Microstimulation in The Brain—Does Microdialysis Influence theActivated Volume of Tissue?

D. Krapohl1,3,∗, S. Loeffler2,∗, A. Moser2 and U.G.Hofmann1,∗∗

1Institute for Signalprocessing, University of Luebeck, Germany2Institute for Neurology, University of Luebeck, Germany3Department of Information Technology and Media, Mid Sweden University, Sweden

∗These authors contributed equally to the presented work.∗∗Corresponding author: Ratzeburger Allee 160, 23538 Lubeck, Germany, hofmann@isip.uni-luebeck.de

Abstract: Deep brain stimulation (DBS) hasbeen established as an effective treatment forParkinson’s disease and other movement disor-ders. The stimulation is currently administeredusing tetrode-macroelectrodes that target thesubthalamic nucleus (STN). This often leadsto side effects which bias the surrounding ar-eas, e.g. the speech centre. Targeting a spe-cific brain region can better be achieved withmicro-stimulation electrodes with directed elec-trical field distribution. Experimental studiesshowed the effectiveness of microelectrode DBSby comparing neurotransmitter outflow beforeand after the stimulation. The neurotransmit-ter outflow in close proximity to the stimulationis hereby measured by means of microdialysis.To establish ideal distances and stimulationstrength, the electric potential around the stim-ulation electrode and microdialysis membranewere modelled using comsol Multiphysics.

Keywords: deep brain stimulation, microelec-trode, microdialysis, electrode-electrolyte inter-face, impedance

1 Introduction

Since the 1990’s tetrode-macroelectrodes areused for DBS in different brain regions. Thebeneficial effects of this stimulation on motor-as well as psychomotor disorders have beenwell established [10, 2]. However, partly severeside effects due to lead misplacement or longterm tissue impact are reported [17, 14]. Com-pared to macroelecrodes, the use of microelec-trodes for stimulation would provide significantadvantages as limitation of the volume of tis-sue activated, electrophysiologically facilitatedaccurate probe placement, less tissue impact

and facilitation of closed-loop applications [16].However, stimulation microelectrodes can onlybe used clinically when their electrical param-eters are within the limitations for safe stim-ulation. Charge per phase and charge densitythresholds of 135 - 400 nC/phase respectively 2.3- 6.7 µC/cm2 with pulse widths of 60 - 200 µshave therefore been determined [7, 12]. Never-theless, charge thresholds depending on the iso-or anisotropy of the tissue, rheobase currentand stimulus waveform have to be exceeded inthe targeted volume area [9]. For microelec-trode stimulation, impedance properties areeven more important than for macroelectrodestimulation. It was reported, that substantiallydifferent volumes of tissue activated are gen-erated from high, medium and low impedanceelectrodes [3, 1]. Electrode impedances origi-nate in the formation of a Helmholtz doublelayer on the electrode-electrolyte interface. Acurrent flow occurs by electrostatic, frequencydependent charging and discharging of the ca-pacitance. But also non-capacitive faradic re-actions as well as electrolytic reactions mayoccur leading to electron transfer across theelectrode-electrolyte interface. The processesat the electrode-electrolyte interface can bemodelled using equivalent circuit representa-tions as shown in figure 1. The series resistanceRs represents the resistance due to electrolytesolution and cables. Rct, the charge transferresistance describes the resistance for electro-chemical reactions taking place [11]. Zcpa isthe frequency dependent constant phase angleelement which comprises real- and imaginarypart of the impedance Z.

Rs

Rct

Zcpa

Figure 1: Equivalent circuit representation of theelectrode electrolyte interface [6, 13].

Because of the small size of the microelectrode’sgeometric surface area (GSA), the charge perunit area at the electrode-electrolyte interfaceis small. Therefore, high charge-injection ca-pacity, depending on the material, is a prereq-uisite for microstimulation electrodes [5]. Thecharge injection capacity Qinj for PtIr alloyhas been calculated to be 300 - 350 µC/cm2 the-oretically, but only about 100 µC/cm2 can be in-jected without causing electrolysis of water [15].However, disregarding all these parameters, theeffectiveness of microelectrode stimulation withcathodic, monopolar, rectangular, 0.5 mA con-stant current pulses with 60 µs duration and124 Hz frequency was proven by showing anenhanced outflow of the neurotransmitter γ-aminobutyric acid (gaba) in close proximityto the stimulation microelectrode [8]. Neu-rotransmitter were sampled with the help ofa microdialysis membrane close to the stim-ulation microelectrode. The influence of themicrodialysis membrane as a dielectricum filledwith conductive liquid may alter the stimula-tion properties of the microelectrode as well asthe direction and volume in which the electricfield is evolving.

2 Measurements

Independent from the modelling approach, volt-ages, developing under 0.5 mA current stim-ulation with 60 µs pulse width and electrodeimpedances were measured. The voltage drop(see figure 2) was measured parallel includingcables and connectors using a tds2004b os-cilloscope (Tektronix Inc., US ) and recordedwith NI Signal Express Software (National In-struments Corp., US ). The signal was down-sampled to 200 datapoints using python pro-gramming language and later used as a voltagefunction for COMSOL.

Figure 2: Voltage function of a 60 µs 0.5 mApulse in 0.9 % sodium chloride solution.

Represents the voltage function applied as electricpotential (V(t)) in the model.

Impedances Z and phase angles Phi of twodifferent electrode tip configurations (see fig-ure 6) were measured using a Gwinstek lcr-821 LCR meter employing the three pointmeasurement method for frequencies rangingfrom 0.1 to 200 kHz at constant voltage of0.1 V . Eight measurements were performedwith 3 electrodes of two different configura-tions. Mean value and standard deviationwere plotted as Bode Plot representation withdouble-logarithmic axes for impedances Z andhalf-logarithmic axes for phase angles Phi (seefigure 3).

Figure 3: Bode Plot representation of impedancesand phase angles for the inner and outer contactarea of the concentric, bipolar electrodes and two

different electrode tip configurations.

Measures of the realistic arrangement of thecbcbg30 concentric bipolar stimulation mi-croelectrode (FHC, Maine, US ) and the cma11 md microdialysis probe (CMA Microdial-ysis, Sweden) were taken from a photographand transfered into a 3d geometric model inCOMSOL drawing mode.

Figure 4: Microdialysis membrane and stimulationelectrode fixed in close proximity to a double tube

guiding cannula

3 Use of COMSOL Multiphysics

COMSOL Multiphysics was used to model themembrane of a microdialysis probe, constantlyperfused with Krebs - Ringer bicarbonatebuffer pH 7.4, closely resembling the cerebralspinal fluid (CSF), and the tip of a concen-tric, bipolar stimulation microelectrode withan outer contact made from stainless steel andan inner contact made from PtIr alloy duringstimulation with cathodic, monopolar, rectan-gular, 0.5 mA constant current pulses of 60 µsduration and 124 Hz frequency. COMSOLElectric Currents (AC/DC) module with Con-ductive Media DC Application Mode solvingthe generalized partial differential equation forcurrent sources (see equation 1).

Qj = −∇ · (σ∇V − Je) (1)

Isotropic conductivity values were set using thematerial library for the defined subdomains inthe model. For all subdomains, we generallyset external current densities, current sourcesand initial electric potentials to zero and usedLagrange quadratic shape functions for approx-imation. No infinite elements applied were ap-plied. Table 1 shows the conductivity as well asgeometry and description for the subdomainsmodelled. Five different boundary conditionswere assigned to different groups. Table 2 com-prises the boundary conditions for groups 1 - 5,shown in figure 5 and their specific properties.

Material V [mm3] A (mm2) σ [S/cm]

grey matter 166.2725 180.6331 0.00228

Stainless Steel 0.342189 7.189776 13888.8

X20CrNi172

CSF 0.907581 7.929236 0.1789

Epoxylite 0.144513 4.001415 1e−11

578EB

PtIr 90/10 0.047968 1.333082 4.081e6

Table 1: Volume, area and conductivity of theemployed material types for the 5 subdomains

modelled.

Boundary parameter equation

condition

1 Ground V 2 = 0

2 Electric n · J = 0

insulation

3 Continuity n · (J1 − J2) = 0

4 Electric σ = 1e−11, n · (J1 − J2) =shielding d = 13e−6 −∇tσd∇tV 2

5 Electric V0 = V 2 = V0

potential V(t)

Table 2: Exterior and interior boundaryconditions assigned to group 1 - 5.

Figure 5: Boundaries group 1 - 5 to which theboundary conditions from table 2 were assigned.

Meshing was performed according to theboundaries.

To establish the role of the constant phaseangel element Zzpa and the charge transferresistance Rct, a thin layer of uniform thick-ness and electrical properties was placed at theelectrode - electrolyte interface as explainedin [4]. Zcpa was calculated using the factors

K = 1.57 m2/s, β, and the electrode surface

area A = 166.61 mm2 with ω = 2 · π · f andf = 124 Hz (see equation 2)

Zcpa =K

A(jω)−β(2)

It was assumed that the overpotential η wasrepresented by the voltage difference betweenthe PtIr electrode contact and the surroundinggrey matter. Thus, instead of η, the V (t) func-tion was used in the description of the chargetransfer resistance Rct as the driving force forfaradic reactions to take place (see equation3 where R = 8.314472 J/K·mole , T = 298 K,F = 96485.3399 C/mole , n = 2 (number ofelectrons), I0 = n · J0 · A (exchange current),nJ0 = 6.41 ·10−4 A/m2 (normalized equilibriumcurrent density), A = 166.61 mm2 (electrodesurface area), V (t) was the overpotential andαa = 0.099 and αc = 0.378 were transfer coef-ficients ).

Rct =V (t)

I0 ·(e(αa

nFRT ·V (t)) − e(αc

nFRT ·V (t))

) (3)

Meshing was performed according to theboundary conditions. The SPOOLES directlinear systems solver was used with standardsettings to solve the model. 91 time stepswere calculated according to the time courseof the input voltage function V (t). Two differ-ent electrode tip configurations were examined(see figure 6). Tip configurations 1 and 2 arebevelled at 45 ◦. Tip configuration 1 has ainner PtIr contact that is on one level withthe outer stainless steel contact and a smoothsurface. For tip configuration 2, the inner PtIrcontact is raised compared to the outer con-tact. The tip possesses a rough surface. Theelectrodes were further modelled having a mi-crodialysis membrane in close promixity, ornot. The microdialysis mebrane was modelledas a dielectric material filled with conductiveliquid.

Figure 6: 3d geometry model of the microdialysismembrane and stimulation electrode in close

proximity. Two different electrode tipconfigurations A and B were used in the model.

4 Results

The streamline plot from postprocessing modein figure 7 shows, qualitatively, that the mi-crodialysis membrane, when included in themodel, effects the spread of the electric fieldfrom stimulation contact to the outer marginsof the tissue volume conductor which were setto ground.

Figure 7: Streamline plots from the differentgeometric models. A + B: Tip configuration 1

with (A), or without (B) microdialysis membrane.C + D: Tip configuration 2 with (C), or without

(D) microdialysis membrane.

For further postprocessing analysis, cross sec-tional plots for the three dimensions along thex, y and z axis were exported. Figure 8 showsthe cross sectional planes in the 3D model.

Figure 8: Cross sectional planes x, y and z forwhich postprocessing analysis was performed.

Figure 9 shows the electric potential for thecross section plots in z-direction including dif-ferent time steps of the stimulation voltagefunction. The electric potential in z directionwas plottet against the logarithmic distance z.The drop of electric potential from the elec-trode surface in z-direction was compared be-tween the two different tip configurations (C+ D). Further, it was compared whether thepresence of the microdialysis membrane affectsthe voltage drop in z-direction (A+B). Figure9 shows that the voltage drop for tip configu-ration 1 is steeper than for tip configuration 2.The presence of the microdialysis membranedoes not affect the voltage drop in z-direction.

Figure 9: Electric potentials in V for Tipconfigurations 1 and 2 as well as the electric

potential for the enabled or disabled microdialysismembrane.

Figure 10 demonstrates the voltage drop alongthe x-axis.

Figure 10: Electric potential in x-direction.

These results show, that the microdialysis mem-brane in x direction, too, has no effect on theelectric potential drop. Again, there is a no-table difference between the two electrode tipconfigurations. The voltage peak at x = 0 rep-resents the electric potential on the stimulationcontact. The potential drops rapidly on bothsides of the stimulation site due to the epoxyinsulation material. Then, from the outer con-tact of the electrode, the potential drops almostlinearly along the distance through the tissue.The y-direction is the axis which leads throughthe contact and the microdialysis membrane.Figure 11 shows the voltage drop of the electricpotential in y-direction.

Figure 11: Electric potential in y-direction.

The effect of the microdialysis membrane isclearly visible on this axis. The electrode tipsare bevelled. Therefore the voltage drop is non-symmetric in y-direction. The voltage drop onthe positive y-axis almost resembles the situa-tion for the x-direction. On the negative y-axis,the steepness of the slope is clearly diminished

on the electrode-tissue boundary. The slopeof the voltage drop is zeros from −0.5mm to−1.0mm. This occurs co-localized with themicrodialysis membrane localization.

5 Discussion

The results of the presented model indicate,that the modification of even minimal tip con-figurations can lead to strong influences on theelectric field distribution in the case of micro-electrodes. Further, it is to assume that themicrodialysis membrane, indeed has an effecton the spread of the electric potential throughthe tissue. This effect does, however, not af-fect the general stimulation behaviour of themicroelectrode. Thus, the model of the co-localized microdialysis and microstimulationcan be compared with other microstimulationtechniques. Our model is based on assumptionswhich were introduced to reduce the complexityof the electrode-electrolyte interface. There-fore, predictions of current densities are errorprone in this state of the model and are notdiscussed here. It can, however, be observed,that the current density drops rapidly on theelectrode-electrolyte interface. That may be anexplanation for the comparatively minor dam-age to the stimulated tissue, which is observedwith microstimulation. Further models shouldemphasize the role of Zzpa Rct and their depen-dency on the overpotential more thoroughly.The monopolar stimulation, which is now car-ried out in the model, should be replaced by abipolar stimulation, which is mostly used forelectrical stimulation of cerebral tissue.

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