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H. Benav, F. Rattay, R. Wilke, D. Feiertag, C. Freystaetter, G. Kitzler, P. Werginz, E. Zrenner; Modeled Responsivity of Retinal Bipolar Cells During Subretinal Stimulation. Invest. Ophthalmol. Vis. Sci. 2010;51(13):3035. doi: https://doi.org/.
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© ARVO (1962-2015); The Authors (2016-present)
To create a computer model of the electrode-neuron interface in retinitis pigmentosa patients carrying an implanted, subretinal microphotodiode-array (MPDA) for restoration of vision. The model has been implemented for simulation of transmembrane voltage (Vm) time courses of retinal bipolar cells (BC) following extracellular stimulation. Vm time courses of BC in different locations relative to a stimulating electrode are compared.
Two steps were involved in simulation of extracellular neuronal excitation:1. A Finite Element Simulation delivered values for the extracellular potential (Ve) in an inhomogeneous volume (2 mm x 2 mm x 0.5 mm) covering a monopolar disc electrode (radius 20 µm, 1V at surface) , a distant return electrode, retinal tissue (electric conductivity sigma = 1.75 S/m), and vitreous.2. A 3D model of a simplified BC was divided into 17 compartments. The axon terminal had 3 bifurcations, total cell length was 113 µm. Ionic, ohmic, and capacitive currents were calculated for each compartment, in each time-step. Ionic currents depend on passive ion channel densities (passive conductivity gpas = 0.041 mS/cm2). Ohmic currents to neighboring compartments depend on compartment volume. The initial impact of Ve on Vm was determined using the activating function (Rattay, Neuroscience 89: 335-46, 1999). A numeric differentiation formula (NDF) solved the cable equation to deliver Vm (resting potential of -70 mV) for a 500 µs pulse. The soma was first located 45 µm from the center of the electrode, and then shifted horizontally in a plane parallel to the electrode. Shifts of 20 µm and 35 µm were investigated since the implanted MPDA has an inter-electrode distance of 70 µm.
The time courses of Vm were calculated for each of the 3 presynaptic endings of the axon. From -70 mV, Vm was raised to 78 mV, 79 mV, and 74 mV. After a 20 µm shift the amplitudes were reduced to 59 mV, 61 mV, and 55 mV; and a 35 µm shift yielded 29 mV, 32 mV, and 25 mV. Therefore, a 20 µm shift reduced Vm by 12.6% ± 0.3%. For 35 µm, Vm was reduced by 32.9% ± 0.8%.
The model is feasible for simulation studies of Vm in BC during extracellular, subretinal stimulation. Different electrode sizes and arrangements can be tested for varying positions of the retinal target cells. Experimental verification of these results will further refine the model. For extension of simulation paradigms, voltage-gated sodium channels should be integrated. (Pan et al. J.Neurophysiol. 84: 2564-71, 2000)
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