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Objective. Trans-corneal electrical stimulation (TcES) produces therapeutic effects on many ophthalmic diseases non-invasively. Existing clinical TcES devices use largely variable design of electrode distribution and stimulation parameters. Better understanding of how electrode configuration paradigms and stimulation parameters influence the electric field distribution on the retina, will be beneficial to the design of next-generation TcES devices. Approach. In this study, we constructed a realistic finite element human head model with fine eyeball structure. Commonly used DTL-Plus and ERG-Jet electrodes were simulated. We then conducted in silico investigations of retina observation surface (ROS) electric field distributions induced by different return electrode configuration paradigms and different stimulus intensities. Main results. Our results suggested that the ROS electric field distribution could be modulated by re-designing TcES electrode settings and stimulus parameters. Under far return location (FRL) paradigms, either DTL-Plus or ERG-Jet approach could induce almost identical ROS electric field distribution regardless where the far return was located. However, compared with the ERG-Jet mode, DTL-Plus stimulation induced stronger nasal lateralization. In contrast, ERG-Jet stimulation induced relatively stronger temporal lateralization. The ROS lateralization can be further tweaked by changing the DTL-Plus electrode length. Significance. These results may contribute to the understanding of the characteristics of DTL-Plus and ERG-Jet electrodes based electric field distribution on the retina, providing practical implications for the therapeutic application of TcES.

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This study develops a modified elliptic harmonic balance method (EHBM) and uses it to solve the force and displacement transmissibility of a two-stage geometrically nonlinear vibration isolation system. Geometric damping and stiffness nonlinearities are incorporated in both the upper and lower stages of the isolator. After using the relative displacement of the nonlinear isolator, we can numerically obtain the steady-state response using the first-order harmonic balance method (HBM1). The steady-state harmonic components of the stiffness and damping force are modified using the Jacobi elliptic functions. The developed EHBM can reduce the truncation error in the HBM1. Compared with the HBM1, the EHBM can improve the accuracy of the resonance regimes of the amplitude-frequency curve and transmissibility. The EHBM is simple and straightforward. It can maintain the same form as the balancing equations of the HBM1 but performs better than it.

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