Monopolar vs. bipolar subretinal stimulation—An in vitro study

Journal of Neuroscience Methods 199 (2011) 26–34

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Monopolar vs. bipolar subretinal stimulation—An in vitro study Matthias Gerhardt a,c,∗ , Gillian Groeger b , Niall MacCarthy a a

Tyndall National Institute, Prospect Row, Cork, Ireland Department of Biochemistry, University College Cork, Ireland c Institut für Physik und Astronomie, University Potsdam, Germany b

a r t i c l e

i n f o

Article history: Received 24 August 2010 Received in revised form 24 March 2011 Accepted 14 April 2011 Keywords: SVD Subretinal Electrodes Monopolar Bipolar Retina Ganglion Cells

a b s t r a c t This study uses an in vitro rd10 mouse model to quantify and compare the ability of the monopolar and the (concentric) bipolar electrode configurations for subretinal stimulation. To allow for results which can be directly compared an identical region of the retina was stimulated due to the circumstance that the bipolar electrode configuration allows also for monopolar stimulation, if the concentric counter-electrode is set potential-free (floating). A ganglion cell, located centrally over the bipolar electrode configuration was selected to extracellularly record action potentials during stimulation. To analyse the recorded action potentials, we introduce a new method which combines the advantages of (a) singular value decomposition (SVD) for weighting similar modulation patterns with which the recorded action potentials are characterized and (b) multi curve fitting to identify a common threshold level, required to finally assemble a strength–duration relationship (SDR). By directly comparing the obtained SDR curves, we found that the efficiency of stimulation with the monopolar electrode configuration is significantly higher than with the bipolar electrode configuration. All obtained SDR curves were fitted using the Lapicque model to estimate the chronaxie times and the rheobase currents. Liquid inclusions, eventually separating the retina from the electrodes are discussed to be a major cause for low ganglion cell responses during stimulation with the bipolar electrode configuration. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The retina of patients suffering from the final stages of retinitis pigmentosa is characterized by nearly complete loss of all photoreceptors (Fariss et al., 2000), therefore the patients lose their vision. Fortunately, during recent years some promising therapeutic approaches were devised to help such patients. One of these therapeutic approaches is called “subretinal stimulation” and was developed by the groups Zrenner et al. (1999) and Chow et al. (2002), 10 years ago. The subretinal stimulation is based on an array of microelectrodes implanted in contact with the outer plexiform layer of a degenerated retina to replace the lost neural input of the photoreceptors by supplying electrical stimulation to the remaining retinal nerve cells. Due to the fact that electrical stimulation of retinal nerve cells causes a phosphene perception (Humayun et al., 2003), it is now proven (Zrenner et al., 2009,2010) that multiphosphene perceptions, generated by a subretinally implanted

∗ Corresponding author at: Institut für Physik und Astronomie, University Potsdam, Karl Liebknecht Str. 24/25, D-14476 Postdam Golm, Germany. Tel.: +49 331 977 5945; fax: +49 331 977 70 5945. E-mail addresses: [email protected], [email protected] (M. Gerhardt). 0165-0270/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2011.04.017

microelectrode array, can code for visual images and scenes, thus creating an artificial sense of vision. The degeneration of photoreceptors caused by retinitis pigmentosa is accompanied by enhanced neurite growth (Fariss et al., 2000) at horizontal and bipolar cells, once the photoreceptor synaptic pedicles and spherules have disappeared (Cuenca et al., 2005). It is not yet clear whether this event induces new atypical synaptic interconnections between bipolar and horizontal cells. A more realistic scenario is that connections between horizontal cells and bipolar cells get entirely lost during degeneration. However, the interconnections between bipolar cells and the amacrine/ganglion cell network in a degenerated retina appear to be intact (Santos et al., 1997; Kohler et al., 2001; Mazzoni et al., 2008). The bipolar cells code neuronal signals by a depolarization of their membrane voltage. If an incoming depolarization reaches voltage gated Ca2+ channels located at the axon terminal of the bipolar cells further signalling to amacrine and ganglion cells is initiated (Ma and Pan, 2003; Pan et al., 2001; Satoh et al., 1998). Numerical simulations have shown that subretinally applied electric fields can also depolarize the axon terminal of bipolar cells (Gerhardt and Stett, 2008; Gerhardt et al., 2010). Therefore it is very likely that bipolar cells are the major targets for electrical stimulation carried out from subretinal space, as also reported in (Zrenner et al., 2010; Benav et al., 2010).

M. Gerhardt et al. / Journal of Neuroscience Methods 199 (2011) 26–34

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Fig. 1. Simplified view (cross section) of a subretinal implanted electrode array in contact with the bipolar cells of a degenerated retina.

However, the native retina is characterized by at least two different signalling pathways – the ON and OFF bipolar cells – which are polarized in a reciprocal manner (Awatramani and Slaughter, 2000; Werblin, 1991). Both pathways are involved in forming the receptive fields of retinal ganglion cells. If bipolar cells are subretinally targeted by electrical stimulation, then both ON and the OFF type bipolar cells are polarized identically which means that either the ON or the OFF type cell would transmits inverse information into the amacrine/ganglion cell network (Gerhardt et al., 2010). Zrenner et al. (2010) have reported the first ever restoration of vision using an approach based on subretinal stimulation. The implanted patients were able to perceive coherent structures, coded by an ‘electrical image’ which was generated by the subretinally implanted electrode array. As reported in Benav et al. (2010) the implanted device is based on the monopolar electrode configuration (Burghartz et al., 2008; Rothermel et al., 2008). A counter electrode is located far away from the implanted electrode array and the stimulation electrodes remain in direct contact with the retina (Fig. 1). If a charge is injected by the stimulating electrodes, it will cause a temporary electrical field inside the space up to the counter electrode. The size of the ‘return’ or counter electrode is several times larger than the size of stimulation electrodes. Thus the highest electric field strength is attained close to the smaller stimulation electrodes (Palanker et al., 2005). In a recent theoretical study (Gerhardt et al., 2010), the monopolar electrode configuration was numerically simulated on its capabilities for depolarizing a cluster of bipolar cells. Due to superposition effects between monopolar electrodes and the physiological threshold for activating the Ca2+ channels located at the axon pre-synaptic terminals of the bipolar cells, it was concluded that the contrast may be dependent on the amplitude used for electrical stimulation. An alternative bipolar electrode configuration (Fig. 2), originally introduced by (Rizzo et al., 2003) was also investigated and compared with the monopolar electrode configuration. For the bipolar electrode configuration, it was found that the contrast coded by the membrane voltage at the pre-synaptic terminals of the bipolar cells is independent of the amplitude used for electrical stimulation. In terms of stimulation efficiency the monopolar electrode configuration was found to be superior over the bipolar electrode configuration – especially if small sized electrodes are used. Despite the theoretical results it is still unclear whether the bipolar electrode configuration is suitable for subretinal stimulation of a degenerated retina and also what efficiency of stimulation really could be reached on a practical level. In this study we compare the stimulation efficiency for subretinal stimulation of the bipolar electrode configuration and of the monopolar electrode configuration based on an in vitro approach originally introduced by Stett et al. (2000). We used explanted retinas from rd10 mouse at an age of 35 days post-natal (p35), because

Fig. 2. Monopolar (on the left) and bipolar (on the right) electrode configurations. The hatched areas on the monopolar or bipolar subunits are the electrodes. The subunit for the bipolar electrode configuration consists of the centrally located stimulation electrode and the return (counter) electrode, which surrounds the stimulation electrode concentrically

according to (Gargini et al., 2007) rd10 mice provide a good model of typical retinitis prigmentosa in humans. The key feature of this study is that an identical subretinal region of the explanted retina was stimulated using both electrode configurations. This was possible, because the bipolar electrode configuration allows also for monopolar stimulation, if the concentric counter electrode is set to potential free (floating) and another far away located counter electrode is used instead. Additionally we present a new method for offline statistical analysis of action potentials recorded from a ganglion cell during stimulation with both the electrode configurations to assemble a strength–duration relationship (SDR) curve, which characterizes the used retina + electrode system. The obtained SDR curves were finally fitted with the Lapicque model (Lapicque, 1906; Reilly, 1998) to compare them on the characteristic parameters: chronaxie – time and rheobase – current. Parts of this method have been previously reported at the MEA Meeting 2008 (Gerhardt and Stett, 2008). 2. Methods Explanted rd10 retinas were in vitro stimulated subretinally using monopolar and bipolar electrode configurations. During the stimulation experiments with both types of electrode configurations, action potentials were recorded extra-cellularly from a ganglion cell located centrally over the stimulating electrode. To determine the effectiveness of both electrode configurations, the ganglion cell activity was recorded and subsequently assembled into raw data matrices. The singular values of those data matrices were determined to weight the stimulus induced modulations of the recorded action potentials. 2.1. Microelectrode arrays According to model calculations performed in Gerhardt et al. (2010) the size of the bipolar electrode design was chosen (Fig. 3) to allow for almost equal addressing of both the ON and OFF retinal bipolar cell types, which were estimated to be the main target for subretinal stimulation. In MacCarthy et al. (2008) the manufacturing process of the microelectrode arrays is described in detail. Starting from a Pyrex wafer a 200 nm platinum layer was deposited and electrodes, tracks and the contact pads were structured using the “lift off” technique. Subsequently an insulation layer of Si3 N4 was deposited and finally vias to the electrode surfaces and to the contact pads were etched using RIE etching technique. The wafer was diced

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M. Gerhardt et al. / Journal of Neuroscience Methods 199 (2011) 26–34

Fig. 3. The center stimulation electrode is surrounded by a quasi-concentric ring electrode. The central electrode area is 7808 ␮m2 . The counter electrode area is 5183 ␮m2 . All diameter measures are given in ␮m.

into 4 mm × 4 mm microelectrode array-cores. These cores were mounted into a printed circuit board (PCB) and wire bonded to the PCB tracks. The wire bonds were finally encapsulated using “Stycast50300HT”. To perform in vitro experiments a culture chamber made of a hollow polycarbonate cylinder (diameter: 24 mm; height: 5 mm) was mounted on top of the microelectrode arrays. 2.2. Stimulation experiments All mice were kept in a local facility with water and food ad libitum, in a 12 h light/dark cycle with illumination level <60 lx. Retinas were explanted from rd10p35 (±5 days) mice (killed by cervical dislocation) and submerged into modified Ringer’s solution [120 NaCl, 5 KCl, 2 CaCl2 , 1 MgCl2 , 30 NaHCO3 , 15 glucose, 0.2 l-Glu, 2 NaH2 PO4 in mM, equilibrated with Carbogen (95% O2 , 5% CO2 )]. The microelectrode arrays were pretreated for 4 min with a 300 mTorr air plasma ∼30 W (PDC-001 Harrick plasma cleaner). A 2 mm × 2 mm retina piece was prepared, maintaining its ganglion cell side up on top of the microelectrode array and subsequently modified Ringer’s solution was added. For the complete duration of the experiment, the modified Ringer’s solution was exchanged continuously using a perfusion system at a flow rate of 1 ml/min and maintained at a temperature of 37 ◦ C. A silver-oxide pellet, submerged into the modified Ringer’s solution surrounding the retina preparation was used for the counter electrode during stimulation with the monopolar electrode configuration. During stimulation with the bipolar electrode configuration, the integrated concentric ring electrode served for the counter electrode. The central electrode of both configurations served for the stimulation electrode (anode). Using the switch S1 shown in Fig. 4 either the monopolar- or the bipolar electrode configuration was selected. The electrical stimulation was performed using mono-phasic current pulses. These current pulses were generated by a current source as shown in Fig. 4. Using rectangular voltage pulses (at P) a current was driven along the resistor R1. This current was mirrored in the feedback loop of an operational amplifier (TL071, Texas Instr.). The micro-electrodes used for stimulation were driven by this feedback loop. Thus the parameters, namely amplitude and duration, of the current pulses can be defined by the same parameters of the rectangular voltage pulses the resistor R1 is driven with. The complete stimulator-circuit was battery powered to isolate it from net ground, optical insulators were used to send and receive trigger signals, required to control the experiment. The amplitude and duration of the rectangular voltage pulses were controlled by a two loop system, where the first loop, which controls for the amplitude, includes the second loop which controls for the duration. Each loop repeated 6 times where the amplitude

Fig. 4. Circuit for generating mono-phase current pulses. To avoid any galvanic “offset-”charging of the microelectrodes a ballast resistor of 0.5 M was connected in parallel to the stimulation- and the counter electrode. Using R1 the maximum voltage amplitude to drive the current constant was adjusted to never exceed 2.5 V compliance for the monopolar- and for the bipolar electrode configuration the voltage compliance was set at 4 V.

and duration, respectively, were increased stepwise. This resulted in 36 different combinations (Fig. 5). By adjusting the pot resistor R1 (50 K), the maximum and minimum amplitude of the 36 stimulus current pulses can be adapted for each electrode configuration without changing the parameters of the driver rectangular voltage pulses. The resulting 36 current pulses were subsequently applied using a 5 s delay between each of the pulses. This procedure was repeated at least 12 times to allow for statistically significant stimulation results. The action potentials of a ganglion cell on top of the center stimulation electrode were recorded based on loose patch technique (Stett et al., 2000) using a 4 M (GB150T) glass-pipette and an Axopatch200B amplifier (gain: 10×, mode: I-Fast, high pass: 1 kHz). The selected ganglion cell was initially tested, whether it responded by a temporal modulation of its action potentials on stimulation using the bipolar- and the monopolar electrode configuration and subsequently the experiment was started with bipolar stimulation trials followed by monopolar stimulation trials. The raw signal delivered from the amplifier was further processed using a “NPI LHBF-48x” (NPI, Germany) band pass filter (FLow = 1 kHz; FHigh = 0.8 kHz) and finally recorded using a “Multi Channel Systems, Reutlingen” AD converter at a sampling frequency of 20 kHz. Appropriate trigger signals were additionally recorded to allow for

Fig. 5. Schematic overview to illustrate the sequence resulting from the two loop system which controls the amplitude and duration.

M. Gerhardt et al. / Journal of Neuroscience Methods 199 (2011) 26–34

later assignment of each particular current pulse with 2 s of recording time and to make sure that only action potentials behind the stimulus artefact were analysed. The 2 s recording time was divided into n = 200 bins (bin width = 10 ms). Using a simple algorithm for threshold detection, the number of action potentials in each bin was counted. The counted values were stored inside a set of vectors Znk,m . The index “k” ranged from 1..36 and indicated for each amplitude and duration, what the current pulse was composed of. The index “m” (1..12) indicated the repetition of a particular stimulation. Finally raw data matrices for each trial (k = 1..36) were constructed from the Znk,m vectors. From each of the obtained raw data matrices the singular values were calculated, using the Matlab (7.0) builds in routine: ‘svd’.

⎛

Akmxn

⎞

Znk,1 ⎜ Znk,2 ⎟ ⎜ ⎟ =⎜ . ⎟ ⎝ .. ⎠ Znk,m

(1)

−1 Amxn = Umxn Snxn Vnxn

(2)

The highest singular value Smax of a raw data matrix is a weight for the similarity between the matrix rows (and of course also the matrix columns). This can be proven as follows by using the rectangular matrices AAT and AT A, by which the contents of U and V can be identified with. Both the matrices AAT and AT A are quadratic and can be decomposed into an orthogonal basis of Eigenvectors (matrices B and C) and Eigenvalues (matrix D). AAT = BDB−1 T

(3) T T

T

AA = USV (USV )

(4)

AAT = USV T VS T U T = USS T U −1 = BDB−1

(5)

AT A = CDC −1

(6)

T T

T

A A = (USV ) USV T

T

T

T

(7)

T

T

A A = VS U USV = VS SV

−1

= CDC

−1

(8) AAT

AT A

and revealed that Closer inspection of the matrix traces in the sum of squared elements in matrix A is equal to the sum of all squared singular values in S. Trace [AAT ] = Trace [BDB−1 ] = Trace [D]

(9)

Trace [AT A] = Trace [CDC −1 ] = Trace [D]

(10)

 m

Trace [AAT ] =

n

aij (aji )T =

i=1 j=1

Trace [AT A] =

n m   i=1 j=1

 m

n

a2ij = Trace [S 2 ]

(11)

a2ji = Trace [S 2 ]

(12)

i=1 j=1

aji (aij )T =

m n   j=1 i=1

The more identical the temporal patterns of action potentials a ganglion cell produces in response to a repeated stimulation, the lower the rank of A. If the sum of matrix elements stays constant, then a low rank of A results in a high Smax value and vice versa ((11) and (12)). The singular values were further used to assemble SDR curves by custom written data-processing software. Since the required methodical steps to perform this task are related to relevant intermediate results, the description of data processing is postponed into the subsequent Section 3. 3. Results In vitro experiments on subretinal electrical stimulation of degenerated retinas, explanted from rd10 mice at an age of p35,

29

were performed. Two electrode configurations, monopolar and bipolar, were compared on their stimulation efficiency. According to Gargini et al. (2007) horizontal cells are still present in retinas of rd10 mice at an age of p35, however the “complexity of the dendrites and axonal arborizations of horizontal cells” is vanished compared with the wild type of the same age. Therefore bipolar cells were estimated to be the most probable target for subretinal stimulation (Zrenner et al., 2010). However bipolar cells were difficult to contact using electrophysiological techniques whereas ganglion cells are connected with bipolar cells and also with amacrine cells to transmit the entire information processed by the retinal nerve cells to the brain. This holds also for degenerated rd10 mouse retinas (Mazzoni et al., 2008). Therefore according to Stett et al. (2000), ganglion cells were contacted using the extracellular recording technique “loose patch”. To allow for direct comparisons between the results obtained, when stimulation was carried out with the bipolar- and the monopolar electrode configuration the same ganglion cell was recorded during electrical stimulation with both electrode configurations. Hence the success of an experiment depended strongly on whether the contacted ganglion cell stayed alive during the entire duration of an experiment. This happened for 9 of the 17 experiments completed. The obtained ganglion cell responses were found to be different regarding their evoked temporal patterns of action potentials. Differences were also found when switching between the two electrode configurations and when the pulse amplitude and duration of the stimulation were changed. In Fig. 6 the evoked action potentials sorted for 12 representative stimulation-parameters of one experiment are graphed in raster plots. Each dot indicates the event when an action potential was detected. The artefact elicited by the stimulation occurred during each trial at t = 1000 ms. The 5 s inter-stimulus interval proved to be sufficiently long enough to avoid any interference between ganglion cell responses of consecutive stimulation trials, because there were never any reproducible modulation patterns in front of the artefact detected. As also reported in Jensen and Rizzo (2006) the main observation is that at different post-stimulation times characteristic modulation patterns of action potentials were evoked by stimulation higher than the threshold level. Appearance and structure of those modulation patterns depends on the current amplitude and pulse duration. Since ganglion cells receive inputs from many bipolar and amacrine cells, a major goal of this study was to develop a suitable method to take the whole evoked ganglion response into consideration to determine a threshold level for stimulation, required to graph SDR curves. This goal was realized as described in the next section. 3.1. Data analysis to obtain SDR curves Since evoked action potentials were assigned in a reproducible manner (Stett et al., 2007; Jensen and Rizzo, 2006), they exhibit a definite time correlation with the stimulus pulse. This is the most relevant information which can be quantified using singular value decomposition (Kaluzny et al., 1991). The mathematical details were described in Section 2. The Smax values obtained from each completed experiment (for each electrode configuration) were graphed into two plots. Into the first plot the Smax values were plotted against the pulse durations. In the second plot the Smax values were plotted against the pulse amplitudes. These resulting two graphs are called: “the tuning functions” (Stett et al., 2007) of the recorded ganglion cell. An example for stimulation using the monopolar electrode configuration is given in Fig. 7. 12 of the singular values, plotted in Fig. 7 were generated from raw data matrices for which the underlying ganglion

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M. Gerhardt et al. / Journal of Neuroscience Methods 199 (2011) 26–34

Fig. 6. Raster plots, representing the detected action potentials, recorded during monopolar stimulation with different pulse durations and amplitudes. Each raster plot contains 12 trials were the stimulation was carried out using identical amplitudes and durations, indicated at the top of each plot. The stimulus has happened at t = 1000 ms.

cell response is also represented by the raster plots shown in Fig. 6. The main feature found from these tuning functions is, that all the functions were characterized by a common lower and upper steady state level. A similar behaviour is also reported from discharge rates of spikes found for retinal ganglion cells during stimulation using light (Deans et al., 2002; Thibos and Werblin,

1978). The Smax values need to scatter consistently around an identical upper and lower level in both tuning function plots. This happened in all experiments for both electrode configurations successfully performed. For interpolating the parameters (the amplitude and duration which would reach stimulation at threshold level), a sigmoid model function (see Eq. (13)) was chosen to further analyse the obtained tuning functions (Tsai et al., 2009).

M. Gerhardt et al. / Journal of Neuroscience Methods 199 (2011) 26–34

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Fig. 7. Tuning curves fitted using a sigmoidal model function. The lower curves were excluded from multi curve fitting, because they do not show an upper steady state level.

Consideration of the feature of a lower and upper steady state level was done by multi-curve least-square fitting. For the multicurve-fit session only such tuning functions were included, which exhibited a common upper and lower steady state level. The shared parameters were the upper and lower steady state levels F1 and F2, whereas slope (dx) and inflection points (xi) are the individual parameters of each curve. f (x, xi, dx, F1, F2) =

F1 − F2 1 + e(x−xi)/dx

+ F1

(13)

The inflection points of the sigmoid curves were interpreted as threshold values (Tsai et al., 2009) and subsequently assembled to form a SDR curve (Figs. 8 and 9). In both plots of Fig. 9, each of the SDR curves assembled for monopolar stimulation (left side) is printed in a certain pattern (color, thickness and symbol) to allow for tracking the corresponding SDR curve for bipolar stimulation of the same retinal nerve cells in the second plot. The significant result is that all curves obtained from stimulation with the bipolar electrode configuration were associated with higher amplitudes and durations than the corresponding curves obtained for monopolar stimulation. To better quantify the SDR curves the Lapicque model (Lapicque, 1906; Reilly, 1998) was used to determine the two characteristic values: the rheobase current: I(rheobase) and the chronaxie duration. The rheobase current gives the lowest current necessary, to trigger a cellular response and the chronaxie is the duration required, to trigger a response at threshold level, if the twofold rheobase current is used. Istim =

Irheobase 1 − e−t/

(14)

Chronaxie = − · ln(0.5)

(15)

The Lapicque model (14) was least square fitted to the SDR curves (compare Fig. 8) and the standard errors associated with parameters:  and Irheobase were indicated by the error bars in Fig. 10 (left side). The higher the amplitudes and the durations the SDR curves were associated with the higher were also that standard errors. The average charge transfer required for subretinal stimulation at chronaxie duration was 7.34 nC for the monopolar electrode configuration and 31.5 nC for bipolar electrode configuration (Fig. 10, right side). Therefore the bipolar electrode configuration needs at least a 5.8 ± 2.1 fold higher charge transfer, than the monopolar electrode configuration for electrical stimulation at chronaxie duration. 4. Discussion Subretinally performed electrical stimulation of the diseased retina in blind patients by means of an electrode array is an option to provide artificial vision. Currently two alternative electrode configurations are possible to use on subretinal implants. These are the monopolar electrode configuration and the bipolar electrode configuration. Recently performed theoretical studies have revealed that a bipolar electrode configuration may be a better alternative in terms of spatial resolution (Loudin et al., 2007; Joucla and Yvert, 2009; Gerhardt et al., 2010). This study investigated the stimulation efficiency of the bipolar electrode configuration for subretinal stimulation by directly comparing it with the well studied monopolar configuration. For this purpose, both the configurations were used alternately to stimulate subretinally an explanted rd10 mice retina. The action potentials of a ganglion cell, located centrally over the stimulating electrode were extracellularly recorded using the “loose clamp” method. The key feature of this study is that the same ganglion cell was recorded during stimulation with both the electrode configurations. Alongside this comparison, a major goal of this study was also to develop a suitable method to assemble SDR curves out of evoked ganglion cell responses. In the next section the advantages and disadvantages of the new method will be analysed followed by a discussion about the efficiency of subretinal stimulation using (concentric) bipolar and monopolar electrodes. 4.1. SDR curves and a method to obtain them

Fig. 8. SDR curves generated by subretinal stimulation using the monopolar- and the bipolar electrode configuration. Both curves were assembled from raw data, measured at the same cell.

Every point of a SDR curve identifies a combination between pulse-amplitudes and pulse-durations required to evoke stimulation at threshold level. The determination of such parameters can be performed online as an experiment is being carried out, if the pulse amplitude and duration are iteratively adjusted until stimulation evokes a response in more than 90% of the trials (Sekirnjak

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Fig. 9. SDR curves obtained from electrical stimulation using monopolar (left) and bipolar (right) electrode configurations. For each of the both stimulation techniques an SDR curve is presented, measured at the same cell. This curve is identified by identical color and pattern.

et al., 2006) or in more than 50% of trials (Jensen and Rizzo, 2006). An offline procedure to carry out this task is described in Tsai et al. (2009). They used a predefined set of parameters having different current amplitudes which were used at identical pulse durations. 20 consecutive stimulation trials for each of the pulse amplitudes were stimulated to later on identify the percentage of trials, where a stimulus evokes a response. The obtained percentages were plotted against the pulse amplitudes and then fitted using a sigmoid function to identify the inflection point for the threshold level. To assemble a SDR curve this procedure was repeated for different pulse durations. Inspired by Tsai et al. (2009), the present study used a predefined set of 36 different current-pulses to perform subretinal stimulation. The 36 current pulses were defined by 6 different amplitudes and 6 different durations. However instead repeating each of the 36 pulses several times before switching to the next one, all current pulses were sequentially applied. If the end of this sequence was reached at the 36th stimulus then the whole sequence was started again. This was done at least 12 times. Although this experimental procedure makes data analysis more complicated, since the recorded ganglion cell responses need initially to be sorted for the pulse parameters which have been used to evoke them, the procedure has the major advantage that every current pulse has an identical history when applied. The relevant information to assemble SDR curves is the threshold level at which amplitudes and durations a response at the stimulated tissue can be evoked. Therefore the ganglion cell responses needed to be quantified to finally compare them. To perform this task Sekirnjak et al. (2006) and Tsai et al. (2009) have focussed on short latency spikes which occurred immediately after the applied current pulse. This simplifies the statistical procedure to

analyse the recorded ganglion cell response, but it also neglects the influence of modulation patterns which are present in the response of retinal ganglion cells (Jensen and Rizzo, 2006). To take the whole ganglion cell response into consideration an offline method based on singular value decomposition was developed (Gerhardt and Stett, 2008) as described in Sections 2 and 3. Although the used raw data matrices were characterized by a dimension of 12 × 200 the following small example shall demonstrate the advantages of singular values to weight and to compare ganglion cell responses.

0

1 0

0 1 0 0 1 0

0 1

0 1 0 1 0 0

0 0

0 1 0 0 1 0 0 1



0

or



1 0

1 0 0 0 0 1

0 0

1 0 1 0 0 1

0 0

1 0 1 0 1 0

0 or



0 or



1

or



0 0

1 or



0 0 1 0 0 0 0 1

1 or

0 0 1 0 0 1

1 1

0 0 0 0 0 0



(16)

yields Smax = 1

yields Smax =

yields Smax =

√

√

2

(17)

3

(18)

The rank of the 3 × 3 matrix (16) is higher than the rank of the 3 × 3 matrix (18). A low rank of a raw data matrix means that either the rows or the columns are very similar. If a recorded ganglion cell produces reproducible modulation patterns which are correlated or time-locked with the stimulus, then also the rows of the raw data matrix are very similar. According to (9)–(12) the largest singular value Smax , which is yielded by singular value decomposition of a raw data matrix is weighting the similarity in between the matrix rows if compared with other raw data matrices. This works if the sum of all elements of the raw data matrices is identical. However ganglion cell responses can also be characterized by an increased amount of spontaneous activity or short latency bursts (see Fig. 6). A higher amount of spontaneous activity will increase the sum of

Fig. 10. Chronaxie and rheobase values found for electrical stimulation of explanted retinas from subretinal side using monopolar and bipolar electrode configurations. The electrical charges necessary, to stimulate at chronaxie level are given in box plots, right side

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all elements in a raw data matrix. Fortunately this also increases the amount of Smax as proven in (9)–(12), and is why a higher level of spontaneous activity evoked by stimulation is considered. The short latency bursts, sometimes evoked by the stimulation like those graphed in Fig. 6 are also considered, because the similarity in between the columns of the raw data matrices will be increased by such bursts. This also decreases the matrix rank as described in Section 2, which results in a higher Smax value. Therefore singular value decomposition allows for holistic weighting of ganglion cell responses including (1) similarity in between the rows of the raw data matrix, (2) increasing and decreasing level of spontaneous activity and (3) randomly evoked short latency bursts. The obtained singular values were further processed in a similar way as performed in Tsai et al. (2009). Plotting them against its underlying amplitudes or durations resulted in an array of curves – the so-called “tuning functions” of the recorded ganglion cells. In Tsai et al. (2009) each tuning function was modelled by a sigmoid model function. This raised the question whether all tuning function were characterized by an identical inflection point which corresponds to the “threshold” response of the recorded ganglion cell. A significant feature found from the tuning functions in this study is the upper and of course also the lower response level, originally observed by Deans et al. (2002) and Thibos and Werblin (1978). Therefore it appeared plausible that each cell has its definite threshold response. However the modulation patterns of each ganglion cell found for stimulation with the monopolar and with the bipolar electrode configuration were different – although in both cases the tuning curves were characterized by an upper and lower response level. Therefore each set of tuning functions obtained for stimulation with both electrode configurations from each ganglion cell was analysed separately for its common threshold level by multi curve fitting to yield threshold currents and its associated pulse durations. For subretinal stimulation using a monopolar stimulation electrode Jensen and Rizzo (2006) have published threshold currents for 9 different pulse durations. The threshold currents they found for 100 and 200 ␮s pulse duration are in the same range as the said currents found in the present study. Least square fitting the published pulse parameters using the Lapicque model yields an average rheobase current of 0.6 ␮A and a chronaxie time of 1.8 ms and therefore a charge transfer to stimulate at chronaxie level of 1.1 nC. Comparing that amount to those found in the present study exhibits a difference. However Jensen and Rizzo (2006) used native retinas without any defects and the surface-area of their electrode was 25 times larger than those used in the present study. Yamauchi et al. (2005) found a charge transfer of 9 nC for subretinal stimulation at threshold level using monopolar electrodes having a 5 times smaller surface area compared with electrodes used the present study. Although they used also native retinas their charge transfer scattered higher than the charge transfer found for stimulation at chronaxie in the present study. Therefore it could be that larger monopolar electrodes like used in Jensen and Rizzo (2006) are more efficient than smaller monopolar electrodes. However fitting the Lapicque model to the obtained SDR curves associated with high threshold currents and pulse duration yielded high standard errors. Therefore in such cases it is difficult to estimate whether the determined rheobase currents and therefore also the chronaxie times are in the correct range. To experimentally estimate the rheobase current a long pulse duration need to be applied which is in the case of the bipolar electrode configuration difficult or impossible because for those configurations the maximum charge transfer for safe stimulation is smaller compared with monopolar electrode configuration. Exceeding that maximum-charge transfer excesses the risk for electrochemical reactions are starting to take place at the electrode surface (Stieglitz, 2008). Therefore it appeared the safest way to approximate the rheobase current and

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Fig. 11. Side view of a concentric bipolar electrode configuration contacting a retina. A liquid inclusion is separating the retina and the electrodes and shortcuts at the same time the stimulation electrode and the counter electrode.

the chronaxie time by least-square-fitting the Lapicque model to the obtained SDR curves. However the Lapicque-model has its limitations (Boinagrov et al., 2010). 4.2. Efficiency The efficiency of electrical stimulation using the bipolar electrode configuration was found to be ∼5.8 times lower than efficiency of the monopolar electrode configuration, which is in general agreement with predictions given in Gerhardt et al. (2010). A few results revealed a similar – even if a little smaller efficiency for the bipolar electrode configuration compared with the monopolar electrode configuration. The efficiency for bipolar stimulation found in the remaining experimental trials was found to be very low if compared with the monopolar stimulation. This raised the question as to how this could be explained. One possibility could be the higher spatial resolution, proposed for the bipolar electrode configuration, as it means that some of the ganglion cells, selected for recording were not inside the stimulation focus of the bipolar electrode configuration. Another possibility could be a leakage current, which is present during stimulation without having a stimulation effect. The reason for such a leakage current could be liquid inclusions (Fig. 11) which separate the retina from the electrodes (Kasi et al., 2011). Karwoski and Xu (1999) and Baker et al. (1988) have shown that the specific resistance of retinal tissue is approximately 5000  cm. If the specific resistance of such liquid inclusions is lower than the resistance of the retina, then the current used for stimulation needs to be higher to reach the threshold level inside the retina tissue if the bipolar electrode configuration is shortcut by the liquid-inclusion. 5. Conclusion The reason for this in vitro study was to experimentally compare the efficiency for subretinal stimulation of a bipolar electrode configuration with the one of a monopolar electrode configuration. This was done using explanted retinas from rd10 mice at the age of 35 days post-natal and custom fabricated electrode arrays containing a bipolar electrode configuration. To get statistically significant results the stimulation experiments have been designed in such a way that the both electrode configurations can be directly compared based on evoked responses which were extra-cellularly recorded from the same ganglion cell. To determine the strength–duration relationship (SDR) a new method was developed to combine the advantages of singular value decomposition to holistically weight recorded ganglion cell responses and multi curve fitting to find threshold amplitudes and dura-

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tions required for stimulation. The developed method proved to be useful to determine SDR curves, which characterised the retina + electrode system. The results (n = 9) revealed that stimulation with the monopolar electrode configuration is significantly more efficient than stimulation with the bipolar electrode configuration. The obtained SDR curves were further analysed by least square fitting the Lapicque model to finally conclude that subretinal stimulation by the bipolar electrode configuration is 5.8 times lesser efficient than the said stimulation with the monopolar electrode configuration. Finally we discuss the possible predisposition of the bipolar electrode configuration for much lower stimulation efficiency caused by liquid inclusions. Acknowledgements This work was supported by the European Commission (Marie Curie Transfer of Knowledge Program, Grant MTKD-CT-2005029568) and by Fighting Blindness Ireland. The authors would like to thank Prof. Tom Cotter for providing rd10p35 mice and John Alderman for experimental support and for discussion and comments on the manuscript the authors thank Dr. Alfred Stett and Prof. Carsten Beta. References Awatramani GB, Slaughter MM. Origin of transient and sustained responses in ganglion cells of the retina. J Neurosci 2000;20:7087–95. Baker CL, Hess RR, Olsen BT, Zrenner E. Current source density analysis of linear and non-linear components of the primate electroretinogram. J Physiol 1988;407:155–76. Benav H, Bartz-Schmidt KU, Besch D, Bruckmann A, Gekeler F, Greppmaier U, et al. Restoration of useful vision up to letter recognition capabilities using subretinal microphotodiodes. Conf Proc IEEE Eng Med Biol Soc 2010:5919–22. Boinagrov D, Loudin J, Palanker D. Strength–duration relationship for extracellular neural stimulation: numerical and analytical models. J Neurophysiol 2010;104:2236–48. Burghartz JN, Engelhardt T, Graf HG, Harendt C, Richter H, Scherjon C, et al. CMOS imager technologies for biomedical applications. In: Proceedings of the IEEE international solid-state circuits conference (ISSCC); 2008. p. 142–602. Chow AY, Pardue MT, Perlman JI, Ball SL, Chow VY, Hetling JR, et al. Subretinal implantation of semiconductor-based photodiodes: durability of novel implant designs. J Rehabil Res Dev 2002;39:313–21. Cuenca N, Pinilla I, Sauvé Y, Lund R. Early changes in synaptic connectivity following progressive photoreceptor degeneration in RCS rats. Eur J Neurosci 2005;22:1057–72. Deans MR, Volgyi B, Goodenough DA, Bloomfield SA, Paul DL. Connexin36 is essential for transmission of rod-mediated visual signals in the mammalian retina. Neuron 2002;36:703–12. Fariss RN, Li ZY, Milam AH. Abnormalities in rod photoreceptors, amacrine cells, and horizontal cells in human retinas with retinitis pigmentosa. Am J Ophthalmol 2000;129:215–23. Gargini C, Terzibasi E, Mazzoni F, Strettoi E. Retinal organization in the retinal degeneration 10 (rd10) mutant mouse: a morphological and ERG study. J Comp Neurol 2007;500:222–38. Gerhardt M, Alderman J, Stett A. Electric field stimulation of bipolar cells in a degenerated retina—a theoretical study. IEEE Trans Neural Syst Rehabil Eng 2010;18:1–10. Gerhardt M, Stett A. Subretinal stimulation with hyperpolarising and depolarising voltage steps. In: Proceedings of the 6th international meeting on substrateintegrated micro electrode arrays, reutlingen (BIOPRO Baden-Württemberg GmbH), vol. 6; 2008. p. 144–7. Humayun MS, Weiland JD, Fujii GY, Greenberg R, Williamson R, Little J, et al. Visual perception in a blind subject with a chronic microelectronic retinal prosthesis. Vision Res 2003;43:2573–81. Jensen RJ, Rizzo JF. Thresholds for activation of rabbit retinal ganglion cells with a subretinal electrode. Exp Eye Res 2006;83:367–73. Joucla S, Yvert B. Improved focalization of electrical microstimulation using microelectrode arrays: a modeling study. PLoS One 2009;4:e4828.

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