A boundary element method of bidomain modeling for predicting cellular responses to

Abstract

A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields Czerwonky DM, Aberra AS, Gomez LJ. A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields. J Neural Eng. 2024 Jun 11. doi: 10.1088/1741-2552/ad5704. Abstract Objective: Commonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or “whole” finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons. Methods: Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios. Main Results: Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh. Significance: Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies. Conclusion We introduced a novel bidomain integral equation for modeling the electric response of neuron cells to device-induced E-fields. Our study includes several canonical test cases with unmyelinated cells, including scenarios with multiple cells, transverse polarization, DBS electrodes at varying proximity to multiple axon geometries, and TMS with a spherical head model. The study results indicate that (1) the hybrid cable-equation approach is a sufficient choice for most simulations, (2) longitudinal stimulation serves as the primary activation mechanism for electromagnetic brain stimulation, and (3) multi-cell studies of advanced mechanisms would greatly benefit from further development of fast-bidomain or hybrid cable-bidomain solvers. Our future efforts will focus on developing fast bidomain solvers to fully incorporate realistic neuron morphologies. Acknowledgements Preliminary results for this work have been presented at the Applied Computational Electromagnetics Society (ACES) 2023 conference (March 2023, Monterey, California, USA)[67], the 2023 IEEE MTTS International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO’2023, June 2023, Winnipeg, Canada), the IEEE International Symposium on Antennas and Propagation Society and USNC-URSI Radio Science Meeting (IEEE-AP-S 2023, July 2023, Portland, Oregon, USA), and the Brain and Human Body Modeling conference 2023 (BHBM 2023, August 2023, Boston, Massachusetts, USA). Additionally, a preprint of this manuscript has been uploaded to biorxiv.org. Research reported in this publication was supported by the National Institute of Mental Health of the National Institutes of Health under Award Number R00MH120046. The content of the current research is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. Additionally, this effort was sponsored by the Central Intelligence Agency (CIA), through CIA Federal Labs. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the U.S. Government or of the Central Intelligence Agency. Open access paper: iopscience.iop.org

AI evidence extraction

Main findings

The authors introduce a bidomain boundary element method (integral equation) to model electromagnetic coupling between stimulation devices and neuronal compartments. Comparison studies in simulated Hodgkin-Huxley axons and spherical cells indicate the boundary element approach produces accurate results for both electric and magnetic stimulation and avoids the need for multi-scale volume meshing; the study also reports that a hybrid cable-equation approach is sufficient for most simulations and that longitudinal stimulation is the primary activation mechanism in electromagnetic brain stimulation scenarios tested.

Outcomes measured

• Modeling accuracy for electric stimulation
• Modeling accuracy for magnetic stimulation
• Predicted neuronal/cellular electric response to device-induced E-fields (intracellular, membrane, extracellular coupling)
• Activation mechanism inference (longitudinal vs transverse stimulation)

Limitations

• Study is computational/simulation-based (no in vivo or clinical outcomes reported in abstract).
• Specific exposure parameters (e.g., frequencies, field strengths, SAR) are not provided in the abstract.
• Validation details and quantitative error metrics are not described in the abstract.

Suggested hubs

• occupational-exposure (0)

{
    "study_type": "engineering",
    "exposure": {
        "band": null,
        "source": "brain stimulation devices (e.g., DBS electrodes, TMS)",
        "frequency_mhz": null,
        "sar_wkg": null,
        "duration": null
    },
    "population": null,
    "sample_size": null,
    "outcomes": [
        "Modeling accuracy for electric stimulation",
        "Modeling accuracy for magnetic stimulation",
        "Predicted neuronal/cellular electric response to device-induced E-fields (intracellular, membrane, extracellular coupling)",
        "Activation mechanism inference (longitudinal vs transverse stimulation)"
    ],
    "main_findings": "The authors introduce a bidomain boundary element method (integral equation) to model electromagnetic coupling between stimulation devices and neuronal compartments. Comparison studies in simulated Hodgkin-Huxley axons and spherical cells indicate the boundary element approach produces accurate results for both electric and magnetic stimulation and avoids the need for multi-scale volume meshing; the study also reports that a hybrid cable-equation approach is sufficient for most simulations and that longitudinal stimulation is the primary activation mechanism in electromagnetic brain stimulation scenarios tested.",
    "effect_direction": "unclear",
    "limitations": [
        "Study is computational/simulation-based (no in vivo or clinical outcomes reported in abstract).",
        "Specific exposure parameters (e.g., frequencies, field strengths, SAR) are not provided in the abstract.",
        "Validation details and quantitative error metrics are not described in the abstract."
    ],
    "evidence_strength": "insufficient",
    "confidence": 0.7399999999999999911182158029987476766109466552734375,
    "peer_reviewed_likely": "yes",
    "keywords": [
        "boundary element method",
        "bidomain modeling",
        "integral equation",
        "neurons",
        "Hodgkin-Huxley axon",
        "electric stimulation",
        "magnetic stimulation",
        "DBS",
        "TMS",
        "head model",
        "electromagnetic coupling"
    ],
    "suggested_hubs": [
        {
            "slug": "occupational-exposure",
            "weight": 0,
            "reason": null
        }
    ]
}

Comments

Log in to comment.

No comments yet.