A fast direct solver for surface-based whole-head modeling of transcranial magnetic stimulation.

When modeling transcranial magnetic stimulation (TMS) in the brain, a fast and accurate electric field solver can support interactive neuronavigation tasks as well as comprehensive biophysical modeling. We formulate, test, and disseminate a direct (i.e., non-iterative) TMS solver that can accurately determine global TMS fields for any coil type everywhere in a high-resolution MRI-based surface model with ~ 200,000 or more arbitrarily selected observation points within approximately 5 s, with the solution time itself of 3 s. The solver is based on the boundary element fast multipole method (BEM-FMM), which incorporates the latest mathematical advancement in the theory of fast multipole methods-an FMM-based LU decomposition. This decomposition is specific to the head model and needs to be computed only once per subject. Moreover, the solver offers unlimited spatial numerical resolution. Despite the fast execution times, the present direct solution is numerically accurate for the default model resolution. In contrast, the widely used brain modeling software SimNIBS employs a first-order finite element method that necessitates additional mesh refinement, resulting in increased computational cost. However, excellent agreement between the two methods is observed for various practical test cases following mesh refinement, including a biophysical modeling task. The method can be readily applied to a wide range of TMS analyses involving multiple coil positions and orientations, including image-guided neuronavigation. It can even accommodate continuous variations in coil geometry, such as flexible H-type TMS coils. The FMM-LU direct solver is freely available to academic users.

A fast direct solver for surface-based whole-head modeling of transcranial magnetic stimulation.

Background: When modeling transcranial magnetic stimulation (TMS) in the brain, a fast and accurate electric field solver can support interactive neuronavigation tasks as well as comprehensive biophysical modeling. Objective: We formulate, test, and disseminate a direct (i.e., non-iterative) TMS solver that can accurately determine global TMS fields for any coil type everywhere in a high-resolution MRI-based surface model with ~200,000 or more arbitrarily selected observation points within approximately 5 sec, with the solution time itself of 3 sec. Method: The solver is based on the boundary element fast multipole method (BEM-FMM), which incorporates the latest mathematical advancement in the theory of fast multipole methods - an FMM-based LU decomposition. This decomposition is specific to the head model and needs to be computed only once per subject. Moreover, the solver offers unlimited spatial numerical resolution. Results: Despite the fast execution times, the present direct solution is numerically accurate for the default model resolution. In contrast, the widely used brain modeling software SimNIBS employs a first-order finite element method that necessitates additional mesh refinement, resulting in increased computational cost. However, excellent agreement between the two methods is observed for various practical test cases following mesh refinement, including a biophysical modeling task. Conclusion: The method can be readily applied to a wide range of TMS analyses involving multiple coil positions and orientations, including image-guided neuronavigation. It can even accommodate continuous variations in coil geometry, such as flexible H-type TMS coils. The FMM-LU direct solver is freely available to academic users.

Degree of improving TMS focality through a geometrically stable solution of an inverse TMS problem.

The Transcranial Magnetic Stimulation (TMS) inverse problem (TMS-IP) investigated in this study aims to focus the TMS induced electric field close to a specified target point defined on the gray matter interface in the M1HAND area while otherwise minimizing it. The goal of the study is to numerically evaluate the degree of improvement of the TMS-IP solutions relative to the well-known sulcus-aligned mapping (a projection approach with the 90∘ local sulcal angle). In total, 1536 individual TMS-IP solutions have been analyzed for multiple target points and multiple subjects using the boundary element fast multipole method (BEM-FMM) as the forward solver. Our results show that the optimal TMS inverse-problem solutions improve the focality - reduce the size of the field "hot spot" and its deviation from the target - by approximately 21-33% on average for all considered subjects, all observation points, two distinct coil types, two segmentation types, two intracortical observation surfaces under study, and three tested values of the field threshold. The inverse-problem solutions with the maximized focality simultaneously improve the TMS mapping resolution (differentiation between neighbor targets separated by approximately 10 mm) although this improvement is quite modest. Coil position/orientation and conductivity uncertainties have been included into consideration as the corresponding de-focalization factors. The present results will change when the levels of uncertainties change. Our results also indicate that the accuracy of the head segmentation critically influences the expected TMS-IP performance.

Imaging G-Ratio in Multiple Sclerosis Using High-Gradient Diffusion MRI and Macromolecular Tissue Volume.

BACKGROUND AND PURPOSE: Remyelination represents an area of great therapeutic interest in multiple sclerosis but currently lacks a robust imaging marker. The purpose of this study was to use high-gradient diffusion MRI and macromolecular tissue volume imaging to obtain estimates of axonal volume fraction, myelin volume fraction, and the imaging g-ratio in patients with MS and healthy controls and to explore their relationship to neurologic disability in MS. MATERIALS AND METHODS: Thirty individuals with MS (23 relapsing-remitting MS, 7 progressive MS) and 19 age-matched healthy controls were scanned on a 3T MRI scanner equipped with 300 mT/m maximum gradient strength using a comprehensive multishell diffusion MRI protocol. Macromolecular tissue volume imaging was performed to quantify the myelin volume fraction. Diffusion data were fitted to a 3-compartment model of white matter using a spheric mean approach to yield estimates of axonal volume fraction. The imaging g-ratio was calculated from the ratio of myelin volume fraction and axonal volume fraction. Imaging metrics were compared between groups using 2-sided t tests with a Bonferroni correction. RESULTS: The mean g-ratio was significantly elevated in lesions compared with normal-appearing WM (0.74 vs 0.67, P < .001). Axonal volume fraction (0.17 vs 0.23, P < .001) and myelin volume fraction (0.17 vs 0.25, P < .001) were significantly lower in lesions than normal-appearing WM. Myelin volume fraction was lower in normal-appearing WM compared with that in healthy controls (0.25 vs 0.27, P = .009). Disability, as measured by the Expanded Disability Status Scale, was significantly associated with myelin volume fraction (ß = -40.5, P = .001) and axonal volume fraction (ß = -41.0, P = .016) in normal-appearing WM. CONCLUSIONS: The imaging g-ratio may serve as a biomarker for the relative degree of axonal and myelin loss in MS.