ABSTRACT
Accurate source localization of the epileptogenic zone (EZ) is the primary condition of surgical removal of EZ. The traditional localization results based on three-dimensional ball model or standard head model may cause errors. This study intended to localize the EZ by using the patient-specific head model and multi-dipole algorithms using spikes during sleep. Then the current density distribution on the cortex was computed and used to construct the phase transfer entropy functional connectivity network between different brain areas to obtain the localization of EZ. The experiment result showed that our improved methods could reach the accuracy of 89.27% and the number of implanted electrodes could be reduced by (19.34 ± 7.15)%. This work can not only improve the accuracy of EZ localization, but also reduce the additional injury and potential risk caused by preoperative examination and surgical operation, and provide a more intuitive and effective reference for neurosurgeons to make surgical plans.
Subject(s)
Humans , Scalp , Brain Mapping/methods , Epilepsy/diagnosis , Electroencephalography/methods , BrainABSTRACT
The inverse problem of diffuse optical tomography (DOT) is ill-posed. Traditional method cannot achieve high imaging accuracy and the calculation process is time-consuming, which restricts the clinical application of DOT. Therefore, a method based on stacked auto-encoder (SAE) was proposed and used for the DOT inverse problem. Firstly, a traditional SAE method is used to solved the inverse problem. Then, the output structure of SAE neural network is improved to a single output SAE, which reduce the burden on the neural network. Finally, the improved SAE method is used to compare with traditional SAE method and traditional levenberg-marquardt (LM) iterative method. The result shows that the average time to solve the inverse problem of the method proposed in this paper is only 1.67% of the LM method. The mean square error (MSE) value is 46.21% lower than the traditional iterative method, 61.53% lower than the traditional SAE method, and the image correlation coefficient(ICC) value is 4.03% higher than the traditional iterative method, 18.7% higher than the traditional SAE method and has good noise immunity under 3% noise conditions. The research results in this article prove that the improved SAE method has higher image quality and noise resistance than the traditional SAE method, and at the same time has a faster calculation speed than the traditional iterative method, which is conducive to the application of neural networks in DOT inverse problem calculation.
Subject(s)
Algorithms , Neural Networks, Computer , Tomography, OpticalABSTRACT
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.
ABSTRACT
The inverse problem of electrical impedance tomography (EIT) is seriously ill-posed, which restricts the clinical application of EIT. Regularization is an important numerical method to improve the stability of the EIT inverse problem as well as the resolution of the imaging. This paper proposes a self-diagnosis regularization method based on Tikhonov regularization and diagonal weight regularization method (DWRM). Firstly, the ill-posedness of the inverse problem is analyzed by sensitivity. Then, the performance of the self-diagnosis regularization is analyzed through the singular value theory. Finally, some simulated experiments including simulations and flume experiment are carried out and verify that the self-diagnosis regularization has better image quality and anti-noise ability than those of traditional regularization methods. The self-diagnosis regularization method weakens the ill-posedness of inverse problem of EIT and can prompt the practical application of EIT.
ABSTRACT
Objective To develop a new algorithm to reconstruct the distribution of acoustic sources of magnetoacoustic tomography with magnetic induction(MAT-MI)in the acoustic inhomogeneous media,which is developed on the basis of generalized finite element method (GFEM) and modified time inversion algorithm. Methods The acoustic and acoustic coupling theory and the basic equations of acoustics were used to study the forward and inverse problems of the acoustic inhomogeneous concentric sphere magneticacoustic coupling model. The solution of acoustic non-uniform media wave equation based on GFEM was proposed.The method solved the problem of acoustically inhomogeneous media sound source reconstruction and conductivity reconstruction.At the same time,the distribution of velocity was reconstructed by rotating the pairs of transducers and the time reversal algorithm. Results The proposed algorithm could accurately reconstruct the acoustic source distribution in acoustic inhomogeneous media,and could obtain the distribution of sound velocity during the reconstruction of sound source and recover the image well. Conclusion The proposed algorithm had its feasibility and effectiveness verified,and gains advantages in MAT-MI reconstruction of acoustic inhomogeneous media.