In vitro Magnetic Stimulation: A Simple Stimulation Device to Deliver Defined Low Intensity Electromagnetic Fields

Abstract

Non-invasive brain stimulation (NIBS) by electromagnetic fields appears to benefit human neurological and psychiatric conditions, although the optimal stimulation parameters and underlying mechanisms remain unclear. Although, in vitro studies have begun to elucidate cellular mechanisms, stimulation is delivered by a range of coils (from commercially available human stimulation coils to laboratory-built circuits) so that the electromagnetic fields induced within the tissue to produce the reported effects are ill-defined. Here, we develop a simple in vitro stimulation device with plug-and-play features that allow delivery of a range of stimulation parameters. We chose to test low intensity repetitive magnetic stimulation (LI-rMS) delivered at three frequencies to hindbrain explant cultures containing the olivocerebellar pathway. We used computational modeling to define the parameters of a stimulation circuit and coil that deliver a unidirectional homogeneous magnetic field of known intensity and direction, and therefore a predictable electric field, to the target. We built the coil to be compatible with culture requirements: stimulation within an incubator; a flat surface allowing consistent position and magnetic field direction; location outside the culture plate to maintain sterility and no heating or vibration. Measurements at the explant confirmed the induced magnetic field was homogenous and matched the simulation results. To validate our system we investigated biological effects following LI-rMS at 1 Hz, 10 Hz and biomimetic high frequency, which we have previously shown induces neural circuit reorganization. We found that gene expression was modified by LI-rMS in a frequency-related manner. Four hours after a single 10-min stimulation session, the number of c-fos positive cells increased, indicating that our stimulation activated the tissue. Also, after 14 days of LI-rMS, the expression of genes normally present in the tissue was differentially modified according to the stimulation delivered. Thus we describe a simple magnetic stimulation device that delivers defined stimulation parameters to different neural systems in vitro. Such devices are essential to further understanding of the fundamental effects of magnetic stimulation on biological tissue and optimize therapeutic application of human NIBS.

Keywords: LI-rMS; computational modeling; electric field; low intensity repetitive magnetic stimulation; magnetic coil design; magnetic field; magnetic stimulation; rTMS.

FIGURE 1

Overview of the culture set-up (A) and induced magnetic (B–D) and electric field (E). (A) Hindbrain explants are dissected so that they contain a central brainstem containing the inferior olive caudally and the 2 hemicerebellar plates at each side (beige). For our lesion model we graft two denervated hemicerebellae (cerise pink) adjacent to an intact explant (left panel). Explants are cultured on Millicell membranes in six-well plates (middle panel). The organotypic hindbrain samples (beige) were cultured on a membrane ∼4 mm above the top of the coil, placed underneath the culture well (right panel). (B) Modeled overview of the coil and its generated magnetic field. Gray squares at the bottom of the image show a cross-section of the coil wiring (see Table 1 for coil components and dimensions). White surround corresponds to the coil’s plastic shell. Colors correspond to the magnetic field strength and black arrows to magnetic field direction . The beige block in the center of the image shows the location of the explant on a horizontal plane 4 mm above the coil. (C) Schematic overview of the different magnetic field components at 4 mm distance from the base of the coil. The magnetic field is almost exclusively comprised of a vertical field component B_z (red line) up to 2.5 mm from the coil axis, whereas thehorizontal component is effectively zero within this region. (D) Modeled overview of magnetic field strength (mT; colors) and direction (red lines) starting at the top of the coil wiring (horizontal plane at 0 mm). The explant lies 4 mm above within the unidirectional magnetic field. (E) Modeled overview of the induced electric field from the top of the coil wiring (Horizontal plane at 0 mm). Colors indicate the electric field strength (V/m). The explant at 4 mm shows that the areas of interest (cerise pink; grafted hemicerebellae and inferior olive) lie in the same electric field.

FIGURE 2

Detailed finite element modeling of the magnetic and electric fields in the explant tissue. (A) Schematic overview of the spatial relation between the coil and the explant. The coil has 119 turns with counter clockwise current flow. Coil dimensions are listed in Table 1. The overall dimension of the explant is 5 mm in width and length, and 1 mm thickness. It is placed 4 mm above the surface of the coil, centered along the coil axis. (B) Simulated magnetic field distribution in the explant. The arrows indicate the direction of the magnetic flux. For illustration purposes, the intensity scale has been limited to between 8 and 10 mT in order to show the intensity gradient throughout the explant. (C) Simulated electric field distribution in the explant. The arrows indicate the direction of the induced current flow. For this figure the upper scale has been limited to 0.1 Vm^-1 to demonstrate the range of E intensity within the explant, as it is not visible in Figure 1E. (D) Electric field distribution looking at the side of the tissue closest to the coil. The areas of interest are outlined in white and all receive the same E intensity.

FIGURE 3

Pulse waveform and parameters. (A) Schematic representation of the trapezoidal waveform used to induce the magnetic field and the resulting predicted induced electric field inside a conductor (E(t)). Three different temporal domains are specified for this set-up: t_rise = rise-time, t_fall = fall-time, t₁ = pulse ON. t_rise /t_fall and t₁ are based on previous experiments and have a value of 100 and 300 μs, respectively. Note that there is a static magnetic field between rise and fall-times (A,C), during which no current flows inside the target tissue. (B) Magnetic field intensity in normalized, arbitrary units (a.u.) induced inside the coil by a single pulse using the waveform shown in (A). The intensity was modeled in TINA (dotted line) and measured via hall-effect (solid gray line), showing a tight correspondence between predicted and measured waveform. (C) Calculated, single pulse induced electric field in a round conductor at a radius of 2 mm from the central axis and 4 mm vertically above the top of the coil’s wiring.

FIGURE 4

(A) Schematic overview of the electronic circuit used to produce the desired current in the coil (L). The microcontroller produces a squared waveform, which triggers the darlington transistor (TIP122) on and off to permit the 24 V power source to drive current through the RL circuit at the desired frequency during the desired period. The zener diode (BZT03-C24) is unidirectional and thus not involved in the active circuit. However, when the transistor is off, it is the energy stored in the coil L, which drives current through the R-BZT03 diode circuit. Thus when the transistor opens, the unidirectional BZT03-C24 diode is the primary limiter of the current level induced by the coils energy to control the fall time. (B) Definition of the characteristic time Tau (τ). Current intensity inside the circuit in response to increasing voltage steps reaches more than 99.9% of its maximum (i.e., t_rise) after a time of ∼5τ.

FIGURE 5

Coil set-up and magnetic shielding. (A) View of a single coil from the top (top panel) and side (bottom panel). (B) Vibration measurement of the coil (top) and background surface (below) in mm/s as measured by a single point vibrometer with OFV-534 compact sensor head for high optical sensitivity. Vibration amplitude of the coil is within background vibration. (C) View of the coil set-up within the incubator. A sheet of Mu-metal (min 1 mm thickness) is placed between adjacent cultures (vertical arrow). Also two wires can be seen passing to each six-well plate. This is because each coil is driven by a separate RL circuit. (D) Measurements of coil temperature during the 10 min stimulation period. For all frequencies and sham (unactivated coils) there was no temperature rise above that of the incubator (35°C). (E) Effect of Mu-metal on the magnetic field. Black lines indicate a produced magnetic field without Mu-metal shielding at a horizontal distance from the center of the active coil. Red line shows the magnetic field in correspondence with a Mu-metal shielding at 35 mm from the coil. Magnetic field intensity is concentrated by Mu-metal, leading to complete shielding with no detectable magnetic field at adjacent cultures beyond that distance (small inset).

FIGURE 6

c-fos labeling following LI-rMS in the cerebellar plates. (A) An example of c-fos labeling after stimulation by BHFS. In this case c-fos (red) is co-labeled with calbindin (green) to reveal Purkinje neurons. C-fos labeling is located in some of the Purkinje cell nuclei (^∗) and in other calbindin-negative profiles (arrowheads), which are the size and location of either granule or stellate neurons. Bar = 25 μm. (B) Histograms show the number of c-fos positive cellular profiles per mm² in sham (unstimulated) controls, and explants stimulated with 1 Hz, 10 Hz or BHFS (n = 4 for each group; all four groups contain explants from the same 3 litters). Error bars are standard error of the mean. Cellular labeling in comparison to sham: ^∗∗∗p < 0.0001; ^∗∗p < 0.01. 1 Hz vs. BHFS between group comparison: ^###p < 0.001 (ANOVA followed by post hoc Tukey pairwise comparisons).

FIGURE 7

BDNF, Pax3, Sia2, and Sia 4 mRNA expression levels in the cerebellar plate (Cb) and inferior olive (ION) normalized to sham (unstimulated) controls. Explants were stimulated with 1 Hz, 10 Hz or BHFS (n = 5 for each group; all four groups contain pooled tissue from the same 15 litters). Histograms show mRNA levels as fold-change relative to sham (horizontal dotted line at threshold change of 1). Error bars are standard error of the mean, ^∗ indicates p < 0.05 and # indicates significantly different compared to sham stimulated controls (p < 0.05) (ANOVA, p < 0.05, followed by post hoc Tukey pairwise comparisons).