Microscopic magnetic stimulation of neural tissue

Electrical stimulation is currently used to treat a wide range of cardiovascular, sensory and neurological diseases. Despite its success, there are significant limitations to its application, including incompatibility with magnetic resonance imaging, limited control of electric fields and decreased performance associated with tissue inflammation. Magnetic stimulation overcomes these limitations but existing devices (that is, transcranial magnetic stimulation) are large, reducing their translation to chronic applications. In addition, existing devices are not effective for deeper, sub-cortical targets. Here we demonstrate that sub-millimeter coils can activate neuronal tissue. Interestingly, the results of both modelling and physiological experiments suggest that different spatial orientations of the coils relative to the neuronal tissue can be used to generate specific neural responses. These results raise the possibility that micro-magnetic stimulation coils, small enough to be implanted within the brain parenchyma, may prove to be an effective alternative to existing stimulation devices.

curvature reduces the numerical staircasing, which occurs for example when a sphere is approximated by tetrahedral elements. The sampling resolution of narrow regions allows for decreasing the element size so that the object would not disappear or become unrealistically magnified in the mesh. Finally, the mesh was also controlled by the physics, which essentially adapts the mesh to the physical solution, for example if there is a point source or electric field generator in the center of a sphere than the center will be sampled more finely in order to represent the electric field more precisely in space. The next step after meshing was to set the boundary conditions or constrain the behavior of the solution at the boundary of its domain; these conditions are very important when solving differential equations of real physical problems. The exterior boundary conditions were set to 0 = ϕ A (i.e., magnetic insulation), except for the vector along the z-axis, which was set to 0 = r (i.e., axial symmetry). The interior boundary conditions were set to 0 = ⋅ J n (i.e., electric insulation) for each turn and the two terminals. In each of the 21 turns the voltage was set to 4V corresponding to our experimental conditions under maximum stimulation.
The initial values for the electric potential and the magnetic vector potential were set to zero. The simulations including meshing converged after 25s of computing time with a Dell Precision T7500 48GB running 64-bit Windows 7.

Finite Element Method Validation:
In order to validate the Finite Element Method we ran a set of simulations to estimate the inductance of the coil and then compare it to the values measured. The inductor was a homogenized coil 41 , or a coil with just one very large turn, instead of 21 for numerical reasons and the solution was normalized to take this idealization in account. The single turn composed of a 25 µm thick copper sheet with a 500×500 µm cross-section square and rounded edges. The homogenized coil is considered to be an ideal magnetic field generator, and it stores the magnetic field energy W generated by the supplied electric current i. This information can be used to estimate the ideal inductance of the coil and compare it with the value measured in each coil for FEM numerical validation purposes. The portion of magnetic energy W lost reduces both the efficiency (i.e., Q-factor) and the measured inductance of the coil. However, this magnetic energy does not really vanish since energy is conserved and therefore is available around the coil where we have reaped its benefits by eliciting neuronal activity. The magnetic fields (B) arising from µMS as well as the electric fields (E) were found by solving numerically the magnetostatics equation (Methods), or the set of Maxwell equations simplified by the assumption that all electric currents are constant (i.e., steady state -DC). The solution of this 3D model returned the values in and around the square inductor of electric (V) and magnetic potentials (A), which was used to calculate the magnetic flux density (i.e.

A B × ∇ =
). In order to obtain this solution we meshed the geometry in approximately 700,000 tetrahedral elements.
All six faces of the box containing the geometry were set to magnetic insulation boundary conditions (i.e., exterior boundary conditions), or the magnetic field is zero in these faces. All the interior surfaces of the model were set to electric insulation boundary conditions except for the two surfaces that are in common to the two halves of the homogenized coil or current sheet. The current density (eq. 5) on one surface was set to generate a current of 10 A (terminal) and the other surface was set to a V 0 =0 V (ground).
The magnetic field inside the coil (Fig. 6a) follows an almost linear path but outside the lines of flux are radially symmetric to the center of the coil. The magnetic field peaks inside the inductor and spreads around the external part of the coil uniformly according to the magnetic conservation law. The inside peak occurs because the volume outside the solenoid is much greater than the volume inside, so the magnitude of magnetic field outside is greatly reduced. The maximum induced electric fields were found at distances of 25-100µm from the lateral side of the coils (Fig. 6b)  Filter) that was mounted with vacuum grease to the recording chamber (~1.0 ml volume). A 2 mm circle in the center of the Millipore paper allowed light from below to be projected onto the photoreceptors so that light-elicited spikes would arise in the ganglion cell. The light stimulus was projected from an LCD projector (InFocus, Portland, OR).
Electrophysiology: Patch pipettes were used to make small holes in the inner limiting membrane, and ganglion cells with large somata were targeted under visual control (Fig. 3c). Spiking was recorded with a patch electrode (4-8 MΩ) that was filled with superfusate and positioned onto the surface of a targeted ganglion cell (cell-attached mode). Two silver-chloride-coated wires served as the ground and were positioned at opposite edges of the recording chamber, each approximately 15 mm from the targeted cell.
The retina was continuously perfused at 4 mL/min with Ames solution (pH 7.4) at 36°C, equilibrated with 95% O 2 and 5% CO 2 . Full-field light stimuli were used to determine whether an appropriate patch seal had been established and also to confirm that the cell was functioning normally; only those cells that generated spiking responses were tested with µMS. The µMS coil assembly was fixed in the micromanipulator such that the main axis of the coil was oriented either parallel or perpendicular to the retinal surface. The coil assembly was lowered into the bath until the coil was 100 µm above the retinal surface. Five repeats were performed every time a parameter was changed, e.g. increase in amplitude, adjustment of the position of the coil, etc.