Erich W. Schmid

Simultaneous vs. sequential and unipolar vs. multipolar stimulation in retinal prostheses

A computational model for research on retinal implants is presented. In this model, the electric field produced by a multi-electrode array in a uniform retina is calculated. It is shown how this model can be used to answer questions as to cross talk of activated electrodes, bunching of field lines in monopole and dipole activation, sequential stimulation, multipolar stimulation, etc. The model is equally applicable to epiretinal, subretinal, and suprachoroidal vision implants.

Operational Design Considerations for Retinal Prostheses

Three critical improvements resulting from computer simulations for present day and future retinal vision implants are proposed and discussed: (1) A time profile for the stimulation current that leads predominantly to transversal stimulation of nerve cells; (2) auxiliary electric currents for electric field shaping with a time profile chosen such that these currents have small probability to cause stimulation; and (3) a local area scanning procedure that results in high pixel density for image/percept formation, except for losses at the boundary of an electrode array.

Operational challenges of retinal prostheses.

Two computational models for research on retinal implants are presented. In the first model, the electric field produced by a multi-electrode array in a uniform retina is calculated. It is shown how cross talk of activated electrodes and the resulting bunching of field lines in monopole and dipole activation prevent high resolution imaging with retinal implants. Furthermore, it is demonstrated how sequential stimulation and multipolar stimulation may overcome this limitation. In the second model a target volume, i.e., a probe cylinder approximating a bipolar cell, in the retina is chosen, and the passive Heaviside cable equation is solved inside this target volume to calculate the depolarization of the cell membrane. The depolarization as a function of time indicates that shorter signals stimulate better as long as the current does not change sign during stimulation of the retina, i.e., mono-phasic stimulation. Both computational models are equally applicable to epiretinal, subretinal, and suprachoroidal vision implants.

Electric stimulation of neurons and neural networks in retinal prostheses

A computational model is presented that can be used as a tool in experimental research in retinal implants. In this model a target volume (i.e., a probe cylinder approximating a bipolar cell) in the retina is chosen, and the passive Heaviside cable equation is solved inside the target volume to calculate the depolarization of the cell membrane. The depolarization as a function of time indicates that shorter signals stimulate better, as long as the current does not change sign during stimulation of the retina. The model is equally applicable to epiretinal, subretinal, and suprachoroidal vision implants.

Lösung der Schrödinger-Gleichung in Oszillatordarstellung

Wir haben in den Kapiteln 13 und 14 die SCHRODINGER-Gleichung als Differentialgleichung kennengelernt. In dieser Form wurde sie 1926 von ERWIN SCHRODINGER aufgestellt [15.1, 15.3]. Bereits ein Jahr fruher fand WERNER HEISENBERG die Quantenmechanik in Form einer Matrixgleichung [15.2, 15.3]. Spater stellte sich dann heraus, das beide Gleichungen dieselbe physikalische Theorie in verschiedener mathematischer Darstellung enthalten: Die Gleichungen von HEISENBERG und SCHRODINGER konnen ineinander transformiert werden.

Die sphärischen Bessel-Funktionen

Wir haben bereits in mehreren Kapiteln die Losungen der Einteilchen-SCHRODINGER-Gleichung

Berechnung elektrischer Felder nach dem Verfahren der sukzessiven Überrelaxation

- \frac{{{h^2}}}{{2m}}\Delta \psi \left( r \right) + V\left( r \right)\psi \left( r \right) = E\psi \left( r \right)

Die Van der Waals’sche Gleichung

(18.1) untersucht. Die Gleichung gilt, wie wir wissen, auch fur die Relativbewegung von zwei Teilchen. In diesem Fall ist r der Abstandsvektor und m die reduzierte Masse der beiden Teilchen. Fur ein kugelsymmetrisches Potential last sich (18.1) relativ leicht losen. Man fuhrt Kugelkoordinaten (r, ϑ, φ) ein und zerlegt die Wellenfunktion in Drehimpuls-Partialwellen (vgl. Kapitel 17),