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We show the construction of 3D solids (volumetric 3D models) of SARS-CoV-2 viral particles from the tomographic studies (videos) of SARS-CoV-2-infected tissues. To this aim, we propose a video analysis (tomographic images) by frames (medical images of the virus), which we set as our metadata. We optimize the frames by means of Fourier analysis, which induces a periodicity with simple structure patterns to minimize noise filtering and to obtain an optimal phase of the objects in the image, focusing on the SARS-CoV-2 cells to obtain a medical image under study phase (MIS) (process repeated over all frames). We build a Python algorithm based on Legendre polynomials called "2DLegendre_Fit," which generates (using multilinear interpolation) intermediate images between neighboring MIS phases. We used this code to generate m images of size M×M, resulting in a matrix with size M×M×M (3D solid). Finally, we show the 3D solid of the SARS-CoV-2 viral particle as part of our results in several videos, subsequently rotated and filtered to identify the glicoprotein spike protein, membrane protein, envelope, and the hemagglutinin esterase. We show the algorithms in our proposal along with the main MATLAB functions such as FourierM and Results as well as the data required for the program execution in order to reproduce our results.
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COVID-19 , SARS-CoV-2 , Humanos , Análisis de Fourier , Tomografía , Virión , AlgoritmosRESUMEN
We tested different optical elements placed in three different positions by applying the irradiance transport equation (ITE), obtaining the wavefront $[ W(x,y) ]$[W(x,y)] and aberration surface [$ \textit{AS}(r,\theta ) $AS(r,θ)]. The existing noise in the captures $ I $I as well as in the $ W $W and $ AS $AS were analyzed applying several filters: first a filter based on Legendre polynomials (LP), generating the most probable points increasing the data resolution; second, a filter based on a 50 deg 2D-LP was used as a multilineal fit (multiple linear regression); and third, an ideal bandpass filter in the Fourier space after inducing a periodicity using Ronchi simulated masks with periods in $ x,y,xy $x,y,xy was used to perform data scanning (similar to the four-step phase-shifting method). Signal-to-noise ratio values were obtained for each proposed filter along with the most probable image free from noise, determined from a linear combination of the original data and the applied filters.
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In this paper, we give a solution to the irradiance transport equation (ITE) using the two-dimensional (2D) Legendre polynomials (LPs) and an interpolator (i-LP) based on the LP. In the first place, we analyze the experimental data; subsequently, we proceed to fit the most probable 2D LPs' surface to the data in order to obtain the wavefront surface (W(x,y) of the elements under test) as a solution of the ITE differential equation associated with a boundary problem; and finally, we interpolate the resulting fitting. The interpolation is built from LP to increase the resolution and sharpness of the data. We apply the ITE to these results in order to obtain the wavefront as a nondeterministic solution that increases the resolution of the ITE as an optical test, and we compare our results regarding the obtained aberration surfaces (AS(x,y)).
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This paper presents a combination of Independent Component Analysis (ICA) with Empirical Mode Decomposition (EMD) to suppress muscle and ocular artifacts in electroencephalographic (EEG) signals: By means of ICA, the EEG signals are decomposed into independent components. To avoid the suppression of artifactual components still containing physiological information, EMD is applied to decompose the components in Intrinsic Mode Functions (IMFs). The IMFs with mainly muscle artifacts are removed, and a new data set of independent components without muscle artifacts is generated. From this set, the components containing ocular artifacts are suppressed and clean data are reconstructed. In this way, the muscle and ocular artifacts are better suppressed than using pure ICA, or pure EMD. The performance of the proposed combination is applied to a semi-simulated data set, and three real EEG data sets from healthy subjects contaminated with both artifacts.
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Artefactos , Electroencefalografía , Algoritmos , Ojo , Músculos , Procesamiento de Señales Asistido por ComputadorRESUMEN
Resumen El presente trabajo describe un prototipo de una silla de ruedas que es dirigido hacia enfrente y hacia atrás usando 2 o 3 parpadeos, respectivamente, y es detenido cuando se alcanzan ciertos niveles de atención. El objetivo principal es que las personas que tienen discapacidad motora en sus extremidades puedan usarlo para desplazarse y les brinde autonomía. Para captar la señal de los parpadeos, se utilizó la diadema MindWave Mobile de Neurosky. Se implementó un circuito electrónico en conjunto con Arduino que permite complementar la ejecución del accionamiento del prototipo. El prototipo se probó con 10 personas cuyas edades oscilan entre 20 y 35 años. Los resultados muestran que, en un 80% de los casos, el prototipo se mueve correctamente. La gran ventaja del presente trabajo es que la interfaz cerebro-computadora con la que cuenta este prototipo no requiere entrenamiento previo del sistema, por lo cual, puede ser usado por cualquier persona. Además, su costo es más accesible comparado con otros dispositivos para el mismo fin.
Abstract The present work describes a prototype of a wheel chair directed by means of eye blinks, which can be moved forwards, and backwards using 2 or 3 eye blinks, respectively, and stopped when a certain attention level is met. The main objective of this work is to help people, who have motor disabilities on their arms and legs, move and have autonomy. In order to register the eye blinking signals, the MindWave Mobile device from Neurosky was used. Moreover, an electronic circuit in combination with Arduino has been used to make the prototype work. This prototype has been tested in 10 healthy people from 20 to 35 years old. According to the results, in 80% of the cases the prototype worked correctly. The main advantage of the present work is that the brain-computer interface, which is part of the prototype, does not require training, and hence, it could be used by most of the people. Moreover, its cost is less than similar devices.
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Resumen Objetivo: Presentar un algoritmo estable que determina, a partir de mediciones electroencefalográficas, los parámetros de fuentes de tipo dipolar asociadas a focos epilépticos ubicados sobre la superficie de la corteza cerebral. Metodología: Se utiliza un problema de contorno para establecer correlaciones entre la fuente y la medición. El problema se divide en dos subproblemas lineales y en cada uno de ellos, se utilizan el método de mínimos cuadrados y la regularización de Tikhonov para encontrar soluciones estables. Estos subproblemas son problemas mal planteados en el sentido de Hadamard, debido a la inestabilidad numérica que presentan, es decir, pequeños cambios en las mediciones pueden producir grandes variaciones en la solución de cada problema. El parámetro de regularización de Tikhonov fue elegido usando el método de la curva L. Para hallar la solución del problema de contorno se utiliza el método de las series de Fourier y el Método del Elemento Finito. Resultados: Se propuso un tipo de fuente para representar a los focos epilépticos en la corteza cerebral y un algoritmo estable para el problema de identificación de los parámetros de dichas fuentes. Se desarrollaron ejemplos sintéticos y programas en MATLAB para el caso de geometría simple bidimensional. Originalidad: La separación del problema original en dos subproblemas así como los ejemplos sintéticos son producto de esta investigación. Conclusión general: Se propuso un algoritmo estable que determina a los parámetros de fuentes de corriente dipolar definidas en la corteza cerebral.
Abstract Objective: To present a stable algorithm that determines, from electroencephalographic measurements, the parameters of dipolar sources associated with epileptic foci located on the cerebral cortex. Methodology: A boundary value problem is used to establish correlations between the sources and the measurements. The problem is divided into two linear subproblems and in each one, the method of Minimum Square and the Tikhonov regularization are used for finding stables solutions. These subproblems are an ill-posed problem in the Hadamard sense, which is due to the numerical instability, that is, small changes in the data can produce substantial variations in the solution of each problem. The Tikhonov regularization parameter was chosen using the L curve method. To find the solution of the boundary value problem are used the Fourier series method and the Finite Element Method. Results: A type of source that represents the epileptic foci on the cerebral cortex and a stable algorithm for finding the parameter of these sources were proposed. Synthetics examples and MATLAB programs were developed for the case of bidimensional geometry. Originality: The separation of the original problem into two subproblems and the synthetics examples are a product of this research. Conclusion: A stable algorithm was proposed for determining the parameters of the dipolar current defined on the cerebral cortex.
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Objective: To analyze the parameter identification problem for volumetric dipolar sources in the brain from measurement of the EEG on the scalp using a simplification which reduces the multilayer conductive medium problem to one homogeneous medium problem with a null Neumann boundary condition. Methodology: The minimum squares technique is used for parameter identification of the dipolar sources. The simple case in which the head is modelled by concentric circles is developed. This case was chosen because we were able to obtain the solution of the forward problem in exact form and for the simplicity of the exposition. Results: The parameter of the dipolar sources can be identified from the EEG on the scalp using the simplification. For the theoretical analysis the results developed for one homogeneous region are used. The numerical implementation is simpler than the multilayer case and the numerical computation requires minor computational cost. Conclusion: The feasibility for solving the parameter identification problem using the simplification is shown. These results can be extended to the case of concentric spheres and complex geometries but the solution cannot be found in exact form.
Objetivo: Analizar el problema de identificación de los parámetros para fuentes dipolares volumétricas en el cerebro a partir de la medición del EEG en el cuero cabelludo mediante una simplificación que reduce el problema de un medio conductor de múltiples capas a un problema en un medio homogéneo con una condición de Neumann nula en su frontera. Metodología: Se utiliza la técnica de mínimos cuadrados para identificar los parámetros de las fuentes dipolares. Se desarrolla el caso simple en el que la cabeza está modelada por círculos concéntricos debido a que la solución del problema directo se puede calcular en forma exacta y por la sencillez de la exposición. Resultados: Se identifican los parámetros de la fuente dipolar a partir del EEG sobre el cuero cabelludo usando la simplificación. Para el análisis teórico se utilizan los resultados desarrollados para una región homogénea. La implementación numérica es más simple y el cálculo numérico requiere menor costo computacional. Conclusión: Se muestra la factibilidad para resolver el problema de identificar los parámetros de una fuente dipolar por medio de la simplificación. Los resultados pueden ser extendidos al caso de esferas concéntricas y al de geometrías complejas pero la solución del problema directo no puede hallarse en forma exacta.
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Objetivo: Presentar una simplificación del Problema Inverso Electroencefalográfico (PIE) del caso de varias capas conductoras a una región homogénea con condición de Neumann Nula. Metodología: Se divide el PIE en tres problemas, dos de los cuales se resuelven usando el potencial medido en el cuero cabelludo y con estas soluciones y el tercer problema se lleva a cabo la simplificación. Para validar la simplificación se genera un ejemplo sintético usando el modelo de esferas concéntricas. Resultados: Por medio de la simplificación la fuente se determina a partir de la ecuación de Poisson con una condición de Neumann nula y un dato adicional sobre la frontera de la región homogénea, el cual se obtiene de la medición. Esto es válido para regiones generales con fronteras suficientemente suaves. Adicionalmente, para el caso de esferas concéntricas, se plantea el PIE para el caso de una fuente dipolar (que representa a focos epilépticos) usando esta simplificación y la técnica de la función de Green. Conclusión: La simplificación presentada aquí permite analizar el PIE en una región lo cual simplifica su estudio teórico y numérico. En particular, puede ser útil para el análisis del problema de identificación de los parámetros de una fuente dipolar.
Objective: To give a simplification of the Inverse Electroencephalographic Problem (IEP) from the case of multilayer conductive medium to the case of a homogeneous region with null Neumann condition. Methodology: IEP is divided in three problems, two of which are resolved using the measurements of potential on the scalp and with these solutions and the third problem the simplification is carried out. In order to validate the simplification a synthetic example is generated using the model of concentric spheres. Results: Through of simplification, the source is determined from the Poisson equation with null Neumann condition and an additional data on the boundary of the homogeneous region, which is obtained from the measurement. This is valid for regions with smooth boundary. Additionally, in the case of concentric spheres, it is statement the identification problem for dipolar sources (representing epileptic focus) using this simplification and Green function. Conclusion: The simplification presented here allows us to analyze the inverse problem in one region, which simplifies the theoretical and numerical study. In particular it may be useful to analyze the problem of parameter identification of a dipolar source.