Charge-Based Brain Modeling Engine with Boundary Element Fast Multipole Method

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ABSTRACT All major open-source brain modeling packages currently available (e.g., SimNIBS, DUNEuro, SciRun, ROAST) as well as their commercial counterparts (e.g., Sim4Life, Ansys Maxwell, COMSOL) use the electric potential- based Finite Element Method (FEM) for electromagnetic modeling. FEM has been continuously improved over the past 60 years, is simple to implement and can model averaged tissue anisotropy. At the same time, FEM may have some intrinsic weaknesses specifically affecting high-definition brain modeling. The present proposal aims to develop and disseminate a novel alternative brain modeling engine. In contrast to FEM which uses the electric potential, it operates with the primary (bio)physical quantity – surface (and volumetric) induced electric charge density. To model charge interactions, it naturally employs the modern Fast Multipole Method (FMM) instead of FEM. For piecewise homogeneous biological media of any complexity, only surface charges at bound- aries are present. Their interactions are most accurately described by the boundary element method (BEM). This combination of BEM and FMM is the new proposed BEM-FMM charge engine. The principal advantage of BEM- FMM is its numerically unconstrained spatial field resolution. AIM 1. Improve and complete the BEM-FMM modeling engine. Sub-aims: (i) major speed up of the BEM-FMM engine; (ii) new adaptive mesh refinement algorithm; (iii) new volumetric anisotropic co-solver, (iv) computing activating function with unconstrained numer- ical resolution and; (v) full-scale numerical verification against established FEM solvers SimNIBS and DUNEuro at meso (submillimeter) scale. AIM 2. BEM-FMM testbed for non-invasive recordings and stimulation. 2A. Develop BEM-FMM source localization stream for EEG/MEG recordings. We will construct and validate an improvement over currently existing BEM EEG/MEG source localization software suites using BEM-FMM. We will deliver a ready-to-use testbed with twenty head models and EEG/MEG experimental data. 2B. Develop a BEM-FMM modeling stream with extracerebral compartments for noninvasive stimulation. For enhanced resolution, we will automatically add fine-resolution major extracerebral compartments into existing segmenta- tions pipelines based on anatomical rules. We will then deliver the ready-to-use BEM-FMM testbed targeting TES and ECT (electroconvulsive therapy) where their effect might be critical for the correct dosage prediction and correct targeting. AIM 3. BEM-FMM testbed for invasive electrical stimulation. 3A. Validate BEM-FMM testbed for modeling activating function in animal axons. Verification for a giant inter-neuronal axon of cray- fish Procambarus clarkia via electrical/magnetic stimulation and compound action potential generation for paral- lel fibers in turtle Pseudemys Scripta Elegans cerebellum will be done. 3B. Verify BEM-FMM testbed for mod- eling DBS responses. Using retrospective clinical data, we will develop a BEM-FMM algorithm for patient- specific multipolar DBS and evaluate whether the model predictions align with clinical observations.