Analyzing approaches to mathematic modeling of heart sounds

The article introduces the findings of the analysis of the existing approaches to the development of mathematical models of acoustic heart phenomena. The analysis of mathematical methods that can be used to model heart sounds has been performed with the use of reference signals from the 3M Open Library (Littmann Library) and a set of signals obtained by the authors during their previous scientific efforts. The analysis findings have allowed revealing the approaches and methods that are most suitable for developing the mathematical models of human phonocardiograms (normal and pathological) for further research efforts meant to develop methods to single out heart beats against the high level of interference and creating intervalograms to characterize the heart rate at the current moments of time. In addition to the generation of model phonocardiograms, the article reviews the methods to analyze model and real-life phonocardiograms with the assessment of an input from random and deterministic components.

Evaluación del comportamiento cardíaco mediante una metodología diagnóstica basada en sistemas dinámicos en 16 horas / Evaluation of the cardiac behaviour with a diagnostic methodology sustained in dynamical systems in 16 hours

Antecedentes: Con conceptos provenientes de la teoría de sistemas dinámicos y la geometría fractal, se ha logrado caracterizar el comportamiento de la dinámica cardíaca, dando resultados objetivos y estableciendo distinciones entre estados de normalidad y enfermedad. Objetivo: Aplicar una ley matemática exponencial de la dinámica cardíaca, inscrita en el contexto de los sistemas dinámicos y la geometría fractal, para evidenciar su utilidad diagnóstica en 16 horas. Materiales y métodos: Fueron empleados 200 Holters y registros electrocardiográficos continuos, entre normales y con diferentes alteraciones cardíacas. Se simuló una secuencia de frecuencias cardíacas en 16 y 21 horas, con la cual se construyó el atractor de cada dinámica. También se calculó la dimensión fractal y la ocupación de los atractores en el espacio fractal. Se estableció el diagnóstico físico-matemático en 16 y 21 horas y la subsecuente validación estadística. Resultados: Fueron obtenidos valores en la rejilla Kp entre 44 y 198 para estados patológicos y entre 221 y 377 para estados de normalidad en 16 horas, la sensibilidad y especificidad fue del 100% y el coeficiente Kappa de 1. Conclusión: Se logró diferenciar de manera adecuada estados normales de patológicos mediante la ley exponencial aplicada en registros de 16 horas

Background: With concepts derived from dynamical systems theory and fractal geometry, it has been possible to characterize the behavior of the cardiac dynamics, giving objective results and estabishing distinctions between states of normality and disease. Objective: To apply an exponential mathematical law of cardiac dynamics, inscribed in the context of dynamical systems and fractal geometry, to demonstrate its diagnostic utility in the context of a reduction in the evaluation time, originally of 21 hours. Materials and methods: There were used 200 Holters and cotinuous electrocardiographic records, between normal and with different cardiac alterations. A sequence of heart rates was simulated in 16 and 21 hours, with which the attractor of each dynamic was constructed. There were also calculated the fractal dimension and the occupation of the attractors in the fractal space. The physical-mathematical diagnosis was establishd at 16 and 21 hours, and the staqtistical validation was performed. Results: Values obtained in the Kp grid were between 44 y 198 for pathological sttes, and between 221 and 377 for normal states in 16 hours. The sensitivity and specificity was 100% and the Kappa coefficient was 1. Conclusion: It was possible to differentiate adequately normal states of pathological by means fo the exponential law applied in registers of 16 hours

Heart Rate and its Variability Assessed by Spectral Analysis in Elderly Subjects with Orthostatic Hypotension: A Case-Control Study / Frequência Cardíaca e sua Variabilidade por Meio da Análise Espectral em Idosos com Hipotensão Ortostática: Estudo de Caso-Controle

Abstract Background: The prevalence of orthostatic hypotension (OH) increases with age and is associated with changes in autonomic regulation of blood pressure (BP) and heart rate (HR). Objective: to assess HR and HR variability (HRV) in elderly subjects with OH and determine OH predictors. Methods: a total of 105 patients aged ≥ 60 years, 39 with OH (case group) and 66 without OH (control group) (age-matched) were studied. Patients underwent clinical assessment, electrocardiogram, biochemistry tests and Holter monitoring for spectral analysis of HRV (Fourier transform) in the supine and orthostatism positions to identify low frequency (LF) and high frequency (HF) components, as well as the LF/HF ratio. Results: median age was 73.0 years, 64 patients were women. In all participants, there was a reduction in HF (133.0 versus 76.0 ms2, p = 0.001) and increase in LF/HF (1.6 vs 2.1; p < 0.001) and no change in LF (233.0 versus 218.0 ms2, p = 0.080). Between-group comparisons revealed significant differences in the median values of HR in the supine position (62.0 vs. 69.0 bpm, p = 0.001) and LF in the supine position (157.0 in case group vs. 275.0 ms2 in the control group, p = 0.014). Spearman's correlation coefficient of 0.27 was found between the groups. Multivariate analysis revealed that HR in the supine position was an independent variable for OH (p = 0.001- 95%CI = -0.022 and -0.006). Using the operating characteristic curve, the best cutoff point was 61 bpm, with a sensitivity of 77.3% and specificity of 51.3%, positive predictive value of 61.3%, and negative predictive value 69.3%. Odds ratio was 3.23 for OH in patients with a HR lower than 61 bpm. Conclusions: lower LF and HR in the supine position were found in patients with OH, regardless of age and gender. The independent predictor for OH was HR in the supine position, with an odds ratio of 3.23 for values lower than 61 bpm.

Resumo Fundamento: A prevalência de hipotensão ortostática (HO) aumenta com a idade e está relacionada a alterações da regulação autonômica da pressão arterial (PA) e da frequência cardíaca (FC). Objetivos: Avaliar a FC e variabilidade da FC (VFC) em idosos com HO e verificar os preditores de HO. Métodos: foram avaliados 105 pacientes, com idade ≥ 60 anos, 39 com HO (grupo caso) e 66 sem HO (grupo controle), pareados por idade. Foram submetidos à avaliação clínica, eletrocardiograma, exames de bioquímica e monitoramento pelo Holter para análise espectral da VFC (transformação de Fourier), na posição supina e em ortostatismo, para detectar os componentes de baixa frequência (LF), de alta frequência (HF) e sua relação LF/HF. Resultados: A mediana de idade foi de 73,0 anos, 64 dos pacientes eram mulheres. Em toda a população, com a mudança de posição, houve redução do HF (133,0 versus 76,0 ms2, p = 0,001) e aumento da relação LF/HF (1,6vs2,1; p < 0,001), sem alteração quanto à mediana do componente LF (233,0 versus 218,0 ms2, p = 0,080). Quando comparado o grupo caso ao grupo controle, houve diferença quanto às medianas da FC nas posições supina (62,0 vs 69,0 bpm, p = 0,001) e do componente LF na posição supina (157,0 no grupo caso vs 275,0 ms2 no grupo controle, p = 0,014). Quanto ao gênero, o coeficiente de Spearman foi de 0,27 entre os grupos. Pela análise multivariada, a FC na posição supina foi a variável independente para a ocorrência de HO (p = 0,001- IC95% = -0,022 e -0,006). Pela curva de operação característica, o melhor ponto de corte para FC foi de 61 bpm, com sensibilidade de 77,3%, especificidade de 51,3%, valor preditivo positivo de 61,3%, e o valor preditivo negativo de 69,3%. A razão de chance foi de 3,23 para HO entre os pacientes com FC < 61 bpm. Conclusões: Houve menor valor do LF e da FC na posição supina entre os pacientes com HO, sem influência da idade e do gênero. O preditor independente para HO foi a FC na posição supina, a qual apresentou uma razão de chance de 3,23 se inferior a 61 bpm.

El análisis de la variabilidad de frecuencia cardiaca como una herramienta para evaluar los efectos de la meditación chi sobre la regulación cardiovascular / Heart Rate Variability analysis as a tool for assessing the effects of chi meditation on cardiovascular regulation

Approximately 30 indices have been proposed for assessing heart rate variability (HRV). Some are mathematically identical or very closely related to each other, and results can be interpreted from completely different viewpoints. Comparing various indices from a tachogram, and combining statistical significance with physiological plausibility could improve the result's interpretation. Using the KubiosHRV package, we studied the chi-meditation R-R database available at Physionet.org, addressing the following questions: i) Which HRV indices are the most suitable for describing meditation effects? ii) Are the effects of meditation beneficial, harmful or insubstantial? iii) Which are the most likely physiological events associated to meditation? It was concluded that power spectrum low frequency component (LF), LF/HF ratio, and nonlinear indices α 1 and α 2, recurrence rate and Shannon entropy performed the best (p<0.05). Observed changes suggest that they harmonize with changes observed in other health-pursuing circumstances as physical training, stress combating; whereas they are in the opposite tendency of changes associated to aging, heavy smoking, high blood glucose levels, autonomic heart denervation and congestive heart failure. Changes induced by chi meditation seem to be associated to increases in respiratory component around0.04 Hz, lower entropy and reduced long-term correlation with higher cardio vascular complexity(AU)

Alrededor de 30 índices han sido propuestos para evaluar la Variabilidad de la Frecuencia Cardiaca. Algunos de esos índices son matemáticamente idénticos o muy semejantes a otros y los resultados pueden ser interpretados desde puntos de vista completamente distintos. Al comparar varios índices estimados a partir de un tacograma y combinando la significación estadística con la plausibilidad biológica pudiera mejorarse la interpretación de los resultados. Utilizando el paquete de análisis KubiosHRV estudiamos la base de datos de señales R-R Chi meditation, disponible en el portal Physionet.org, centrándonos en las interrogantes siguientes: i) ¿cuáles índices son los más adecuados para describir los efectos de la meditación? ii) ¿son los efectos de la meditación beneficiosos, nocivos o insustanciales? iii) ¿cuáles son los eventos fisiológicos asociados a la meditación? Se concluye que el componente de baja frecuencia del espectro de potencia (LF), la relación LF/HF y los índices no lineales α 1 yα 2, la razón de recurrencia y la entropía de Shannon, fueron los indicadores más apropiados (p < 0.05). Los cambios observados parecen armonizar con cambios observados en otras acciones promotoras de salud como entrenamiento físico, combatir el estrés, mientras que exhiben una tendencia opuesta a los cambios asociados al envejecimiento, hábito de fumar, elevados niveles de glucosa, denervación cardiaca, e insuficiencia cardiaca congestiva. Los cambios inducidos por la meditación chi parecen estar asociados a incrementos en el componente respiratorio próximo a los 0.04 hertzios, a una menor entropía y una menor correlación a largo término combinadas a una mayor complejidad cardiovascular(AU)

Caracterización matemática de dinámicas cardiacas neonatales normales a partir de la teoría de la probabilidad / Mathematical Characterization of Normal Neonatal Cardiac Dynamics Based on Probability Theory

Introducción: la dinámica cardiaca se ha evaluado desde teorías físico' matemáticas como la probabilidad y los sistemas dinámicos, lo que ha permitido desarrollar diagnósticos y predicciones de aplicación clínica. Objetivo: medir la probabilidad de distribuciones de frecuencias cardiacas (FC) neonatales normales, para hacer una caracterización matemática, objetiva y reproducible. Metodología: se analizaron diez dinámicas normales mediante registros continuos y holters, tomando los máximos y mínimos de FC por hora durante 21 horas. Se generaron rangos de 5 latmin, y se estableció cuántas frecuencias pertenecen a cada rango. Se analizaron las distribuciones obtenidas en el espacio de probabilidades para las frecuencias cardiacas, en busca de características matemáticas de normalidad para la dinámica cardiaca neonatal. Resultados: las probabilidades de los rangos evaluados variaron entre 0,02272 y 0,2826-, y en tres de los rangos, todas las dinámicas presentaron probabilidad mínima o cero. Conclusiones: se desarrolló una caracterización general de la dinámica cardiaca neonatal normal, objetiva y reproducible.

Background: Cardiac dynamics have been evaluated from physicah mathematical theories like probability and dynamícal Systems, allowing to developing diagnosis and dinical application predictions. Objective: To measure the probability of normal neonatal heart rates distribution, for doing a mathematical characterization, objective and reproducible. Methods: It have been analyzed 10 normal dynamics through continuous records and holters, taking máximum and mínimum valúes of heart rates per hour during 21 hours. Ranges of 5 beats/min were generated; obtained distributions in probability space for heart rates were analyzed, to search normality mathematical characteristics for neonatal cardiac dynamics. Results: The probabilities of the evaluated ranges varied between 0.02272 and 0.2826; also, in three of the ranges, all the dynamics showed a minimum probability or zero. Condusions: A general characterization, objective and reproductible, of normal neonatal cardiac dynamics, was developed.

Heart Rate Variability Analysis Based on Photoplethysmographic Signals

An algorithm for extracting tachograms for Heart Rate Variability (HRV) analysis on the basis of Photoplethysmographic (PPG) signals (instead of electro cardiograms) has been proposed. The main feature of this proposal is to detect peaks from correlograms between a pattern waveform and a sliding time window in the PPG signal. Analysis was carried out with a set of two groups of patients (young and elderly).HRV variables were estimated using the publicly available Kubios HRV package. Results showed that both the sympathetic component of the autonomous nervous system (assessed by LF/HF) and the cardiovascular complexity (assessed by correlation dimension) are reduced with age. These results are supported by literature and may be taken as a support for the validity of the proposed algorithm. Since oximeters for getting PPG signals are affordable even in poor settings, this allows extending autonomic nervous system studies into remote areas of developing countries(AU)

Se propone un algoritmo para obtener tacogramas con la finalidad de realizar estudios de variabilidad de la frecuencia cardiaca, partiendo de registros de señales fotopletismográficas (PPG). La principal peculiaridad de esta propuesta lo es la detección de los picos en las ondas de la señal PPG a partir de un correlograma obtenido como una secuencia de correlaciones entre una onda patrón y una ventana deslizante de la señal PPG. Se realizó un análisis de variabilidad de frecuencia cardiaca sobre dos grupos de pacientes (jóvenes y de avanzada edad). Las variables de variabilidad de frecuencia cardiaca seleccionadas se obtuvieron a partir del programa Kubios HRV, de acceso público y gratuito. Los resultados mostraron que tanto el componente simpático del Sistema Nervioso Autónomo (evaluado a través de la variable LF/HF) como la complejidad cardiovascular (evaluada a través de la dimensión de correlación) disminuyeron con la edad. Estos resultados encuentran apoyo en datos de la literatura que apoyan así la validez del algoritmo propuesto. Por cuanto el oxímetro utilizado para obtener las señales PPG está al alcance de instituciones primarias de salud se hace posible de esta manera extender estudios del sistema nervioso autónomo hacia áreas remotas de países en desarrollo(AU)

On the use of Auto Regressive Dimensional Index for the evaluation of heart rate variability changes associated to yoga meditation

Changes induced by Yoga meditation upon the complexity of Heart Rate Variability were explored via the Auto-Regressive Dimensionality Index (ARDI). Data were downloaded from the Physionet.org website, and corresponded to HRV traces recorded before and during meditation with two Yoga techniques. Statistical support was found for the changes in ARDI being inversely dependent upon the basal ARDI levels before meditation (p<0.01). This suggests that Yoga meditation exerts a set-point mechanism at the level of overall complexity. This is in agreement with the documented effects of Yoga upon different components of the human body. At the same time, the possibility to regulate the level of complexity might be a novel mechanism of action for this ancient technique(AU)

Se exploraron los cambios inducidos por la meditación Yoga sobre la complejidad de la Variabilidad de la Frecuencia Cardiaca evaluada mediante el índice ARDI (Auto-Regressive Dimensionality Index). Los datos fueron obtenidos desde el sitio Physionet.org y se correspondían con trazos de Variabilidad de Frecuencia Cardiaca registrados antes y durante meditación con dos técnicas Yoga. Se obtuvo apoyo estadístico para la correlación negativa entre el cambio en ARDI y los niveles basales de ARDI antes de la meditación. Esto apoya la idea de que la práctica sostenida de Yoga ejerce un mecanismo regulador sobre la complejidad. Esto se corresponde con los efectos beneficiosos reportados por el Yoga sobre diferentes componentes del organismo. Al mismo tiempo, la posibilidad de regular los niveles de complejidad puede ser un mecanismo novedoso para esta técnica tan antigua(AU)