Design of Electrode Placement for Presenting Phosphenes in the Lower Visual Field Based on Electric Field Simulation

Abstract

Presenting visual information, called phosphenes, is a critical method for providing information on the position of obstacles for users of walking support tools for the visually impaired. A previous study has established a method for presenting phosphenes to the right, center, and left of the visual field. However, a method for presenting information on the position of obstacles around the feet using phosphenes, which is essential for the visually impaired, has not been clarified. Therefore, in this study, a method for presenting phosphenes in the lower visual field is presented, towards the aim of realizing a safe walking support tool. Electrode placement is proposed in this paper for the presentation of phosphenes to the right, center, and left of the lower visual field based on the electrode placement method used in the previous study, which presents the phosphene in three locations of the visual field. In addition, electric field simulation is performed, focusing on the electric field value on the eyeball surface, in order to observe whether the proposed electrode placement is able to stimulate the intended region. As a result, it is shown that the intended region on the eyeball surface can be stimulated locally with each of the proposed electrode placements.

1. Introduction

Visually impaired people mostly use white sticks as a support tool while walking. Since the conventional white stick has limitations with respect to its area of detection, various wearable support systems incorporating audio and tactile sense navigation have been introduced [1]. For example, electronic travel aids obtain outside information using sonar and convey this information through another sense, such as through audio or electronic tactile stimulation. Although these existing wearable support systems are able to provide information on the locations of obstacles, the user’s senses are disturbed because the locations of obstacles are presented using those senses. Moreover, some support systems use sensors attached to the hands. As a result, the user needs to keep their hands in place [1]. Therefore, hands-free walking support tools that do not interfere with other senses are needed. As a methodology to overcome the above issues, methods for communicating information on obstacle locations using phosphenes, which are visual information that can be perceived by visually impaired people, have been investigated. This visual information enables visually impaired people to achieve intuitive obstacle recognition and to live their other senses being free from interference. In addition, presenting the locations of obstacles with visual information makes it possible to realize hands-free walking support tools. Hence, phosphenes are an effective way of presenting obstacle locations for the visually impaired. Phosphenes are a phenomenon in which light can be recognized by magnetic and electric stimulation of the visual pathway. Generally, non-invasive stimulation methods include TMS (transcranial magnetic stimulation) [2,3,4], TES (transcorneal electrical stimulation) [5,6], and tACS (transcranial alternating current stimulation) [3,7]. TMS uses magnetic stimulation, and it is possible to generate an induced current in a specific brain region using a coil through which an electric current is passed [2,3]. However, the TMS device is costly, and it has been reported that TMS can cause severe side effects such as convulsions during stimulation [4]. TES stimulates the cornea on the eyeball surface by means of a contact lens with embedded coils being worn [5]. Since stimulation by TES directly stimulates the cornea, it is necessary to protect the cornea with a drug. In addition, since the electrodes are placed on the cornea, it is difficult to change the position of the electrodes. Additionally, the phosphene induced by TES is generally perceived in the center of the visual field, because TES generally stimulates the retina located on the contralateral cornea [6]. tACS is a method using two electrodes, and the area beneath the electrodes is stimulated with alternating current [3,7]. The side effects of tACS have been discussed in several studies, and include dizziness, sensations on the skin, perception of pressure, itching at the stimulus location, aching, headache, sensation of heat, and discomfort [8,9]. However, no severe side effects, such as those reported when using TMS, have been reported. In other words, it is considered to be possible to present a phosphene with a greater degree of safety than when using TMS or TES. Therefore, in this study, we discuss the presentation of phosphenes using tACS.

The position at which the phosphene is presented when using tACS has been reported previously. Higuchi et al. placed electrodes around the eyeball and reported the position of the presented phosphene [10]. Their report states that when the electrodes were located around the eyeball, the phosphene was perceived to be close to the electrodes. In other words, when the electrodes were located below the eyeball, the phosphene was perceived to be in the lower visual field. Our previous study also described a method by which a phosphene could be presented in three different locations, namely, to the right, center, and left of the visual field, by means of electric field simulation [11]. That study focused on the transition of the electric field value on the eyeball surface, and electrode placements that were capable of stimulating the nasal, central, and temporal sides of both eyeballs were described. The reported electrode placements were able to present a phosphene in three locations in the visual field for use as a walking support tool for the visually impaired. Obstacle recognition in these three directions is extremely important in walking support tools [12,13]. This is because visually impaired people need to be able to recognize obstacles in the forward direction, as well as obstacles in the left–right direction, in order to support spatial understanding [12]. However, dangerous are not only present at head height when walking outside. There is much information even in the lower part of the visual field that needs to be recognized, including train station platform edges, steps, and obstacles around their feet, in order to avoid tripping hazards. Nevertheless, methods for increasing the presentation accuracy of phosphenes in order to be able to present them in the lower part of the visual field have not been described. Therefore, in this paper, a method for presenting a phosphene in the lower visual field is described with the aim of developing a safer walking support tool for the visually impaired. For the purposes of validation, electric field simulation was selected to compare the results with the previous study, which demonstrated the presentation of phosphenes in three locations [11]. The contribution of this paper lies in describing the electrode placements that permit the presentation of phosphenes the lower visual field. Moreover, a method for controlling the local stimulated area around the eyeball is described by comparing the stimulated area with the electrode placements used in the previous study. Despite methods of obstacle detection and presentation being a necessary topic of discussion for the development of a walking support tool for visually impaired people, obstacle detection methods are not within the scope of this paper. Sonar-based obstacle detection and smartphone-based control of tACS devices are assumed as obstacle detection method in our walking support tool.

The rest of the paper is organized as follows: the related work and background knowledge are described in Section 2, and Section 3 presents the hypothesis for designing electrode placements for presenting phosphenes in three locations of the lower visual field. The simulation conditions and evaluation results are presented in Section 4, and Section 5 discusses the results. Finally, the conclusions of this study are drawn in Section 6.

2. Related Work and Background Knowledge

This section describes related studies on phosphene presentation by stimulation near the eye with alternating current. Additionally, related studies reporting the electrical stimulation of the eyeball area during phosphene presentation are also described.

2.1. Presentation Position of Phosphene

The location at which phosphenes are perceived when stimulating the eyeball with electrodes placed around the eyes and applying a square wave alternating current of 0.3 mA and 10 Hz was investigated by Higuchi et al. [10]. In their investigation, the electrodes were placed on the top, bottom, left, and right of both eyes. As mentioned in Section 1, it was reported that phosphenes were perceived at locations near the electrodes. In other words, when the electrodes were placed sandwiching the right eyeball at the top and bottom, is the phosphenes were also perceived in the upper and lower parts of the right visual field. Therefore, there is a correspondence between the position at which the phosphene is presented and the electrode placement. The stimulation method used in their study was similar to that used in tACS, and the current was assumed to flow along the eye’s, stimulating the optic nerve. However, there is a discrepancy between the inferred current pathway and the experimental results. In the work by Higuchi et al. [10], the phosphene was perceived on the right side of the visual field when the electrode stimulated the temporal right eyeball, even though the temporal retina of the right eyeball controls the left side of the visual field, as shown in Figure 1 [14].

The current path around the eyeball was verified with respect to the discrepancy between the current pathway and the phosphene presentation position in our previous work. Manami et al. focused on the fact that the visual retina was not exposed to the anterior side when the eyeball was gazing forward and investigated the path of the current around the eyeball [15]. The human eye achieves vision by applying a light stimulus to the visual retina, which has photoreceptors. However, this visual retina is exposed to the anterior side only when eye movement is performed. When performing eye movement towards the right side, the right eyeball’s nasal retina and the left eyeball’s temporal retina are exposed to the anterior side. In the eye movement to the left side, the right eyeball’s temporal retina and the left eyeball’s nasal retina are exposed to the anterior side. Therefore, a hypothesis was posited in this study [15] that the visual retina exposed to the anterior side can only be stimulated during eye movement to the left or right. In this study, the position of the phosphene was investigated with three electrodes placed on the right side of the forehead and three electrodes placed on the left side of the forehead. Using this setup, phosphenes were perceived on the side in the visual field area that was processed by the exposed retina, regardless of the electrode placement. Additionally, area in which the phosphene was perceived when gazing forward was different from that when gazing towards the left or the right, even though the same electrode placement was used. This result indicates that the current path around the eyeball directly stimulates only the area exposed to the anterior side, and that the current does not flow along the sclera of the eyeball. Since the visual retina is not exposed to the anterior side when gazing forward, only the cornea is directly stimulated by the electric current. In this stimulus condition, a phosphene is perceived near the electrode, as in the previous study [10], even though the visual retina is not stimulated directly. Methods in which phosphenes are generated without directly stimulating the visual retina, such as when gazing forward, can be referred to as indirect stimulation. A previous study in which TES was used to stimulate the cornea reported that phosphenes were generally perceived in the central visual field [6]. As shown in Figure 1, the central visual field is processed in the retina located on the contralateral side of the stimulated cornea. Therefore, it can be inferred that TES is able to indirectly stimulate the retina that controls the central visual field, which is located on the contralateral side of the electrode. If the current flows along the sclera and directly stimulates the retina, the outer retinal layer, including the photoreceptors, should be stimulated by the current. However, according to a report by Mihashi et al., the current stimulates ganglion cells and amacrine cells located in the inner retinal layer rather than the photoreceptors located in the outer layer [16,17]. On the basis of their report, the current around the eyeball does not flow along the sclera. Additionally, it can be inferred that the area that is exposed to the anterior side is stimulated directly, and that the inner retinal layer located on the contralateral side of the electrode is stimulated indirectly.

2.2. Adjustment of Stimulated Region on Eyeball by Electrical Stimulation

It is possible to present a phosphene at an intended position by stimulating the correct region of the eyeball surface, since this indirectly stimulates the inner retinal layer at the contralateral side of the stimulated position on the eyeball surface. A shown in Figure 2, our previous study [11] reported electrode placements enabling the stimulation of the temporal, central, and nasal sides of the eyeball in order to present phosphenes in the right, center, and left of the visual field, respectively. Moreover, the previous study focused on the transition of the electric field across the eyeball surface. The pink-colored electrodes shown in Figure 2 are anodes, and the blue-colored electrodes are cathodes.

In order for a phosphene to be presented to the right of the visual field, it is necessary to stimulate the temporal right eyeball surface, as shown in Figure 2A. In order to for a phosphene to be presented in the center of the visual field, it is necessary to stimulate the central part of the cornea of either the right or left eyeball, as shown in Figure 2B,E. In order for a phosphene to be presented around the center of the visual field, it is necessary to stimulate the nasal part of the cornea of either the right or left eyeball, as shown in Figure 2C,D. In order for a phosphene to be presented to the left of the visual field, it is necessary to stimulate the temporal left eyeball, as shown in Figure 2F. There are three methods for designing electrode placements that stimulate these intended areas of the eyeball surface, as follows [11]:

• The forehead electrode should be moved in the direction towards where the phosphene is to be presented.
• The electrodes should be closer to the eyeball when the eyeball surface needs to be stimulated more strongly.
• The electrode placement should be set in consideration of the shape of the facial surface in order to achieve local stimulation of the eyeball.

The reasons why each method is essential when designing electrode placements are described below. In order to successfully present phosphenes at the desired positions, it is necessary to design electrode placements such that the value of the electric field in the intended region on the eyeball surface is greater than that in the other regions. By arranging the electrodes close to the region to be stimulated using method 1, it is possible to design an electrode placement that provides local electrical stimulation. Next, with respect to method 2, the body tissues located between the cathode and the anode of the electrode can be considered to be resistors in the electric circuit. Therefore, when the electrodes are arranged close to the eyeball, as in method 2, the distance between the eyeball and the electrodes becomes shorter; hence, the electric field on the eyeball surface can be affected more directly. This method was used to stimulate the central part of the eyeball, which previous studies have described as being difficult to stimulate strongly [11]. Finally, with respect to method 3, when the electrodes are arranged on the surface of the face, the current will not flow through the linear space between the electrodes, but rather along the shape of the facial surface. Therefore, the intended region can be stimulated by arranging the electrodes using method 3. As shown in Figure 2, it is possible to present a phosphene in both the lower and upper sides of the visual field if the electrode is placed above and below the eyeball. This phosphene presentation was also described in a previous study by Higuchi et al. [10]. Therefore, it is difficult for a phosphene to be presented in the right, center, or left direction in the lower visual field only when using the currently reported electrode placements. However, it seems that an electrode placement capable of presenting a phosphene at the intended position in the lower visual field could be determined by means of the “method for designing the electrode placement for stimulating the intended region on the eyeball surface”, described in the previous study [11].

3. Method for Designing Electrode Placements to Induce Phosphenes in the Lower Visual Field

In Section 2.2, methods for placing electrodes in order to induce phosphenes in three positions in the human visual field were described. In reality, it is necessary to determine electrode placements for the presentation of phosphenes in three positions in the lower visual field so that users will be able to avoid tripping hazards. The previous study [11] on the presentation of phosphenes in three positions never discussed whether the phosphenes were presented in the upper or lower visual field. This section presents hypotheses related to the design of electrode placements with the aim of presenting phosphenes in three positions in the lower visual field. These hypotheses were developed in the following two steps.

• Hypothesize which target areas of the eyeball need to be stimulated in order to present phosphenes in the lower visual field.
• Hypothesize electrode placements that will stimulate the hypothesized target areas.

The part of the retina that controls the lower portion of the visual field is located in the upper half of the eyeball. Its contralateral side corresponds to the lower part of the eyeball surface. This is the part that needs to be stimulated in order to induce a phosphene in the lower portion of the human visual field, according to a previous study [15]. Moreover, as described in Section 2.1, when a phosphene is to be presented on the right side of the visual field, it is necessary to stimulate the temporal right eyeball surface. When a phosphene is be presented on the left side of the visual field, it is necessary to stimulate the temporal left eyeball. Therefore, in order to present a phosphene on the right side of the lower visual field, the lower temporal right eyeball surface should be stimulated, as shown in Figure 3(1). In order to present a phosphene on the left side of the lower visual field, the lower temporal left eyeball surface should be stimulated, as shown in Figure 3(2). Since stimulating the central cornea of both eyeballs results in the presentation of a phosphene in the center of the visual field [6,11], by stimulating the lower central eyeball surface, as shown in Figure 3(3),(4), it is possible to induce phosphene presentation in the lower central visual field. On the other hand, when the nasal side of both eyeball surfaces is stimulated, the temporal retinas of both eyes are stimulated. As shown in Figure 1, the retina on the temporal side of each eye controls a wide area, including the central visual field. Therefore, along with the method described above, namely, the stimulation of the lower central region of the eyeball surface, shown in Figure 3(3),(4), it is possible to induce phosphene presentation in the lower central visual field by stimulating the lower nasal side of both eyeball surfaces, as shown in Figure 3(5).

Now, we will briefly describe our hypotheses regarding the placements of electrodes that with allow the desired target areas be stimulated. In the case of Figure 3(1), in which a phosphene is presented in the lower visual field on the right side, the electrode placement can be determined with reference to that which presents a phosphene on the right side of the visual field, as used in the previous study [11] and shown in Figure 2A. In Figure 2A, the area around the temporal right eyeball might be subjected to a broad area of stimulation. It is presumed that a more local stimulus would be possible by locating the electrode on the forehead closer to the lower side of the right eyeball, in accordance with method 1. Similarly, in the case of Figure 3(2), in which a phosphene is presented on the left side of the lower visual field, the electrode placement can be determined with reference to that which presents a phosphene on the left side of the visual field, as used in the previous study and shown in Figure 2F. In the case of Figure 3(3)–(5), the phosphenes are presented in the lower central visual field. In the case of Figure 3(3),(4), since it is necessary to stimulate the lower part of the center of the eyeball, it is necessary to consider the difficulty of stimulating the central part of the eyeball, as previously described in Section 2.2 [11]. Therefore, it is necessary to place one electrode near the lower part of the eyeball in accordance with method 2 in order to stimulate the lower central part of the eyeball, as shown in Figure 3(3),(4). In addition, when stimulating the lower nasal side of both eyeballs, as shown in Figure 3(5), the electrode placement can be determined with reference to that which presents a phosphene around the central visual field, as shown in Figure 2C,D. Since there is a nose and the bone near the nasal side of both eyeballs, it is assumed that local stimulation will be more difficult. Therefore, the electrode placement must be designed on the basis of method 2. In concrete terms, the electrode located between the eyes in Figure 2C,D should be moved to closer to the lower side of the eyeballs. Moreover, it is necessary to place all of the cheek electrodes along the shape of the face in accordance with method 3 in order to stimulate the target area in a local manner.

On the basis of the subsequent evaluation, these hypotheses will be verified with respect to whether these electrode placements are able to stimulate the intended area of the eyeball.

4. Evaluation

In this paper, we focus on the transition of the electric field value across the surface of the eyeball, following previous research [11], and verify whether the proposed electrode placements are able to stimulate the intended region on the eyeball surface. This section describes the simulation conditions, including the electrode placement used to simulate the electric field on the eyeball surface. Finally, the results of the evaluation are shown in this section.

4.1. Simulation Condition for Evaluation

In this subsection, we firstly describe the simulation method used to verify the hypothesis. Then, we describe the simulation conditions.

There are various types of electric field analysis methods that can be used in the human body, including FDTD (finite difference time domain method) [18] and FEM (finite element method) [19]. FDTD is a method that divides a finite region into cubic cells and obtains an electromagnetic field value for each cell on the basis of Maxwell’s equations. It is possible to handle complicated objects by setting a medium for each cell. However, the FDTD method is time consuming. This is because FDTD requires an enormous number of iterations to perform the calculations for the low frequency band [20]. Although solutions have been investigated to overcome the problem of time consumption for FDTD in the low frequency band, most existing studies focus on frequency ranges of more than 100 Hz [20,21]. Since the frequency range of the stimulation used in this study is supposed to be 10 Hz, based on our previous studies [11,22], it is difficult to perform FDTD under our simulation conditions. An addition problem is that the staircase approximation is required for objects that have many curved surfaces, causing large errors. Therefore, FDTD is not suitable for the analysis of more complex tissues such as the human brain. FEM is a method that decomposes an object into small elements and finds electromagnetic fields inside each element. Although it is computationally expensive, it is suitable for performing electromagnetic field analysis on small objects such as the human body. Moreover, FEM can be performed even in the low frequency band. Therefore, we also used electric field analysis using the FEM method in our previous studies [11,22].

SimNIBS is a free software package that supports the use of FEM to perform electric field simulations for Non-Invasive Brain Stimulation (NIBS) [23,24,25,26]. SimNIBS was also been used in the previous studies, and divides the human body, which is the object of analysis, into tetrahedrons for simulation. Any model can be used as the human body model for the purposes of analysis using SimNIBS, but Ernie is given as an example. Ernie is a young and healthy man. His head model was created by applying the average facial data from five subjects, thus concealing his face. Informed consent was given in writing to disclose MR (magnetic resonance) data, and the data were completely anonymized following confirmation by the radiologist. High-resolution T1- and T2-weighted images and diffusion MR images were used for Ernie’s dataset. Ernie’s is a highly detailed dataset, with voxel sizes of 1 × 1 × 1 ${\mathrm{mm}}^3$ for the T1- and T2-weighted images and 2 × 2 × 2 ${\mathrm{mm}}^3$ for the diffusion MR images. SimNIBS is able to simulate stimulation using TMS and tDCS (transcranial direct current stimulation) as the initial setting, and the simulation result of tDCS can be used for the use of tACS in the low-frequency band. Since the frequency value in this study is supposed to be 10 Hz, as previously mentioned in this subsection, the tDCS simulation can be used to perform the evaluation. The simulation of tDCS in SimNIBS follows Laplace’s equation to find the potential.

$$\nabla ·\left(\mathsf{\sigma }\nabla \mathsf{\phi }\right)=0 \left(in \mathsf{\Omega }\right),$$

(1)

$$\mathbb{E}=-\nabla \mathsf{\phi } \left(in \mathsf{\Omega }\right),$$

(2)

$\mathsf{\Omega }$ is the range covered by the numerical calculations. In Equation (1), $\mathsf{\sigma }$ is the conductivity and $\mathsf{\phi }$ is the potential caused by an external stimulus. $\mathbb{E}$ in Equation (2) represents the electric field and is obtained by the gradient of the potential. In FEM, it is necessary to establish a partial differential equation, as shown in Equation (1), within the range of all regions $\mathsf{\Omega }$. In SimNIBS, the weak form of the partial differential equation is derived, and the desired potential is obtained using the Galerkin method. Regarding the boundary conditions in SimNIBS, the electrodes and the other areas have different initial conditions. The initial conditions of the electrodes are determines using the Dirichlet boundary condition, while those of other areas are determined using the Neumann boundary condition.

The electrical conductivity of each tissue varies depending on the frequency of the stimulation, and arbitrary values can be set in SimNIBS. Therefore, in this study, the electrical conductivity values [27,28] shown in

Table 1. Comparison of electrical conductivity between the default value obtained in SimNIBS and the value obtained with 10 Hz stimulation [27,28].

Tissues	Electrical Conductivity (Default) [S/m]	Electrical Conductivity (10 Hz) [S/m]
White matter	0.12600	0.027656
Gray Matter	0.27500	0.027512
$CSF{ }^1$	1.6540	2.0000
Bone	1.0000 × ${10}^{-2}$	0.020028
Head skin	0.46500	2.0000 × ${10}^{-4}$
Eye ball	0.50000	0.41113

¹CSF (Cerebral Spinal Fluid).

are used for the simulation. These electrical conductivity values are assumed to be linear and isotropic. Regarding the other stimulation conditions, an alternating current stimulation at 1 mA will be simulated, which is in accordance with the previous work [11,22]. Moreover, the electric field on the eyeball surface is simulated, and the default value is used as the electric field value. The default value of the electric field is calculated on the basis of the magnitude of the electric field vector, and it is always a positive value.

Using the method for designing electrode placements that are able to stimulate intended regions on the lower side of the eyeball surface described in Section 3, in this subsection, the electrode placements used in the simulation presented in this study are shown. Figure 4 shows the electrode placements used in this simulation, and

Table 2. Coordinates of each stimulus electrode on the human face.

Electrode	Anode’s Coordinate [mm]	Cathode’s Coordinate [mm]	Electrode	Anode’s Coordinate [mm]	Cathode’s Coordinate [mm]
1	(63.36, 59.78, −24.16)	(18.1, 78.77, −95.18)	4	(−38.82, 78.54, −27.97)	(−37.49, 65.82, −93.9)
2	(−67.2, 59.45, −24.09)	(−27.79, 75.21, −97.31)	5	(−1.03, 99.96, −23.91)	(18.1, 78.77, −95.18)
3	(34.79, 78.28, −27.44)	(36.84, 60.07, −94.86)

shows the coordinates. In correspondence with the stimulation regions of each of the conditions shown in Figure 3, five electrode placements are shown in Figure 4. The pink-colored electrodes shown in Figure 4 are anodes, and the blue-colored electrodes are cathodes. The size of the electrode is determined with reference to the gel pad of foc.us [29] used in the previous research [15], which has a size of 42 mm × 42 mm. The coordinates in Table 2 represent the x, y, and z coordinates from left to right. The origin of the coordinates corresponds to the center of the human head model, as shown in Figure 5.

4.2. Method for Evaluating Simulation Results

In this subsection, firstly, the default output style of SimNIBS simulation is described, along with the method for transforming the output value of the simulation in order to be able to perform the evaluation. In the default output style of SimNIBS, the electric field transition on the specific tissues is described visually. As described in Section 4.1, the human tissues are divided into tiny elements by means of FEM using SimNIBS. Therefore, the default value of the electric field is assigned to one tiny element as a simulation result. The simulation results are represented as changes in the color of the electric field on the surface of the eyeball, which is composed of tiny triangles. This output style makes it easy to observe the stimulated area in a specific tissue. However, it is difficult to compare the spatial information numerically. Therefore, it is necessary to employ a method that makes it easy to perform numerical comparisons. In this study, the eyeball surface is transformed into a plane surface in order to be able to compare the stimulated area on the eyeball surface numerically.

We employed a method in which the spherical eyeball is output as a plane, similar to the Mercator projection of the globe. In SimNIBS, each of the many tiny triangles dividing the surface of the tissues has a single electric field value, and these triangles are not always equilateral triangles. It is challenging to transform the eyeball surface formed by this set of triangles into a plane. Therefore, as shown in the first step in Figure 6, an electric field value is assigned to a single point at the center of gravity of the triangle, in order to be able to handle it easily. As a result of this, only a single coordinate value is processed for each electric field value. Regarding the electric field values obtained by the simulation, the range of electric field values is normalized in order to be able to compare them with the results obtained using other electrode placements. The maximum electric field value is converted to 1, and the minimum electric value is converted to 0 in the second step of Figure 6. After dividing the electric field value data obtained with both eyes into data for each eye, as shown in the third step shown in Figure 6, in the fourth step, the rectangular coordinates of each element’s center of gravity on the eyeball surface are converted into the polar coordinates. This conversion is a preliminary step for the transformation of the eyeballs into a plane, in a similar manner to the Mercator projection. In the 3D conversion of the polar coordinates, the provided coordinates correspond to the radius of the eyeball, the degrees of longitude, and the height in the eyeball. Therefore, the vertical axis of the transformed plane shown in the final step of Figure 6 represents the height coordinate in the eyeball, while the horizontal axis of the plane corresponds to the angular coordinates of the eyeball. The range of values on the vertical axis reflects the radius of the eyeball, and the range of values on the horizontal axis is approximate −π to π. The eyeball is not a perfect sphere; therefore, the shape of the transformed plane shown in Figure 6 is not a perfect rectangle. The stimulated area is indicated by yellow to orange color in the plane, while the unstimulated area is indicated by blue color in the plane. If the stimulated area is below the half-line on the vertical axis, this means that the lower part of the eyeball surface is being stimulated correctly. Moreover, the range from 0 to π on the horizontal axis is the anterior side of the eyeball surface. Therefore, by dividing the range from 0 to π into three areas, it is possible to evaluate whether the temporal, central or nasal region of the anterior eyeball surface is being stimulated.

4.3. Evaluation Results

The simulation results for the proposed electrode placements for stimulating the lower side of the eyeball surface in order to present phosphenes in the lower portion of the human visual field are shown in Figure 7. Each cell in Figure 7 represents the simulation results for a different electrode, and consists of two transformed 2D planes corresponding to the surfaces of the right and left eyeballs. The vertical axis is the height coordinate of the eyeball, and the horizontal axis is the angular coordinate of the eyeball. The stimulated area is colored yellow to orange, and the blue area is not stimulated. The area below the red line on the vertical axis corresponds to the lower part of the eyeball surface. The area from around zero to three on the horizontal axis is further divided into three areas in Figure 7. The left side of the divided area corresponds to the temporal right eyeball or the nasal left eyeball. The central part of the divided area corresponds to the central area of the right or left eyeball. The right side of the divided area corresponds to the nasal right eyeball or the temporal left eyeball.

Our hypotheses, and the expected area stimulated by each electrode, are summarized in

Table 3. Summary of the hypotheses for each electrode.

Electrode	Expected Stimulation Area	Hypothesis
1	the lower temporal right eyeball	- One electrode should be located around the lower temporal right eyeball - The other electrode should be located in consideration of the shape of the face
2	the lower temporal left eyeball	- One electrode should be located around the lower temporal left eyeball - The other electrode should be located in consideration of the shape of the face
3	the lower central right eyeball	- One electrode should be located near the lower central right eyeball - The other electrode should be located in consideration of the shape of the face
4	the lower central left eyeball	- One electrode should be located near the lower central left eyeball - The other electrode should be located in consideration of the shape of the face
5	the lower nasal both eyeballs	- One electrode should be located near the lower nasal both eyeballs - The other electrode should be located in consideration of the shape of the face

. On the basis of Figure 7, all of the hypotheses regarding the areas stimulated by particular electrodes were validated. All of the areas that were stimulated by each electrode placement were located below the red line on the horizontal axis. Therefore, it can be seen that all of the proposed electrodes can potentially allow the the stimulation of the lower side of the eyeball. Regarding the target stimulated area, all of the proposed electrodes stimulated the expected stimulated area on the eyeball surface, as stated in Table 3. However, local stimulation remains an issue, in the sense that the electrode placements stimulate areas outside the target area, in addition to the target area. For example, electrode 3, designed to stimulate the lower central area of the right eyeball, as shown in Table 3, also stimulated the lower temporal area of the right eyeball, which is outside of the target stimulation area.

5. Discussion

In this section, the positional relationships between the electrodes and the eyeballs that affect the stimulated area are discussed. This is done on the basis of a comparison between the electrode placements described in our previous study [11] and the ones proposed in this study. The electrode placements reported in the previous study presents phosphenes in three positions within the visual field. On the other hand, the electrode placements proposed in Section 4 present phosphenes in the lower visual field. Then, the manner in which the positional relationships between the electrodes and the eyeball affect the stimulated area is discussed. Moreover, solutions to the problem of local stimulation in the simulation results described in Section 4 re also discussed.

5.1. Comparison of the Stimulated Areas between Previously Described Electrodes and Proposed Electrodes

In this subsection, we present a comparison between the electrode placements described in our previous study [11] and the ones proposed in this study. To perform this comparison, simulations with the electrode placements described in our previous study were performed under the same simulation conditions as the placements proposed in this study.

Table 4. Coordinate of each stimulus electrode used in previous study.

Electrode	Anode’s Coordinate [mm]	Cathode’s Coordinate [mm]	Electrode	Anode’s Coordinate [mm]	Cathode’s Coordinate [mm]
A	(62.68, 57.05, 27.99)	(44.43, 76.69, − 36.22)	D	(−0.81, 90.4, 20.72)	(−53.77, 65.46, −56.93)
B	(23.16, 88.73, 34.62)	(51.05, 66.06, −59.22)	E	(−24.47, 88.32, 33.67)	(−53.77, 65.46, −56.93)
C	(−0.81, 90.4, 20.72)	(51.05, 66.06, −59.22)	F	(−64.06, 54.13, 28.95)	(−45.91, 77.21, −35.86)

shows the electrode placement coordinates for the presentation of phosphenes in three positions of the visual field. In order to evaluate the simulation results, they were converted using the method described in Section 4.2.

Figure 8 shows the simulation results obtained using the electrodes described in the previous study [11]. In this figure, the vertical axis is the height coordinate of the eyeball, and the horizontal axis is the angular coordinate of the eyeball. The stimulated area is colored yellow to orange, and the blue area is not stimulated. The area below the red line on the vertical axis corresponds to the lower part of the eyeball surface. Additionally, the area from around zero to three on the horizontal axis is divided into three areas in Figure 8. The left, central, and right sides of the divided area correspond to the temporal right eyeball or nasal left eyeball, the central area of the right or left eyeball, and the nasal right eyeball or temporal left eyeball, respectively.

Electrodes A and F were used to stimulate the temporal side of the eyeball surface. Electrodes C and D were used to stimulate the nasal side of the eyeball surface. Electrodes B and E were used to stimulate the central side of the eyeball surface. It can be seen from Figure 8 that all of the electrode placements are able to stimulate the desired stimulation area on the eyeball surface. However, electrodes A and F still face challenges with respect to local stimulation.

On the basis of the simulation results shown in Figure 8, we determine why, even though all anodes were placed on the forehead and all cathodes were placed on the cheek, the electrode placements determine whether the upper or lower side of the eyeball will be stimulated. Moreover, we discuss why it was possible to stimulate the target area on the lower eyeball surface by all of the proposed electrode placements. In electrodes A and F, which stimulate the temporal side of the eyeball, the electric current flows from the electrode on the forehead to the electrode on the cheek, stimulating the temporal eyeball surface along the shape of the facial surface. The anode of electrodes A and F, as used in the previous study [11], is located on the forehead in a region as close to the ear as possible, and the cathode is located just below the eyeball. Therefore, electrodes A and F broadly stimulate the region on the temporal side of the eyeball surface, and then stimulate the central region of the eyeball surface near the cathode. On the other hand, as shown in Figure 4, electrodes 1 and 2, proposed in this study, which stimulate the temporal side of the eyeball surface, have the anode located significantly lower than the anode of electrodes A and F described in the previous study [11]. It can be seen that it is possible to avoid stimulating the upper side of the eyeball surface by locating the electrode at coordinates below the eyeball. In addition, by moving the cathode of electrodes A and F, used in the previous study, from the position under the eyeball to the jaw, it is possible to avoid stimulating the central eyeball surface, which is an unintended stimulation area, thus enabling local stimulation.

When placing the electrode to stimulate the nasal area of the eyeball surface, such as in electrodes C and D, the anode is located at the point between the eyebrows, which is close to the upper nasal area of both eyeballs, and the cathode is located on the lower cheek in consideration of the shape of the facial surface. Therefore, the upper side of the eyeball surface will be more strongly stimulated, since the anode is located closer to the eyeball than the cathode. On the other hand, as shown in Figure 4, electrode 5, which stimulates the nasal area of both eyeball surfaces, has the anode located just on the nasal bridge, which is close to the lower nasal area of both eyeballs. It is considered that, using the proposed electrode placement 5, it is possible to intensively stimulate the nasal part of both eyeballs due to the location of the anode. Moreover, the cathode is located near the jaw, so that it is possible to stimulate only the lower side of the eyeball surface.

When placing the electrode to stimulate the central eyeball surface, such as in electrodes B and E, the anode is located just above the center of the surface of the eyeball, and the cathode is located on the lower cheek in consideration of the shape of the facial surface. Therefore, the upper eyeball surface will be more strongly stimulated, since the anode is located closer to the eyeball than the cathode. On the other hand, as shown in Figure 4, electrodes 3 and 4, which stimulate the center of the eyeball surface, have the anode located just below the center of the surface of the eyeball. It is considered that, using the proposed electrode placements 3 and 4, it is possible to intensively stimulate the lower central part of the eyeball due to the location of the anode.

5.2. Solution for Local Stimulation for the Central Part of the Eyeball Surface

In this subsection, a method for achieving better placement of electrode 3 placements, which had difficulty performing local stimulation, is presented. As stated in Section 5.1, local stimulation potentially depends on the adjustment of the positional relationship between the electrodes and the eyeball. If a wide area of eyeball surface is stimulated, the electrode located near the eyeball should be moved to the side of the expected stimulated area, and the electrode located on the cheek should be moved close to the jaw. Therefore, in this subsection, a method for locally stimulating the lower central eyeball surface by adjusting the positional relationships between the electrodes and the eyeball is discussed. As mentioned in Section 3, there is a correspondence between the position of the electrode and the stimulated eyeball surface. When stimulating the temporal right eyeball, it is necessary to position an electrode close to the temporal right eyeball. Similarly, positioning an electrode close to the nasal side of the eyeball is necessary in order to stimulate the nasal side. Figure 7c shows that, although electrode 3 is able to stimulate the lower central area of the right eyeball, it also stimulates the temporal area. Therefore, it can be hypothesized that moving the anode of electrode 3, located under the eyeball, to the nasal side may make it possible to stimulate only the lower central area of the right eyeball. On the other hand, the electrode cheek electrode of electrode 3 is already positioned near the jaw. Since the cathode of electrode 3 does not have a large effect on the electric field value on the eyeball surface due to its large distance from the eye, it is not necessary to move the cathode of electrode 3. In addition, it was found in a previous study [15] that the stimulation value on the eyeball surface can be adjusted by reducing the current value. Therefore, it is conceivable that a more limited stimulation may be enabled by performing stimulation with a smaller current than the 1 mA used in the simulation.

Therefore, the coordinates of the anode used in electrode 3 were moved to the nasal side for verification. Moreover, the stimulated position on the eyeball surface when using 1 mA was compared with that when using 0.8 mA.

In evaluating the simulation results obtained using the revised coordinates of electrode 3, the simulation was performed on the basis of the simulation conditions described in Section 4.1, except that the electric current value in the simulation was different.

Table 5. Coordinate of revised electrodes that stimulate lower central area of right eyeball.

Electrode	Anode’s Coordinate [mm]	Cathode’s Coordinate [mm]
Revised Electrode 3	(20.72, 82.38, −29.32)	(36.84, 60.07, −94.86)

shows the revised coordinates of electrode 3, shown in Figure 4, locally stimulating the lower central area of the right eyeball. The revised electrode placement is shown in Figure 9. The pink-colored electrode is the anode, and the blue-colored electrode is the cathode. In order to evaluate the simulation results, they were converted using the method described in Section 4.2. However, step 2, indicated in Figure 6, was skipped in order to compare the stimulus intensity between simulations performed at 1 mA and at 0.8 mA.

The simulation results obtained for the stimulated area on the eyeball surface using the revised electrode 3 are presented in Figure 10. Figure 10a shows the simulation results obtained at 1 mA, and Figure 10b shows the simulation result obtained at at 0.8 mA. It can be seen that by moving the anode below the right eyeball to the nasal side, the stimulated area on the eyeball surface can be limited to the lower central area. These simulation results indicate that the stimulated area on the eyeball surface can be localized by moving the electrode close to the eyeball in the direction of the target stimulation position. Therefore, it can be stated that the hypothesis mentioned earlier in this subsection is validated. With stimulation at 0.8 mA, as shown in Figure 10b, the simulation results are presented using the same maximum and minimum values for the color bars as those for stimulation at 1 mA, in order to be able to compare the stimulated area with that obtained using 1 mA. On the basis of the stimulated area shown in Figure 10b, no region other than the lower central eyeball was stimulated, which is different from the simulation results obtained with 1 mA. Therefore, when the peak of the stimulated area is within the target stimulating area, making an adjustment to a smaller current value makes it possible to achieve local stimulation.

6. Conclusions

In this study, electrode placements enabling phosphenes to be presented in three locations in the lower visual field, with the aim of enhancing the safety of walking support for the visually impaired, were determined. A hypothesis on the determination of electrode placement for the presentation of phosphenes in the lower visual field was posited based on the electrode placement strategies for achievement desired phosphene location reported in our previous study [11]. As a result, it was shown that it is possible to stimulate the surface of the target eyeball using all of the proposed electrode placements. In addition, the proposed electrode placements in this study enabled local stimulation of the lower eyeball surface more reliably than the electrode placements described in the previous study [11]. Moreover, based on the hypothesis stated in Section 5, it was shown that adjusting the coordinates of the anode of electrode 3, which had difficulty performing local stimulation in the simulation results presented in Figure 7, made it possible to stimulate only the target area on the eyeball surface. This study makes an important contribution to improving phosphene presentation, increasing the number of locations at which phosphenes can be presented in the human visual field. In the future, the obstacles at eye height, which are difficult to detect using currently available walking support tools, such as a white cane, will be addressed by describing a method enabling the presentation of phosphenes not only in the lower portion of the visual field, but also in the upper visual field.