Direct localised measurement of electrical resistivity profile in rat and embryonic chick retinas using a microprobe

Wistar ( Rattus norvegiens)rats (Charles River or Janvier, France) in their postnatal period between 14 and 16 days and Lohmann race chicks (Animalco AG, Switzerland) in their embryonic stages of 12 and 18 days (E12/E18) were employed animal models in this study.

Rectangular electrodes with rounded corners were used to reduce fringing effects. The dimensions and design of the microprobe used in this study is presented in Fig. 1.

Fig. 1

The rectangular electrodes are spaced 10μm apart. The spacing between electrodes is based on a compromise between a localised measurement (high resolution) and maximum current penetration in the retina (sensitivity). Average retinal thickness for rat is 150μm (11) and chicken is 175μm (12. High resolution measurements are required to probe the different layers within the rat and embryonic chick retinas. An electrode spacing of 10 μm is sufficient to obtain an elaborate resistivity profile of the retina accounting for typical retinal cell sizes ranging from 10 μm. Both an analytic analytical (9) and finite element method based computation (Comsol Multiphysics 4.0a) of electric field penetration depth in saline (ρ=1.5Ω⋅m) for a 10 μm spacing between electrodes revealed an approximate depth of 8.3 μm (see supplementary information). The he large enough penetration depth ensures probing retinal cells making an electrode spacing of 10μm appropriate for the application under consideration.

The choice of measurement method depends on the degree of sample homogeneity and the measurement hardware (i.e. whether the measurement hardware is better at detecting absolute or relative changes) (9). . By virtue of the he similarity of cells within a retinal layer, we can consider each layer to be homogeneous. Owing to their high sensitivity to small changes near the electrodes, electrodes, bipolar measurements record the resistivity of the layer. Bipolar impedance measurement method is used in this study as it requires a simpler experimental setup compared to multielectrode schemes.

The polyimide-based flexible microprobe 10-12μm thick consisted of two recessed Platinum electrodes (40μm×25μm), separated by 10μm was fabricated based on an established process (13). A photograph of the complete microprobe assembled on a plastic base for easy manipulation is shown in Fig. 2.

Fig. 2

In order to measure a resistivity profile of the retina, it is essential to extract the resistance in each layer. layer For the extraction of the tissue resistance from the measured impedance, one of the approaches is to consider the impedance of an electrode-retina configuration represented by an equivalent passive electrical circuit model as shown in Fig. 3. The model consists of contributions due to the electrodes-electrolyte interface and the complex tissue impedance in series with it. it. The constant phase element (CPE), Z Z_{CPE_E} accounts for the non-ideal capacitive behaviour observed in solid metal electrodes (14). The complex tissue impedance is represented by a Cole model (15; 16) of a resistance (R _tissue ) in parallel with a series combination of an intracellular resistance (R_intra) and a CPE (Z_{CPE_T}). The model is suitable for AC analysis alone.

Fig. 3

A typical impedance/phase spectrum along with its model fit at a depth in the retinal tissue is presented in Fig. 4. Tissue resistance can be extracted from experimental data involving impedance/phase spectra by using fitting algorithms applied on the equivalent circuit model. Alternatively, tissue resistance has been extracted using the peak resistance frequency (PRF) method in brain tissue impedance measurements (17).

Fig. 4

The PRF method involves finding the frequency at which the measured impedance is least capacitive (or closest to resistive behaviour). Below this frequency, electrode CPE increases the measured impedance; above this frequency frequency, the tissue CPE and C_PAR each separately or jointly decrease the measured impedance. A single choice of frequency to determine tissue resistance is usually defined by the cut-off frequency calculated from the electrode capacitance and tissue resistance itself. The PRF approach helps to define the best measurement frequency for identifying tissue resistance from a typical tissue impedance spectrum spectrum. Although Although, the tissue resistance can be extracted using fitting methods on the electrical equivalent (Fig. 3), its reliability is limited to uncertainties in the various fitting parameters (Z_{CPE_E}, Z_{CPE_T}, R_tissue, Z_PAR).

The tissue resistance is extracted from the impedance magnitude at the PRF. At three different depths in the retina, magnitudes magnitude at PRFs (Z_PRF) associated with raw experimental data compared within 10% of their corresponding fitted tissue resistance (R_tissue) values. We do not observe tissue relaxation as a result of the dominating electrode interface impedance (owing to the small electrode size). In view of possible misinterpretation (curbed tissue relaxation) and algorithmic errors in the fitting method using equivalent circuits, it was proposed to apply the PRF method to extract tissue resistance from impedance spectra recorded at different depths in the retina.

The resistivity (ρ) at any depth in the retina can be determined from the measured tissue resistance (R) using a simple direct relationship given by ρ = R/k (18), , where k is the cell constant. The cell constant of the geometry used in this study was analytically calculated as 232 232.75cm ^-1 according to the method described by Jacobs et al.(19). A 3D finite element simulation revealed a cell constant value of 232 232.2cm^-1 indicating a good agreement with the analytical value (see supplementary information). The theoretical and simulated values will be used later to verify the proper functioning of fabricated electrodes. Conversion of measured electrode advance to percentage of retinal depth corrects the resistivity profiles for deviation of the microelectrodes from a plane normal to the retina and accounts for tissue shrinkage problems due to dehydration during sample preparation.

Experimental apparatus – The experimental apparatus consisted of a three-axe Eppendorf micromanipulator 5171 used for positioning the microprobe with respect to the retina sample as shown in Fig. 5. The micromanipulator enables a uniform advancement of the electrodes into the tissue leading to a reliable impedance measurement. The extracted retina slices from a rat or embryonic chick were placed on a 3-5mm thick Agar (Sigma Aldrich, Switzerland) gel (1% in Ringer’s solution

composition (in mM) of Ringer's solution (Sigma Aldrich, Switzerland): Sodium Chloride (NaCl) – 115, Potassium Chloride (KCl) – 5, Calcium Chloride (CaCl₂) – 2, Sodium Bicarbonate (NaHCO₃) – 25, Magnesium Sulphate (MgSO₄) – 2, Monopotassium phosphate ( KH₂PO₄) – 1 and Glucose ( C₆H₁₂O₆)- 30

Fig. 5

Electrode cleaning and validation – Before every new experiment, the electrodes were either cleaned with 2% mild soap solution (rat trials) or chemically treated with the RCA-1 cleaning process (20) (chick embryo trials) for removing any organic contaminants. They were subsequently treated under a nitrogen gun to dry and blow away dust particles. The impedance spectrum of electrodes was obtained in standard Ringer’s solution to validate their proper functioning.

Slice preparation – A common protocol for retinal slice extraction was followed for both wild-type juvenile rats and embryonic chicks. Eye balls were extracted from decapitated animals. Under low light conditions, the cornea, iris, and lens were removed from the eye ball followed by transection of the eyecup to float pieces of retina into a dish of Ringer’s solution to obtain isolated retinal slices without the retinal pigment epithelium. The slices were then perfused in Ringer’s solution continuously bubbled in 95% O₂//5% CO₂ until it was placed on the Agar gel. The surface on the Agar gel was pre-treated with a solution of cellulose nitrate (0.14mg/ml in methanol) and dried. This acted as an adhesion promoter for the retina to stay on the gel preventing it from being washed away when in contact with the Ringer’s solution. A few moments before the experiment was conducted, the retinal slice was taken out from the perfusion and was placed on the treated area of the gel with the retinal ganglion cell side facing upwards and the photoreceptor cells in contact with the gel. The Ringer’s solution was then added to fill the petri-dish to a certain level submerging the retina-gel structure.

– In every trial trial, at least three impedance measurements at different depths (every 10μm) in the bath (Ringer’s solution) before entering the retina were performed. The first considerable change in impedance magnitude at PRF indicate indicated the entry into the retina. Visual control using a pair of binoculars confirm confirmed this first electrode-retina contact. Subsequent impedance measurements at every 10μm depth were recorded until an impedance value similar to the one observed in the bath was encountered. Each measurement was recorded with a wait time of 30 seconds for the signal to stabilise after the micromanipulator made the 10μm vertical movement into the retina. This time was determined based on measurement of time taken for the impedance value to stabilise at a random depth in the retina (see supplementary information) information). Three more recordings at 10μm intervals were made to ensure the electrodes contact with the Agar gel before terminating the experiment and retracting the electrodes to the initial position. The system was under ambient laboratory conditions of 21°C during the impedance measurements.

To o be able to compute the resistivity from the measured tissue resistance at PRF, the cell constant needs to be experimentally determined. The cell constant of the bipolar electrodes used in this study was calculated using the impedance/phase spectrum of Ringer’s solution of predetermined conductivity conductivity. The spectrum is as shown in Fig. 6. Based on an average of such measurements with different batches of electrodes, an average experimental cell constant was found to be 225cm^-1 (less than 5% error). This value is within 3.5% of the theoretical and simulated values of cell constant for the electrode configuration used in this study. The close agreement of the cell constant with previously calculated values validates the proper working of the electrodes for an experiment.

Fig. 6

Following the functional validation of electrodes, they can be employed for impedance measurements at different depths in the retina of the chosen animal model. During these experiments, a shift in the PRF was observed at each depth in the retina as present presented ed in Fig. 7. Starting from the retinal ganglion cell layer as we go deeper into retina towards the photoreceptor layer, the PRF moved to lower frequencies and the impedance magnitude rose from a low to a high value between 80-85% of retinal depth spanned during the experiment. With reference to Fig. 7, a 10% retinal depth corresponded to an approximate microprobe displacement of 14μm in the rat retina.

Fig. 7

Impedance spectroscopic measurements at different depths of isolated retinal slices from three rat (14-16 days postnatal) and five chick (three E18 and two E12 embryos) samples were performed. Resistivity values were calculated from the extracted impedance value at the PRF using the direct relation between both for each depth in the retina sample. A resistivity depth of 100% was denoted as the last measurement in the retina before an identical value of resistivity obtained in Ringer’s solution is reached (electrodes in Agar gel). Point zero represent represented the last measurement in the Ringer’s solution before there is a significant change in the resistivity, i.e., an appreciable shift in the PRF is observed observed. Resistivity versus retinal depth profiles for both rats and embryonic chicks are presented in Fig. 8 and Fig. 10 respectively.

Fig. 8

Fig. 9

Fig. 10

In both rat (Fig. 8) and embryonic chick (Fig. 10) measurements, an increasing resistivity-depth profile is observed rising gradually from the retinal ganglion cell layer towards the photoreceptor layer. At an approximate depth of 65%, the resistivity reaches a maximum value and then gradually decreases to attain a value obtained in Agar gel. There is a close interspecies resemblance in the studied resistivity profile shapes.

The maximum mean resistivity reached in rat retina samples is 4.2 ± 0.9 Ω⋅m and for E12 chick is 4.5 ± 0.2 Ω⋅m occurring between 65-70% retinal depths. On the other hand, the maximum mean resistivity in E18 chick retina samples is 7.9 ± 0.6 Ω⋅m which is approximately double the value measured in rats and E12 chicks at the same retinal depth. In rat and E18 chick resistivity profile measurements, at around 80% depth into the retina, there is a definite dip in the resistivity profile gradually decreasing into a low value similar to a measurement in Ringer’s solution.

The he standard deviation (SD) of resistivity from the mean resistivity value at each depth was examined examined. For the embryonic chick resistivity profiles profiles, it is determined that the SD is low in the Ringer’s solution and the Agar gel. gel In contrast, the rat data demonstrates large SD in the these two regions of the resistivity profile profile.

It is known that there is a PRF shift with a resistivity change in different retinal layers. A representation of the relationship between PRF and resistivity based on the experiments on rat and embryonic chick retinal slices is depicted in Fig. 9 and Fig. 11 respectively. The log resistivity is linearly dependent on the log PRF for both the species. For embryonic chicks, owing to similarity in the data across various trials, it can be observed that there is a unique PRF for each resistivity. On the contrary, the three rat trials suggest multiple PRFs for each resistivity.

Fig. 11