Example of Steady-State Electric-Current Modeling of a Complicated Cellular Topology with Boundary Element Fast Multipole Method
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ABSTRACT:
SUBMITTER: Makarov S
PROVIDER: S-EPMC7403854 | biostudies-literature | 2020 Apr
REPOSITORIES: biostudies-literature
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Project description:Objective. To formulate, validate, and apply an alternative to the finite element method (FEM) high-resolution modeling technique for electrical brain stimulation-the boundary element fast multipole method (BEM-FMM). To include practical electrode models for both surface and embedded electrodes.Approach. Integral equations of the boundary element method in terms of surface charge density are combined with a general-purpose fast multipole method and are expanded for voltage, shunt, current, and floating electrodes. The solution of coupled and properly weighted/preconditioned integral equations is accompanied by enforcing global conservation laws: charge conservation law and Kirchhoff's current law.Main results.A sub-percent accuracy is reported as compared to the analytical solutions and simple validation geometries. Comparison to FEM considering realistic head models resulted in relative differences of the electric field magnitude in the range of 3%-6% or less. Quantities that contain higher order spatial derivatives, such as the activating function, are determined with a higher accuracy and a faster speed as compared to the FEM. The method can be easily combined with existing head modeling pipelines such as headreco or mri2mesh.Significance.The BEM-FMM does not rely on a volumetric mesh and is therefore particularly suitable for modeling some mesoscale problems with submillimeter (and possibly finer) resolution with high accuracy at moderate computational cost. Utilizing Helmholtz reciprocity principle makes it possible to expand the method to a solution of EEG forward problems with a very large number of cortical dipoles.
| S-EPMC8783394 | biostudies-literature
Project description:ObjectiveA new numerical modeling approach is proposed which provides forward-problem solutions for both noninvasive recordings (EEG/MEG) and higher-resolution intracranial recordings (iEEG).MethodsThe algorithm is our recently developed boundary element fast multipole method or BEM-FMM. It is based on the integration of the boundary element formulation in terms of surface charge density and the fast multipole method originating from its inventors. The algorithm still possesses the major advantage of the conventional BEM - high speed - but is simultaneously capable of processing a very large number of surface-based unknowns. As a result, an unprecedented spatial resolution could be achieved, which enables multiscale modeling.ResultsFor non-invasive EEG/MEG, we are able to accurately solve the forward problem with approximately 1 mm anatomical resolution in the cortex within 1-2 min given several thousand cortical dipoles. Targeting high-resolution iEEG, we are able to compute, for the first time, an integrated electromagnetic response for an ensemble (2,450) of tightly packed realistic pyramidal neocortical neurons in a full-head model with 0.6 mm anatomical cortical resolution. The neuronal arbor is comprised of 5.9 M elementary 1.2 μm long dipoles. On a standard server, the computations require about 5 min.ConclusionOur results indicate that the BEM-FMM approach may be well suited to support numerical multiscale modeling pertinent to modern high-resolution and submillimeter iEEG.SignificanceBased on the speed and ease of implementation, this new algorithm represents a method that will greatly facilitate simulations at multi-scale across a variety of applications.
| S-EPMC7704617 | biostudies-literature
Project description:The numerical solution of the Poisson-Boltzmann (PB) equation is a useful but a computationally demanding tool for studying electrostatic solvation effects in chemical and biomolecular systems. Recently, we have described a boundary integral equation-based PB solver accelerated by a new version of the fast multipole method (FMM). The overall algorithm shows an order N complexity in both the computational cost and memory usage. Here, we present an updated version of the solver by using an adaptive FMM for accelerating the convolution type matrix-vector multiplications. The adaptive algorithm, when compared to our previous nonadaptive one, not only significantly improves the performance of the overall memory usage but also remarkably speeds the calculation because of an improved load balancing between the local- and far-field calculations. We have also implemented a node-patch discretization scheme that leads to a reduction of unknowns by a factor of 2 relative to the constant element method without sacrificing accuracy. As a result of these improvements, the new solver makes the PB calculation truly feasible for large-scale biomolecular systems such as a 30S ribosome molecule even on a typical 2008 desktop computer.
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Project description:OBJECTIVE:We develop a new accurate version of the boundary element fast multipole method for transcranial magnetic stimulation (TMS) related problems. This method is based on the surface-charge formulation and is using the highly efficient fast multipole accelerator along with analytical computations of neighbor surface integrals. RESULTS:The method accuracy is demonstrated by comparison with the proven commercial finite-element method (FEM) software ANSYS Maxwell 18.2 2017 operating on unstructured grids and with adaptive mesh refinement. Five realistic high-definition head models from the Population Head Repository (IT'IS Foundation, Switzerland) have been acquired and augmented with a commercial TMS coil model (MRi-B91, MagVenture, Denmark). For each head model, simulations with our method and simulations with the FEM software ANSYS Maxwell 18.2 2017 have been performed. These simulations have been compared with each other and an excellent agreement was established in every case. SIGNIFICANCE:At the same time, our new method runs approximately 500 times faster than the ANSYS FEM, finishes in about 200 s on a standard server, and naturally provides a submillimeter field resolution, which is justified using mesh refinement. CONCLUSIONS:Our method can be applied to modeling of brain stimulation and recording technologies such as TMS and magnetoencephalography, and has the potential to become a real-time high-resolution simulation tool.
| S-EPMC7388683 | biostudies-literature
Project description:In order to compute polarization energy of biomolecules, we describe a boundary element approach to solving the linearized Poisson-Boltzmann equation. Our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface. State of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation. We perform a variety of computational experiments, testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy.
| S-EPMC3110014 | biostudies-literature
Project description:Objective.In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems.Approach.We propose, describe, and systematically investigate an AMR method using the boundary element method with fast multipole acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy. The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a 'silver-standard' solution found by subsequent 4:1 global refinement of the adaptively-refined model.Main results.Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models.Significance.This error has especially important implications for TES dosing prediction-where the stimulation strength plays a central role-and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.
| S-EPMC10902857 | biostudies-literature
Project description:OBJECTIVE:A study pertinent to the numerical modeling of cortical neurostimulation is conducted in an effort to compare the performance of the finite element method (FEM) and an original formulation of the boundary element fast multipole method (BEM-FMM) at matched computational performance metrics. APPROACH:We consider two problems: (i) a canonic multi-sphere geometry and an external magnetic-dipole excitation where the analytical solution is available and; (ii) a problem with realistic head models excited by a realistic coil geometry. In the first case, the FEM algorithm tested is a fast open-source getDP solver running within the SimNIBS 2.1.1 environment. In the second case, a high-end commercial FEM software package ANSYS Maxwell 3D is used. The BEM-FMM method runs in the MATLAB® 2018a environment. MAIN RESULTS:In the first case, we observe that the BEM-FMM algorithm gives a smaller solution error for all mesh resolutions and runs significantly faster for high-resolution meshes when the number of triangular facets exceeds approximately 0.25 M. We present other relevant simulation results such as volumetric mesh generation times for the FEM, time necessary to compute the potential integrals for the BEM-FMM, and solution performance metrics for different hardware/operating system combinations. In the second case, we observe an excellent agreement for electric field distribution across different cranium compartments and, at the same time, a speed improvement of three orders of magnitude when the BEM-FMM algorithm used. SIGNIFICANCE:This study may provide a justification for anticipated use of the BEM-FMM algorithm for high-resolution realistic transcranial magnetic stimulation scenarios.
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Project description:Lymphangiogenesis plays pivotal roles in diverse physiological and pathological conditions. Steady direct-current electric fields (DC EFs) induce vascular endothelial behaviors related to angiogenesis have been observed. This study investigated the effects of DC EFs on the lymphangiogenic response of lymphatic endothelial cells (LECs). We demonstrated that EFs stimulation induced directional migration, reorientation, and elongation of human LECs in culture. These lymphangiogenic responses required VEGF receptor 3 (VEGFR-3) activation and were mediated through the PI3K-Akt, Erk1/2, and p38 MAPK signaling pathways in relation to the reorganization of the actin cytoskeleton. Our results indicate that endogenous EFs may play a role in lymphangiogenesis in vivo, and VEGFR-3 signaling activation may be involved in the cellular function of LECs driven by EFs.
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Project description:The control of cellular processes by direct electronic interface will facilitate the development of biosensors, synthetic biology, and nanobiotechnology by providing the means to pass information from synthetic to living elements of hybrid systems. To investigate the potential of manipulating cellular gene expression by means of electric current, Escherichia coli cultures were screened for electric current inducible genes using global gene expression profiling. Cells in stationary phase were subjected to a DC current density of 2.5 mA/cm2 for 2 min after which the cells were lysed and the total RNA extracted. Of the 4290 expressed genes in E. coli , 432 genes were found to be significantly differentially expressed at an effective alpha value of 5.8 X 10-6. Of these, 333 genes were induced and 99 repressed. Several genes were verified as differentially expressed by quantitative real-time RT-PCR. The set of differentially expressed genes were examined for the presence of regulatory factors, subsidiary regulon genes, and biological function, particularly redox functions. Transcripts for the regulatory proteins fnr, sspB, soxS, oxyR, creB and yeiL were found to be up-regulated, and crp was down regulated. While soxS and oxyR were up-regulated, the downstream genes controlled by these regulatory proteins were not differentially expressed, suggesting that the oxidative stress level of low-current electric exposure is small. Genes controlled by FNR and CRP, many of which have redox function, were found to be differentially expressed suggesting modulation by direct reduction that can only be partially explained as a response to the reducing environment created by the electrolytic generation of H2 at the cathode. Genes associated with phosphate metabolism and membrane proteins were also differentially expressed. Keywords: electric current induced gene expression
2008-02-12 | GSE5192 | GEO
Project description:The control of cellular processes by direct electronic interface will facilitate the development of biosensors, synthetic biology, and nanobiotechnology by providing the means to pass information from synthetic to living elements of hybrid systems. To investigate the potential of manipulating cellular gene expression by means of electric current, Escherichia coli cultures were screened for electric current inducible genes using global gene expression profiling. Cells in stationary phase were subjected to a DC current density of 2.5 mA/cm2 for 2 min after which the cells were lysed and the total RNA extracted. Of the 4290 expressed genes in E. coli , 432 genes were found to be significantly differentially expressed at an effective alpha value of 5.8 X 10-6. Of these, 333 genes were induced and 99 repressed. Several genes were verified as differentially expressed by quantitative real-time RT-PCR. The set of differentially expressed genes were examined for the presence of regulatory factors, subsidiary regulon genes, and biological function, particularly redox functions. Transcripts for the regulatory proteins fnr, sspB, soxS, oxyR, creB and yeiL were found to be up-regulated, and crp was down regulated. While soxS and oxyR were up-regulated, the downstream genes controlled by these regulatory proteins were not differentially expressed, suggesting that the oxidative stress level of low-current electric exposure is small. Genes controlled by FNR and CRP, many of which have redox function, were found to be differentially expressed suggesting modulation by direct reduction that can only be partially explained as a response to the reducing environment created by the electrolytic generation of H2 at the cathode. Genes associated with phosphate metabolism and membrane proteins were also differentially expressed. Three biological replicates were exposed to electric current along with three biological replicate controls.
2010-06-25 | E-GEOD-5192 | biostudies-arrayexpress