A multi-sphere particle numerical model for non-invasive investigations of neuronal human brain activity

In this paper, a multi-sphere particle method is built-up in order to estimate the solution of the Poisson's equation with Neumann boundary conditions describing the neuronal human brain activity. The partial differential equations governing the relationships between neural current sources and the data produced by neuroimaging technique, are able to compute the scalp potential and magnetic field distributions generated by the neural activity. A numerical approach is proposed with current dipoles as current sources and going on in the computation by avoiding the mesh construction. The current dipoles are into an homogeneous spherical domain modeling the head and the computational approach is extended to multilayered con¯guration with different conductivities. A good agreement of the numerical results is shown and, for the first time compared with the analytical ones

The smoothed particle hydrodynamics method via residual iteration

In this paper we propose for the first time an iterative approach of the Smoothed Particle Hydrodynamics (SPH) method. The method is widespread in many areas of science and engineering and despite its extensive application it suffers from several drawbacks due to inaccurate approximation at boundaries and at irregular interior regions. The presented iterative process improves the accuracy of the standard method by updating the initial estimates iterating on the residuals. It is appealing preserving the matrix-free nature of the method and avoiding to modify the kernel function. Moreover the process refines the SPH estimates and it is not affected by disordered data distribution. We discuss on the numerical scheme and experiments with a bivariate test function and different sets of data validate the adopted approach

Polynomial mapped bases: theory and applications

In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge's and Gibbs effects

An advanced variant of an interpolatory graphical display algorithm

In this paper an advanced interpolatory graphical display algorithm based on cardinal B-spline functions is provided. It is well-known that B-spline functions are a flexible tool to design various scale rapresentations of a signal. The proposed method allows to display without recursion a function at any desiderable resolution so that only initial data and opportune vectors weight are involved. In this way the structure of the algorithm is independent across the scale and a computational efficiency is reached. In this paper mono and bi-dimensional vectors weight generated by means of centered cubic cardinal B-spline functions have been supplied

IL METODO DELLE SOLUZIONI FONDAMENTALI PER LA SOLUZIONE DEL PROBLEMA DIRETTO M/EEG

The research already started on the mesh-free solution of the M / EEG direct problem has led to the development of a solver based on the method of fundamental solutions (MFS, method of fundamental solutions) able to manage the physical-geometric complexity of realistic models of the head more efficiently than traditional

Electrical analogous in viscoelasticity

In this paper, electrical analogous models of fractional hereditary materials are introduced. Based on recent works by the authors, mechanical models of materials viscoelasticity behavior are firstly approached by using fractional mathematical operators. Viscoelastic models have elastic and viscous components which are obtained by combining springs and dashpots. Various arrangements of these elements can be used, and all of these viscoelastic models can be equivalently modeled as electrical circuits, where the spring and dashpot are analogous to the capacitance and resistance, respectively. The proposed models are validated by using modal analysis. Moreover, a comparison with numerical experiments based on finite difference time domain method shows that, for long time simulations, the correct time behavior can be obtained only with modal analysis. The use of electrical analogous in viscoelasticity can better reveal the real behavior of fractional hereditary materials