arXiv subjects

Maryam Samavaki

Publications and source records attributed to Maryam Samavaki.

10 recordsLinked to original sources

arXiv2025

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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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.

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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

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.

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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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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.

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arXiv2020

On the numerical computation of Killing and conformally Killing vector fields on compact Riemannian manifolds

The defining equations for Killing vector fields and conformal Killing vector fields are overdetermined systems of PDE. This makes it difficult to solve the systems numerically. We propose an approach which reduces the computation to the solution of a symmetric eigenvalue problem. The eigenvalue problem is then solved by finite element techniques. The formulation itself is valid in any dimension and for arbitrary compact Riemannian manifolds. The numerical results which validate the method are given in two dimensional case.

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arXiv2019

On some classes of Riemannian manifolds

We study several classes of Riemannian manifolds which are defined by imposing a certain condition on the Ricci tensor. We consider the following cases: Ricci recurrent, Cotton, quasi Einstein and pseudo Ricci symmetric condition. Such conditions can be interpreted as overdetermined PDE systems whose unknowns are the components of the Riemannian metric, and perhaps in addition some auxiliary functions. Hence even if the dimension of the manifold is small it is not easy to compute interesting examples by hand, and indeed very few examples appear in the literature. We will present large families of nontrivial examples of such manifolds. The relevant PDE systems are first transformed to an involutive form. After that in many cases one can actually solve the resulting system explicitly. However, the involutive form itself already gives a lot of information about the possible solutions to the given problem. We will also discuss some relationships between the relevant classes.

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arXiv2018

Navier-Stokes equations on Riemannian manifolds

We study properties of the solutions to Navier-Stokes system on compact Riemannian manifolds. The motivation for such a formulation comes from atmospheric models as well as some thin film flows on curved surfaces. There are different choices of the diffusion operator which have been used in previous studies, and we make a few comments why the choice adopted below seems to us the correct one. This choice leads to the conclusion that Killing vector fields are essential in analyzing the qualitative properties of the flow. We give several results illustrating this and analyze also the linearized version of Navier-Stokes system which is interesting in numerical applications. Finally we consider the 2 dimensional case which has specific characteristics, and treat also the Coriolis effect which is essential in atmospheric flows.

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