arXiv subjects

Fernando Galaz Prieto

Publications and source records attributed to Fernando Galaz Prieto.

5 recordsLinked to original sources

arXiv2026

Multi-Compartment Volume Conductor with Complete Electrode Model: Simulated Stereo-EEG Source Localization using Brainstorm-Zeffiro Plugin

This study introduces a novel integration of the Brainstorm (BST) software and the Zeffiro Interface (ZI) to enable whole-head, multi-compartment volume conductor modeling for electroencephalography (EEG) source imaging, with a particular focus on stereotactic EEG applications. We present the BST-2-ZI plugin, a MATLAB-based tool that facilitates seamless transfer of tissue segmentations and anatomical atlases from BST into ZI for finite element (FE) mesh generation as well as forward and inverse modeling. The generated FE meshes support variable spatial resolution and implement the complete electrode model (CEM), allowing for precise modeling of both invasive depth electrodes and non-invasive scalp electrodes. Using the ICBM152 template and synthetic source simulation, we demonstrate the end-to-end pipeline from MRI data to lead field (LF) computation and source localization in a stereotactic EEG (stereo-EEG) setting. Our numerical experiments highlight the capability of the pipeline to accurately model multi-compartment head geometry and conductivity with a stereotactic CEM-based electrode configuration. Our preliminary source localization results show how a synthetic stereo-EEG probe corresponding to a bidirectional deep brain stimulation (DBS) probe with four omnidirectional contacts can, in principle, be coupled with scalp electrodes to improve source localization in its vicinity.

physics.med-ph↗

arXiv2025

In Silico Study for Optimizing Intensity and Focality Electrode Configurations for Directional DBS Under Uncertainty Using Metaheuristic L1L1 Method

Background and Objective: As Deep Brain Stimulation (DBS) advances toward directional leads and optimization-based current steering, selecting electrode contact configurations becomes complex. This study formulates configuration selection as an inverse mapping between target activation and electrode currents using metaheuristic L1-norm regularized L1-norm fitting (L1L1). L1L1 incorporates lead-field uncertainty arising from electrode placement, tissue properties, and forward modeling assumptions. Methods: The framework introduces lead-field perturbations and restricts the controllable domain through a sensitivity-based feasibility criterion within a finite element formulation derived using the Complete Electrode Model. Current distributions were optimized for 8- and 40-contact leads. Performance was evaluated using focused current density, nuisance current density, and their ratio under safety and sparsity constraints. Results: L1L1 was evaluated using noiseless and noisy lead fields, with noise selected to reflect attenuation within the volume of tissue activated. The method produced sparse, spatially selective stimulation patterns across perturbation levels. Hyperparameter optimization yielded bipolar or multipolar configurations. Compared with the Reciprocity Principle (RP), which produced strictly bipolar configurations, and Tikhonov-regularized least squares (TLS), which produced more distributed solutions, L1L1 enabled controlled transitions between sparse and multipolar patterns. It concentrated stimulation within the target while limiting unintended current spread, particularly under noisy conditions. Conclusions: L1L1 can assist specialists in optimizing DBS configurations. By incorporating uncertainty directly into optimization, it provides robust and interpretable current steering across lead configurations while accounting for forward-model variability.

math.OC↗

arXiv2023

Pressure-Poisson Equation in Numerical Simulation of Cerebral Arterial Circulation and Its Effect on the Electrical Conductivity of the Brain

This study considers dynamic modelling of the cerebral arterial circulation and reconstructing an atlas for the electrical conductivity of the brain. While high-resolution 7-Tesla (T) Magnetic Resonance Imaging (MRI) data allow for reconstructing the cerebral arteries with a cross-sectional diameter larger than the voxel size, electrical conductivity cannot be directly inferred from MRI data. Brain models of electrophysiology typically associate each brain tissue compartment with a constant electrical conductivity, omitting any dynamic effects of cerebral blood circulation. Incorporating those effects poses the challenge of solving a system of incompressible Navier-Stokes equations in a realistic multi-compartment head model. We postulate that circulation in the distinguishable arteries can be estimated via the pressure-Poisson equation, which is coupled with Fick's law of diffusion for microcirculation. To establish a fluid exchange model between arteries and microarteries, a boundary condition derived from the Hagen-Poisseuille model is applied. The relationship between the estimated volumetric blood concentration and the electrical conductivity of the brain tissue is approximated through Archie's law for fluid flow in porous media. Through the formulation of the PPE and a set of boundary conditions based on the Hagen-Poisseuille model, we obtained an equivalent formulation of the incompressible Stokes equation. Thus, allowing effective blood pressure estimation in cerebral arteries segmented from open 7T MRI data. As a result of this research, we developed and built a useful modelling framework that accounts for the effects of dynamic blood flow on a novel MRI-based electrical conductivity atlas. The electrical conductivity perturbation obtained in numerical experiments has an appropriate overall match with previous studies on this subject.

math.AP↗

arXiv2023

Multi-compartment human head modeling: generating adaptive tetrahedral mesh with GPU acceleration

This paper introduces a highly adaptive and automated approach for generating Finite Element (FE) discretization for a given realistic multi-compartment human head model obtained through magnetic resonance imaging (MRI) dataset. We aim at obtaining accurate tetrahedral FE meshes for electroencephalographic source localization. We present recursive solid angle labeling for the surface segmentation of the model and then adapt it with a set of smoothing, inflation, and optimization routines to further enhance the quality of the FE mesh. The results show that our methodology can produce FE mesh with an accuracy greater than 1 millimeter, significant with respect to both their 3D structure discretization outcome and electroencephalographic source localization estimates. FE meshes can be achieved for the human head including complex deep brain structures. Our algorithm has been implemented using the open Matlab-based Zeffiro Interface toolbox with it effective time-effective parallel computing system.

math.AP↗

arXiv2022

L1-norm vs. L2-norm fitting in optimizing focal multi-channel tES stimulation: linear and semidefinite programming vs. weighted least squares

This study focuses on Multi-Channel Transcranial Electrical Stimulation, a non-invasive brain method for stimulating neuronal activity under the influence of low-intensity currents. We introduce mathematical formulation for finding a current pattern which optimizes a L1-norm fit between a given focal target distribution and volume current density inside the brain. L1-norm is well-known to favor well-localized or sparse distributions compared to L2-norm (least-squares) fitted estimates. We present a linear programming approach which performs L1-norm fitting and penalization of the current pattern (L1L1) to control the number of non-zero currents. The optimizer filters a large set of candidate solutions using a two-stage metaheuristic search in from a pre-filtered set of candidates. The numerical simulation results, obtained with both a 8- and 20-channel electrode montages, suggest that our hypothesis on the benefits of L1-norm data fitting is valid. As compared to L1-norm regularized L2-norm fitting (L1L2) via semidefinite programming and weighted Tikhonov least-squares method, the L1L1 results were overall preferable with respect to maximizing the focused current density at the target position and the ratio between focused and nuisance current magnitudes. We propose the metaheuristic L1L1 optimization approach as a potential technique to obtain a well-localized stimulus with a controllable magnitude at a given target position. L1L1 finds a current pattern with a steep contrast between the anodal and cathodal electrodes meanwhile suppressing the nuisance currents in the brain, hence, providing a potential alternative to modulate the effects of the stimulation, e.g., the sensation experienced by the subject.

math.OC↗