A multi-conductivity 3D human eye model, incorporating essential structures such as the cornea, atria, lens, vitreous body (VB), retina, choroid, and sclera (Lyu et al., 2020; Cvetkovic et al., 2006), was constructed using the AC/DC module in COMSOL Multiphysics (Figure 1).

Additionally, the model also incorporated additional biological components, including the optic nerve, cerebrospinal fluid (CSF), the optic nerve sheath on the nasal side, and surrounding tissues such as muscle and fat.

Specifically, the optic nerve segment was positioned at a 22.5° angle relative to the model’s central axis, oriented horizontally toward the nasal side. The section intersecting the eyeball resembled a truncated cone, while the extended portion was cylindrical. Eventually, the optic nerve, CSF, and optic nerve sheath were aligned as coaxial cylinders. Based on reported data, the anterior segment of intraconal fat and muscle was shaped like hemispheres, while the posterior segment resembled a cone deviated from the optic nerve (Wang et al., 2016; Xu et al., 2017; Alireza et al., 2018). A single extraocular electrode was composed of a platinum (Pt) disc, measuring 500 μm in diameter and 50 μm in thickness, which was used to form extraocular multi-channel electrode montages for TI stimulation.

Table 1 outlines the conductivities of all tissues and Pt electrodes at 100 Hz, which were isotropic, except for the optic nerve. Given that the optic nerve was not perfectly aligned with the central axis of the eye, causing a 22.5° shift to the nasal side, the conductivity parameters listed in Table 1 assumed that the optic nerve was independent and aligned with the central axis. Therefore, the conductivity of the optic nerve was adjusted to account for this offset angle for ease of understanding.

We initially employed multi-channel electrode montages based on our eye model to analyze the spatial distribution of generated TIEFs through extraocular TI stimulation.

The 2D montage (Figure 1A) included two stimulating-return electrode pairs positioned horizontally around the eye and symmetrically aligned with the model’s central axis.

The specific positions of the stimulating and return electrodes were defined by the angles (θ₁ and θ₂, respectively) created between the lines connecting their centers to the eye’s center (point O) and the central axis of the asymmetric eye model. The 3D montage introduced another two symmetrical electrode channels around the vertical plane of the eyeball model (Figure 1B). In this setup, the stimulating and return electrodes on the horizontal plane were designated as θ_1H and θ_2H, while those on the vertical channels were labeled as θ_1V and θ_2V, respectively.

Furthermore, we defined current ratio indexes (illustrated as Equations 1, 2) as follows to explore the modulation principles of the TIEF on the retinal surface mediated by the existence of the optic nerve:

Here, αX represented the ratio of output currents from the nasal (I1) and temporal (I2) side of the horizontal stimulating electrodes, its value ranged from 0 to 1. Similarly, αY expressed the current ratio from stimulating channels on the superior (I3) and inferior (I4) sides of the vertical plane. The condition αX/αY=0.5 represented equal current amplitudes across all channels.

Our previous study comprehensively described the basic calculating principles of the generated TIEF (Su et al., 2021). Briefly, a unit vector n→ represented any direction in space, and a 3D Cartesian coordinate system was utilized to pinpoint the spatial position of the envelope modulation amplitude resulting from the superposition of the n→ direction generated by multi-channel current sources at the position r→xyz could be denoted as E→AMn→r→, which emerged as the vector sum of electric fields generated by two dependent current sources E→1r→ and E→2r→. Therefore, the envelope amplitude that yields TIEF at a specific point within the eye model was given by Equation 3 (Grossman et al., 2017):

As the electric field was vectorial, the maximum amplitude of its directional component at the position r→xyz could be expressed as|E→AM−MAXr→|, which was also the maximal modulated envelope amplitude (MMEA) of the TIEF at this location. Therefore, the MMEA of the 2D electrode montage could be described as Equation 4:

Under 3D montage, as the incorporation of electrode channels, the MMEA of the generated TIEF at each point could be approximately calculated by Equation 5 (Grossman et al., 2017):

For the analysis of TIEF’s spatial properties, we first calculated normalized MMEA values on the posterior retinal surface (red area in Figure 2A) and within the macula (Figure 2B) and further fitted MMEA curves to visualize the spatial distribution of generated TIEFs mediated by the optic nerve along horizontal, vertical, or diagonal directions (blacked dotted lines in Figure 2A). Moreover, we calculated the full width at half maxima (FWHM) and the full width at 80% maxima (80% width) of MMEA distribution curves to describe the spatial resolution of generated convergent TIEFs (Figure 2C), which physiologically represented excitation areas on the retinal surface under 2- and 1.25-times threshold stimulation intensities, respectively (Su et al., 2021).

Additionally, the peak values of retinal MMEA at the horizontal, vertical, diagonal edges, and center points were calculated and fitted to allow us to accurately compare variations of generated TIEFs under different simulation conditions. Finally, we determined the 80% intensity contour range and central peak offsets of different directional MMEA curves on the retinal surface and macula to further evaluate modulation patterns of TIEFs among different electrode montages and current ratios and reveal alternations of convergence and steerability mediated by the optic nerve.

Initially, we demonstrated that altering the location of stimulating electrodes had minimal impact on the spatial patterns of the generated TIEFs when the optic nerve was present (Supplementary Figure S1). To ensure electrical safety, reduce potential invasiveness, and simplify implantation for clinical application, we fixed the stimulating electrodes at θ₁ = 30° for all subsequent studies, approximately aligning with the electrode position employed in applied TES research (Xie et al., 2012).

Subsequently, we explored the effects of varying the positions of the return electrodes, revealing trends consistent with our previous findings (Su et al., 2021). Regardless of whether a 2D (Figure 3A) or 3D (Figure 3B) electrode montage was used, as θ₂ increased (with return electrodes moving closer to the retinal center), the strongest TIEF shifted from the peripheral edge to the retinal center. When θ₂ ≥ 105°, a convergent electric field emerged in the central retina, with its range narrowing as the return electrodes approached the posterior eye. Additionally, the 3D montage improved the convergence of generated TIEF along the vertical axis, which was less pronounced compared to the horizontal axis, forming an approximately elliptical convergent area under the 2D montage.

However, since the optic nerve cross-section was on the nasal side of the retinal surface, an increased axial anisotropy emerged within the convergent TIEF. The most notable phenomenon was the sudden alternation observed in the MMEA distribution curve along the horizontal line for most electrode positions that could generate TIEFs with convergence (blue curve of each inset of Figure 3, except for θ₂ = 170°). Additionally, the center of the convergent area shifted either temporally or nasally, depending on the relative position of the return electrodes to the optic nerve segment (θ₂ ≤ 145° or = 170°). Moreover, compared to the square-shaped convergent TIEFs observed under all electrode positions in previous research (Su et al., 2021), the shapes of the TIEFs turned into near-rectangles when θ₂ ≤ 145° in this study.

Quantitative analyses of MMEA properties indicated that as return electrodes progressively moved toward the posterior part of the eye, MMEA values at the retinal central point increased at a faster rate compared to those derived from horizontal, vertical, and edge points under both 2D and 3D montages (Figures 4A,C).

Specifically, when θ₂ exceeded 105°, the MMEA at the central point gradually surpassed the edge values, indicating the generation of an increasingly intense electric field with a convergent peak in the central retina.

Figures 4B,D further illustrate the influence of return electrode positions on the TIEF’s spatial resolution. Under the 2D montage, while more posterior return electrodes improved the spatial resolution of the generated TIEF along both axes, the FWHM and 80% width of the horizontal line were always smaller than those of the vertical line, which was consistent with the elliptical convergent area displayed in Figure 3A. Another noteworthy finding was that the FWHMs and 80% widths of horizontal MMEA distribution curves were not always equal to those calculated from the vertical lines under the 3D montage (red and blue solid and hollow triangles in Figure 4D). This discrepancy further confirmed the anisotropy between the horizontal and vertical axes, as displayed in Figure 3B.

Considering the increased axial anisotropy mediated by the optic nerve to the convergent TIEF generated under initial current conditions (αX/αY=0.5), as well as the asymmetry that would elevate its modulation complexity confirmed by our previous study (Su et al., 2021). We attempted to balance the horizontal and vertical convergence of the TIEF generated under 3D montages with return electrode positions ranging from 105° to 145° (the convergent area generated by θ₂ = 170° maintained an almost square form and necessitated no adjustment). Figure 5 illustrated corresponding TIEF distributions, while Table 2 summarized resulting FWHMs and 80% widths of MMEA distribution curves along both axes, following alternations to the vertical electrode positions. As values marked by red boxes in Table 2, which demonstrated that TIEF generated under related electrode position could possess an optimal convergence accompanied by comparable axial isotropy, we finally determined θ_2H = 105° and θ_2V = 107° to represent θ₂ = 105°, θ_2H = 120° and θ_2V = 121° to represent θ₂ = 120°, θ_2H = 135° and θ_2V = 136° for θ₂ = 135°, θ_2H = 145°, and θ_2V = 146° for θ₂ = 145°, respectively.

The influence of the optic nerve on the steerability of convergent TIEFs was investigated by changing current ratios of horizontal (αX) and vertical (αY) electrode channels under 3D montage and displaying modulation patterns on the retinal surface and within the macular area (Figure 6).

Taking the return electrodes fixed at θ₂ = 135° as an example (illustrated in Figure 6A, θ_2H = 135°, θ_2V = 136°), the convergent area shifted on the retinal surface with alterations in αX or αY, or both simultaneously. Specifically, decreasing αY caused the convergent TIEF to gradually move to the superior side of the retinal surface and vice versa. Similarly, smaller/larger αX resulted in the convergent region slowly shifting to the nasal/temporal side. Concurrent alternations of both αX and αY could theoretically steer the generated TIEF across the entire retinal surface, even covering the full extent of the optic nerve cross-section. Modulation patterns under other return electrode positions exhibited similar tendencies, as displayed in Supplementary Figure S2. The steering behavior of the convergent TIEF around the macular area is shown in Figure 6B, where return electrodes were fixed at θ₂ = 170°. Unlike the pattern presented in Figure 6A, the convergent area remained confined to the macula across all current ratios and exhibited a relatively regular shape, even when steered away from the retinal center.

To further explore modulation diversities of the generated TIEF on the retinal surface mediated by the optic nerve, we calculated 80% intensity contour ranges of normalized MMEAs and presented three typical and distinct patterns in Figure 7 (θ₂ = 105°, 135°, and 170°, respectively). Contour ranges assessed under θ₂ = 120° and 145°were shown in Supplementary Figure S3. When return electrodes were fixed relatively close to the anterior retina (Figure 7A), alternations in current ratios resulted in a majority of the 80% intensity contours on the retinal surface remaining unclosed (marked by green boxes); additionally, some contours overlapped partially or completely with the optic nerve cross-section (red boxes), while a few could be modulated in the vicinity of the macula, displaying a convergent pattern. As return electrodes approached the posterior eye (Figure 7B), under various combinations of current ratios, generated TIEFs maintained convergent areas both in the central and peripheral retina. Notably, only in a few instances did the TIEFs partially or completely overlap with the optic nerve (marked by red boxes). While return electrodes were located surrounding the macula (Figure 7C), all generated TIEF contours exhibited a convergent pattern and were confined to the perifovea region; nevertheless, the degree of freedom in steering the TIEF contours with the macula was constrained by adjustments to the current ratios among electrode channels.

A comprehensive quantitative exploration was undertaken to investigate the modulation rules of TIEFs generated by different electrode positions and current ratios under the mediation of the optic nerve. We calculated central peak values and central peak offsets of MMEA curves in horizontal, vertical, and diagonal directions relative to the retinal center, along with their 80% peak widths in Figure 8 and Table 3. It is worth noting that these indices primarily focus on describing the spatial characteristics of closed and convergent TIEFs formed on the retinal area by altering current ratios. Therefore, we excluded conditions that generated a major proportion of unclosed TIEF (such as θ₂ = 105°) or overlapped with the cross-section of the optic nerve (marked by red boxes in Figure 7).

Typically, the largest central peaks were observed when θ₂ = 170° and the current ratio was 1:1 (i.e., αX = αY). These peaks varied significantly as the convergent TIEF moved in all directions across the retinal surface (green lines in Figures 8A–C); however, they remained relatively stable under other return electrode montages. As shown in Figures 8D–F, changing αX or αY steered the generated TIEF from the central to the peripheral retinal surface, which led to a negative (nasal side) or positive (temporal side) increase in central peak offsets. Due to the presence of the optic nerve, the offset ranges under most return electrode positions (except θ₂ = 170°) along the horizontal direction (Figure 8D) were anisotropic and predominantly confined to the temporal sides of the optic nerve cross-section.

Moreover, although the steerable range of the convergent area narrowed as return electrodes approached the posterior eye, its convergence presented more predominantly (the absolute values of 80% widths were smaller in a larger return electrode position illustrated in Figures 8G–I). Theoretically, the optic nerve did not limit the steerable regions along vertical and diagonal directions (Figures 8B,E,F). Notably, a relatively high-intensity electric field might be generated in the peripheral retina or the optic nerve cross-section.

Table 3 summarizes the central peak offsets of the convergent TIEFs and the variation ranges of their 80% width (indicating convergence or spatial resolution) of the distribution curves along three directions. Briefly, the central points of convergent TIFFs generated and steered when θ₂ ≤ 145° exhibited a similar horizontal offset range (roughly 25°) without crossing the optic nerve, and its range narrowed along vertical and diagonal directions with return electrodes moving posteriorly. The minimum 80% widths in different directions also decreased with larger θ₂ values, indicating an improvement of the convergence or spatial resolution with a more posterior return electrode location. At θ₂ = 170°, the convergent area under various steerable conditions was primarily limited in the parafovea region of the macula, with absolute offset ranges not exceeding 10° horizontally and vertically. The most convergent sites were generated in the fovea with an 80% width of less than 6° along all directions (last row in Table 3).

In comparison to a previous study that used an idealized symmetrical eye model to simulate the retinal electric fields generated by the TI approach (Su et al., 2021), this study initially demonstrated similar trends in the convergence and steerability of the generated TIEF: (1) A convergent area was established when the return electrodes were positioned relatively close to the posterior side of the retina (θ₂ > 105°); (2) the TIEF could be steered in the direction with smaller current ratios, regardless of whether the adjustment was made horizontally, vertically, or diagonally. However, incorporating more intricate biological tissues, such as the optic nerve segment, in this study introduced variations in the distribution and modulation patterns of the TIEF.

Electrical stimulation has been widely applied to the therapy of various retinal diseases, including retinitis pigmentosa (RP), age-related macular degeneration (AMD), optic neuropathy (ON), and retinal artery occlusion (RAO)(Meral et al., 2022; Nagasato et al., 2023; Stett et al., 2023; Miura et al., 2023; Parkinson et al., 2023). Presently, micro-current stimulation is delivered via a single stimulating and return electrode channel through trans-corneal, palpebral, or orbital approaches, resulting in a diffuse electric field limited to specific retinal regions (Inomata et al., 2008; Sabel et al., 2021; Xie et al., 2012; Xie et al., 2011; Hernández-Sebastián et al., 2023). However, lesion locations differ among retinal diseases and may spread or change as the pathology progresses. For example, damage in early to mid-stage RP patients initially affects the peripheral retina. It gradually spreads to the central area, while in AMD, the lesion expands from the macula to the entire retina (Shepherd et al., 2013). Similarly, central and branch retinal artery occlusions (CRAO and BRAO) occur in the corresponding macula or peripheral region (Scott et al., 2020). Therefore, traditional single-channel electrical stimulation strategies may not realize selective therapy for local retinal lesions on a small scale.

Recent studies have demonstrated that combining multi-channel electrical stimulation with optimized current parameters can somewhat activate neurons in the posterior retina (Lee et al., 2021). Relative research also suggested that multi-channel stimulation offers advantages in selectively activating the local retina and generating specific stimulation patterns, potentially beneficial for treating central, peripheral, or entire visual field injuries (Hernández-Sebastián et al., 2023). In contrast, the present study adopted the TI strategy, which incorporated multiple extraocular stimulating-return electrode pairs and resulted in convergent electric fields under several electrode montages. Moreover, due to the consideration of the presence of the optic nerve, this strategy generated diverse electric field distribution and modulation patterns on the retinal surface. How to effectively leverage this diversity could offer the potential for the selective treatment of various retinal and optic nerve diseases.

Current TES devices primarily consisted of a stimulating electrode attached to the corneal surface, eyelids, or orbital skin, along with a return electrode located at the occipital pole, forearm, or thigh, and either an external or integrated microcurrent stimulator (de Rossi et al., 2020; Stett et al., 2023; Parkinson et al., 2023). The electric current reaches the retina through a minimally invasive or even non-invasive manner, with the most severe side effects being tolerable symptoms, such as mild inflammation and dry eyes, which are easily treatable (Schatz et al., 2017; Wagner et al., 2017).

In contrast, the extraocular TI stimulation proposed here involves a more invasive approach, as the return electrodes are implanted in the posterior eye (θ₂ ≥ 105°). In practical applications, stimulating electrodes can be modified as contact lenses that are attached to the corneal surface (Xie et al., 2012). During the implantation of the return electrodes, minimally invasive surgery is necessary to incise the skin and muscular tissue at the corner of the eye (Soleymanzadeh et al., 2023), position the return electrodes at the appropriate location behind the eyeball, and subsequently suture it to the adjacent tissues. The wired connection between the electrodes and the external simulator can also hinder eye movement. However, this extraocular electrode implantation procedure requires no incision or destruction of the eyeball, nor does it harm the retina (Weiland and Humayun, 2014), enabling multiple repeated surgical implantations. We anticipate that advancements in novel electrode materials [such as carbon nanotube electrodes (Devi et al., 2021)] and wireless coding technologies will facilitate the implantation of multiple flexible electrode contacts with excellent conductivity and biocompatibility in the posterior eyeball simultaneously. The wireless return electrode array on the retinal surface will possess various spatial configurations, such as a concentric ring: the inner return electrodes can be fixed at the temporal side of the optic nerve cross-section, aiming for targeted and steerable stimulation of the macular area, while the outer ring is located at a more anterior position to achieve peripheral visual field or optic nerve therapy. Prior to each treatment session, the stimulating electrode array could be positioned on the corresponding corneal surface based on the lesion area and the corresponding return electrodes to generate a steerable TIEF through the TI strategy.

Besides, current TES devices are limited to generating a single current waveform at once, typically a charge-balanced rectangular pulse with a certain amplitude, phase duration, and frequency (Nagasato et al., 2023; Stett et al., 2023). The retina, however, is an intricate tissue composed of multiple neural layers (such as photoreceptors, bipolar, and ganglion cells), and each neuron type prefers a different frequency of electrical stimulation (Freeman et al., 2010; Hadjinicolaou et al., 2016). Traditional TES methods may not be able to selectively activate multiple impaired neurons in the lesion area simultaneously. Conversely, an innovative retinal electrical stimulation device equipped with multi-extraocular stimulation channels will have the potential to generate several TIEFs with distinct envelope frequencies, distributed either separately or concentratedly through the TI approach (Zhu et al., 2019).

In this study, we conducted computational calculations to investigate the distribution patterns and modulation principles of TIEFs generated by extraocular TI stimulation in a biologically detailed human eye model. However, in practical applications, additional non-ocular structures, including the skull, skin, and even brain tissues, may influence the spatial characteristics of the TIEF (Lu et al., 2022; Lee et al., 2021), exemplifying the abrupt change in the MMEA curve around the optic nerve along the horizontal axis (middle illustrations in Figure 3). In the future, it is imperative to integrate our detailed eyeball model into a realistic human head model derived from medical imaging techniques, such as MRI (Cvetković et al., 2017; Haberbosch et al., 2019), which may provide more practical guidance for clinical electrode implantation.

Furthermore, the optic nerve serves as the crucial link between the eye and the brain, comprising millions of ganglion cell axons responsible for transmitting action potentials to the lateral geniculate nucleus (Selhorst and Chen, 2009). Several studies have demonstrated that electrical stimulation can partially restore visual functions compromised by optic neuropathy (Miura et al., 2023; Gall et al., 2016; Gall et al., 2010; Fedorov et al., 2011; Sabel et al., 2011; Bola et al., 2014). In our study, the extraocular TI electrical stimulation also exhibited a relatively convergent TIEF that covered the optic cross-section under certain strategies, but distributions of the generated TIEF along the axial direction of its depth remain unexplored.

Finally, our study mainly focused on spatial characteristics of simulated electrostatic fields, neglecting the potential neural responses evoked by the generated TIEF. For example, current intensity is a critical parameter that affects neuronal response and safety in assessing the effectiveness of electrical strategies in restoring visual function (Schatz et al., 2011; Schatz et al., 2017; Perin et al., 2019). Additionally, it has been suggested that the carrier frequency of TI stimulation should be high enough (− kHz) to elicit the desired neuronal response (Twyford et al., 2014; Esmaeilpour et al., 2021), while the envelope frequency should match the optimal response frequency of target neurons (5–100 Hz)(Freeman et al., 2010; Hadjinicolaou et al., 2016; Su et al., 2022). Related studies based on a population retinal ganglion cell (RGC) model demonstrated that when return electrodes were fixed in the macular (θ₂ ≥ 170°), the threshold for activating RGC populations in response to TI stimulation was lower than 2 mA and increased with higher carrier frequency (Song et al., 2024), which indirectly confirmed that in our study when θ₂ = 170° and αX=αy=0.5, the central peak value of the MMEA generated on the retinal surface was sufficient to elicit a neural response. For other electrode montages or steerable patterns, it might be appropriate to increase the current intensity of stimulating channels or apply electrodes with stronger charge injection capabilities, such as carbon nanotube electrodes (Devi et al., 2021). However, in vitro or in vivo experiments were still necessary to determine the current safety limits required to elicit robust retinal responses with minimal side effects and to investigate the characteristics of specific retinal neurons in response to different stimulation parameters. Furthermore, the physiological feasibility of TI strategy in visual function restoration should be verified in clinical trials.