Methods and System for Modeling Electromagnetic Brain Stimulation and Brain Recordings with Boundary Element Approach with Fast Multipole Acceleration

Abstract

The present invention relates bringing a new accessible and accurate computational modeling approach to compute electric and magnetic fields in the brain to clinical practice.

Claims

1. A method for making a new BEM-FMM computational approach applicable to practical electromagnetic brain modeling for clinical applications including both neurophysiological recordings and neuro stimulation, comprising: Solving a first integral equation, Eq. (4), and a second integral equation, Eq. (7), for surface charge density ρ(r) residing on tissue conductivity interfaces within a human head model with the new BEM-FMM computational approach, wherein a tissue conductivity interface is a boundary between any two distinct tissues from a plurality of cranial and intracranial tissues, wherein the first integral equation, Eq. (4), on the tissue conductivity interfaces is discretized into a plurality of pulse bases on a plurality of triangular facets as shown in a first discretizing equation, Eq. (8a), wherein the second integral equation, Eq. (7), on an electrode surface is discretized into a plurality of pulse bases on a plurality of triangular facets as shown in a second discretizing equation, Eq. (8b), wherein a special diagonal preconditioner for the second discretizing equation, Eq. (8b), on an electrode interface in the form of an equation, Eq. (9), as an inverse integral electric potential of a uniform charge distribution on a surface of a given facet, is applied, wherein the resulting system of coupled equations, Eq. (8a) and Eq. (8b), is solved using a standard fast multipole method and a plurality of iterative methods including a generalized residual method and a bi-conjugate gradient method, wherein a set of neighbor double surface potential integrals in the form of an Eq. (6) and an Eq. (10) are precomputed analytically, Inclusion and modeling at least one non-nested human head topology, Inclusion and modeling at least one anisotropic tissue of the head, Inclusion and modeling at least one external and at least one internal voltage electrode, Inclusion and modeling at least one external and at least one internal current electrode, Improving the convergence of an iterative solution using a charge conservation law, Restoring at least one near-surface normal electric field from a computed charge distribution without postprocessing.

2. The method of claim 1 wherein the inclusion and modelling of the at least one non-nested head topology further comprises: Defining non-nested head topology as such where an object 1 and an object 2 may have a joint interface, Counting the joint interface between the object 1 and the object 2 only once, Assigning conductivity of the object 1 as an inner conductivity and assigning conductivity of the object 2 as an outer conductivity in a direction of an outer normal vector of object 1, Interchanging a meaning of objects 1 and 2 if necessary, Solving the first integral equation, Eq. (4), and the second integral equation, Eq. (7), for the surface charge density ρ(r) residing on conductivity interfaces within a human head model with the new BEM-FMM computational approach as described in claim 1, Applying this method to a plurality of non-nested head compartments.

3. The method of claim 1 wherein the inclusion and modeling at least one anisotropic tissue further comprises: Defining an anisotropic tissue as such where a local electrical conductivity and a local dielectric constant are different in different directions, Defining an elementary dipole source as combination of an electric current source and an electric current sink of equal strength, located closely to each other in a three-dimensional space, Replacing an anisotropic medium by a volumetric density of such dipole sources uniformly distributed in the three-dimensional space, wherein the space further comprises an x-direction, a y-direction and a z-direction in Cartesian coordinates, wherein local volumetric dipole density in the x-direction is proportional to (σ.sub.x−σ.sub.ref)/(σ.sub.x+σ.sub.ref) where σ.sub.x is the electrical conductivity in the x-direction, and σ.sub.ref is a reference conductivity, and is further proportional to an applied electric field, wherein local volumetric dipole density in the y-direction is proportional to (σ.sub.y−σ.sub.ref)/(σ.sub.y+σ.sub.ref) where σ.sub.y is the electrical conductivity in the y-direction, and σ.sub.ref is a reference conductivity, and is further proportional to an applied electric field, wherein local volumetric dipole density in the z-direction is proportional to (σ.sub.z−σ.sub.ref)/(σ.sub.z+σ.sub.ref) where σ.sub.z is the electrical conductivity in the z-direction, and σ.sub.ref is a reference conductivity, and is further proportional to an applied electric field, Solving the first integral equation, Eq. (4), and the second integral equation, Eq. (7), for the surface charge density ρ(r) residing on conductivity interfaces within a human head model with the new BEM-FMM computational approach as described in claim 1, wherein the primary field E.sup.p(r) on the right hand side of the first integral equation, Eq. (4), now contains the field of the said volumetric density of dipole sources.

4. The method of claim 1 wherein inclusion and modeling at least one external and at least one internal voltage electrode further comprises, Defining an external voltage electrode as such located on a skin surface and assigned a certain voltage V, Defining an internal voltage electrode as such located within the human head model and assigned a certain voltage V, Solving the first integral equation, Eq. (4), and the second integral equation, Eq. (7), for the surface charge density ρ(r) residing on conductivity interfaces within the human head model with the new BEM-FMM computational approach as described in claim 1.

5. The method of claim 1 for inclusion and modeling an external current electrode and an internal current electrode further comprises, Defining an external current electrode as such located on a skin surface and assigned a certain current I.sub.e, Defining an internal current electrode as such located within the human head model and assigned a certain current I.sub.e, Setting a primary electric field E.sup.p(r) in the first integral equation, Eq. (4), in the form n(r).Math.E.sup.p(r)=±I.sub.e(σ.sub.eA.sub.e), wherein the electrode has a local normal vector n(r) and a certain electrode area A.sub.e, wherein the electrode is enclosed in a medium with conductivity σ.sub.e for the internal electrode, wherein σ.sub.e is a scalp conductivity for the external electrode. Solving only the first integral equation, Eq. (4), for the surface charge density ρ(r) residing on conductivity interfaces within a human head model with the new BEM-FMM computational approach as described in claim 1.

6. The method of claim 1 further comprising, Adding a charge conservation law, Eq. (11), to the first integral equation, Eq. (4), with a certain weight value, wherein S in Eq. (11) is a combination of all interfaces in the first integral equation, Eq. (4), wherein a weight value on the order of 1 is assigned to Eq. (11), more preferably the weight value is one half, Solving only the first integral equation, Eq. (4), for the surface charge density ρ(r) residing on conductivity interfaces within a human head model with the new BEM-FMM computational approach as described in claim 1.

7. The method of claim 1 further comprising, Using an algebraic equation, Eq. (12) which directly expresses a normal electric field in terms of local surface charge density ρ(r) residing on tissue conductivity interfaces and two interfacial conductivities σ.sub.in and σ.sub.out, wherein the normal electric field is the normal field just inside any tissue conductivity interface and just outside any tissue conductivity interface, and the normal field discontinuity across an interface, wherein the surface charge density ρ(r) residing on conductivity interfaces within a human head model is found with the new BEM-FMM computational approach as described in claim 1.

8. The method of claim 1 further comprising, Including a dielectric permittivity ε of a human tissue into consideration by replacing the two interfacial conductivity values in the first integral equation, Eq. (4), by a complex conductivity in the form of an equation σ.sub.in/out.fwdarw.σ.sub.in/out+jωε.sub.in/out for a harmonic excitation with an angular frequency ω where the dielectric permittivity ε is a relative dielectric constant of the tissue, Solving the first integral equation, Eq. (4), and the second integral equation, Eq. (7), for the surface charge density ρ(r) residing on conductivity and dielectric interfaces within a human head model with the new BEM-FMM computational approach as described in claim 1.

9. The method of claim 1 further comprising, Defining a primary field E.sup.p(r) on the right hand side of the first integral equation, Eq. (4), through a magnetic vector potential, A, of a transcranial magnetic stimulation (TMS) coil in the form E.sup.p(r)=−∂A/∂tA, without a current or at least one voltage electrode, Solving only the first integral equation, Eq. (4), for the surface charge density ρ(r) residing on conductivity interfaces within a human head model with the new BEM-FMM computational approach as described in claim 1.

10. The method of claim 1 further comprising, A plurality of head models and a plurality of compositions while each may include at least one of the following: a conducting tissue component, a dielectric tissue component, and an anisotropic tissue component.

11. A tangible, non-transitory computer-readable medium storing instructions, the instructions when read by one or more processors, cause the one or more processors to: Acquire the human head model with a plurality of head compartments and a plurality of tissue properties, wherein the human head model may have a plurality of shapes and may include at least one of the following: a conducting tissue component, a dielectric tissue component, and an anisotropic tissue component, Compute an electric and a magnetic field for a plurality of excitations, E.sup.p(r), in the first integral equation, Eq. (4), and a plurality of excitations, V, in the second integral equation, Eq. (7), as described in claim 1, wherein keeping only the excitation in the form E.sup.p(r) corresponds to transcranial magnetic stimulation (TMS) modeling, wherein keeping only the excitation in the form E.sup.p(r) also corresponds to electroencephalography (EEG) modeling with a plurality of volumetric current dipole distributions, wherein keeping only the excitation in the form V corresponds to transcranial electrical stimulation (TES) or deep brain stimulation (DBS) or intracortical micro stimulation (ICMS) modeling.

12. The medium of claim 11, wherein the instructions further cause the one or more processors to optimize performance of a medical diagnostic tool.

13. A device comprising one or more processors configured to: Acquire the human head model with a plurality of head compartments and a plurality of tissue properties, wherein the human head model may have a plurality of shapes and may include at least one of the following: a conducting tissue component, a dielectric tissue component, and an anisotropic tissue component, Compute an electric and a magnetic field for a plurality of excitations, E.sup.p(r), in the first integral equation, Eq. (4), and a plurality of excitations, V, in the second integral equation, Eq. (7), as described in claim 1, wherein keeping only the excitation in the form E.sup.p(r) corresponds to transcranial magnetic stimulation (TMS) modeling, wherein keeping only the excitation in the form E.sup.p(r) also corresponds to electroencephalography (EEG) modeling with a plurality of volumetric current dipole distributions, wherein keeping only the excitation in the form V corresponds to transcranial electrical stimulation (TES) or deep brain stimulation (DBS) or intracortical micro stimulation (ICMS) modeling.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0089] FIG. 1. Examples of neurostimulation and neurophysiological recordings.

[0090] FIG. 2. Block diagram showing an example of the systems of this disclosure.

[0091] FIG. 3. Block diagram showing an example of a technical computing environment of this disclosure.

[0092] FIG. 4. Flow diagram of an example process for computing electric and magnetic fields within a high-resolution multi-compartment head model.

[0093] FIG. 5. Method of modeling non-nested geometries.

[0094] FIG. 6. Distributed dipole method for anisotropic medium.

[0095] FIG. 7. Method of improving the convergence using the charge conservation law.

DETAILED DESCRIPTION OF THE DRAWINGS

[0096] FIG. 1. Examples of TES or transcranial electrical stimulation, DBS or deep brain stimulation, ICMS or intracortical microstimulation and neurophysiological recordings (EEG). and. All applications require fast and accurate computations of the electric field and the electric potential within the head. Neurophysiological recordings additionally include magnetic field measurements (MEG, not shown in FIG. 1) and intracortical EEG (similar to ICMS but with a recording function instead of stimulation).

[0097] FIG. 2 shows the system example, a client device 110 accesses and interacts with a server device 150 through a network 140 to obtain information about scattering/radiation of a target or choose a target model for use. A user may interact with the client device 110 directly or through one or more input devices 120. The input device(s) 120 can be part of the client device 110 and can be a user device. In some implementations, the client device 110 can provide the desired information without needing to access the server device 150. The server device 150 hosts a technical computing environment (TCE) 130 in which the historical data is processed and the target models are processed and/or generated. In some implementations, the client device 110 may employ a TCE 130 to provide a display, e.g., a webpage. In some implementations, a user interacts with the server device 150 via the displayed webpage. The displayed TCE 130 operating on the client device 110 can be the same as or be part of the TCE 130 hosted by the server device 150.

[0098] FIG. 3 shows block diagram showing an example of a technical computing environment of this disclosure. The TCE 130 is supported by an application programming interface (API) 260. The API 260 can be visible to a user within the TCE 130, or can be invisible to the user. An example of a portion of programming code is an optimizer 266 that is capable of optimizing parameters. Other examples of the programming code portions can include, but not limited to, a target model generator, equation solver, and graphical user interface (not shown). The API 260 can receive one or more TCE inputs 262 from the TCE 130, or on behalf of a user or a user device, and output one or more TCE outputs 264 to the TCE 130. Examples of TCE inputs 262 include, for example, specifications for the target models to be processed or generated, incident field data, testing data, etc. Examples of TCE outputs 264 include generated models, results of model comparisons, and other user specified information.

[0099] FIG. 4. Flow diagram of an example process for estimating electric and magnetic fields in the brain. The systems of this disclosure can perform process 300 to generate or acquire head target models of the physical subject of interest, and solve for the electric and magnetic fields and other results. Initially, upon receipt of a request, step 302 to perform brain modeling e.g., from a user or a user device, the system may prompt the user or user device to input complete information about the target model(s), step 304. These inputs can be the same as TCE inputs 262 of FIG. 3. Once the target surface head model is imported and described, some implementations then begin to model the fields within the head and performance estimation process (Step 308). Mathematical details of certain exemplary implementations of process 308 are described in much greater detail below as including numerous sub-processes. In step 306, the target head surface mesh model is also processed internally to enable a proper treatment of the non-nested head geometry. In Step 310, a uniform dipole mesh is introduced into an anisotropic head compartment. In Step 312, the electrodes with known parameters are either imprinted or embedded automatically and their mesh labels are generated. In Step 314, neighbor potential integrals necessary for accurate integration are computed as described below. In steps 316, 318, 320, 322, 324, the resulting system of BEM equations is solved iteratively using fast multipole method (FMM) acceleration and generalized minimum residual method (GMRES). Results, such as described above, of the electric and magnetic field estimation process 308 may be output in Step 330. A determination (Step 332) may then be made to establish whether the determined performance characteristics of the electrode system and its readings meet user's requirements. If the requirements are satisfied, the process may then proceed to other target modeling tasks, or progress to prototype development (Step 334). If the performance measures output does not meet the specified requirements, the process may iterate, e.g., from step 332, permitting the user to enter additional and/or different input parameters or change the electrode assembly.

[0100] FIG. 5. For two objects (1 and 2) in contact with each other, the joint interface between them should be counted only once. In the figure, this interface is counted only for object 1 with σ.sub.1 being the inner conductivity and σ.sub.2 being the outer conductivity (in the direction of the normal vector n.sub.1). Facets of object 2 at the interface are removed to avoid double-counting.

[0101] FIG. 6. Model of elementary dipoles uniformly distributed in space used to for taking into account the effect of the anisotropic medium. Three orthogonal dipoles are responsible for three different conductivity values in the x, y, and z directions.

[0102] FIG. 7. Typical convergence rate of the solution with generalized minimum residual method (GMRES) for a multi-compartment head model with the charge conservation law; b)—the same result when the charge conservation law is ignored.