arXiv subjects

Santtu Söderholm

Publications and source records attributed to Santtu Söderholm.

7 recordsLinked to original sources

arXiv2026

Advanced EEG Source Models from the Perspective of FEM and Inverse Solutions

In this study, we compare forward solutions computed with finite element methods in Zeffiro Interface and DUNEuro, using the different source models they provided. We compared two of the source models from DUNEuro, called Whitney basis and Local subtraction, and the divergence-conforming model of Zeffiro Interface. For source estimation, we applied sparsity-promoting standardized hierarchical adaptive L1 regression (SHAL1R), standardized Kalman filtering (SKF), classical sLORETA, and dipole scanning. Analyses include Earth Mover's Distance, depth bias scatter plots, and qualitative assessments of amplitude distribution and focality. Preliminary experiments with source interpolation for each method revealed that Local subtraction closely matches expectations for the local behavior of the lead field at various depths. The main results reveal that the success of an inverse method depends strongly on the compatibility between its assumptions about the focality of the source and the chosen source model, with point-source models performing best when paired with methods designed for such sources, i.e., sparsity-promoting methods and methods that scan for a single source. Moreover, source models that admit patch sources with a wide distribution are more sensitive to additional noise.

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arXiv2026

Forward--Inverse Interplay in FEM-Based EEG Source Imaging: Distributional Signatures of Advanced Source Models and Inverse Solvers

Electroencephalography (EEG) source imaging aims to infer brain activity from electrical potentials measured on the scalp. This is a difficult problem because many different source patterns can explain the same measurements. The result depends strongly on two things: the forward model and the inverse method. In this work, we study how these two parts work together. We focus not only on where the activity is located, but also on how the reconstructed activity is distributed in space. We suggest that different source models create different signatures in the reconstructed activity. We use realistic head models and compute forward solutions with the finite element method using Zeffiro Interface and DUNEuro. We test different source models, including 2 implementations of a divergence-conforming model, and one implementation of Local subtraction approach. For inverse methods, we use advanced methods such as standardized hierarchical adaptive L1 regression (SHAL1R), standardized Kalman filtering (SKF), and classical dipole scanning. To understand the complex interplay between the forward and inverse approaches, we analyze the inverse source localization results using distributional quantitative measures, including Earth Mover's Distance and depth bias scatter plot, and qualitatively assess the amplitude distribution and focality. The results show that there is a strong dependence between the choice of source model and the success rate of a given inverse method: a source model that corresponds well with a single point-like source is a good match with an inverse method that presupposes such a source.

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arXiv2026

A Complete-Electrode-Model-Based Forward Approach for Transcranial Temporal Interference Stimulation with Linearization: A Numerical Simulation Study

Background and Objective: Transcranial temporal interference stimulation (tTIS) is a promising non-invasive brain stimulation technique in which interference between electrical current fields extends the possibilities of electrical brain stimulation. The objective of this study is to develop an efficient mathematical tTIS forward modelling scheme that allows for realistic and adaptable simulation and can be updated accurately when the contact resistance is modified in one or more electrodes. Such a model is vital, for example, in optimization processes that seek the best possible stimulation currents to exhibit or inhibit a given brain region. This study aims to establish and evaluate the complete electrode model (CEM), i.e., a set of boundary conditions incorporating electrode impedance and contact patch, as a forward finite-element-method-based simulation technique for tTIS and investigate linearized CEM as a surrogate. Results: The CEM-based forward simulation successfully reproduced the volumetric stimulating fields induced by tTIS. Sensitivity analysis showed that variations in electrode resistance affects the field distribution, especially in regions where the interfering currents have nearly equal amplitudes. The linearized CEM model closely matched the full nonlinear model within a predefined peak signal-to-noise ratio (PSNR) threshold for relative error. Both models exhibited the highest sensitivity near the focal region.

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arXiv2024

A Coupled Diffusion Approximation for Spatiotemporal Hemodynamic Response and Deoxygenated Blood Volume Fraction in Microcirculation

Background and Objective: This proof of concept study investigates mathematical modelling of blood flow and oxygen transport in cerebral microcirculation, focusing on understanding hemodynamic responses. By coupling oxygen transport models and blood flow dynamics, the research aims to predict spatiotemporal hemodynamic responses and their impact on blood oxygenation levels, particularly in the context of deoxygenated and total blood volume (DBV and TBV) fractions. Methods: A coupled spatiotemporal model is developed using Fick's law for diffusion, combined with the hemodynamic response function derived from a damped wave equation. The diffusion coefficient in Fick's law is based on Hagen-Poiseuille flow, and arterial blood flow is approximated numerically through pressure-Poisson equation (PPE). The equations are then numerically solved with the finite element method (FEM). Numerical experiments are performed on a high-resolution 7-Tesla Magnetic Resonance Imaging (MRI) dataset for head segmentation, which facilitates the differentiation of arterial blood vessels and various brain tissue compartments. Results: The applicability of the model is further demonstrated through numerical experiments utilizing a 7 Tesla magnetic resonance imaging (MRI) dataset for head segmentation, which facilitates the differentiation of arterial blood vessels and various brain tissue compartments. By simulating hemodynamical responses and analyzing their impact on volumetric DBV and TBV, this study offers valuable insights into spatiotemporal modelling of brain tissue and blood flow. Conclusions: This study utilizes spatiotemporal modelling with high-resolution 7 Tesla-MRI head data to explore cerebral blood flow, oxygen transport, and brain dynamics. It enhances understanding of cardiovascular conditions, improves simulation accuracy, and offers potential clinical applications for targeted interventions.

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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.

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arXiv2023

The Effects of Peeling on Finite Element Method -based EEG Source Reconstruction

The problem of reconstructing brain activity from electric potential measurements performed on the surface of a human head is not an easy task: not just because the solution of the related inverse problem is fundamentally ill-posed (not unique), but because the methods utilized in constructing a synthetic forward solution themselves contain many inaccuracies. One of these is the fact that the usual method of modelling primary currents in the human head via dipoles brings about at least 2 modelling errors: one from the singularity introduced by the dipole, and one from placing such dipoles near conductivity discontinuities in the active brain layer boundaries. In this article we observe how the removal of possible source locations from the surfaces of active brain layers affects the localisation accuracy of two inverse methods, sLORETA and Dipole Scan, at different signal-to-noise ratios (SNR), when the H(div) source model is used. We also describe the finite element forward solver used to construct the synthetic EEG data, that was fed to the inverse methods as input, in addition to the meshes that were used as the domains of the forward and inverse solvers. Our results suggest that there is a slight general improvement in the localisation results, especially at lower noise levels. The applied inverse algorithm and brain compartment under observation also affect the accuracy.

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arXiv2023

Navier-Stokes Modelling of Non-Newtonian Blood Flow in Cerebral Arterial Circulation and its Dynamic Impact on Electrical Conductivity in a Realistic Multi-Compartment Head Model

Background and Objective: This study aims to evaluate the dynamic effect of non-Newtonian cerebral arterial circulation on electrical conductivity distribution (ECD) in a realistic multi-compartment head model. It addresses the importance and challenges associated with electrophysiological modalities, such as transcranial electrical stimulation, electro-magnetoencephalography, and electrical impedance tomography. Factors such as electrical conductivity's impact on forward modeling accuracy, complex vessel networks, data acquisition limitations (especially in MRI), and blood flow phenomena are considered. Methods: The Navier-Stokes equations (NSEs) govern the non-Newtonian flow model used in this study. The solver comprises two stages: the first solves the pressure field using a dynamical pressure-Poisson equation derived from NSEs, and the second updates the velocity field using Leray regularization and the pressure distribution from the first stage. The Carreau-Yasuda model establishes the connection between blood velocity and viscosity. Blood concentration in microvessels is approximated using Fick's law of diffusion, and conductivity mapping is obtained via Archie's law. The head model used corresponds to an open 7 Tesla MRI dataset, differentiating arterial vessels from other structures. Results: The results suggest the establishment of a dynamic model of cerebral blood flow for arterial and microcirculation. Blood pressure and conductivity distributions are obtained through numerically simulated pulse sequences, enabling approximation of blood concentration and conductivity within the brain. Conclusions: This model provides an approximation of dynamic blood flow and corresponding ECD in different brain regions. The advantage lies in its applicability with limited a priori information about blood flow and compatibility with arbitrary head models that distinguish arteries.

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