80 de dinámicas normales y 320
de dinámicas anormales. Se generó una sucesión pseudoaleatoria con el número de
latidos/hora y las frecuencias máximas y mínimas cada hora; luego, se construyó el
atractor de cada dinámica, para así calcular los espacios de ocupación y la dimensión
fractal. Finalmente, se estableció el diagnóstico físico-matemático en 18 y 21 horas y se
comparó con el diagnóstico clínico tomado como Gold Standard, obteniendo valores de
sensibilidad, especificidad y coeficiente Kappa.
Resultados: se encontraron valores de ocupación espacial en la rejilla Kp para normalidad
entre 236 y 368 y para estados patológicos entre 22 y 189, lo que permitió diferenciar
entre normalidad, enfermedad, y estados de evolución hacia la enfermedad en 18 horas.
Se obtuvieron valores de sensibilidad y especificidad del 100% y coeficiente Kappa igual
a 1.
Conclusión: la ley matemática permitió dictaminar diagnósticos reduciendo el tiempo
de evaluación a 18 horas confirmando así su aplicabilidad clínica.
Background: Dynamical systems theory aims to study the evolution of systems. With this theory and fractal geometry, it was developed a mathematical law of diagnostic utility in cardiac dynamical systems that may differentiate normality from disease and evolution between these two states. Objective: To confirm the diagnostic capacity of the exponential mathematical law initially developed for cardiac dynamics in 21 hours, for dynamics evaluated in 18 hours. Method: There were taken 400 electrocardiographic records, 80 from normal dynamics and 320 from abnormal dynamics. A pseudorandom sequence was generated with the number of beats per hour and the maximum and minimum frequencies each hour; then, the attractors were built for each dynamic, in order to calculate the space occupation and the fractal dimension. Finally the physical and mathematical diagnosis in 18 and 21 hours was established, and compared to clinical diagnosis taken as Gold Standard, obtaining values of sensitivity, specificity and Kappa coefficient. Results: There were found values for spatial occupation in the Kp grid between 236 and 368 for normal cases, and between 22 and 189 for pathological states, which allowed distinguish normality from disease and states of progression to disease in 18 hours. There were obtained values for sensitivity and specificity of 100% and a Kappa coefficient equal to 1. Conclusion: The mathematical law allowed to stablish diagnostics by reducing the evaluation time to 18 hours confirming its clinical applicability.
Background: Dynamical systems theory aims to study the evolution of systems. With this theory and fractal geometry, it was developed a mathematical law of diagnostic utility in cardiac dynamical systems that may differentiate normality from disease and evolution between these two states. Objective: To confirm the diagnostic capacity of the exponential mathematical law initially developed for cardiac dynamics in 21 hours, for dynamics evaluated in 18 hours. Method: There were taken 400 electrocardiographic records, 80 from normal dynamics and 320 from abnormal dynamics. A pseudorandom sequence was generated with the number of beats per hour and the maximum and minimum frequencies each hour; then, the attractors were built for each dynamic, in order to calculate the space occupation and the fractal dimension. Finally the physical and mathematical diagnosis in 18 and 21 hours was established, and compared to clinical diagnosis taken as Gold Standard, obtaining values of sensitivity, specificity and Kappa coefficient. Results: There were found values for spatial occupation in the Kp grid between 236 and 368 for normal cases, and between 22 and 189 for pathological states, which allowed distinguish normality from disease and states of progression to disease in 18 hours. There were obtained values for sensitivity and specificity of 100% and a Kappa coefficient equal to 1. Conclusion: The mathematical law allowed to stablish diagnostics by reducing the evaluation time to 18 hours confirming its clinical applicability.
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Palabras clave
Ley, Dinámica cardiaca, Atractor, Diagnóstico, Law, Cardiac dynamics, Attractor, Diagnosticen