Simple estimation of induced electric fields in nervous system tissues for human exposure to non-uniform electric fields at power frequency

Most results regarding induced current in the human body related to electric field dosimetry have been calculated under uniform field conditions. We have found in previous work that a contact current is a more suitable way to evaluate induced electric fields, even in the case of exposure to non-uniform fields. If the relationship between induced currents and external non-uniform fields can be understood, induced electric fields in nervous system tissues may be able to be estimated from measurements of ambient non-uniform fields. In the present paper, we numerically calculated the induced electric fields and currents in a human model by considering non-uniform fields based on distortion by a cubic conductor under an unperturbed electric field of 1 kV m−1 at 60 Hz. We investigated the relationship between a non-uniform external electric field with no human present and the induced current through the neck, and the relationship between the current through the neck and the induced electric fields in nervous system tissues such as the brain, heart, and spinal cord. The results showed that the current through the neck can be formulated by means of an external electric field at the central position of the human head, and the distance between the conductor and the human model. As expected, there is a strong correlation between the current through the neck and the induced electric fields in the nervous system tissues. The combination of these relationships indicates that induced electric fields in these tissues can be estimated solely by measurements of the external field at a point and the distance from the conductor.

by means of an external electric field at the central position of the human head, and the distance between the conductor and the human model. As expected, there is a strong correlation between the current through the neck and the induced electric fields in the nervous system tissues. The combination of these relationships indicates that induced electric fields in these tissues can be estimated solely by measurements of the external field at a point and the distance from the conductor.
Keywords: numerical human model, cubic conductor, induced current through the neck, brain, spinal cord (Some figures may appear in colour only in the online journal)

Introduction
Stimulations based on currents induced in the human body by extremely low frequency (ELF) electric and magnetic fields can be regarded as a factor in adverse health effects in humans. Accordingly, induced currents in a numerical human body model from electric and magnetic fields have been calculated in several previous studies , Dimbylow 1998, Dimbylow 2000, Stuchly and Dawson 2002, Leitgeb and Cech 2008. Most results were calculated under uniform fields, with very few results under realistic non-uniform magnetic fields, such as those in a substation and from home appliances (Cheng et al 1995, Dawson et al 1999, Gandhi et al 2001. In the case of magnetic field exposure, estimations of induced currents in a spherical model or a human model by non-uniform magnetic fields that are produced by currents from single and double wires were carried out (IEC 2004a, Yamazaki et al 2005, 2007. In the IEC 62226-2-1, the coupling factors for nonuniform magnetic fields for several different types of magnetic sources are indicated. In addition, understanding of magnetic field exposure has been advanced by a number of numerically dosimetric studies, including studies using models of specific tissues such as the retina and skin (Hirata et al 2011, Santis et al 2016, Schmid and Hirtl 2016. In the case of electric field exposure, meanwhile, induced electric fields in a spheroid model in a uniform electric field were theoretically derived (Shiau and Valentino 1981). Also, currents induced in both ankles of a grounded human body were measured and formulated (Deno and Zaffanella 1982). These calculated results (i.e. short circuit currents) are consistent with numerically calculated results using anatomical human models that have often been used recently , Tarao et al 2013. However, these calculations do not consider non-uniform field exposure, which is unrealistic because electric fields are readily perturbed by a conductor. In the IEC 62226-3-1 (2004b), methods to calculate currents induced by electric field exposures are described, but non-uniform field exposures are not covered.
Experimental data concerning external electric fields in substations and induced currents through the necks of workers were reported (Korpinen et al 2009(Korpinen et al , 2012, and the results showed that there is a rough correlation between them. Furthermore, in our previous work we found that a contact current or a short circuit current is a more suitable factor for evaluating induced electric fields, even in the case of a non-uniform field exposure (Tarao et al 2013). Therefore, if the relationship between ambient non-uniform electric fields and induced currents in the body can be made clear, induced electric fields in nervous system tissues such as the brain and spinal cord could possibly be estimated by measuring ambient non-uniform electric fields.
In the present paper, in relation to the electrical safety of workers in substations, our goal is to develop an estimation technique for induced electric fields in the nervous system tissues of workers based on measurements of ambient external electric fields. The EU Directive 2013/35/EU, which is intended to improve regulations for workplace safety, seeks to limit workers' exposure to electric and magnetic fields. EU member nations must apply it by July 2016 (The European Parliament and the Council of the European Union 2013). Thus, there is a clear need for a practical method of estimating induced electric fields for these workers.
First, we numerically calculated the induced currents in a human model by considering a non-uniform electric field that is distorted by a cubic conductive object, which assumes a grounded metal structure in a substation, under an unperturbed electric field at power frequency. In the calculations, the height of the conductive object and the distance between the human model and the object are varied to consider the different types of non-uniformity. Then, from the calculated results, we examined the relationship between the external electric field and the induced current through the neck of the model. We have a good record of using a current through the neck, and we confirmed that the induced electric fields in the nervous system tissues of the model correlate with the currents through the neck. Finally, we investigated an approximate expression to obtain induced electric fields in those tissues from experimental measurements of ambient non-uniform electric fields.

Numerical method
Electric fields and currents induced in a voxelized human model exposed to ELF external electric fields were calculated based on the scalar potential finite difference (SPFD) method (Dimbylow 1998). This method was originally used for low-frequency induction by magnetic fields, but has been improved for use with electric field exposure. In the case of the SPFD method of magnetic induction, only the region inside a numerical human model is required as the computational domain. However, in the case of the improved method for electric field exposure, the computational domain includes a large region outside the human model as well as the region inside the human model. Therefore, this numerical computation for electric field exposures using the improved method requires very large nodes. A detailed description of the numerical method and its validation is available from Tarao et al (2013).

Human model
A realistic human model of an adult male (Duke), 1.80 m in height, comprising 77 tissues and organs, was used for the numerical calculations (Christ et al 2010). The model has a bounding box of 0.61 m × 0.31 m × 1.86 m for the x-, y-, and z-axes, respectively. The voxel size of the model can be adjusted from 0.1 mm to a maximum of 5 mm. Selecting the maximum size results in approximately 2.8 million voxels for the bounding box itself. This size was selected for the present study, because in our case we had to locate the model within a much larger computational area (discussed in the next section). The typical conductivity values at power frequency corresponding to particular tissues were used based on the measurements reported by Gabriel et al (1996Gabriel et al ( , 2009 and were assigned to each voxel of the numerical model.

Exposure condition
The entire computational domain used in the study was a cubic space with dimensions 20 m × 10 m × 16 m for the x-, y-, and z-axes, respectively. A high potential electrode (16 kV) on the top surface of the domain and a ground electrode on the bottom surface of the domain were attached to generate a vertical uniform electric field of 1 kV m −1 at 60 Hz in the computational domain. The numerical human model (Duke) stood on the center of the ground plane and was grounded. A conductive object with dimensions 0.5 m × 0.5 m for the x-and y-axes, which was also grounded, was placed in front of the human model so that the human model would encounter non-uniform electric fields that were distorted by the object. As illustrated in figure 1, the height of the object (h) varied from 2 m up to 5 m, and the distance (d) between the surface of the object and the center axis of the human model also varied from 0.25 m up to 4 m, to produce different types of non-uniformity around the object. The computational domain was divided into various voxel sizes, ranging from 5 mm for the bounding box of the numerical human model to 1.28 m for the edge of the domain. The selected sizes reduced the total number of voxels to about 20 million.
After the numerical calculations were performed by varying the height (h) of the conductive object and the distance (d) from the object, the relationship between the ambient external electric fields and the induced currents flowing through the neck of the human model, and the relationship between the induced currents in the neck and the induced electric fields in the nervous system tissues (i.e. the brain, heart, nerves, and spinal cord) of the human model were investigated. Here, the external field is defined as the electric field strength (E ext ) at the central position of the numerical human head (1.7 m height from the ground) with no human present (see figure 1), since currents induced in the neck are caused by potential differences based on the electrification charges on the human head. Figure 1 shows the distribution of the equipotential line and electric field vector around the conductive object with no human present. It is clear from the figure that the electric field around the object is distorted and becomes non-uniform. In the IEC 62110 (2009), the nonuniformity of electric fields (E NU ) is defined as,

External electric field and its non-uniformity
where E 1.5 is the electric field strength at 1.5 m above the ground, which is the value at the largest difference in the numerator, and E avg is the electric field level at heights of 0.5 m, 1.0 mm, and 1.5 m above the ground. Table 1 indicates the electric field strengths calculated with no human present and the averaged value (E avg ), which also shows the non-uniformity (E NU ). In the table, the electric fields at a point 1.5 m near the object exceed 1 kV m −1 . For example, the electric field strengths at 1.5 m for h = 2 m are 1.7 kV m −1 , 1.3 kV m −1 , and 1.1 kV m −1 for d = 0.25 m, 0.45 m, and 0.65 m, respectively, where the non-uniformity ranges from 30% to 55%. In contrast, the non-uniformity reduces by a small percentage 2 m from the object, becoming more uniform. Only a few measured non-uniform electric fields related to the non-uniformity were reported, because electric field meters are generally calibrated under a uniform field. One example is the measurement of electric fields in a corridor of an EHV substation (Deno and Zaffanella 1982). The measured data were 3.7, 4.43, and 6.7 kV m −1 at 0.5, 1.0, and 2.0 m above the ground, respectively. In this case, the non-uniformity was 35.5%; however, note that the highest measured point was not 1.5 m. Therefore, the range of the non-uniformity investigated in the present study covers a practical situation encountered in a substation. Figure 2 shows the calculated results of both the equipotential line and electric field vector around the human model for the different distances from the surface of the object. It can be seen from figure 2 that the electric field interacting with the human body (in particular, the frontal side of the human) decreases with a closer approach to the conductive object because of the existence of the object. This results in the induced current through the human body also decreasing. Figure 3 shows the induced current flowing downward, perpendicular to each horizontal layer of the human body for the different distances from the surface of the conductive object. From the figure, the induced current through the neck in the case of a uniform field of 1 kV m −1 at 60 Hz is 5 μA, which is about 27% of the total current through the ankles (i.e. short circuit current). The induced current decreases as the distance from the object decreases, since the electric field getting through the human body decreases, as expected. Figure 4 shows the induced current through the neck of the human model as a function of the external field (E ext ) for the different h and d. The straight line in the figure represents the current through the neck in the case of a uniform electric field, which is based on the fact that the current value in the neck for the uniform field exposure shown in figure 3, as expressed by:

Currents through the neck
(2)   where E uni is the external electric field strength for a uniform exposure and f is the frequency. In the case of an electric field exposure at low frequency, induced electric fields and currents in the body are proportional to the frequency as the complex conductivity outside the body (i.e. air) can be regarded as ωε 0 , and its magnitude is very small compared with the magnitude of the complex conductivity inside the body (Shiau andValentino 1981, Kaune et al 1997). As indicated in figure 4, all the plots stay below the straight line, even when the point electric field at 1.7 m above the ground exceeds 1 kV m −1 , and show a non-linear relationship against E ext .  The currents through the neck decrease non-linearly as the body moves closer to the object for any object height, since the electric potentials at the head position (but with no human present) decrease (see figure 1). In contrast, the plots coincide with the case of a uniform field exposure when the distance (d ) is large. External electric fields around power equipment in 400 kV substations and currents in the heads of workers during their maintenance were previously measured (Korpinen et al 2009, 2012). The results showed that there was a rough correlation between the current through the neck and the external field at 1.7 m above the ground, but the distance from the equipment is not completely described. Consequently, all data regarding current through the neck, as indicated in the literature, seem to be lower than those obtained from equation (2), which shows a similar tendency to figure 4. Figure 5 shows the ratio of the current through the neck (I neck ) under non-uniform exposure with E ext to another current through the neck by a uniform field with strength equal to E ext , as a function of distance (d ). For a distance greater than about 4 m, the ratio reaches 100%, so it can be regarded as a uniform field. In contrast, for distances below 4 m, the ratio depends only on the distance. Using curve fitting based on the calculated results, the reduction rate can be expressed by: which is shown in figure 5 and demonstrates that the reduction rate can be determined by the distance from the object, regardless of the height. In equation (3), K I becomes zero if d is about 0.1 m, which is the situation in which the largest area of the human body contacts the conductive object, and which is not covered in this study. For d = 0.45 m and h = 2 m, K I is 40.9% from equation (3). Because the external field strength and the current in the neck were 1.5 kV m −1 and 3.09 μA, respectively, K I can be estimated as 41.2% with a current of 7.5 μA in the neck for uniform exposure taken into consideration. Therefore, these reduction rates are in excellent agreement with each other. Figure 6 shows the 99th percentile values of the induced electric fields (E tissue ), which are based on the International Commission on Non-Ionizing Radiation Protection (ICNIRP) guidelines (2010), in the brain, heart, peripheral nerves, and spinal cord against the current through the neck (I neck ). It is clear from figure 6 that the induced electric fields in these nervous system tissues are strongly correlated with the induced currents through the neck under all conditions, as predicted by previous work (Tarao et al 2013), which indicates that these induced electric fields can be estimated from the currents through the neck, expressed approximately by:

Induced electric fields in nervous system tissues
where K tissue is the slope of the straight line shown in figure 6, as indicated in table 2. From the calculation for d = 0.45 m and h = 2 m, the current in the neck and induced electric field in the brain were 3.09 μA and 1.64 mV m −1 , respectively. Therefore, the slope can be estimated as 530.7, with an error of 5.8%. Korpinen et al (2012) tabulated induced electric fields in the head estimated by measurements of currents through the necks of humans working in substations. This induced field was calculated by dividing averaged current density in the neck by a conductivity of 0.1-0.2 S m −1 , which are typical values of tissue conductivity. These induced electric fields are comparable with the values obtained from equation (4). Figure 7 shows an example of the induced electric field distribution on the horizontal crosssection, including the brain of the human model, for the different distances from the object. It can be seen that the induced electric fields in the tissues existing between the skull and skin, such as subcutaneous adipose tissues, are higher than those in the brain. In particular, the induced fields in the frontal side of the head increase as the distance increases, as is obvious from figure 2. The vectors in figure 7 are all unit vectors. However, the lengths of the vectors in the brain seem to be somewhat shorter, which means that the vertical component of the induced fields is dominant.

Estimation of induced field by measuring the external field
By combining equations (2)-(4), the approximated E tissue can be derived by: In the proposed estimation, measurements of the external electric field at a point in the center of the human head and the distance from the conductive object are needed to obtain the maximum value of the induced electric fields in the nervous system tissues.

Validation
3.5.1. Ungrounded human. The calculations in the present paper were carried out with the numerical human model grounded. If an ungrounded human stands beside the conductive object, currents induced in the neck of the human body should be smaller than in the case of a grounded human. Therefore, the reduction rate should be smaller than that in the curve indicated in equation (3), which can be thought of as underestimation. However, if an ungrounded human touches a conductor, a contact current, which is the total current flowing out from the body to the ground, has the same value as in a short-circuit current from the feet of a grounded human (Tarao et al 2013), allowing the application of our method. In any case, the relationship between the current in the neck and the induced electric fields in the nervous system tissues does not change. 3.5.2. 99th percentile value of induced field. According to the ICNIRP guidelines established in 2010 (ICNIRP 2010), the induced electric field to be compared with the basic restrictions is recommended as a vector average of the electric field in a small contiguous tissue volume of 2 × 2 × 2 mm 3 , although we used a voxel size of 5 mm in the present study. The effects of averaging the volume of the voxels on induced electric fields in the brain of a numerical human model exposed to a uniform electric field were previously investigated (Hirata et al  2010). These authors concluded that the 99th percentile value of an electric field in nerve tissue is more stable than that of the maximal value for the different averaging volumes. Figure 8 shows the percentile values of the induced electric field in the nervous system tissues of a Duke model for a uniform electric field (1 kV m −1 at 60 Hz) with a voxel size of 2 mm  and 5 mm. The result in the case of a voxel size of 2 mm was obtained using a two-stage approach (Tarao et al 2013). It is noted that the currents induced through each horizontal cross-section of the body obtained from the numerical human models, such as in figure 3, with different voxel sizes are in agreement with each other. However, the induced electric fields differ depending on the voxel size as an electric field is a kind of density. It can be seen in figure 8 that the results obtained for the 2 mm and the 5 mm voxels were almost consistent up to about 99%, except for the spinal cord. The maximum value of the induced fields in the nerves can be observed to have a staircase error even for a voxel size of 5 mm. It has been reported that the 99th percentile value could significantly underestimate the actual induced field level (Chen et al 2013). Further work could be necessary to fully understand the maximum value. 3.5.3. Comparison with the previous report. We reported previously the induced currents and electric fields in a worker engaging in the maintenance of an operational circuit breaker in a substation, considering human exposure to a non-uniform electric field (Tarao et al 2013). In this case, the external electric fields at 1.7 m were 21.0, 15.6, and 12.8 kV m −1 at 50 Hz for the distances of 0.25, 0.45, and 0.65 m, respectively. It is noted that the distance is adapted to that defined in the present study. Substituting these values in equation (5), the induced electric fields in the tissues (E tissue ) can be calculated, as indicated in table 3. The estimated values are in greater agreement with the previous results shown in parentheses as the distance increases. In part icular, in the case of a distance of 0.65 m, which is generally maintained in a substation, these values are in excellent agreement with each other.
3.5.4. Effect of conductor size. Finally, in the present calculations, a non-uniform electric field encountered in a substation was given by assuming a geometrically complex metal structure as the simply configured conductive object. The method presented here provides for estimating induced electric fields in various nervous system tissues of a worker near a conductive object with a certain width, as used in the present calculation. Assuming that the worker stands beside a metal pole in a substation, the reduction rate will exceed the upper bound indicated in equation (3) and figure 5, because the worker is exposed to more electric fields as they emanate from both sides of the pole. Also, figure 9 shows the reduction rate for the different The value in parentheses shows the results from the previous work (Tarao et al 2013). distances (d ) from the object as a function of the height of the object. We found that the reduction rate increases sharply when the object height is below the human model height. This method has some room for improvement. However, even in such cases, the induced fields in the nervous system tissues correlated closely with the current through the neck.

Conclusion
In the present paper, to provide a simple method for the estimation of induced electric fields in the nervous system tissues of an adult human exposed to a non-uniform electric field, induced electric fields and currents in the numerical human model were examined under different types of non-uniformity.
As expected, induced currents through the neck of the model were non-linear to the external electric fields when there was no human present. However, the induced currents depend on the distance from the surface of the object, regardless of the height of the object considered, and can be approximately formulated. Meanwhile, we confirmed that there was a strong correlation between the induced current through the neck and the induced electric fields in the nervous system tissues in all conditions. Consequently, the combination of these findings facilitates the estimation of the induced electric fields in those tissues from the external electric field at the central position of the human head and the distance from the object, both of which can be readily measured. The present simple estimation method can be applied in limited cases, such as when a conductive object is a device or a piece of equipment with a certain width and is taller than a human's height. Further investigations of accounting for non-uniformity in estimation methods are needed to extend the coverage of the applicable conditions.