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Heval Benav, Rattay Frank, Robert Wilke, Eberhart Zrenner; An Active Model of Retinal Bipolar Cell Responses To Sinusoidal Subretinal Electrical Stimulation. Invest. Ophthalmol. Vis. Sci. 2011;52(14):4965.
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© ARVO (1962-2015); The Authors (2016-present)
To create a computer-model for calculation of transmembrane voltage (Vm) of retinal bipolar cells during subretinal electric stimulation in patients carrying the Tuebingen subretinal implant (Zrenner et al., Proc. Roy. Soc. B 2010). A passive model (Benav et al., ARVO 2010) was equipped with voltage gated (active) ion channels. We here compare sinusoidal stimulation in a range of different frequencies (f) and electrode voltages (Ve).
A simplified 3D geometry with 17 compartments was used. For each compartment, active ion channels were built into the membrane. The underlying Hodgkin-Huxley style equations were adopted from (Publio et al., PLOS one 2009). Initial conditions for the ion-channel gating variables were determined at Vrest = -41 mV. Calculation of the following ion currents was implemented: Na+ (INa, conductance: g = 120 mS/cm² ), K+ (IK, g = 12 mS/cm²), delayed rectifying K+ current (IKv, g = 0.318 mS/cm²), hyperpolarization activated current (Ih, g = 31.1 mS/cm²), Ca++ (ICa, g = 2 mS/cm²), Ca++ dependent K+ current (IKCa, g = 1.4 mS/cm²) and leakage current ( IL, g = 0.3 mS/cm²). Specific membrane resistance was set to 24 kOhm*cm², specific axial resistance 130 Ohm*cm, membrane capacitance 1.1 µF/cm². The sinusoidal stimulation began after a 0.1 ms delay and had duration of 0.3 ms (end at 0.5ms). Sinusoids with f = 1,100,200...,1500 and 2000 Hz were simulated at Ve = 0.25,0.5,075,1,1.25 and 1.5V.
The highest changes in Vm were achieved at 1100Hz. The maximal/minimal (at 1Hz) synaptic Vm values were -17.8mV/-26.47mV (Ve=0.25), 0.83mV/-16.27mV (Ve=0.5), 18.9mV/-6.8mV (Ve=0.75), 38.18mV/2.2mV (Ve=1), 54.66mV/11.42mV (Ve=1.25) and 70.83mV/21.3mV (Ve=1.5V).The ionic currents ICa,INa, IKCa and passive current (Ipas) were observed. ICa was close to zero at Ve=0.25V, for Ve=1V it reached 0.07µA at 1Hz and 0.23µA at 1400Hz, for Ve=1 V it yielded 0.13µA at 1Hz and 0.34µA at 1200Hz. IK had similar results for Ve=1V, but for Ve=0.25 fluctuated around 0.12µA for all f. Ipas and INa increased linearly with Ve.
Synaptic Vm exhibits frequency dependency and is highest at 1100Hz in these simulations, at which a 0.3ms stimulation contains one third of a sinusoid. At 1000Hz a 1V pulse creates larger Vm changes than a 1.5V pulse at 1Hz. ICa was most affected by f and peaked around f=1000Hz. IKCa f-dependency increased with Ve. Further studies using neurons with differing ion channels can clarify the f-dependency observed by Freeman at al., J. Neurophysiol. 2010.
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