Teoría de la complejidad y los sistemas de salud / Complexity theory and health systems

En la investigación en salud es todavía poco frecuente el uso de la Teoría de la Complejidad y de la Fractalidad (más aún en tópicos no relacionados directamente con la biología molecular o con la clínica). La complejidad nos propone complementar con propuestas desde nuevas perspectivas el pensamiento lineal y cuantitativo predominante todavía en la metodología de producción del conocimiento científico. El estudio de los sistemas de salud necesita un enfoque que se aparte de la linealidad, lo rígido y lo direccional, dado que los mismos son sistemas complejos en los que el todo es más que la simple suma de sus partes. La crisis global generada ante la pandemia por COVID-19 nos puso frente a la oportunidad (y a la obligación) de repensar tanto nuestra praxis cotidiana como nuestra forma de producir conocimiento (AU)

In health research, the use of the Complexity and Fractality Theory is still infrequent (even more so in topics not directly related to molecular or clinical biology). The complexity proposes us to complement with proposals from new perspectives the linear and quantitative thinking still predominant in the methodology of production of scientific knowledge. The study of health systems needs an approach that moves away from linearity, rigidity and direction, since they are complex systems in which the whole is more than the simple sum of its parts. The global crisis generated by the COVID-19 pandemic presented us with the opportunity (and the obligation) to rethink both our daily praxis and our way of producing knowledge (AU)

Fractal evaluation in retinographies of individuals with different grades of diabetic retinopathy / Avaliação fractal de retinografias de indivíduos com diferentes graus de retinopatia diabética

ABSTRACT Purpose To evaluate the retinal blood vascular network of the retinographies of patients with different grades of diabetic retinopathy. Methods Ninety Retinographies (MESSIDOR database) were used, with different grades of diabetic retinopathy divided into 4 groups: no retinopathy (n=23), grade one (n=20), grade two (n=20) and grade three (n=27) diabetic retinopathy. The grades of diabetic retinopathy were classified according to the number of microaneurysms, number of hemorrhages and the presence of neovascularization. The images were skeletonized and quantified by fractal methods: dimension of box-counting (Dbc) and information (Dinf). Results The means of Dbc values of groups were around 1.25, without statistically significant difference in the dimension values between groups for whole retina. There was also no statistical difference in Dinf values between groups, whose means ranged between 1.294 ± 0.013 (group of grade 1) and 1.3 ± 0.017 (group of grade 3). The retinographies were divided into regions of equal areas. The fractal values of some retinal regions showed statistical differences, but these differences were not enough to show the sensitivity of fractal methods in identifying diabetic retinopathy. Conclusion The fractal methods were not able to identify the different grades of diabetic retinopathy in retinographies.

RESUMO Objetivo Avaliar a rede vascular sanguínea da retina a partir de retinografias de pacientes com diferentes graus de retinopatia diabética. Métodos Foram utilizadas 90 retinografias (banco de dados MESSIDOR), com diferentes graus de retinopatia diabética divididas em quatro grupos: sem retinopatia (n=23), retinopatia diabética de grau um (n=20), grau dois (n=20) e grau três (n=27). Os graus de retinopatia foram classificados conforme o número de microaneurismas, número de hemorragias e presença de neovascularização. As imagens foram esqueletizadas e quantificadas pelos métodos fractais: dimensão da contagem de caixas e informação. Resultados As médias dos valores das dimensões de contagem de caixas para todos os grupos foram próximas a 1,25, sem diferença estatisticamente significativa nos valores das dimensões entre os grupos para retina inteira. Também não houve diferença estatística nos valores da dimensão de informação entre os grupos, cujas médias variaram entre 1,294 ± 0,013 (grupo do grau 1) e 1,3 ± 0,017 (grupo do grau 3). As imagens retinianas foram divididas em regiões de áreas iguais. Os valores fractais de algumas regiões retinais mostraram diferenças estatísticas, mas estas não foram suficientes para mostrar a sensibilidade dos métodos fractais na identificação da retinopatia diabética. Conclusão Os métodos fractais não foram capazes de identificar os diferentes graus de retinopatia diabética em retinografias.

Cortical bone modifications after radiotherapy: cortex porosity and osteonal changes evaluated over time

Abstract Aiming to evaluate cortical bone microarchitecture and osteonal morphology after irradiation, twelve male New Zealand rabbits were used. The animals were divided: control group (no radiation-NIr); and 3 irradiated groups, sacrificed after: 7 (Ir7d); 14 (Ir14d) and 21 (Ir21d) days. A single radiation dose of 30 Gy was used. Computed microtomography analyzed the cortical microarchitecture: cortical thickness (CtTh), bone volume (BV), total porosity (Ct.Po), intracortical porosity (CtPo-cl), channel/pore number (Po.N), fractal dimension (FD) and degree of anisotropy (Ct.DA). After scan, osteonal morphology was histologically assessed by means: area and perimeter of the osteons (O.Ar; O.p) and of the Haversian canals (C.Ar; C.p). Microtomographic analysis were performed by ANOVA, followed by Tukey and Dunnet tests. Osteon morphology analyses were performed by Kruskal-Wallis, and test Dunn's. Cortical thickness was significant difference (p<0.010) between the NIr and irradiated groups, with thicker cortex at Ir7d (1.15±0.09). The intracortical porosity revealed significant difference (p<0.001) between irradiated groups and NIr, with lower value for Ir7d (0.29±0.09). Bone volume was lower in Ir14d compared to control. Area and perimeter of the osteons were statistically different (p<0.0001) between NIr and Ir7d. Haversian canals also revealed lower values (p<0.0001) in Ir7d (80.57±9.3; 31.63±6.5) compared to NIr and irradiated groups. Cortical microarchitecture was affected by radiation, and the effects appear to be time-dependent, mostly regarding the osteons morphology at the initial days. Cortex structure in Ir21d revealed similarities to control suggesting that microarchitecture resembles normal condition after a period.

Resumo Com o objetivo de avaliar a microarquitetura óssea cortical e a morfologia dos osteons após irradiação, foram utilizados doze coelhos machos da Nova Zelândia. Os animais foram divididos: grupo controle (sem radiação-NIr); e 3 grupos irradiados, sacrificados após: 7 (Ir7d); 14 (Ir14d) e 21 (Ir21d) dias. Foi utilizada uma dose única de radiação de 30 Gy. A microtomografia computadorizada analisou a microarquitetura cortical: espessura cortical (CtTh), volume ósseo (BV), porosidade total (Ct.Po), porosidade intracortical (CtPo-cl), número de canal/ poro (Po.N), dimensão fractal (DF) e grau de anisotropia (Ct.DA). Após a varredura, a morfologia dos osteosn foi avaliada histologicamente por meio de: Área e perímetro do osteon (O.Ar; O.p) e dos canais de Havers (C.Ar; C.p). A análise microtomográfica foi realizada por ANOVA, seguida pelos testes de Tukey e Dunnet. As análises morfológicas do osteon foram realizadas por Kruskal-Wallis e testadas por Dunn. A espessura cortical foi diferente (p<0,010) entre os grupos controle e irradiados, com córtex mais espesso no Ir7d (1,15±0,09). A porosidade intracortical revelou diferenças significativas (p<0,001) entre os grupos irradiados e o controle, com menor valor para Ir7d (0,29±0,09). O volume ósseo foi menor no Ir14d em relação ao controle. Área e perímetro do osteon foi diferente (p<0,0001) entre o controle e Ir7d. Os canais haversianos também revelaram valores mais baixos (p<0,0001) em Ir7d (80.57±9.3; 31.63±6.5) em relação ao controle e demais grupos irradiados. A microarquitetura cortical é afetada pela radiação e os efeitos parecem ser dependentes do tempo, principalmente em relação à morfologia dos osteons nos dias iniciais. A estrutura cortical em Ir21d revelou semelhanças com o controle, sugerindo que a microarquitetura se assemelha à condição normal após um período.

Fractal features of soil texture and physical attributes in indian dark earth under different uses in Western Amazon / Características fractais da textura e atributos físicos do solo em áreas com terra preta de índio sob diferentes usos na Amazônia Ocidental

Studying particle size distribution is important to understand soil structure and formation processes. This research aimed to assess the fractal dimension of soil texture in Indian Dark Earth (IDE) areas in southern Amazonas state under different land uses, as follows: two areas in the municipality of Apuí, one growing cocoa and the other coffee; a grassland area in the municipality of Manicoré; and a forest area in the municipality of Novo Aripuanã. A sampling grid containing 88 collection points (intersecting points on the grid) was established in each area, measuring 80 x 42 m for the cocoa and coffee-growing sites, and 80 x 56 m and 60 x 42 m for the grassland and forest areas, respectively. Soil samples were collected in soil core and as clumps at a depth of 0.0-0.20m to determine the structural physical properties and texture of the soil. The following physical attributes were assessed: texture (PSD), bulk density (BD), macroporosity (Macro), microporosity (Micro), total porosity (TP) and aggregate stability (GMD and WMD). The fractal dimension (D) of the soil texture was determined, followed by analysis of variance and comparison of the means using Tukey's test (p≤0.05). Pearson's correlation was applied to assess the correlation between variables. There was a significant difference between the IDEs studied, with a higher D value in the cocoa-growing area in relation to the other sites. Additionally, the larger the clay fraction, the higher the D value. Fractal dimension (D) showed a positive correlation with sand, clay, BD, Macro, GMD and WMD, and a negative correlation with silt, micro, TP. Based on the D values obtained, the ADE cultivated with cocoa showed superior quality in relation to the other areas studied.KEYWORDS: Fractal dimension. Soil physics. Soil use. INTRODUCTION Applications of fractal geometry in soil science have shown that soil exhibits fractal characteristics, being a porous medium having different particle compositions, with irregular shape and self-similar structure (TYLER; WHEATCRAFT, 1989; KRAVCHENKO; ZHANG, 1998). Fractal geometry, proposed and established by Mandelbrot (1982), is a method for describing systems with non-characteristic scales and self-similarity. In recent years, this theory has been used to quantitatively describe the particle size distribution of soil, attracting the interest of pedologists worldwide (DENG et al., 2017). Particle size distribution is one of the most important physical characteristics of soil because of its significant influence on water flow and soil erosion (XU; LI; LI, 2013). In this respect, broad and precise knowledge of particle size distribution is vital to understanding soil structures and formation, since it is closely related to soil erosion, organic matter content and moisture content (DU et al., 2017). Deng et al. (2017) studied the fractal features of soil particle size distribution and found an association between fractal dimensions and the physical and chemical properties of the soil analyzed, indicating that the lower the fractal dimension, the worse the soil physical and chemical properties. Recently, the fractal method was applied to estimate soil structure and proved to be an efficient tool in analyzing soil Received: 01/04/2019 Accepted: 30/01/2020

Estudar a distribuição do tamanho das partículas é importante para entender a estrutura do solo e os processos de formação. Esta pesquisa teve como objetivo avaliar a dimensão fractal da textura do solo em áreas de Terra Preta de Índio (TPI) no sul do Estado do Amazonas sob diferentes usos da terra: duas áreas no município de Apuí, uma com cultivo de cacau e outra de café; uma área de pastagem no município de Manicoré; e uma área florestal no município de Novo Aripuanã. Uma malha de amostragem contendo 88 pontos de coleta (pontos de interseção na grade) foi estabelecida em cada área, medindo 80 x 42 m para as áreas de cacau e café, e 80 x 56 m e 60 x 42 m para as áreas de pastagem e floresta, respectivamente. Amostras de solo foram coletadas em torrões a uma profundidade de 0,0-0,20 m para determinar as propriedades físicas estruturais e a textura do solo. Os seguintes atributos físicos foram avaliados: textura, densidade do solo (DS), macroporosidade (Macro), microporosidade (Micro), porosidade total (PT) e estabilidade de agregados (DMG e DMP). Determinou-se a dimensão fractal da textura do solo (D), seguida da análise de variância e comparação das médias pelo teste de Tukey (p≤0,05). A correlação de Pearson foi aplicada para avaliar a correlação entre as variáveis. Houve uma diferença significativa entre as TPIs estudadas, com um maior valor D na área de cultivo de cacau em relação aos outros locais. Além disso, quanto maior a fração argila, maior o valor de D. A dimensão fractal (D) apresentou correlação positiva com areia, argila, DS, Macro, DMG e DMP, e correlação negativa com silte, micro, PT. Com base nos valores de D obtidos, as TPIs cultivadas com cacau apresentaram qualidade superior em relação às demais áreas estudadas.PALAVRAS-CHAVES: Dimensão Fractal. Física do solo. Uso do solo. REFERENCES ALVARENGA, R. C.; FERNANDES, B.; SILVA, T. C. A.; RESENDE, M. Estabilidade de agregados de um Latossolo Roxo sob diferentes métodos de preparo do solo e de manejo da palha do milho. Revista Brasileira de Ciência do Solo, Viçosa, v. 10, n. 2, p. 273-277, 1986.

Comportamiento estocástico de la COVID-19 en la República Bolivariana de Venezuela. ¿Persistencia o antipersistencia en los contagios? / Stochastic behavior of covid-19 in the Bolivarian Republic of Venezuela: persistence or antipersistence in infections?

La novedosa pandemia por coronavirus, etiquetada por la Organización Mundial de la Salud OMS, 2020) como la covid-19, se reportó por primera vez en Wuhan, China, el 31 de diciembre de 2019 y a la fecha, según estimaciones de la misma OMS (2020), en la medida en que se ha extendido a nivel planetario, ha infectado a más de 9,2 millones de personas, de las cuales se reportan más de 500.000 fallecidos y 5.2 millones de pacientes recuperados. En este estudio, aplicaremos el exponente de Hurst (1951) asociado con la estadística fractal para simular la propagación de la covid-19, considerando series temporales de fluctuaciones de nuevos casos diarios de la enfermedad, disponibles a través de un sitio web de referencia de la República Bolivariana de Venezuela, como lo es el Observatorio Nacional de Ciencia, Tecnología e Innovación (ONCTI). Se parte de la hipótesis de que la propagación de la covid-19, puede analizarse en función de las fluctuaciones del crecimiento de nuevos casos diarios de contagio. Para ello, se empleó un método de rango reescalado R/S que permitió calcular el Exponente de Hurst, parámetro estocástico cuyo valor permitió inferir sobre la presencia de correlaciones de largo alcance en la transmisión del virus entre la población. Estudiaremos los efectos de correlación en la propagación de COVID-19 en Venezuela mediante el análisis de las series temporales de nuevos casos después del decreto de Alerta dictado por el Ejecutivo Nacional que convocó a la ciudadanía a "quedarse en casa" mediante una cuarentena social obligatoria. Simularemos el comportamiento a mediano plazo (180 días) considerando las fluctuaciones de los nuevos casos de contagio diarios sobre la base de dos factores: los casos de contagio importados y los contagios comunitarios. En consecuencia, inicialmente examinaremos el origen de correlaciones con grandes fluctuaciones, y posteriormente analizaremos en base a las series de tiempo de nuevos casos diarios de la covid-19 en Venezuela, para luego establecer las correlaciones de largo alcance e inferir sobre la posible la persistencia o antipersistencia de la misma(AU)

The novel coronavirus pandemic, labeled by the World Health Organization (WHO) as Covid-19, was first reported in Wuhan, China, on December 31, 2019. To date, according to the WHO's estimates, it has infected more than 9.2 million people, of whom more than 500,000 are reported dead, and 5.2 million patients have recovered. To deepen in its study, we apply the Hurst exponent, associated with fractal statistics to simulate the spread of Covid-19, considering time series of fluctuations of new daily cases, which are available in a site reference website of the Bolivarian Republic of Venezuela, such as the National Observatory for Science, Technology, and Innovation (ONCTI). This work starts from the hypothesis that the spread of Covid-19 can be analyzed based on the fluctuations in the increase of new daily cases. For this, an R / S rescaled range method was used that allowed calculating the Hurst Exponent, a stochastic parameter whose value allowed inferring the presence of long-range correlations in the virus transmission among the population. We will study the correlation effects in the spread of COVID-19 in Venezuela by analyzing the time series of new cases after the alert decree issued by the Executive branch, which called on citizens to "stay at home" through a mandatory social quarantine. Consequently, initially, we will examine the origin of correlations with large fluctuations, followed by an analysis based on the time series of new daily cases of Covid-19 in Venezuela, in order to establish the long-range correlations and infer about the possible persistence or anti persistence of it(AU)

Caracterización geométrica euclidiana y fractal de células falciformes / Geometric euclidean and fractal characterization of sickle cells

Resumen Introducción. Estudios recientes proponen nuevas metodologías que permiten hacer el reconocimiento de las diferentes alteraciones en la forma de los glóbulos rojos, estableciendo patrones de comparación matemáticos y geométricos en el contexto de la geometría fractal y euclidiana. Objetivo. Caracterizar la forma de las células falciformes mediante una metodología diseñada en el contexto de la geometría fractal y euclidiana. Metodología. Se realizó un reconocimiento de 30 imágenes de células falciformes en frotis de sangre periférica. Las células falciformes fueron delineadas y se superpusieron dos rejillas Kp de 5 x 5 píxeles y Kg de 10 x 10 píxeles, para calcular el espacio ocupado por estas células y la dimensión fractal mediante el método de Box Counting. Resultados. Los espacios ocupados por las células falciformes variaron con la superposición de la rejilla de Kp entre 36 y 56; la superficie de células falciformes varió entre 969 y 1872 píxeles y las proporciones entre la superficie y los valores de la rejilla Kp variaron entre 23.1 y 39.6. Conclusiones. El presente estudio revela la posibilidad de hacer caracterizaciones más precisas en las células falciformes, a partir de los espacios de ocupación de estas, al superponer la rejilla Kp y las proporciones entre la superficie, y no mediante los valores de la dimensión fractal, contribuyendo de esta manera en el diseño de metodologías que mejoren el reconocimiento de este tipo de células.

Abstract Introduction. Recent studies propose new methodologies that allow the recognition of the different alterations in the shape of red blood cells, establishing mathematical and geometric comparison patterns in the context of fractal and Euclidean geometry. Objective. To characterize the shape of sickle cells using a methodology designed in the context of fractal and Euclidean geometry. Methodology. 30 images of sickle cells were obtained in peripheral blood smears. The sickle cells were delineated and two grids were superimposed (Kp of 5 x 5 pixels and Kg of 10 x 10 pixels), to calculate the space occupied by these cells and the fractal dimension by means of the Box Counting method. Results. the spaces occupied by the sickle cells varied with the superposition of the Kp grid between 36 and 56; the surface of sickle cells varied between 969 and 1872 pixels, and the proportions between the surface and the values of the Kp grid varied between 23.1 and 39.6. Conclusions. The present study reveals the possibility of making more precise characterizations in sickle cells, from the occupation spaces of the sickle cell by superposing the Kp grid and the proportions between the surface and the Kp grid, and not by the values of the fractal dimension, contributing in this way in the design of methodologies that improve the recognition of this type of cells.

Aplicación de la ley de Zipf-Mandelbrot al diagnóstico de la dinámica cardíaca normal y aguda / Application of the law of Zipf-Mandelbrot to the diagnosis of normal and acute cardiac dynamics

Introducción: Es conocida la capacidad de los fractales estadísticos en la evaluación de la complejidad de diferentes sistemas cuya dinámica pueda ser evaluada a partir de las frecuencias de una variable; para esto, se utiliza la medida de la dimensión fractal estadística, la cual puede ser calculada con la ley de Zipf-Mandelbrot. Esta ley matemática ha sido aplicada en cardiología para evaluar el grado de complejidad de la dinámica cardíaca. En el presente trabajo se aplicó la ley de Zipf-Mandelbrot junto con la metodología diagnóstica desarrollada previamente para evaluar dinámicas cardíacas normales y con enfermedad aguda. Materiales y métodos: Se tomaron 15 registros Holter; 10 con diagnóstico normal y 5 con patologías agudas de pacientes de la Unidad de Cuidados Intensivos. Se organizaron jerárquicamente las frecuencias de aparición de las frecuencias cardíacas de cada dinámica en rangos de a 15 lat/min, en busca del comportamiento hiperbólico necesario para la aplicación de la ley de Zipf-Mandelbrot. Posteriormente se realizó una linealización y se obtuvo la dimensión fractal estadística para cada dinámica. Resultados: Los valores de la dimensión fractal estadística para una dinámica cardíaca aguda variaron entre 0.4925 y 0.6061, mientras que para una dinámica normal variaron entre 0.7134 y 0.9749, evidenciando la diferenciación entre ambos grupos. Conclusiones: El comportamiento fractal estadístico de la dinámica cardíaca fue corroborado, de igual forma la pérdida de complejidad para las dinámicas agudas respecto a las dinámicas normales

Background: The capacity of statistical fractals in the evaluation of the complexity of different systems whose dynamics can be evaluated from the frequencies of a variable is known. This is why the measure of the statistical fractal dimension is used, which can be calculated with the Zipf-Mandelbrot law, this mathematical law has been applied in cardiology evaluating the degree of complexity of cardiac dynamics. In the present work, the Zipf-Mandelbrot law was applied together with the diagnostic methodology previously developed to evaluate normal cardiac dynamics and acute disease. Material and methods: 15 Holter records were taken; 10 with normal diagnosis and 5 with acute pathologies of patients of the Intensive Care Unit. The frequencies of occurrence of the heart frequencies of each dynamics were organized hierarchically in ranges of 15 lat/min, in search of the hyperbolic behavior required for the application of the law of Zipf-Mandelbrot. Subsequently, a linearization was performed and the statistical fractal dimension was obtained for each dynamics. Results: The values of the statistical fractal dimension for acute cardiac dynamics varied between 0.4925 and 0.6061, whereas for normal dynamics they varied between 0.7134 and 0.9749, evidencing the differentiation between both groups. Conclusions: The statistical fractal behavior of the cardiac dynamics was corroborated, as well as the loss of complexity for the acute dynamics with respect to the normal dynamics

Análise fractal do padrão espacial de plantas em pastagem / Fractal analysis of plant spatial patterns in natural grasslands under different managements

Avaliou-se o uso da análise fractal como ferramenta na determinação de padrões na escala de pastejo em pastagens naturais submetidas a diferentes manejos. Os tratamentos testados em Santa Maria foram: pastejo com queima, pastejo sem queima, exclusão com queima, exclusão sem queima. Em Bagé, os tratamentos avaliados foram: pastagem natural e pastagem natural com introdução de azevém, trevo-branco e cornichão. A caracterização da composição florística da pastagem foi realizada pelo método Botanal. A diversidade da pastagem foi calculada pelos índices de Shannon (H') e equitabilidade. A informação da dimensão fractal foi calculada pela regressão entre H'(ε) e o logaritmo natural de ε, sendo a inclinação da linha a informação da dimensão fractal. Os índices de Shannon e equitabilidade demonstraram dependência em relação à área amostral, onde a maior diversidade florística e a homogeneidade da frequência de distribuição de plantas entre espécies foram observadas no intervalo amostral de 0,87 e 1,03m2. A dimensão fractal pode ser uma ferramenta na determinação de padrões na comunidade vegetal na escala reduzida de pastejo. A limitação do emprego dessa técnica para escalas reduzidas é a necessidade de um número maior de repetições.(AU)

The use of fractal analysis was evaluated as a tool in the determination of grazing patterns in natural grasslands submitted to different managements. The treatments tested in Santa Maria were grazing with burning, grazing without burning, exclusion with burning and exclusion without burning. In Bagé, the evaluated treatments were natural pasture and introduction of ryegrass, white clover and birdsfoot trefoil in a natural grassland. The characterization of the floristic composition of the pasture was performed by the BOTANAL method. The pasture diversity was calculated by Shannon (H') and Evenness (J) indexes. The fractal dimension information was calculated by regression between H'(ε) and ε natural algorithm, with the line's slope being the fractal dimension information. Shannon and Evenness indexes showed dependence on the sample area, where the highest floristic diversity and homogeneity of the distribution frequency of plants between species were observed in the sample range of 0.87 to 1.03m2. The fractal dimension can be a tool in determining patterns in the plant community on the reduced grazing scale. The limitation of the use of this technique for reduced scales is the need for a greater number of repetitions.(AU)

Sistemas dinámicos y teoría de la probabilidad aplicados al diagnóstico de la dinámica cardiaca en dieciséis horas / Dynamic systems and probability theory applied to the diagnosis of cardiac dynamics in 16 hours

Resumen Introducción: se han establecido diagnósticos cuantitativos de los sistemas cardiacos, partiendo de teorías como los sistemas dinámicos, la geometría fractal y la teoría de probabilidad. Objetivo: evaluar la dinámica cardiaca con base en una metodología fundamentada en la teoría de probabilidad y los sistemas dinámicos, en dieciséis horas. Metodología: a partir de ochenta registros electrocardiográficos de dinámicas cardiacas, diez normales y setenta con enfermedad, se tomaron los valores máximos y mínimos de la frecuencia cardiaca y el número de latidos/hora durante cada hora, con los cuales se construyó el atractor. Posteriormente, se calculó la dimensión fractal por el método de box counting, los espacios de ocupación y la probabilidad de los espacios de ocupación del atractor. Se determinó el diagnóstico matemático y se hizo una validación estadística respecto al diagnóstico convencional, tomado como estándar de oro. Resultados: se evidenció que la probabilidad de ocupación espacial de los atractores de dinámicas patológicas estuvo entre 0,029 y 0,144 y para dinámicas en estado de normalidad entre 0,164 y 0,329. Se hallaron valores de sensibilidad, especificidad, valor predictivo positivo y negativo de 100% y coeficiente kappa de 1. Conclusiones: se pudo confirmar la capacidad diagnóstica y predictiva de la metodología para diferenciar estados normales de patológicos a nivel clínico.

Abstract Introduction: Quantitative diagnostics of cardiac systems have been established using theories such as, dynamic systems, fractal geometry, and probability theory. Objective: To evaluate cardiac dynamics using a methodology based on probability theory and dynamic systems in sixteen hours. Methods: Using a total of 80 cardiac dynamic electrocardiograph traces (10 normal and 70 with disease), a record was made of the maximum and minimum heart rate values, as well as the number of heart beats/hour during each hour. These values were used to construct the attractor. The fractal dimension was then calculated using the "box counting" method, the spatial occupation, and the probability of spatial occupation by the attractor. The mathematic diagnosis was determined, and a statistical validation was made as regards the conventional diagnosis, which was taken as the reference standard. Results: It was shown that the probability of spatial occupation of the pathological attractor dynamics was between 0.29 and 0.144, and for dynamics in the normal state it was between 0.164 and 0.329. The sensitivity, specificity, positive and negative predictive values were 100%, and the kappa coefficient was 1. Conclusions: The diagnostic and predictive capacity of the methodology to differentiate normal from disease states at clinical level was demonstrated.

Evaluation by fractal dimension of muscle regeneration after photobiomodulation / Avaliação por meio da dimensão fractal da regeneração muscular após fotobiomodulação

Abstract Introduction: Many treatment modalities are used for muscle tissue recovery. Photobiomodulation is a modality that can be employed to improve the quality of tissue repair. The use of fractal dimension (FD) is an innovative methodology in the quantitative evaluation of treatment efficacy. Objective: Use FD as a quantitative analysis method to evaluate the effect of photobiomodulation of 904 nanometers (nm) in the initial phase of the muscle regeneration process. Method: Thirty male Wistar rats were divided into three groups: Control Group (CG), Injured and Untreated Group (IUT), and Injured and Treated Group (IT). Muscle injury was induced by cryoinjury in the central region of the anterior tibial (AT) belly of the left posterior limb. This was performed by an iron rod that was previously immersed in liquid nitrogen. Applications started 24 hours after the injury and occurred daily for five days. They were performed at two points in the lesion area. The rats were euthanized on the seventh day. The AT muscles were removed and frozen in liquid nitrogen. Then, the histological sections were stained using the Hematoxylin-Eosin (HE) technique and submitted to FD analysis performed by the box-counting method using ImageJ software. The Kolmogorov-Smirnov test was used for data normality, and the Kruskall-Wallis test and Dunn's post-test were used for group comparison (p<0.05%). Results: Differences between IT and IUT groups were statistically significant, and it was possible to observe the reduction of fractability with p=0.0034. Conclusion: FD is a useful tool for the analysis of skeletal muscle disorganization in the initial phase of regeneration and confirms the potentially beneficial effects of photobiomodulation to this process.

Resumo Introdução: Diversas modalidades de tratamento são utilizadas para recuperação do tecido muscular, dentre elas a fotobiomodulação pode ser empregada para melhorar a qualidade da regeneração e a dimensão fractal se apresenta como uma metodologia inovadora na avaliação quantitativa da eficácia do tratamento. Objetivo: Utilizar a dimensão fractal como método de análise quantitativa do efeito do Laser de Arseneto de Gálio (AsGa) na fase inicial do processo de regeneração muscular. Método: Foram utilizados trinta ratos Wistar, machos divididos em: Grupo Controle (CT), Grupo lesado e não tratado (LNT) e Grupo Lesado e tratado (LT). A lesão muscular foi induzida por criolesão na região central do ventre do músculo tibial anterior (TA) do membro posterior esquerdo, por meio de uma haste de ferro previamente imersa em nitrogênio líquido. As aplicações foram iniciadas 24 horas após a lesão, diariamente, durante cinco dias, em dois pontos na área da lesão. No sétimo dia os animais foram eutanasiados; o músculo TA retirado, congelado em nitrogênio líquido e os cortes histológicos corados com a técnica de Hematoxilina-Eosina para serem então submetidos à análise de dimensão fractal realizada pelo método boxcounting através do software Image J. Para a normalidade dos dados utilizou-se Kolmogorov Smirnov, para as comparações teste de Kruskall-Wallis com pós teste de Dunn (p<0,05%). Resultados: A comparação entre LT e LNT foi estatisticamente significativa, sendo possível observar a redução da fractabilidade com p=0,0034. Conclusão: A dimensão fractal é uma ferramenta útil para análise da desorganização músculo esquelética na fase inicial da regeneração e mostra o potencial efeito benéfico da fotobiomodulação nesse processo.

Evaluación de la Saturación Venosa de Oxígeno (SvO2) desde la teoría de los sistemas dinámicos / Evaluation of SvO2 from the Theory of Dynamic Systems

Introducción: La evolución de un sistema dinámico se puede caracterizar a partir de la construcción de atractores caóticos. Objetivo: Desarrollar una metodología de evaluación de la saturación venosa de oxígeno, fundamentada en los sistemas dinámicos, para pacientes en Unidad de Cuidados Intensivos. Metodología: Se seleccionaron 10 pacientes con diferentes patologías de la Unidad de Cuidados Intensivos Postquirúrgicos, y registró la saturación venosa de oxígeno durante su tiempo de estancia. Con base en estos valores se construyeron atractores caóticos en el mapa de retardo y se evaluaron los valores mínimos y máximos ocupados por el atractor. Resultados: Se halló que la saturación venosa de oxígeno tiene un comportamiento caótico; los valores máximos y mínimos de los atractores en el mapa de retardo variaron entre 22,10 mmHg y 93,70 mmHg. Conclusiones: Se plantea una nueva metodología capaz de caracterizar el comportamiento de la variable monitorizada para la evaluación del paciente crítico(AU)

Introduction: The evolution of a dynamic system can be characterized from the construction of chaotic attractors. Objective: To develop a methodology based on dynamic systems, for the evaluation of venous oxygen saturation of patients in the Intensive Care Unit. Methodology: 10 patients with different pathologies of the Post-surgical Intensive Care Unit were selected, and recorded venous oxygen saturation during their time of stay. Based on these values, chaotic attractors were constructed on the delay map and the minimum and maximum values occupied by the attractor were evaluated. Results: It was found that venous oxygen saturation has a chaotic behavior; the maximum and minimum values of the attractors on the delay map varied between 22.10 mmHg and 93.70 mmHg. Conclusions: A new methodology is proposed capable of characterizing the behavior of this monitored variable for the evaluation of the critical patient(AU)

Means of communication for visually impaired people. Fractalyphlotechnologies of data communication

This article describes technical means of data communication for blind and visually impaired people. Radically new method of haptic and fingerspelling data coding is proposed based on fractal self-similarity of binary code. It would be possible to develop numerous typhlo-appliances at reasonable and low price, thus simplifying teaching Braille system both in conventional, manual, and computer variants. Coding of typhlodata on the basis of fractal self-similarity is referred to as fractal Braille. On the basis of fractal self-similarity of binary code, the concept of haptic and fingerspelling alphabet has been developed which combines essentially different methods of data coding in a single morphological base.

Fractalidad en un patrón de cristalización de moco cervical humano obtenido en período periovulatorio / Fractality in a pattern of crystallization of human cervical mucus obtained at periovulatory period

Introducción: La secreción cervical cumple una función importante en el proceso reproductivo humano y algunas sus características (e.g., el cristalizar) cambian dependiendo de las variaciones en los niveles de hormonas esteroidales sexuales. Objetivo: Reportar la fractalidad observada en un patrón de cristalización de moco cervical humano. Métodos: El moco fue obtenido de una paciente en período periovulatorio. La imagen de un patrón cristalino de moco cervical fue transformada a blanco y negro y analizada mediante Fractalyse v. 2.4, el cual determina la dimensión fractal (DF) para cada imagen estudiada. Se analizaron tres zonas para la imagen seleccionada. Resultados: Se encontró, para la Zona 1, DF (± desviación estándar) = 1,36 ± 0,02 (r² = 0,9985); para la Zona 2, DF = 1,35 ± 0,02 (r² = 0,9979); y para la Zona 3, DF = 1,36 ± 0,03 (r² = 0,9958). Las DF encontradas para las zonas estudiadas fueron estadísticamente iguales entre sí. Conclusiones: El moco cervical humano en período periovulatorio puede seguir un patrón de cristalización tipo fractal, especialmente en lo referente a la semejanza de sus componentes estructurales (criterio de autosimilitud) (AU)

Introduction: Cervical secretion plays an important role in the human reproductive process and its characteristics (e.g., crystallization) change depending on variations in the levels of sex steroid hormones. Objective: The purpose of this brief communication is to report the fractality observed in a crystallization pattern of human cervical mucus. Methods: Mucus samples were obtained from a patient in the periovulatory period and an image of the crystalline pattern of cervical mucus was transformed to black and white and analysed by Fractalyse v. 2.4, which determines the fractal dimension (FD) for each studied image. Three zones were analysed for the selected image. Results: It was found that, for Zone 1, FD (± standard deviation) = 1.36 ± 0.02 (r² = 0.9985); for Zone 2, FD = 1.35 ± 0.02 (r² = 0.9979); and for Zone 3, FD = 1.36 ± 0.03 (r² = 0.9958). Zones studied were statistically equal to each other regarding their FD. Conclusions: Human cervical mucus obtained at periovulatory period can follow a fractal-like pattern of crystallization, especially in relation to the similarity of its structural components (criterion of self-similarity) (AU)

Evaluacion diagnóstica de la dinámica cardíaca caótica fetal a partir de la evolución del sistema dinámico / Diagnostic evaluation of fetal chaotic cardiac dynamics from the evolution of the dynamic system

Objetivo: Desarrollar una nueva metodología física y matemática para diagnosticar la dinámica cardíaca caótica fetal a partir de atractores de la frecuencia cardíaca. Metodología: Se realizó una inducción matemática con tres trazados de monitorias fetales; una reactiva sin dudas en su evaluación, una plana y una con pérdida aguda de bienestar fetal, para cada una de ellas se generó un atractor caótico a partir de las frecuencias cardíacas, se evaluaron los espacios de ocupación de cada atractor en dos rejillas, y se establacieron diferencias matemáticas entre trazados de monitorias reactivas y no reactivas. Posteriormente se analizaron otros 15 trazados de monitorias fetales, para refinar los parámetros diagnósticos. Resultados: Los espacios evaluados para los atractores de monitorias normales presentaron valores entre 53 y 117 para la rejilla más pequeña; mientras que las monitorias anormales presentaron valores menores a 41 y mayores a 123. Conclusiones: se desarrolló una nueva metodología de ayuda diagnóstica para evaluar la dinámica cardíaca caótica fetal, que diferencia normalidad de enfermedad de forma objetiva y reproducible (AU)

Objective: To develop a new physical and mathematical methodology to diagnose fetal chaotic cardiac dynamics from heart rate attractors. Methods: A mathematical induction was performed with three fetal monitoring tracings;one of them, reactive without doubt in its evaluation, other plane and other with acute loss of fetal well-being, for each of them a chaotic attractor was generated from the cardiac frequencies, the spaces of occupation of each attractor in two grids were evaluated, and mathematical differences were established between reactive and non-reactive monitorin tracings. A further 15 fetal monitoring tracings were then analyzed to refine the diagnostic parameters. Results: The spaces evaluated for the normal monitor attractors presented values between 53 and 177 for the smallest grid; while abnormal monitoring had values lower than 41 and greater than 12.3. conclusions: a new methodology of diagnostic aid was developed to evaluate fetal chaotic cardiac dynamics, which distinguishes normality of disease in an objective and reproductible way (AU)

Ley exponencial de la dinámica cardiaca caótica aplicada a 18 horas / Exponential law of chaotic cardiac dynamics applied to 18 hours

Resumen Introducción: La aplicación de una ley exponencial para los sistemas dinámicos caóticos cardiacos ha sido reducida a 18 horas para el análisis del Holter, cuantificando las dinámicas cardiacas normales y patológicas, así como la evolución entre estos estados. Metodología: Se analizaron 80 registros electrocardiográficos, 15 con dinámicas normales y 65 con diferentes patologías. Se construyó un atractor caótico para cada dinámica cardiaca a partir de la simulación de la secuencia de las frecuencias cardiacas durante 18 horas, posteriormente se halló la dimensión fractal de cada atractor y su ocupación espacial. Los parámetros diferenciadores de la ley caótica exponencial fueron aplicados diferenciando dinámicas cardiacas normales de aquellas patológicas, finalmente se calculó la sensibilidad, especificidad y coeficiente Kappa. Resultados: Las dinámicas normales presentaron espacios de ocupación por encima de 200 en la rejillla Kp, y para la rejilla Kg por encima de 67. Para los casos de enfermedad aguda los valores en las rejillas Kp y Kg estuvieron por debajo de 73 y 22 respectivamente. Los valores de sensibilidad y especificidad fueron de 100% y el coeficiente Kappa fue de 1. Conclusión: La aplicación de la ley exponencial durante 18 horas mostro que fue posible caracterizar matemáticamente las dinámicas cardiacas, permitiendo reducir el tiempo de evaluación.

Abstract Introduction: The application of an exponential law for chaotic dynamic cardiac systems has been reduced to 18 hours for Holter analysis, quantifying normal and pathological cardiac dynamics, as well as the evolution between these states. Methodology: 80 electrocardiographic records were analyzed, 15 with normal dynamics and 65 with different pathologies. A chaotic attractor was constructed for each cardiac dynamic based on the simulation of the cardiac frequency sequence for 18 hours, after the fractal dimension of each attractor and its spatial occupation were found. The differentiating parameters of the chaotic exponential law were applied differentiating normal cardiac dynamics from those pathological, finally the sensitivity, specificity and Kappa coefficient were calculated. Results: The normal dynamics presented occupancy spaces above 200 in the Kp grid, and for the Kg grid above 67. In the cases of acute disease, the values in the Kp and Kg grids were below 73 and 22 respectively. The values of sensitivity and specificity were 100% and the Kappa coefficient was 1. Conclusion: The application of the exponential law for 18 hours showed that it was possible to characterize mathematically the cardiac dynamics, allowing reducing the time of evaluation.

New metallophamaceutic reduced renal injury induced by non-steroidal anti-inflammatory

Abstract Purpose To evaluate the effect of Rut-bpy (Cis-[Ru(bpy)2(SO3)(NO)]PF 6), a novel nitric oxide donor, able to modulate the histological changes caused by the NASID (meloxicam). Methods Wistar rats were assigned into three groups (n=6 rats/group): Sham group (saline solution), NSAID group (meloxicam - 15 mg/kg) and Rut-bpy group (100 mg/kg of Rut-bpy associated with 15mg/kg of meloxicam). At the end of experiments, kidneys were removed for histological study, fractal dimension and lacunarity in all animals. Results At the histological examination, all animals (six animals - 100 %) in the NSAID group had membrane thickening and other changes (necrosis, acute tubular congestion and vascular congestion); on the other hand, only one animal (16.6 %) of the Rut-bpy group had congestion. The fractal dimension and lacunarity were greater in the control and Rut-bpy group than in NSAIDs group (p<0.05). Conclusion Rut-bpy may prevent renal histological changes in rats caused by meloxicam.

Effect of Fractal Tones on the Improvement of Tinnitus Handicap Inventory Functional Scores among Chronic Tinnitus Patients: An Open-label Pilot Study

Abstract Introduction Music-based sound therapies become recently a trend in the treatment of tinnitus. Few publications have studied the therapeutic use of fractal tones to treat chronic tinnitus. Objective The aim of this study was to determine the benefits of using fractal tones as a unique sound therapy for chronic tinnitus sufferers. Methods Twelve participants were recruited; however, six could not be assigned. At baseline and at 1, 3 and 6 months, the participants were provided with the Tinnitus Handicap Inventory (THI) and Hearing Handicap Inventory for Adults (HHIA) questionnaires, and their visual analog scale score was recorded. Tinnitus pitch and loudness matching was performed before fitting and after 6 months of use. Results The visual analog scale (VAS) score, pitch and loudness matching and minimal masking levels did not result in significant improvement at the end of the treatment. The mean THI measured at baseline was 45, and the final one was 25. A paired sample t-test showed that this 20-point difference was statistically significant. Conclusions We measured the benefits of using fractal tone therapy for the treatment of chronic tinnitus and found that most of the benefits were in the THI functional domain, which includes concentration, reading, attention, consciousness, sleep, social activities, and household tasks. For all patients with bothersome chronic tinnitus and high scores on the THI functional scale, fractal tones should be considered a promising initial sound therapy strategy. The findings from this open-label pilot study are preliminary, and further trials are needed before these results can be generalized to a larger tinnitus population.

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

Comportamiento fractal de infecciones asociadas al cuidado de la salud en el Hospital de Meissen ESE II Nivel, para los años 2011, 2012 y 2013 / Fractal behavior of infections associated with health care at Meissen Hospital ESE II Level, for the years 2011, 2012 and 2013

Introducción: la dimensión fractal estadística ha sido de utilidad para la caracterización de diversos fenómenos, incluyendo la dinámica cardiaca fetal y del adulto, así como comportamientos asociados al sistema inmune. Las Infecciones Asociadas al Cuidado de la Salud son un problema de salud de alta importancia a nivel mundial. Objetivo: establecer el comportamiento fractal estadístico de la frecuencia de aparición de Infecciones Asociadas al Cuidado de la Salud. Material y métodos: Se aplicó la ley de Zipf-Mandelbrot a la distribución de frecuencias de aparición agrupadas por especialidad de Infecciones Asociadas al Cuidado de la Salud en el Hospital Meissen ESE II Nivel, para los años 2011, 2012 y 2013. Se calculó la dimensión fractal estadística para cada año, hallando los rangos en los que se desenvuelve la dinámica en estos años y posteriormente se realizaron simulaciones de estas dinámicas anuales. Resultados: Se observó un comportamiento a escala de la dinámica de aparición de Infecciones Asociadas al Cuidado de la Salud por especialidad, los valores de la dimensión fractal fue de 0,6104, 0,7560 y 0,4332 para los años 2011, 2012 y 2013 respectivamente. Conclusión: La ley de Zipf/Mandelbrot permite caracterizar de forma objetiva y reproducible el comportamiento de la frecuencia de aparición de las Infecciones Asociadas al Cuidado de la Salud en el tiempo; las dimensiones fractales acotadas consecutivas en el tiempo permitirían generar predicciones, constituyendo una herramienta de ayuda para la vigilancia epidemiológica y la clínica.

Introduction: The statistical fractal dimension has been useful for the characterization of diverse phenomena, including the fetal and adult cardiac dynamics, as well as the behaviors associated with the immune system. Health Care Associated Infections are a major health problem worldwide. Objective: to establish the statistical fractal behavior of the frequency of occurrence of Health Care Associated Infections. Material and methods: The Zipf-Mandelbrot law was applied to the frequency distribution of occurrences grouped by Health Care Associated Infections in II level at Meissen ESE Hospital for the years 2011, 2012 and 2013. The statistical fractal dimension was calculated for each year, finding the ranges in which the dynamics develops in these years and later simulations of these annual dynamics were carried out. Results: Scale behavior of the dynamics of occurrence of Health Care Associated Infections by specialty was observed; the values of fractal dimension were 0.6104, 0.7560 and 0.4332 for the years 2011, 2012 and 2013 respectively. Conclusion: The law of Zipf / Mandelbrot allows to characterize objectively and reproducibly the behavior of the frequency of occurrence of Health Care Associated Infections over time; the consecutive bounded fractal dimensions over time would allow predictions to be generated, constituting an aid tool for epidemiological and clinical surveillance.

Diagnostic methodology of cardiac dynamics based on the Zipf-Mandelbrot law: evaluation with 50 patients / Metodología diagnóstica de la dinámica cardiaca basada en ley de Zipf-Mandelbrot: evaluación con 50 pacientes

Abstract: Objective: Zipf-Mandelbrot law has been used to assess the complexity of cardiac systems. The objective of this work is to corroborate the clinical applicability of a diagnostic methodology developed from Zipf-Mandelbrot law, in the differentiation of normality and acute cardiac disease. Material and methods: there were taken 50 continuous electrocardiographic Holter monitoring records, 20 normal and 30 with acute alterations of the cardiac dynamics. The frequencies of occurrence of heart rates in ranges of 15 lat/min were organized hierarchically to demonstrate the hyperbolic behavior of dynamics and to apply the Zipf-Mandelbrot law. A linearization was performed and the statistical fractal dimension of each dynamic was obtained, giving rise to the mathematical diagnosis. Sensitivity, specificity and Kappa coefficient were calculated. Results: The values of the statistical fractal dimension of the acute cardiac dynamics were between 0.7123 and 0.9327, whereas for the normal dynamics were found between 0.4253 and 0.6698, evidencing quantitative differences between states of normality and disease. Sensitivity and specificity values of 100% were found and the kappa coefficient was 1. Conclusions: The clinical and diagnostic utility of the mathematical methodology based on Zipf-Mandelbrot law was verified, observing a decrease of dynamics complexity in cases of acute heart disease.(AU)

Resumen: Objetivo: La ley de Zipf-Mandelbrot ha sido utilizada con el fin de evaluar la complejidad de los sistemas cardiacos. El objetivo de este trabajo es corroborar la aplicabilidad clínica de una metodología diagnóstica desarrollada a partir de la ley de Zipf-Mandelbrot, en la diferenciación de normalidad y enfermedad cardiaca aguda. Material y métodos: Se tomaron 50 Holter cardiacos (monitoreo electrocardiográfico continuo ambulatorio), 20 normales y 30 con alteraciones agudas de la dinámica cardiaca. Se organizaron jerárquicamente las frecuencias de aparición de frecuencias cardiacas en rangos de a 15 lat/min, para evidenciar el comportamiento hiperbólico de las dinámicas y aplicar la ley de Zipf-Mandelbrot. Se realizó una linealización y se obtuvo la dimensión fractal estadística de cada dinámica, dando lugar al diagnóstico matemático. Fueron calculadas la sensibilidad, especificidad y el coeficiente Kappa. Resultados: Los valores de la dimensión fractal estadística de las dinámicas cardiacas agudas se encontraron entre 0.7123 y 0.9327, mientras que para las dinámicas normales se hallaron entre 0.4253 y 0.6698, evidenciando diferencias cuantitativas entre estados de normalidad y enfermedad. Se encontraron valores de sensibilidad y especificidad del 100% y el coeficiente kappa fue de 1. Conclusiones: Fue comprobada la utilidad clínica y diagnóstica de la metodología matemática basada en la ley de Zipf-Mandelbrot, observando un decremento de la complejidad de la dinámica en casos de enfermedad cardiaca aguda.(AU)