Yolanda Soracipa

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

BackgroundFractal 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.MethodsStarting 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.ResultsA 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.ConclusionsThe 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.

Predictions of CD4 lymphocytes’ count in HIV patients from complete blood count

BackgroundHIV 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).MethodsSets 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.ResultsIntersection (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.ConclusionsUsefulness 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.

Predicción de unión de péptidos de MSA-2 y AMA-1 de Plasmodium falciparum al HLA clase II

The aim of this research is apply the predictive nonameric binding methodology to HLA class II central region, to nonameric peptides of MSA-2 and AMA-1 proteins FROM Plasmodium falciparum, and to 492 nonameric overlapped peptides for three theoretical proteins with size of 500 residues. It was applied a predictive binding theory to HLA class II based on S/k proportion in order to predict binding peptides of MSA-2 and AMA1 proteins to all sequences with 20 residues size from these proteins. The probability, combinatory and entropy values were calculated for 300 nonameric overlapped sequences of MSA-2 and 372 of AMA-1. Finally it was made three theoretical proteins of 500 residues each one, starting from a computational simulation and it was applied the theory, quantifying binding for all nonameric overlapped peptides for these proteins. It was predicted 35 sequences for MSA-2 and 60 for AMA-1 associated to binding macrostate while 265 for MSA-2 and 317 for AMA-1 associated to non binding macrostate. It was predicted 102, 104 and 101 sequences associated to binding macrostate for the theoretical proteins while the others 390, 388, and 391 associated to non binding macrostate respectively. The theoretical prediction developed can facility choose peptides implied in vaccine development, showing that mathematical and physical order lies to antigenic presentation.

Aplicación de la probabilidad y la entropía a la proteína EBA-140. Caracterización matemática de péptidos de alta unión

Resumen Una de las proteinas del merozoito de Plasmodium falciparum, la EBA-140, tambien conocida como BAEBL o PfEBP-2, comparte caracteristicas estructurales y homologia con EBA-175 y EBA-181. Estudios de la localizacion sub-celular sugieren que esta localizada en los micronemas. Por medio de la construccion de un espacio de probabilidad, donde se cuantifico la posibilidad de aparicion por posicion para los 20 aminoacidos en peptidos con tamano de 20 residuos para 6 secuencias de alta union de la proteina EBA-140, se calculo la probabilidad, sumatoria de probabilidad y Entropia para las 61 secuencias de 20 residuos de la proteina EBA-140, para posteriormente caracterizar matematicamente los peptidos de alta union y los que no lo son. Adicionalmente se realizaron las mismas medidas para peptidos teoricos analogos, donde se cambiaron por Glicinas aminoacidos comprobados experimentalmente como criticos, y se efectuaron los calculos. Los valores de probabilidad, Sumatoria de Probabilidad y Entropia para las secuencias comprobadas experimentalmente de alta union varian entre los rangos asociados al macroestado union, mientras que todos estos mismos valores para los peptidos comprobados de baja union se encuentran fuera de los rangos asociados al macroestado de union. Los valores de probabilidad, sumatoria de probabilidad y Entropia diferencian los peptidos de alta union de los de baja union, acertando en el 100% de los casos estudiados, segun estudios experimentales. El fenomeno de union de la proteina estudiada presenta un orden subyacente, que es caracterizable a partir de las leyes de la probabilidad y de la Entropia de forma objetiva y reproducible.

Entropía proporcional de dinámicas cardiacas normales y con arritmia en la unidad de cuidados intensivos

Background Based on the theory of probability and not equiprobable entropy ratios in the context of dynamical systems theory, a methodology for cardiac dynamic evaluation was developed. Objectives To confirm the clinical applicability of the diagnostic methodology based on probability and entropy for patients with different types of arrhythmia assessing the degree of intensification in the ICU through its characteristic proportions. Methods 80 Holter records from ICU diagnosed with arrhythmia and 20 normal were analyzed. Holter clinical findings were masked and were taken from them the maximum and minimum values of heart rate and total number of beats per minute to build the numerical attractor for each dynamics. Probability, entropy, S/k ratio, and proportions of entropy were evaluated, establishing its mathematical diagnosis and quantifying its severity level. Results It was shown that the methodology difference in all cases normal of abnormal dynamics, obtaining a sensitivity and specificity of 100 % and Kappa coefficient of 1, showing that it is also possible to establish quantitatively the degree of exacerbation. Conclusions The methodology developed is useful in clinical practice to correlate the severity of arrhythmias with physical and mathematical predictions of exacerbation.

Predicción de la dinámica temporal de egresos hospitalarios por obesidad en niños y jóvenes en Estados Unidos

La prevalencia de sobrepeso en ninos a nivel mundial tiende al incremento especialmente en paises en via de desarrollo. Enfermedades asociadas al sobrepeso infantil como asma, apnea del sueno y diabetes mellitus, siendo esta ultima la mas frecuente en ninos y adolescentes, implican otra problematica como es el alto costo en salud, el cual ha sido analizado por el Centro Nacional de Estadisticas de la Salud en los Estados Unidos. El objetivo de esta investigacion fue estudiar matematicamente la dinamica del porcentaje de altas hospitalarias por sobrepeso y obesidad de pacientes de 6 a 17 anos de edad en los Estados Unidos con el fin de predecir el porcentaje de altas hospitalarias por obesidad en Estados Unidos para el ano 1999, en el contexto de la caminata al azar probabilista, especificamente a partir de un espacio total de probabilidades que permite analizar el comportamiento probabilista de aumentos y disminuciones, a partir de los anos comprendidos entre 1983 y 1998, en Estados Unidos. El rango predicho para el ano 1999 fue de 1,17%, valor que fue posteriormente comparado con los datos del NCHS, que reporto un 1,15%, logrando una prediccion del 98,01%. Se establecio un orden fisico y matematico subyacente a la dinamica del porcentaje de altas hospitalarias por obesidad en ninos, logrando realizar predicciones en su trayectoria