Modeling the response of ON and OFF retinal bipolar cells during electric stimulation

Abstract

Retinal implants allowing blind people suffering from diseases like retinitis pigmentosa and macular degeneration to regain rudimentary vision are struggling with several obstacles. One of the main problems during external electric stimulation is the co-activation of the ON and OFF pathways which results in mutual impairment. In this study the response of ON and OFF cone retinal bipolar cells during extracellular electric stimulation from the subretinal space was examined. To gain deeper insight into the behavior of these cells sustained L-type and transient T-type calcium channels were integrated in the synaptic terminals of reconstructed 3D morphologies of ON and OFF cone bipolar cells. Intracellular calcium concentration in the synaptic regions of the model neurons was investigated as well since calcium influx is a crucial parameter for cell-to-cell activity between bipolar cells and retinal ganglion cells. It was shown that monophasic stimulation results in significant different calcium concentrations in the synaptic terminals of ON and OFF bipolar cells. Intracellular calcium increased to values up to fourfold higher in the OFF bipolar model neuron in comparison to the ON bipolar cell. Furthermore, geometric properties strongly influence the activation of bipolar cells. Monophasic, biphasic, single and repetitive pulses with similar lengths, amplitudes and polarities were applied to the two model neurons.

Keywords: Compartment model; Electric stimulation; Retinal bipolar cells; Retinal implant.

Fig. 1

Tübingen subretinal implant and its location relative to the retina –The micro-photodiode-array (MPDA) is surgically inserted between the retinal pigment epithelium (RPE) and the bipolar cell layer into the area formerly occupied by photoreceptors. Each unit of the MPDA contains a photodiode capturing incident light, an amplifier circuit and a stimulating electrode. The light-dependent voltage generated by these electrodes primarily stimulates bipolar cells. Iso-potential lines generated by one stimulating element are shown in red. The visual information is then projected to the brain through ganglion cell axons after activation of the retinal network.

Fig. 2

Volume used to calculate the extracellular potential generated by an electrode – Edge length is 2000 μm. (A) Chip layer, height 100 μm. (B) Retinal layer, height 300 μm. (C) Silicone tamponade, height 300 μm. (D) The outer boundaries of the retinal layer were used as current sink and had an electric potential of 0 V. To calculate the external voltage $V_e$ at each compartment center the potentials at given coordinates were evaluated, i.e. the morphology was virtually placed into the volume.

Fig. 3

Current densities for CaT and CaL-type during voltage clamp mode – (A) Current density over time for one synaptic compartment of the OFF CBC with T-type calcium channels during voltage clamp simulations. Holding voltage was set to −80 mV, pulses of 25, 50, 75, 100 and 125 mV were applied. (B) The same simulations were conducted for the ON CBC with L-type channels. Holding voltage was −70 mV and pulses to −45, −20, +5, +30 and  + 55 mV were delivered for 300 ms.

Fig. 4

Morphological 3D models of traced rat CBCs and stimulation configuration – The images are based on 2D images (Euler & Wässle, 1995) and were created with a custom made Matlab program. (A) Type 9 ON CBC in frontal view (top left), lateral view (top right) and top view (bottom). (B) Type 3 OFF CBC in frontal view (top left), lateral view (top right) and top view (bottom). The stimulating electrode (50 μm in diameter) was positioned 25 μm from the dendritic tree in all simulations. Dendrites, soma, axon and terminals are indicated in red, green, purple and yellow, respectively.

Fig. 5

Stimulus paradigm used for the parametric investigation of biphasic anodic first pulses – The length of the first pulse determined the parameter x. Areas A and B were equal for each simulation. Biphasic cathodic first simulations were conducted analogously.

Fig. 6

Different excitation of the two model neurons without ion channels (passive model) – Every line shows the temporal response of a single compartment during an cathodic 1 V/1 ms electrode pulse. The ON CBC (A) synaptic compartments depolarize to a higher peak membrane potential than the OFF CBC (B) whereas the dendritic compartments hyperpolarize to a similar membrane voltage in both geometries.

Fig. 7

Maximum de- and hyperpolarization of the ON CBC with different axonal length – When the axon of the ON CBC is shortened, the depolarization (A) and hyperpolarization (B) become weaker. If the ON CBC has the same length as the OFF CBC (40%) the de- and hyperpolarization characteristics are totally different in both geometries.

Fig. 8

Axonal length and pulse amplitude influence synaptic [Ca⁺⁺]_i – The OFF CBC geometry was manipulated by elongating the axonal and synaptic parts in axial direction. Multiplicators in the legend correspond to the elongation factor, i.e. ‘1x’ means the standard OFF CBC and ‘2x’ a twice as long axonal and synaptic portion. (A) A 0.5 V pulse leads to a depolarization of 43 mV (standard OFF CBC, ‘1x’) and up to 58 mV (‘2x’). The longer the cell gets, the higher increases synaptic [Ca⁺⁺]_i with a difference of over 200% between the standard geometry and the longest version. (B) The situation changes when a 1 V pulse is applied. Again, depolarization varies between the different morphologies, however, synaptic [Ca⁺⁺]_i only changes little.

Fig. 9

Identical Ca⁺⁺ channels on ON and OFF morphology – If both model geometries have the same channel equipment the intracellular calcium concentration depends on how strong the neuron is depolarized. (A) Panel (a) shows [Ca⁺⁺]_i over time for all synaptic compartments of the ON (blue traces) and OFF (red traces) CBC when the L-type channel is implemented in both geometries. The ON CBC depolarizes more than the OFF CBC during a 0.5 V pulse as also shown in Fig. 6. Intracellular calcium concentration raises more in the ON CBC as well. Although the ON CBC still gets stronger depolarized this changes when a 1 V pulse is applied (panel (b)). When both cells are depolarized similar which can be achieved by stimulating the ON CBC with a 0.5 V pulse and the OFF CBC with a 0.8 V pulse (synaptic membrane voltage increases in both cases up to  + 20 mV) synaptic calcium concentration does not differ between both cells (panel (c)). (B) If the T-type channel is implemented in both geometries and a 0.5 V pulse is applied synaptic calcium again increases higher in the ON CBC whereas a 1 V pulse leads to similar levels of [Ca⁺⁺]_i in ON and OFF CBC. An equal depolarization (panel (c)) leads to higher calcium levels in the OFF CBC due to a faster depolarization characteristic (see Fig. 6). Pulse length was 0.5 ms in all simulations. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 10

Maximum [Ca⁺⁺]_i in synaptic terminals for different cell positions relative to the electrode – The standard position of the electrode is represented by the center pixel in the bottom row. This position corresponds to a centered electrode above the cell soma (x- and y-axis) and 25 μm distant from the dendritic tree in z-direction. (A) Synaptic compartments of the ON CBC increase their [Ca⁺⁺]_i up to 0.75 μM. Interestingly, the peak calcium concentration was found to be at a position further away from the stimulating electrode than in the standard case, however, variations are quiet small. (B) Changes of synaptic [Ca⁺⁺]_i are larger in the OFF CBC. Stimulation from the standard electrode position results in maximum [Ca⁺⁺]_i of approximately 4.5 μM.

Fig. 11

Monophasic stimulation with three different stimulus amplitudes – Three 0.5 ms cathodic pulses with amplitudes of 0.5 V (blue trace), 1 V (red trace) and 2 V (yellow trace) were applied. (A) One synaptic compartment of the ON CBC depolarizes to membrane voltages (a) of  + 21 mV, +93 mV and  + 236 mV during the three pulses, the internal calcium concentration (b) increases to 0.61 μM, 0.74 μM and 0.73 μM, respectively. Current densities of the L-type calcium channels are shown in (c). (B) The membrane voltage (a) of one synaptic terminal of the OFF CBC depolarizes to lower values than the ON CBC (-7 mV, 41 mV, +130 mV) during the three pulses. Synaptic [Ca⁺⁺]_i (b) raises to 0.7 μM during the 0.5 V stimulus and to 3.05 μM and 3.6 μM during the stronger pulses. In (c) the current density of the calcium channel shows similar characteristics as in the ON CBC. The green bars at the bottom indicate the stimulus on- and offset.

Fig. 12

Membrane voltage over time and synaptic [Ca⁺⁺]_i during biphasic stimulation – (A) The time course of the membrane voltage of all synaptic compartments of the ON CBC is depicted in the left panel. During the anodic-first pulse (black trace), the terminals depolarize slightly more than for the cathodic-first case (blue trace). The anodic-first pulse applied on the ON CBC leads to a peak [Ca⁺⁺]_i of approximately 0.39 μM (right panel) whereas a cathodic-first pulse results in an intracellular calcium concentration of 0.77 μM. (B) Synaptic terminals of the OFF CBC depolarize to approximately 45 mV in both stimulating configurations. [Ca⁺⁺]_i increases to a maximum value of 2.9 μM (cathodic-first) and 3.1 μM (anodic-first). The green and red bars at the bottom indicate the length of the stimulus as well as the switch between cathodic and anodic pulse phase.

Fig. 13

Repetitive stimulation results in different [Ca⁺⁺]_i in ON and OFF CBC terminals – (A) The ON CBC responds to 5 consecutive monophasic cathodic pulses (0.5 ms pulse length, 0.5 ms inter stimulus interval, 1 V) with a peak [Ca⁺⁺]_i of approximately 1 μM. (B) Because of persistent calcium T-type currents, the calcium concentration in the synaptic compartments raises up to 3.8 μM during repetitive stimulation in the OFF CBC. Again, the green bars at the bottom indicate pulse on- and offset.

Fig. 14

Ion channel activation is stimulus frequency-dependent – A mono-compartment model was established with three voltage gated ion channels to investigate how those are activated during sinusoidal stimulation. Calcium L-type (solid trace), calcium T-type (dashed trace) and a sodium channel (dashed-dotted trace) from a previous study (Benison et al., 2001) were tested. The calcium T-type channel activates strongly at frequencies around 3–5 Hz and is still open at high frequencies. L-type currents peak at slightly higher frequencies, however, the channel closes when frequency increases. Maximum sodium current is evoked by stimulation around 200 Hz.