Analysis of antepartum cardiotocography based on S/k proportions and probability in 20 minutes / Análisis de la cardiotocografía anteparto mediante las relaciones S/k y la probabilidad en 20 minutos

Abstract Objectives: although mortality and perinatal asphyxia in newborns have been considerably reduced, there are still deficiencies in screening and diagnosis methods for intrapartum fetal well being that aim to detect its early alterations. Therefore, the purpose of this research was to apply a methodology based on probability and entropy and confirm its capacity to detect normal and abnormal fetal cardiac dynamics from 20-minute cardiotocographic tracings. Methods: 80 cardiotocographic tracings of pregnant women in the last trimester were collected, of which the minimum and maximum fetal heart rate were evaluated every 10 seconds, as well as its repetitions along with their probability and the diagnostic S/k ratio. Finally, the statistical analysis was carried out to establish the diagnostic capacity of the method concerning the clinical evaluation and interpretation of the cardiotocographic tracing, taken as the Gold Standard. Results: it was confirmed that S/k ratio values differentiated normal from abnormal fetal cardiac dynamics with sensitivity and specificity values of 100% and a Kappa coefficient of 1. Conclusion: the applicability of a diagnostic mathematical method of cardiotocography was confirmed, which suggests its implementation in the clinical context to detect alterations in fetal well-being in 20 minutes.

Resumo Objetivos: aunque se ha logrado reducir considerablemente la mortalidad y asfixia perinatal en neonatos, aún hay deficiencias en los métodos de tamizaje y diagnóstico del bienestar fetal intraparto que detecten sus alteraciones tempranas. Por lo anterior, el propósito de esta investigación fue aplicar una metodología basada en la probabilidad y la entropía y confirmar su capacidad para diagnosticar la dinámica cardíaca fetal normal de la anormal a partir de trazados cardiotocográficos de 20 minutos. Métodos: se recolectaron 80 trazados cardiotocográficos de gestantes en el último trimestre, de los cuales se evaluaron frecuencia cardíaca fetal mínima y máxima cada 10 segundos al igual que sus repeticiones, su probabilidad y la proporción S/k diagnóstica. Finalmente, se realizó un análisis estadístico para establecer la capacidad diagnóstica del método con respecto a la interpretación el trazado cardiotocográfico y la evaluación clínica, tomadas como Gold Standard. Resultados: se confirmó que los valores de la proporción S/k diferenciaron las dinámicas cardíacas fetales normales de las anormales con valores de sensibilidad y especificidad del 100% y un coeficiente Kappa de 1. Conclusión: se confirmó la aplicabilidad de un método matemático diagnóstico de la cardiotocografía, lo cual sugiere que su implementación en la clínica para detectar alteraciones del bienestar fetal en 20 minutos.

Geometrical nuclear diagnosis and total paths of cervical cell evolution from normality to cancer.

BACKGROUND: The diagnosis of cervix cytology has problems of inter-observer reproducibility. Methodologies based on fractal geometry objectively differentiated normal, low-grade squamous intraepithelial lesion (L-SIL) and high-grade squamous intraepithelial lesion (H-SIL) states. AIMS: The aim was to develop a mathematical-physical diagnosis and a theoretical generalization of the evolution paths of cervical cells from normal to carcinoma based on their occupation in the box-counting space. SUBJECTS AND METHODS: Overlaying a grid of 8 x 8 pixels, the a number of squares occupying the nucleus surface and cytoplasm of 5 normal cells, 5 ASCUS, 5 L-SIL and 5 H-SIL were evaluated, as well as the ratio C/N, establishing differences between states. Sensitivity, specificity, negative likelihood ratio, and Kappa coefficient over the gold standard were calculated. Also was developed a generalization of all possible paths from normality to carcinoma. RESULTS: The occupancy spaces of the nuclear surface allow differentiating normal L-SIL and H-SIL thus avoiding the indeterminacy of ASCUS cells. Compared to the Gold Standard, this method has sensitivity and specificity of 100%, negative likelihood ratio of 0, and Kappa coefficient of 1. 62,900 possible routes of evolution were determined between normal and H-SIL, states, based on the structural basis of the cells. CONCLUSIONS: it was obtained an objective and reproducible diagnostic methodology of the development of preneoplastic and neoplastic cervical cells for clinical application. Additionally were developed all possible paths of preneoplastic cellular alteration to carcinoma which facilitates the tracking of patients over time to clinical level, warning of alterations that lead to malignancy, based on the spatial occupation measurements of the nucleus in fractal space regardless of causes or risk factors.

[A method for forecasting the seasonal dynamic of malaria in the municipalities of Colombia]. / Método para la predicción de la dinámica temporal de la malaria en los municipios de Colombia.

OBJECTIVE: To develop a methodology for forecasting the seasonal dynamic of malaria outbreaks in the municipalities of Colombia. METHODS: Epidemiologic ranges were defined by multiples of 50 cases for the six municipalities with the highest incidence, 25 cases for the municipalities that ranked 10th and 11th by incidence, 10 for the municipality that ranked 193rd, and 5 for the municipality that ranked 402nd. The specific probability values for each epidemiologic range appearing in each municipality, as well as the S/k value--the ratio between entropy (S) and the Boltzmann constant (k)--were calculated for each three-week set, along with the differences in this ratio divided by the consecutive sets of weeks. These mathematical ratios were used to determine the values for forecasting the case dynamic, which were compared with the actual epidemiologic data from the period 2003-2007. RESULTS: The probability of the epidemiologic ranges appearing ranged from 0.019 and 1.00, while the differences in the S/k ratio between the sets of consecutive weeks ranged from 0.23 to 0.29. Three ratios were established to determine whether the dynamic corresponded to an outbreak. These ratios were corroborated with real epidemiological data from 810 Colombian municipalities. CONCLUSIONS: This methodology allows us to forecast the malaria case dynamic and outbreaks in the municipalities of Colombia and can be used in planning interventions and public health policies.

Método para la predicción de la dinámica temporal de la malaria en los municipios de Colombia / A method for forecasting the seasonal dynamic of malaria in the municipalities of Colombia

Objetivo: Desarrollar una metodología para la predicción de la dinámica temporal de los brotes de malaria en los municipios de Colombia. Métodos: Se definieron rangos epidemiológicos, definidos por los múltiplos de 50 casos para el grupo de seis municipios con mayor incidencia, de 25 casos para los municipios que ocuparon las posiciones 10 y 11 por su incidencia, de 10 para el municipio que ocupó la posición 193 y de 5 para el municipio que ocupó la posición 402. Se calcularon los valores de probabilidad específica de la aparición de cada rango epidemiológico en cada municipio, así como el valor de S/k -como la relación entre la entropía (S) y la constante de Boltzmann (k)- para cada grupo de tres semanas y las restas de esta relación entre los grupos consecutivos de semanas. Con estas relaciones matemáticas se establecieron los valores de predicción de la dinámica de casos y se compararon con los datos epidemiológicos reales en el período 2003-2007. Resultados: La probabilidad de aparición de los rangos epidemiológicos varió entre 0,019 y 1,00, mientras que las restas de la relación S/k de grupos de semanas consecutivas variaron entre -0,23 y 0,29. Se establecieron tres relaciones que determinan si la dinámica corresponde a un brote. Estas relaciones se confirmaron con los datos epidemiológicos reales de los 810 municipios colombianos. Conclusiones: Esta metodología permite predecir la dinámica de los casos y los brotes de malaria en los municipios de Colombia y se pueden aplicar en la planificación de intervenciones y políticas de salud pública.

Objective: To develop a methodology for forecasting the seasonal dynamic of malaria outbreaks in the municipalities of Colombia. Methods: Epidemiologic ranges were defined by multiples of 50 cases for the six municipalities with the highest incidence, 25 cases for the municipalities that ranked 10th and 11th by incidence, 10 for the municipality that ranked 193rd, and 5 for the municipality that ranked 402nd. The specific probability values for each epidemiologic range appearing in each municipality, as well as the S/k value-the ratio between entropy (S) and the Boltzmann constant (k)- were calculated for each three-week set, along with the differences in this ratio divided by the consecutive sets of weeks. These mathematical ratios were used to determine the values for forecasting the case dynamic, which were compared with the actual epidemiologic data from the period 2003-2007. Results: The probability of the epidemiologic ranges appearing ranged from 0.019 and 1.00, while the differences in the S/k ratio between the sets of consecutive weeks ranged from 0.23 to 0.29. Three ratios were established to determine whether the dynamic corresponded to an outbreak. These ratios were corroborated with real epidemiological data from 810 Colombian municipalities. Conclusions: This methodology allows us to forecast the malaria case dynamic and outbreaks in the municipalities of Colombia and can be used in planning interventions and public health policies.