Predictions of CD4 lymphocytes' count in HIV patients from complete blood count.

BACKGROUND: HIV diagnosis, prognostic and treatment requires T CD4 lymphocytes' number from flow cytometry, an expensive technique often not available to people in developing countries. The aim of this work is to apply a previous developed methodology that predicts T CD4 lymphocytes' value based on total white blood cell (WBC) count and lymphocytes count applying sets theory, from information taken from the Complete Blood Count (CBC). METHODS: Sets theory was used to classify into groups named A, B, C and D the number of leucocytes/mm3, lymphocytes/mm3, and CD4/µL3 subpopulation per flow cytometry of 800 HIV diagnosed patients. Union between sets A and C, and B and D were assessed, and intersection between both unions was described in order to establish the belonging percentage to these sets. Results were classified into eight ranges taken by 1000 leucocytes/mm3, calculating the belonging percentage of each range with respect to the whole sample. RESULTS: Intersection (A ∪ C) ∩ (B ∪ D) showed an effectiveness in the prediction of 81.44% for the range between 4000 and 4999 leukocytes, 91.89% for the range between 3000 and 3999, and 100% for the range below 3000. CONCLUSIONS: Usefulness and clinical applicability of a methodology based on sets theory were confirmed to predict the T CD4 lymphocytes' value, beginning with WBC and lymphocytes' count from CBC. This methodology is new, objective, and has lower costs than the flow cytometry which is currently considered as Gold Standard.

Diagnóstico fractal de disfunción cardéaca severa: Dinámica fractal de la ramificación coronaria izquierda / Fractal diagnosis of severe cardiac dysfunction: Fractal dynamic of the left coronary branching

INTRODUCCIÓN Y OBJETIVOS: la geometría fractal evalúa la irregularidad de los objetos naturales, permitiendo caracterizar de forma imparcial la totalidad de la ramificación coronaria izquierda a diferencia de la metodología actual que evalúa únicamente partes de ésta. Con base en esta medida se generalizó una nueva metodología diagnóstica para detectar cualquier tipo de disfunción cardiaca severa. MÉTODOS: estudio de concordancia diagnóstica en el que se utilizó el método de box counting para medir dimensiones fractales de imágenes consecutivas entre sístole y diástole de la ramificación coronaria izquierda en proyección oblicua derecha anterior de angiografías de ocho pacientes con enfermedad arterial oclusiva leve. Así mismo, se evaluaron sus cambios por medio de los conceptos de variabilidad y diferencia neta y se compararon estos resultados con pacientes sin enfermedad arterial oclusiva, con enfermedad arterial oclusiva moderada y severa evaluados previamente de igual forma, para obtener una metodología matemática que evalúa el impacto de cualquier patología en la dinámica cardiaca. RESULTADOS: los casos que presentan diferencias netas de cero corresponden a pacientes con disfunciones cardiacas severas, independientemente del grado o ausencia de enfermedad arterial oclusiva diagnosticada. CONCLUSIONES: se generalizó una nueva metodología diagnóstica de aplicación clínica que detecta disfunciones cardiacas severas sub-diagnosticadas con las metodologías actuales, mediante la caracterización de la dinámica total de la ramificación coronaria izquierda.

INTRODUCTION AND OBJETIVES: fractal geometry evaluates the irregularity of natural objects, allowing impartially characterize the entire left coronary branching unlike the current methodology which evaluates only parts of it. Based on this measure, a new diagnostic method was generalized to detect any type of severe cardiac dysfunction. METHODS: Concordance study using the box counting method to measure fractal dimensions of consecutive images between systole and diastole of the left coronary branch in right anterior oblique projection in angiograms of eight patients with mild arterial occlusive disease. Likewise, we evaluated its changes through the concepts of variability and net difference and compared these results with patients without occlusive arterial disease, with moderate to severe arterial occlusive disease previously and similarly evaluated, to obtain a mathematical methodology to assess the impact of any pathology in cardiac dynamics. RESULTS: The cases with zero net differences occur in patients with severe cardiac dysfunction, regardless of the degree or absence of diagnosed occlusive arterial disease. Conclusions: a new diagnostic methodology of clinical application to detect sub-diagnosed severe heart dysfunction was generalized with current methodologies, through the characterization of the total dynamics of the left coronary branch.

Theoretical generalization of normal and sick coronary arteries with fractal dimensions and the arterial intrinsic mathematical harmony.

BACKGROUND: Fractal geometry is employ to characterize the irregular objects and had been used in experimental and clinic applications. Starting from a previous work, here we made a theoretical research based on a geometric generalization of the experimental results, to develop a theoretical generalization of the stenotic and restenotic process, based on fractal geometry and Intrinsic Mathematical Harmony. METHODS: Starting from all the possibilities of space occupation in box-counting space, all arterial prototypes differentiating normality and disease were obtained with a computational simulation. Measures from 2 normal and 3 re-stenosed arteries were used as spatial limits of the generalization. RESULTS: A new methodology in animal experimentation was developed, based on fractal geometric generalization. With this methodology, it was founded that the occupation space possibilities in the stenotic process are finite and that 69,249 arterial prototypes are obtained as a total. CONCLUSIONS: The Intrinsic Mathematical Harmony reveals a supra-molecular geometric self-organization, where the finite and discrete fractal dimensions of arterial layers evaluate objectively the arterial stenosis and restenosis process.

Diagnóstico matemático de ecocardiografías pediátricas con medidas de dimensión fractal evaluadas con armonía matemática intrínseca / Mathematical diagnosis of pediatric echocardiograms with fractal dimension measures evaluated through intrinsic mathematical harmony

Antecedentes y objetivos: la geometría permite la caracterización matemática objetiva de las formas; la geometría fractal caracteriza objetos irregulares. La forma de los estados dinámicos del ventrículo izquierdo que se observa mediante eco-cardiografía, puede evaluarse de manera objetiva a partir de medidas de dimensiones fractales. Métodos: se midió la dimensión fractal a través del método de Box-Counting de tres objetos definidos en 28 imágenes eco-cardiográficas, 16 de infantes normales (grupo A) y 12 enfermos (grupo B), a fin de establecer diferencias entre salud y estados patológicos a partir de su comparación con las dimensiones fractales de dos prototipos de normalidad y dos de enfermedad. Resultados: se desarrolló una nueva metodología diagnóstica de aplicación clínica basada en el concepto de "armonía matemática intrínseca", y se halló que las dimensiones fractales de los objetos definidos para un ecocardiograma enfermo presentan similitudes hasta en su cuarta cifra significativa, con lo que se evidencia la posibilidad de seguir la evolución de normalidad a enfermedad. De acuerdo con los cálculos realizados 68,75% de los casos del grupo A podrían tener mejor evaluación con el diagnóstico desarrollado y los enfermos podrían diagnosticarse de modo más efectivo. Conclusiones: las imágenes ecocardiográficas pediátricas pueden caracterizarse de manera objetiva con medidas de dimensión fractal, lo cual permite desarrollar una metodología de diagnóstico clínico de la eco-cardiografía en menores de edad, a partir del concepto de armonía matemática intrínseca.

Background and objectives: Geometry allows the objective mathematical characterization of forms. Fractal geometry characterizes irregular objects. The left ventricle dynamical states form observed through echocardiography can be objectively evaluated through fractal dimension measures. Methods: A measurement of fractal dimension was performed using the Box-counting method of three defined objects in 28 echocardiographic images, 16 from normal children (group A) and 12 ill children (group B), in order to establish differences between health and illness from its comparison with the fractal dimensions of 2 normality prototypes and 2 disease prototypes. Results: A new diagnostic, clinical application methodology was developed based in the "intrinsic mathematical harmony" (IMH) concept, and it was observed that the fractal dimensions of the defined objects for an abnormal echocardiogram show similarity to its fourth significant number, thus demonstrating the possibility of following up the evolution from normality towards disease. According to the performed calculations, 68.75% of the cases in group A could be better evaluated with the developed diagnostic methodology, and the ill ones could be diagnosed more effectively. Conclusions: The pediatric echocardiography images can be objectively characterized with fractal dimension measurements, thus enabling the development of a clinical diagnostic methodology of echocardiography in children from the IMH concept.