Radiation Protection Dosimetry (2014), Vol. 162, No. 3, pp. 244 – 253 Advance Access publication 11 November 2013
doi:10.1093/rpd/nct281
INDUCED ELECTRIC FIELDS IN THE MAXWEL SURFACE-BASED HUMAN MODEL FROM EXPOSURE TO EXTERNAL LOW FREQUENCY ELECTRIC FIELDS R. P. Findlay* EMFcomp, Wantage, Oxfordshire OX12 8HG, UK *Corresponding author: [email protected]
This work presents calculations of internal induced electric fields in the anatomically realistic surface-based model of the male human body, MAXWEL, from exposure to external low frequency electric fields under grounded and isolated conditions. The maximum 99th percentile induced electric fields calculated in the MAXWEL central nervous system were 3.49 (grounded) and 1.54 (isolated) mV m21 per kV m21 at 50 Hz. The application of 2, 1 and 0.5 mm resolution voxel models derived from the surface-based version to the calculations of induced electric fields is described. 2 mm and 1 mm resolution maximum 99th percentile induced electric field values calculated in selected tissues of the eye at 50 Hz were within 30 % of those calculated at 0.5 mm resolution. The calculated electric field values in MAXWEL were compared with values from the male model NORMAN and female model NAOMI. The maximum 99th percentile value for NAOMI, calculated by Dimbylow in bone, was 49.4 mV m21 per kV m21 at 50 Hz under grounded conditions. The corresponding value calculated in MAXWEL was 15.7 mV m21 per kV m21, considerably lower due to anatomical differences between the male and female models.
INTRODUCTION The International Commission on Non-Ionizing Radiation Protection (ICNIRP) has produced guidelines(1) on human electromagnetic field exposure to protect against adverse health effects at low frequencies. Basic restrictions, presented in terms of induced internal electric fields in the body and reference levels, expressed using applied external electric field values, are stated in these guidelines. ICNIRP recommends that the 99th percentile value of the electric field (E99), averaged over a contiguous tissue region of 2` 2` 2 mm3, is used to determine the induced electric field for comparison with the basic restrictions. Separate frequency dependent values are stated for the central nervous system (CNS) tissues in the head and all tissues in the head and body. Human dosimetric studies of induced electric fields from exposure to low frequency external electric fields are limited. Dawson et al.(2) used a quasi-static finitedifference time-domain (FDTD) method to calculate surface charge densities from exposure to electric fields and interpolate onto a 3.6 mm resolution University of Victoria phantom. These provided source terms for internal dose calculations using the scalar-potential finite-difference (SPFD) method(3). Furse and Gandhi (4) used the FDTD method to calculate induced current densities in a 6 mm resolution voxel phantom resulting from electric field exposure at 10 MHz using 60 Hz conductivities. These authors then linearly scaled the values with frequency to obtain current densities at 60 Hz. Hirata et al.(5)
calculated induced electric fields in a 5-y-old child model for exposure to an applied electric field using the hybrid approach(2). The calculated induced electric fields were found to be consistently lower in the child head tissues when compared with those in the adult. Dimbylow(6) used a series of nested sub-grids to solve the potential equation and calculate induced current densities in a 2 mm resolution version of the male NORMAN phantom from exposure to electric fields. Dimbylow also calculated induced electric fields in the CNS for NORMAN and NAOMI due to electric field exposure and induced electric fields in all tissues for NAOMI at 50 Hz(7). More recently, Hirata et al.(8) calculated induced electric fields from exposure to an external electric field in the Japanese voxel models TARO and HANAKO using the quasi-static FDTD method. Dimbylow and Findlay(9) calculated induced current densities in 25 different voxel models at 50 Hz from exposure to electric fields using the SPFD method; however, this study did not extend to the calculation of induced electric fields. The ICNIRP reference levels were based on simulations using only two voxel models of the human body, NORMAN and NAOMI, due to the limited number of induced electric field dosimetric studies for low frequency electric field exposure(10). Furthermore, that paper gives conversion factors between basic restrictions and external field values for just one model, the NAOMI female phantom(7), for non-CNS tissues. The induced electric fields in the body due to an applied external electric field will be different for
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Received 5 September 2013; revised 15 October 2013; accepted 16 October 2013
INDUCED ELECTRIC FIELDS IN MAXWEL
HUMAN MODEL The development of anatomically realistic models of the human body has mostly concentrated on voxel models(4, 11, 12, 13). Recently, a limited number of surface-based computational human models have emerged for the application to ionising and non-ionising exposure problems(14, 15). In these models, the boundary of each tissue type can be mathematically described by a form of parameterised surface that might be as simple as a planar quadrilateral or as sophisticated as a two-dimensional spline. The surface-based model can provide a closer geometrical approximation to the interface of adjacent materials by using a non-orthogonal, and sometimes curved, mesh. Surface-based phantoms combine the advantages of stylised and anatomically realistic voxel models. They are flexible, allowing changes to organ position and posture to occur, but they also present accurate models of the human anatomy and can be voxelised to a desired resolution. EMFcomp, an independent research microenterprise that specialises in computational electromagnetics, has developed a male, anatomically realistic surface-based model MAXWEL (MAle fleXible Whole-body modEL). Volume-rendered images of MAXWEL are shown in Figure 1. The opacity has been varied to show the internal structure of the model. In Figure 1a, the opacity of the skin is high to show the outer surface of the phantom. In Figure 1b, the skin and fat layers have been removed and the muscle layer has been given a reduced opacity to show the internal tissues and organs. In Figure 1c, the muscle layer has been removed to indicate the skeleton, liver, heart and intestines. The MAXWEL phantom presents a model in which the surfaces tend to be less smoothed than some other surface-based
models as these anatomical details are more important in non-ionising exposure problems. An advantage of employing the MAXWEL surface-based anatomical model is demonstrated in Figure 2. This figure displays the model of the eye in the MAXWEL human phantom, based on the Yoriyaz eye model(16). A cutaway view of the surfacebased model is shown in Figure 2a. The humour has been removed for clarity. Voxelised representations of this eye are then shown at 2, 1 and 0.5 mm resolution. The use of a fixed, say 2 mm, resolution voxel model limits the accurate representation of small organs in the body like the eye as the resolution of the model can never be higher than 2 mm—regardless of the grid size used to perform a calculation. It can be seen in Figure 2 that there is an obvious loss of the detailed anatomical structure of the eye at this 2 mm resolution when compared with higher resolutions. A surface-based model allows the model to be voxelised at very fine resolutions such as the displayed 0.5 mm, limiting the staircasing of the structure. The model on which MAXWEL is based originated from whole-body high-resolution magnetic resonance imaging (MRI) scans obtained by Fairfield Imaging. No information was available about the subject, except that he is a healthy young adult male (no known organic disease) of 23 year with a height of 1.70 m and a mass of 68 kg. The horizontal resolution of the data was 2 mm per pixel. The head of the model, however, was constructed from a separate 1 mm sagittal data volume, to give higher resolution, and rescaled to match the rest of the model. The MRI data were segmented into the various tissue types by a process of manual definition, assigning specific voxel intensities to organs by filling them individually on each data slice. The segmentation was then checked by using an intersecting orthogonal display that displayed the segmented area in relation to the whole data set. This was carried out on successive x–y slices throughout the volume. An automated procedure was also used to pre-process parts of the volume by sequentially loading slices into memory for segmentation of skin, fat and muscle. This was possible as the MRI data values for skin, muscle and fat are often well separated from other tissue types. In this way, a number of intermediate volumes could be generated during the segmentation process. Final post-processing of the entire segmented volume was used to remove artefacts so that every voxel belongs to one or other of the defined objects in the final volume. This was followed by a check of the resultant volume by a medical anatomical expert. The phantom consists of 45 different tissue types. These tissue types were, in addition to those listed in Table 1, spinal cord, tendon, cartilage, duodenum, trachea, background air, eye lens, humour, sclera, cornea, retina, optic nerve and choroid. MAXWEL was scaled to ‘reference man’(17) dimensions of 1.76 m tall and a mass of 73 kg.
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different human models due to variations in anatomical details. Studies into how these induced electric fields change with different models are important to ensure that accurate electromagnetic guidelines are produced. The object of this paper is to investigate how the use of a different human model changes the calculated internal electric fields when exposed to an external applied low frequency electric field. It is also to study the effect of voxel resolution on the induced electric fields in small organs from exposure to external electric fields by calculating internal fields in 2, 1 and 0.5 mm resolution voxel models of the eye produced from the surface-based version. The MAXWEL human model is described in the next section. This is followed by a description of the numerical methods used to calculate the induced electric fields. Results for applied, vertically aligned electric fields are then given and conclusions are presented in the final section.
R. P. FINDLAY
Table 1 presents the comparison between selected organ masses in MAXWEL and those identified in the International Commission on Radiation Protection (ICRP) values for ‘reference man’ and NORMAN(18). Values for tongue, small intestine (wall), large intestine (wall), bone (trabecular and cortical), tongue and blood in NORMAN were not listed in the study by Dimbylow(18) and so are not present in Table 1. The totals of the individual masses in Table 1 are 69.1 and 68.0 kg for ICRP and MAXWEL, respectively, presenting a discrepancy between these values and the total mass of 73 kg. This is because ICRP does not provide reference values for all organs within the body. Although some of the masses of organs along with the height and mass of the phantom were normalised, inevitable
differences appear in some of the tissue masses listed. However, in general, good agreement is shown. Good agreement did not exist in the tissue or organ masses for the stomach wall and contents, cortical and trabecular bone, blood and skin. The stomach wall and content masses differed for the ICRP model and MAXWEL; however, the total masses of 500 g for the reference man and 524 g for MAXWEL showed reasonable agreement. Similarly, the cortical and trabecular bone masses for the MAXWEL and ICRP models displayed differences of 16 and 26 %, respectively, but this percentage difference reduces to 10 % for the total bone masses. Blood was not segmented in the model beyond the major blood vessels; thus, any correspondence between the mass values for MAXWEL and ICRP would not be expected. The
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Figure 1. Volume-rendered images of MAXWEL at a resolution of 2 mm, (a) the opacity of the skin is high, (b) the skin and fat layers have been removed and (c) the muscle layer has been removed to indicate the skeleton, liver, heart and intestines.
INDUCED ELECTRIC FIELDS IN MAXWEL Table 1. Comparison of selected tissue and organ masses in MAXWEL with ICRP 89(17) and NORMAN(18). Organ mass (g) ICRP
generalised fat/connective (adipose) tissue values agree well, with the value for MAXWEL being only slightly lower. The skin values do not agree as the skin thicknesses of the ICRP and MAXWEL models are 1.3 and 2 mm, respectively, due to the skin in MAXWEL being treated as a composite cell, i.e. 1.3 mm skin and 0.7 mm subcutaneous fat. The segmented stomach was differentiated into wall and contents, as were the gall bladder (wall and bile) and urinary bladder into the MAXWEL model. The prostate is represented by an elliptical, truncated cone of mass of 17 g. The centre of the breast was identified, and the fat under the skin was replaced such that the mass of each breast was the same as the ICRP reference value of 14 g. The lung was not differentiated and in MAXWEL is considered a mixture of 2/3 air and 1/3 lung tissue. To create a surface-based model of the numerical phantom, the MAXWEL volume was then imported into 3D CAD software and surface models of the various tissues were generated. The software utilised Non-Uniform Rational B-Spline based tools to create surface models of the previously voxelised tissue data. A wire-framed model of the surface was produced, which could then be smoothed and surface-rendered. Interpolation or smoothing processes after inserting a volume object can cause the appearance of artefacts in regions where the surface of the object blends with other tissue surfaces. To minimise these artefacts, resizing by decimation and noise/speckle reduction through median filters was used. A series of programming tools were written in FORTRAN to allow manipulation of surface geometries and the insertion of
Height (m) Mass (kg)
18 200 14 73 40 150 350 650 350
17 737 15 77 41 226 298 669 481
1127 (total)
300 225
426 307
763 (total)
1800 10 58
1952 11 31
1877 10 30
140 1450 25 330 5600 3300 29 000 1000 4400 1100 150 25 20 310 50 35 17
101 1471 25 340 2039 5310 28 602 1044 5248 870 165 21 20 348 50 36 17
108 1532 27 355
1.76 73
1.76 73
17 221 15 44 221 305
5106 5106 1029 177 21 21 332 51 38 17 1.76 73
segmented surface tissue types into the developing model of the human body. Images of some tissue surface-based representations are shown in Figure 3. In places, it was necessary to rotate the sub-volume slightly as well as rescaling and shifting within the three-dimensional space. This was to prevent the overlapping of different tissue types within the model. The final CAD volume is presented as a series of 3D tissue surfaces within a domain. Once the process was complete, the surfacebased representations of the tissue types could be revoxelised to a desired resolution using in-house code. An evaluated review of the dielectric properties of all tissue types in MAXWEL was performed by Gabriel et al.(19 – 22) A 4-Cole-Cole dispersion model was fitted to the data for each tissue type to parameterise the conductivity and permittivity as a function of
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Figure 2. Cutaway (a) surface-based, (b) 2 mm voxelised, (c) 1 mm voxelised and (d) 0.5 mm voxelised representations of the eye in the MAXWEL phantom. The eye humour has been removed for clarity.
Adipose tissues Adrenals (2) Tongue Oesophagus (wall) Stomach (wall) Stomach (contents) Small intestine (wall) Small intestine (contents) Large intestine (wall) Large intestine (contents) Liver Gall bladder (wall) Gall bladder (contents) Pancreas Brain Breast Heart (tissue only) Blood Skin Muscle Lung Bone (cortical) Bone (trabecular) Spleen Thymus Thyroid Kidneys (2) Urinary bladder Testes (2) Prostate
MAXWEL NORMAN
R. P. FINDLAY
frequency. The dielectric properties for the eye tissues have been taken from the study by Dimbylow(10). NUMERICAL METHODS The quasi-static potential equation(6) was solved to calculate the interaction of low frequency fields with the human body. The solution is divided into two parts. First, the coupling between the externally applied field and the human body, defined as a conductor at low frequencies, is calculated to provide the surface charge. This charge is then used as a boundary condition to calculate the internal potential and hence induced fields and current densities in the body. The outer region must extend sufficiently so the perturbation of the applied field due to the phantom is small at the periphery. However, the resolution of the calculation must be sufficiently fine so as to adequately represent the internal structure of the anatomical model. To do this, a nested grid technique was used(7). The outermost grid resolution was 32 mm. The field values from this initial run were used to set the outer boundary conditions at a closer boundary for the next iteration at 16 mm resolution. Successive calculations were then performed at 8 mm, 4 mm and finally either a 2, 1 or 0.5 mm resolution. The electrical properties of the composite cells were volume-weighted averages of the non-air voxels. Once the external potential had been calculated, the internal potentials and therefore the induced internal electric fields could be computed. The quasi-static approximation is approaching the limit of its validity at 10 MHz; however, induced electric field values are presented at this frequency for comparison with the Dimbylow(7) results. A check on the numerical method used to calculate induced fields and currents from exposure to external electric fields can be made by calculating the short-
circuit current ISC. ISC can be defined as the current flowing through the cross section of the feet when the phantom is grounded and can be calculated by performing the integral (Equation 1) over the base of the grounded feet. ð ð1Þ ISC ¼ Ji dS S
where dS is the unit vector normal to the section, S, and Ji is the induced current density in the body and dependent on the conductivity of the tissues and the induced electric fields within the phantom. ISC can also be related to the total surface charge and therefore the external field. ð ð2Þ ISC ¼ v 10 ðn Eo ÞdS S
where v is the angular frequency, 10 is the permittivity of free space, n is the normal vector to the surface, E0 is the external field and S is taken over the entire surface of the phantom. Figure 4 displays how the ISC value obtained from the current flowing through the base of the feet (Equation 1) converges to the identity (Equation 2) calculated from the external field values as the number of steps in the internal region simulation progresses. This is for the MAXWEL phantom grounded at 50 Hz and 2 mm resolution. This figure shows that the discrepancy between the two values is 1.05 % after 477 iterations and 0.07 % after 8000 iterations. ISC can also be used to indicate the correct distance to place the boundaries of the outermost grid away from the phantom for the 32 mm computational run. The outer domain must be sufficiently far away from the numerical phantom so that the perturbation due to the presence of the phantom is small. If the
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Figure 3. Surface-based representations of the (a) bone, (b) subcutaneous fat, (c) muscle and (d) cerebro-spinal fluid (csf ) tissue types in the head and shoulder region of the MAXWEL phantom.
INDUCED ELECTRIC FIELDS IN MAXWEL
domain is truncated too close to the phantom, a conservative estimation of ISC (and hence the induced current density and electric field) will be produced. Figure 5 displays the way in which the short-circuit current converges as the separation distance between the phantom and the boundary of the outermost region is increased. From these results, a boundary separation of 150 cells (4.8 m) was chosen for the initial 32 mm computational run. The potentials from this run are then used for the 16 mm computational run, and so on. As described previously, this process is continued using successively finer resolution grids until the calculations at the final desired resolution have been completed. To compare calculated ISC values for grounded phantoms when exposed to an external electric field, ISC for MAXWEL at 50 Hz was 15.2 mA per kV m21 using the SPFD method. For NORMAN, from the study by Dimbylow(7) at 50 Hz, this value was 14.8 mA per kV m21 using the SPFD method and 14.0 mA per kV m21 using the FDTD method. For the Gandhi phantom (1.76 m, 71 kg) in the Furse and Gandhi work(4), the short-circuit current was 14.3 mA per kV m21, linearly scaled from 17.2 mA per kV m21 at 60 Hz. Also in this paper, Furse and Gandhi calculated induced current densities in the brain from exposure to external electric fields. Conversion of their results to 50 Hz yields minimum, average and maximum values of 0.059, 0.157 and 0.694 mA m22 per kV m21, respectively, compared with average values of 0.201 mA m22 for MAXWEL, 0.184 mA m22 for NAOMI and 0.178 mA m22 for NORMAN. For the University of Victoria phantom (1.77 m, 76 kg) in Dawson et al.(2) the short-circuit current was 14.7 mA per kV m21, linearly scaled from 17.6 mA per kV m21 at 60 Hz. Dimbylow and Findlay(9)
Figure 5. The percentage difference between the shortcircuit current calculated at a particular separation distance (solid line with symbols) with the short-circuit current calculated at the highest separation value (line without symbols).
calculated the short-circuit current for NORMAN in different postures for an applied electric field at 50 Hz under grounded conditions. The values varied from11.6 mA per kV m21 (sitting) to 19.2 mA per kV m21 (arms out to the side). RESULTS Table 2 shows the calculated maximum 99th percentile induced electric field values (E99), i.e. the value exceeded in 1 % of the voxels of that organ, in the CNS of the MAXWEL model for exposure to an external electric field under grounded (denoted as GRO) and isolated (denoted as ISO) conditions. The first entries are for the standard tissue conductivity values at 50 Hz from Gabriel et al.(19 – 22) The suffixes in the remainder in the table refer to modified conductivity values used for the same calculations. For GROa, the conductivities of brain, spinal cord and retina were multiplied by 2.0. For GROb, the conductivities of the brain, spinal cord and retina were multiplied by 0.5. For GROc, the conductivity of the spinal cord was set to the averaged brain value, 0.08 S m21. The highest induced electric field values usually occurred in the lower conductivity tissues. The brain and spinal cord have a lower conductivity than the retina. Therefore, in contrast to the induced current density, it is unusual for the retina to represent the maximum E99 value in the CNS. The highest E99 value for calculations performed in this study always occurred in the spinal cord. The values for MAXWEL were 3.49 mV m21 per kV m21 for grounded conditions and 1.54 mV m21 per kV m21 for isolated conditions. These values were 2 % higher
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Figure 4. The convergence of the short-circuit current calculated by using Equation (1) (solid line) as the internal region calculation progresses. The short-circuit current calculated by using Equation (2) is shown as a line without symbols.
R. P. FINDLAY Table 2. Maximum 99th percentile electric field (E99) voxel values in mV m21 per kV m21 for an applied electric field at 50 Hz and 2 mm resolution. Phantom and geometry
Maximum electric field (mV m21) per kV m21 for 99th percentile
External field (kV m21)
Brain Spinal cord Retina Maximum brain/spinal cord/retina Maximum brain/spinal cord/retina MAXWEL, GRO MAXWEL, ISO MAXWEL, GROa MAXWEL, GROb MAXWEL, GROc
1.87 0.884 1.36 2.53 1.87
3.49 1.54 3.03 3.85 2.86
0.604 0.287 0.398 0.950 0.605
3.49 sc 1.54 sc 3.03 sc 3.85 sc 2.86 sc
28.7 (5.73) 64.9 (13.0) 33.0 (6.60) 30.0 (5.19) 35.0 (6.99)
Table 3. Maximum E99 voxel values in mV m21 per kV m21 for MAXWEL as a function of frequency from exposure to an applied electric field at 2 mm resolution under grounded conditions. Frequency
1 kHz 10 kHz 100 kHz 1 MHz 10 MHz
Maximum electric field (mV m21) per kV m21 for 99th percentile
NORMAN
Brain
Spinal cord
Retina
Maximum brain/spinal cord/retina
Maximum brain/spinal cord/retina
0.0350 0.322 2.92 28.4 227
0.0610 0.535 4.51 40.8 253
0.0117 0.110 1.03 9.51 86.6
0.061 sc 0.535 sc 4.51 sc 40.8 sc 253 sc
0.0621 0.562 4.81 35.3 223
The corresponding values for NORMAN calculated by Dimbylow(7) are presented for comparison. sc denotes spinal cord.
and 6 % lower than the corresponding values for NORMAN(7) under grounded and isolated conditions, respectively. Table 3 lists the maximum E99 values, as a function of frequency for an applied electric field in MAXWEL and NORMAN. The values for NORMAN were derived from external magnetic flux densities required to produce ICNIRP(1) basic restrictions on induced electric field in the study by Dimbylow(7). The maximum E99 values in MAXWEL under grounded conditions occurred in the spinal cord for all frequencies considered in this work. These E99 values compared well with corresponding values calculated by Dimbylow(7) for NORMAN. The percentage differences between the two values were 2, 5, 6, 15 and 13 for 1, 10, 100 kHz, 1 and 10 MHz values, respectively. In Table 4, the E99 and maximum electric field (Emax) values for selected tissues within the eye and the spinal cord for different voxel resolutions for applied electric fields at 50 Hz under grounded and isolated conditions are presented. The resolutions used were 2, 1 and 0.5 mm. The E99 values for 2 and
1 mm resolutions were within 30 % of the 0.5 mm resolution values for tissues within the eye. It can be seen that similar differences in E99 and Emax values exist regardless of the resolution. This may be due to the presence of sharp corners in the voxelised models, even at higher resolution, resulting in staircasing errors. The values for the spinal cord were considerably higher than the induced electric fields in the eye due to its relatively low conductivity. The values in the spinal cord were also relatively insensitive to voxel resolution as this organ is larger than the small components making up the eye. Table 5 gives the maximum E99 values and conductivities at 50 Hz for the different tissue types in MAXWEL when exposed to an external electric field under grounded and isolated conditions. The highest E99 value for MAXWEL from Table 5 was 15.7 mV m21 per kV m21 in bone for exposure under grounded conditions. Dimbylow’s calculations of the maximum E99 value in all tissues using the female model NAOMI form the basis of the ICNIRP reference levels for peripheral nerve stimulation. The
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The external field value (in kV m21) required to produce a maximum induced electric field in the brain, retina or spinal cord of 100 (20) mV m21 is shown. The values in brackets refer to public exposure. Suffixes refer to different conductivities. a—the conductivities of brain, spinal cord and retina are multiplied by 2.0. b—the conductivities of the brain, spinal cord and retina are multiplied by 0.5. c—the conductivity of the spinal cord is set to brain, 0.08 S m21. sc denotes spinal cord.
INDUCED ELECTRIC FIELDS IN MAXWEL Table 4. The maximum (Emax) and 99th percentile (E99) induced electric fields in mV m21 per kV m21 at 50 Hz for selected tissues in the MAXWEL eye when exposed to an applied electric field under grounded and isolated conditions at 2, 1 and 0.5 mm resolution.
Table 5. Maximum E99 and conductivity values in selected MAXWEL tissue types at 50 Hz and 2 mm resolution for an applied electric field under grounded and isolated conditions.
s (S m21)
Maximum E99 values (mV m21 per kV m21)
Resolution 2 mm
1 mm
Grounded
Isolated
15.7 15.5 14.9 14.8 14.4 7.27 7.11 5.66 5.36 4.03 3.49 2.50 2.43 2.43 2.00 1.87 1.77 1.55 1.54 1.52 1.47 1.45 1.34 1.29 1.26 1.03 1.01 0.967 0.955 0.929 0.807 0.730 0.727 0.605 0.596 0.547 0.333 0.307
2.57 2.41 2.29 2.08 2.22 1.51 1.60 1.25 1.29 1.03 1.54 1.06 1.05 1.19 0.884 0.992 0.816 0.708 0.440 0.697 0.721 0.745 0.593 0.633 0.561 0.531 0.397 0.405 0.363 0.433 0.347 0.197 0.297 0.296 0.329 0.238 0.179 0.173
0.5 mm
Emax
E99
Emax
E99
Emax
Grounded Retina Optic nerve Sclera Lens Humour Spinal cord
0.605 1.31 0.596 0.333 0.307 3.49
0.646 1.43 0.625 0.625 0.333 6.74
0.750 1.32 0.619 0.446 0.292 3.42
0.791 1.65 0.654 0.549 0.311 7.58
0.718 1.15 0.625 0.453 0.264 3.45
0.817 1.83 0.687 0.627 0.273 9.26
Isolated Retina Optic nerve Sclera Lens Humour Spinal cord
0.296 0.611 0.329 0.179 0.173 1.54
0.350 0.695 0.502 0.212 0.173 2.68
0.313 0.594 0.447 0.220 0.143 1.58
0.324 0.715 0.522 0.324 0.158 3.12
0.370 0.568 0.375 0.210 0.165 1.60
0.541 0.684 0.649 0.378 0.238 3.92
maximum 99th percentile value for NAOMI, calculated by in bone, was 49.4 mV m21 per kV m21 at 50 Hz under grounded conditions. This is considerably higher than the corresponding value calculated in the MAXWEL male phantom. The large difference is due to anatomical differences between male and female models. It is intended in future work to investigate the location and nature of the differences in maximum tissue E99 values between various human models, to determine why such large variations exist. Figure 6 shows the induced electric fields in the MAXWEL model for exposure to an external electric field at 50 Hz under grounded and isolated conditions. The map is a greyscale spectrum, with the highest values in white and the lowest values in black. The values have been normalised to the highest value in the whole phantom. The map was then stretched to enhance the higher part of the spectrum. This colour map is intended to give a general view of the field patterns for comparison. Figure 6 demonstrates the difference in the induced electric fields in the sections of low cross-sectional area such as the knees and ankles for the grounded and isolated cases. The layer current will increase as one goes down the body to the grounded feet. It will then be further enhanced by narrow cross sections, and so the induced electric field also depends inversely of the cross-sectional areas of the section. Therefore, higher electric field values are to be expected in these ankle and knee sections and also to a lesser extent in the neck. The joints of the knees and ankles are
Bone Tendon Trabec bone Skin Fat Muscle Cartilage Blood Bladder Prostate Spinal cord Liver Spleen Heart muscle Lung White matter Stomach Oesophagus Lower LI Kidney Grey matter Thyroid Pancreas Thymus Adrenals Csf Small intestine Gall bladder Upper LI Breast Duodenum Testis Bile Retina Sclera Urine Lens Humour
0.02 0.27 0.07 0.1 0.04 0.35 0.18 0.70 0.21 0.42 0.03 0.07 0.09 0.08 0.07 0.06 0.52 0.52 1.20 0.09 0.1 0.52 0.21 0.52 0.09 2.00 1.09 0.90 1.28 0.06 1.09 0.42 1.40 0.50 0.50 3.30 0.26 1.50
The table is sorted in descending order of the grounded E99 value. Csf, cerebro-spinal fluid.
mainly made up of low conductivity bone and connective tissue with little high conductivity tissue, so there is a further enhancement of the induced electric field. The enhanced absorption in these low conductivity sections as the current flows through the feet in the grounded case demonstrates why, in Table 4 for the grounded exposure of MAXWEL to an external electric field, the induced electric field value in bone was higher than for the corresponding isolated exposure case.
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E99
R. P. FINDLAY
CONCLUSIONS This article presents simulations of the induced electric field in the body of the male surface-based phantom, MAXWEL, from exposure to external low frequency electric fields. It investigates how the use of a different human model changes the calculated internal electric fields when exposed to external electric fields, by comparing the results from MAXWEL simulations with corresponding calculations using the NORMAN and NAOMI phantoms. The work also studies the effect of voxel resolution on the induced electric fields in small organs from exposure to
external electric fields by calculating internal fields in 2, 1 and 0.5 mm resolution voxel models of the eye produced from the surface-based version present in the MAXWEL phantom. The maximum 99th percentile induced electric fields calculated in the MAXWEL CNS were 3.49 (grounded) and 1.54 (isolated) mV m21 per kV m21 at 50 Hz. These calculations compared well with corresponding simulations performed by Dimbylow in the male NORMAN model of 3.42 (grounded) and 1.63 (isolated) mV m21 per kV m21. The 2 and 1 mm resolution maximum 99th percentile induced electric field values calculated in selected tissues of the eye at 50 Hz were within
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Figure 6. The induced electric field in (a) whole-body, (b) coronal and (c) sagittal views of the MAXWEL phantom for exposure to an applied electric field under isolated conditions at 50 Hz. The map is a greyscale spectrum, with the highest values in white and the lowest values in black.
INDUCED ELECTRIC FIELDS IN MAXWEL
30 % of those calculated at 0.5 mm resolution. Calculations of induced electric field values for the female model NAOMI in all tissues form the basis of the ICNIRP Reference Levels for peripheral nerve stimulation. The maximum 99th percentile value for NAOMI, calculated by Dimbylow in bone, was 49.4 mV m21 per kV m21 at 50 Hz under grounded conditions. The corresponding value calculated in bone tissue using the MAXWEL phantom was 15.7 mV m21 per kV m21, considerably lower due to anatomical differences between the male and female models.
9.
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The author thanks Dr Peter Dimbylow for his kind support and comments made on the methods used in this article. 13.
FUNDING This work was partially supported by National Grid. 14.
REFERENCES 1. ICNIRP. Guidelines for limiting exposure to time varying electric, magnetic fields (1 Hz to 100 kHz). Health Phys. 99, 818–836 (2010). 2. Dawson, T. W., Caputa, K. and Stuchly, M. A. Highresolution organ dosimetry for human exposure to low frequency electric fields. IEEE Trans. Power Deliv. 13, 366 –373 (1998). 3. Dawson, T. W., De Moerloose, J. and Stuchly, M. A. Comparison of magnetically induced ELF fields in humans computed by FDTD and scalar potential FD codes. Appl. Comput. Electromagn. Soc. J. 11(3), 63–71 (1996). 4. Furse, C. M. and Gandhi, O. P. Calculation of electric fields and currents induced in a millimetre-resolution human model at 60 Hz using the FDTD method. Bioelectromagnetics 19, 293– 299 (1998). 5. Hirata, A., Caputa, K., Dawson, T. W. and Stuchly, M. A. Dosimetry in models of child and adult for low-frequency electric field. IEEE Trans. Biomed. Eng. 48(9), 1007–1012 (2001). 6. Dimbylow, P. J. Current densities in a 2 mm resolution anatomically realistic model of the body induced by lowfrequency electric fields. Phys. Med. Biol. 45, 1013–1022 (2000). 7. Dimbylow, P. J. Development of the female voxel phantom, NAOMI, and its application to calculations of induced current densities and electric fields from applied low frequency magnetic and electric fields. Phys. Med. Biol. 50, 1047–1070 (2005). 8. Hirata, A., Takano, Y., Kamimura, Y. and Fujiwara, O. Effect of the averaging volume and algorithm on the in
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ACKNOWLEDGEMENTS
situ electric field for uniform electric- and magnetic-field exposures. Phys. Med. Biol. 55, N243–N248 (2010). Dimbylow, P. J. and Findlay, R. P. The effects of body posture, anatomy, age and pregnancy on the calculation of induced current densities at 50 Hz. Radiat. Prot. Dosim. 139(4), 532– 538 (2010). Dimbylow, P. J. Spherical polar co-ordinate calculations of induced fields in the retina and head for applied magnetic fields at 50 Hz. Phys. Med. Biol. 56, 4597–4611 (2011). Dimbylow, P. J. FDTD calculations of the whole-body averaged SAR in an anatomically realistic voxel model of the human body from 1 MHz to 1 GHz. Phys. Med. Biol. 42, 479–490 (1997). Dawson, T. W. and Stuchly, M. A. A comparison of analytical and numerical solutions for induction in a sphere with equatorially varying conductivity by low frequency uniform magnetic fields of arbitrary orientation. Proceedings of 1997 Symposium of the Applied Computational Electromagnetics Society 533–540 (1997). Nagaoka, T., Watanabe, S., Sakurai, K., Kuneida, E., Watanabe, S., Taki, M. and Yamanaka, Y. Development of realistic high-resolution whole-body voxel models of Japanese adult males and females of average height and weight, and application of models to radio-frequency electromagnetic field dosimetry. Phys. Med. Biol. 49, 1–15 (2004). Lee, C., Lodwick, D., Hurtado, J., Pafundi, D., Williams, J. L. and Bolch, W. E. The UF family of reference hybrid phantoms for computational radiation dosimetry. Phys. Med. Biol. 55, 339–363 (2010). Christ, A. et al. The Virtual Family —development of surface-based anatomical models of two adults and two children for dosimetric simulations. Phys. Med. Biol. 55, N23– N38 (2010). Yoriyaz, H., Sanchez, A. and dos Santos, A. A new human eye model for ophthalmic brachytherapy dosimetry. Radiat. Prot. Dosim. 115, 316–319 (2005). ICRP. Basic anatomical and physiological data for use in radiological protection: reference values. ICRP Publication 89 32(3– 4), (2002). Dimbylow, P. J. The development of realistic voxel phantoms for electromagnetic field dosimetry. Proceedings of an International Workshop on Voxel Phantom Development; NRPB Report, 1–7 (1996). Gabriel, C. Compilation of the dielectric properties of body tissues at RF and microwave frequencies. Report prepared for the NRPB by Microwave Consultants Ltd (1995). Gabriel, C., Gabriel, S. and Corthout, E. The dielectric properties of biological tissues: 1. Literature survey. Phys. Med. Biol. 41, 2231– 2249 (1996). Gabriel, S., Lau, R. W. and Gabriel, C. The dielectric properties of biological tissues: 2. Measurements in the frequency range 10 Hz to 20 GHz. Phys. Med. Biol. 41, 2251–2269 (1996). Gabriel, S., Lau, R. W. and Gabriel, C. The dielectric properties of biological tissues: 3. Parametric models for the dielectric spectrum of tissues. Phys. Med. Biol. 41, 2271–2293 (1996).
doi:10.1093/rpd/nct281
INDUCED ELECTRIC FIELDS IN THE MAXWEL SURFACE-BASED HUMAN MODEL FROM EXPOSURE TO EXTERNAL LOW FREQUENCY ELECTRIC FIELDS R. P. Findlay* EMFcomp, Wantage, Oxfordshire OX12 8HG, UK *Corresponding author: [email protected]
This work presents calculations of internal induced electric fields in the anatomically realistic surface-based model of the male human body, MAXWEL, from exposure to external low frequency electric fields under grounded and isolated conditions. The maximum 99th percentile induced electric fields calculated in the MAXWEL central nervous system were 3.49 (grounded) and 1.54 (isolated) mV m21 per kV m21 at 50 Hz. The application of 2, 1 and 0.5 mm resolution voxel models derived from the surface-based version to the calculations of induced electric fields is described. 2 mm and 1 mm resolution maximum 99th percentile induced electric field values calculated in selected tissues of the eye at 50 Hz were within 30 % of those calculated at 0.5 mm resolution. The calculated electric field values in MAXWEL were compared with values from the male model NORMAN and female model NAOMI. The maximum 99th percentile value for NAOMI, calculated by Dimbylow in bone, was 49.4 mV m21 per kV m21 at 50 Hz under grounded conditions. The corresponding value calculated in MAXWEL was 15.7 mV m21 per kV m21, considerably lower due to anatomical differences between the male and female models.
INTRODUCTION The International Commission on Non-Ionizing Radiation Protection (ICNIRP) has produced guidelines(1) on human electromagnetic field exposure to protect against adverse health effects at low frequencies. Basic restrictions, presented in terms of induced internal electric fields in the body and reference levels, expressed using applied external electric field values, are stated in these guidelines. ICNIRP recommends that the 99th percentile value of the electric field (E99), averaged over a contiguous tissue region of 2` 2` 2 mm3, is used to determine the induced electric field for comparison with the basic restrictions. Separate frequency dependent values are stated for the central nervous system (CNS) tissues in the head and all tissues in the head and body. Human dosimetric studies of induced electric fields from exposure to low frequency external electric fields are limited. Dawson et al.(2) used a quasi-static finitedifference time-domain (FDTD) method to calculate surface charge densities from exposure to electric fields and interpolate onto a 3.6 mm resolution University of Victoria phantom. These provided source terms for internal dose calculations using the scalar-potential finite-difference (SPFD) method(3). Furse and Gandhi (4) used the FDTD method to calculate induced current densities in a 6 mm resolution voxel phantom resulting from electric field exposure at 10 MHz using 60 Hz conductivities. These authors then linearly scaled the values with frequency to obtain current densities at 60 Hz. Hirata et al.(5)
calculated induced electric fields in a 5-y-old child model for exposure to an applied electric field using the hybrid approach(2). The calculated induced electric fields were found to be consistently lower in the child head tissues when compared with those in the adult. Dimbylow(6) used a series of nested sub-grids to solve the potential equation and calculate induced current densities in a 2 mm resolution version of the male NORMAN phantom from exposure to electric fields. Dimbylow also calculated induced electric fields in the CNS for NORMAN and NAOMI due to electric field exposure and induced electric fields in all tissues for NAOMI at 50 Hz(7). More recently, Hirata et al.(8) calculated induced electric fields from exposure to an external electric field in the Japanese voxel models TARO and HANAKO using the quasi-static FDTD method. Dimbylow and Findlay(9) calculated induced current densities in 25 different voxel models at 50 Hz from exposure to electric fields using the SPFD method; however, this study did not extend to the calculation of induced electric fields. The ICNIRP reference levels were based on simulations using only two voxel models of the human body, NORMAN and NAOMI, due to the limited number of induced electric field dosimetric studies for low frequency electric field exposure(10). Furthermore, that paper gives conversion factors between basic restrictions and external field values for just one model, the NAOMI female phantom(7), for non-CNS tissues. The induced electric fields in the body due to an applied external electric field will be different for
# The Author 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
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Received 5 September 2013; revised 15 October 2013; accepted 16 October 2013
INDUCED ELECTRIC FIELDS IN MAXWEL
HUMAN MODEL The development of anatomically realistic models of the human body has mostly concentrated on voxel models(4, 11, 12, 13). Recently, a limited number of surface-based computational human models have emerged for the application to ionising and non-ionising exposure problems(14, 15). In these models, the boundary of each tissue type can be mathematically described by a form of parameterised surface that might be as simple as a planar quadrilateral or as sophisticated as a two-dimensional spline. The surface-based model can provide a closer geometrical approximation to the interface of adjacent materials by using a non-orthogonal, and sometimes curved, mesh. Surface-based phantoms combine the advantages of stylised and anatomically realistic voxel models. They are flexible, allowing changes to organ position and posture to occur, but they also present accurate models of the human anatomy and can be voxelised to a desired resolution. EMFcomp, an independent research microenterprise that specialises in computational electromagnetics, has developed a male, anatomically realistic surface-based model MAXWEL (MAle fleXible Whole-body modEL). Volume-rendered images of MAXWEL are shown in Figure 1. The opacity has been varied to show the internal structure of the model. In Figure 1a, the opacity of the skin is high to show the outer surface of the phantom. In Figure 1b, the skin and fat layers have been removed and the muscle layer has been given a reduced opacity to show the internal tissues and organs. In Figure 1c, the muscle layer has been removed to indicate the skeleton, liver, heart and intestines. The MAXWEL phantom presents a model in which the surfaces tend to be less smoothed than some other surface-based
models as these anatomical details are more important in non-ionising exposure problems. An advantage of employing the MAXWEL surface-based anatomical model is demonstrated in Figure 2. This figure displays the model of the eye in the MAXWEL human phantom, based on the Yoriyaz eye model(16). A cutaway view of the surfacebased model is shown in Figure 2a. The humour has been removed for clarity. Voxelised representations of this eye are then shown at 2, 1 and 0.5 mm resolution. The use of a fixed, say 2 mm, resolution voxel model limits the accurate representation of small organs in the body like the eye as the resolution of the model can never be higher than 2 mm—regardless of the grid size used to perform a calculation. It can be seen in Figure 2 that there is an obvious loss of the detailed anatomical structure of the eye at this 2 mm resolution when compared with higher resolutions. A surface-based model allows the model to be voxelised at very fine resolutions such as the displayed 0.5 mm, limiting the staircasing of the structure. The model on which MAXWEL is based originated from whole-body high-resolution magnetic resonance imaging (MRI) scans obtained by Fairfield Imaging. No information was available about the subject, except that he is a healthy young adult male (no known organic disease) of 23 year with a height of 1.70 m and a mass of 68 kg. The horizontal resolution of the data was 2 mm per pixel. The head of the model, however, was constructed from a separate 1 mm sagittal data volume, to give higher resolution, and rescaled to match the rest of the model. The MRI data were segmented into the various tissue types by a process of manual definition, assigning specific voxel intensities to organs by filling them individually on each data slice. The segmentation was then checked by using an intersecting orthogonal display that displayed the segmented area in relation to the whole data set. This was carried out on successive x–y slices throughout the volume. An automated procedure was also used to pre-process parts of the volume by sequentially loading slices into memory for segmentation of skin, fat and muscle. This was possible as the MRI data values for skin, muscle and fat are often well separated from other tissue types. In this way, a number of intermediate volumes could be generated during the segmentation process. Final post-processing of the entire segmented volume was used to remove artefacts so that every voxel belongs to one or other of the defined objects in the final volume. This was followed by a check of the resultant volume by a medical anatomical expert. The phantom consists of 45 different tissue types. These tissue types were, in addition to those listed in Table 1, spinal cord, tendon, cartilage, duodenum, trachea, background air, eye lens, humour, sclera, cornea, retina, optic nerve and choroid. MAXWEL was scaled to ‘reference man’(17) dimensions of 1.76 m tall and a mass of 73 kg.
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different human models due to variations in anatomical details. Studies into how these induced electric fields change with different models are important to ensure that accurate electromagnetic guidelines are produced. The object of this paper is to investigate how the use of a different human model changes the calculated internal electric fields when exposed to an external applied low frequency electric field. It is also to study the effect of voxel resolution on the induced electric fields in small organs from exposure to external electric fields by calculating internal fields in 2, 1 and 0.5 mm resolution voxel models of the eye produced from the surface-based version. The MAXWEL human model is described in the next section. This is followed by a description of the numerical methods used to calculate the induced electric fields. Results for applied, vertically aligned electric fields are then given and conclusions are presented in the final section.
R. P. FINDLAY
Table 1 presents the comparison between selected organ masses in MAXWEL and those identified in the International Commission on Radiation Protection (ICRP) values for ‘reference man’ and NORMAN(18). Values for tongue, small intestine (wall), large intestine (wall), bone (trabecular and cortical), tongue and blood in NORMAN were not listed in the study by Dimbylow(18) and so are not present in Table 1. The totals of the individual masses in Table 1 are 69.1 and 68.0 kg for ICRP and MAXWEL, respectively, presenting a discrepancy between these values and the total mass of 73 kg. This is because ICRP does not provide reference values for all organs within the body. Although some of the masses of organs along with the height and mass of the phantom were normalised, inevitable
differences appear in some of the tissue masses listed. However, in general, good agreement is shown. Good agreement did not exist in the tissue or organ masses for the stomach wall and contents, cortical and trabecular bone, blood and skin. The stomach wall and content masses differed for the ICRP model and MAXWEL; however, the total masses of 500 g for the reference man and 524 g for MAXWEL showed reasonable agreement. Similarly, the cortical and trabecular bone masses for the MAXWEL and ICRP models displayed differences of 16 and 26 %, respectively, but this percentage difference reduces to 10 % for the total bone masses. Blood was not segmented in the model beyond the major blood vessels; thus, any correspondence between the mass values for MAXWEL and ICRP would not be expected. The
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Figure 1. Volume-rendered images of MAXWEL at a resolution of 2 mm, (a) the opacity of the skin is high, (b) the skin and fat layers have been removed and (c) the muscle layer has been removed to indicate the skeleton, liver, heart and intestines.
INDUCED ELECTRIC FIELDS IN MAXWEL Table 1. Comparison of selected tissue and organ masses in MAXWEL with ICRP 89(17) and NORMAN(18). Organ mass (g) ICRP
generalised fat/connective (adipose) tissue values agree well, with the value for MAXWEL being only slightly lower. The skin values do not agree as the skin thicknesses of the ICRP and MAXWEL models are 1.3 and 2 mm, respectively, due to the skin in MAXWEL being treated as a composite cell, i.e. 1.3 mm skin and 0.7 mm subcutaneous fat. The segmented stomach was differentiated into wall and contents, as were the gall bladder (wall and bile) and urinary bladder into the MAXWEL model. The prostate is represented by an elliptical, truncated cone of mass of 17 g. The centre of the breast was identified, and the fat under the skin was replaced such that the mass of each breast was the same as the ICRP reference value of 14 g. The lung was not differentiated and in MAXWEL is considered a mixture of 2/3 air and 1/3 lung tissue. To create a surface-based model of the numerical phantom, the MAXWEL volume was then imported into 3D CAD software and surface models of the various tissues were generated. The software utilised Non-Uniform Rational B-Spline based tools to create surface models of the previously voxelised tissue data. A wire-framed model of the surface was produced, which could then be smoothed and surface-rendered. Interpolation or smoothing processes after inserting a volume object can cause the appearance of artefacts in regions where the surface of the object blends with other tissue surfaces. To minimise these artefacts, resizing by decimation and noise/speckle reduction through median filters was used. A series of programming tools were written in FORTRAN to allow manipulation of surface geometries and the insertion of
Height (m) Mass (kg)
18 200 14 73 40 150 350 650 350
17 737 15 77 41 226 298 669 481
1127 (total)
300 225
426 307
763 (total)
1800 10 58
1952 11 31
1877 10 30
140 1450 25 330 5600 3300 29 000 1000 4400 1100 150 25 20 310 50 35 17
101 1471 25 340 2039 5310 28 602 1044 5248 870 165 21 20 348 50 36 17
108 1532 27 355
1.76 73
1.76 73
17 221 15 44 221 305
5106 5106 1029 177 21 21 332 51 38 17 1.76 73
segmented surface tissue types into the developing model of the human body. Images of some tissue surface-based representations are shown in Figure 3. In places, it was necessary to rotate the sub-volume slightly as well as rescaling and shifting within the three-dimensional space. This was to prevent the overlapping of different tissue types within the model. The final CAD volume is presented as a series of 3D tissue surfaces within a domain. Once the process was complete, the surfacebased representations of the tissue types could be revoxelised to a desired resolution using in-house code. An evaluated review of the dielectric properties of all tissue types in MAXWEL was performed by Gabriel et al.(19 – 22) A 4-Cole-Cole dispersion model was fitted to the data for each tissue type to parameterise the conductivity and permittivity as a function of
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Figure 2. Cutaway (a) surface-based, (b) 2 mm voxelised, (c) 1 mm voxelised and (d) 0.5 mm voxelised representations of the eye in the MAXWEL phantom. The eye humour has been removed for clarity.
Adipose tissues Adrenals (2) Tongue Oesophagus (wall) Stomach (wall) Stomach (contents) Small intestine (wall) Small intestine (contents) Large intestine (wall) Large intestine (contents) Liver Gall bladder (wall) Gall bladder (contents) Pancreas Brain Breast Heart (tissue only) Blood Skin Muscle Lung Bone (cortical) Bone (trabecular) Spleen Thymus Thyroid Kidneys (2) Urinary bladder Testes (2) Prostate
MAXWEL NORMAN
R. P. FINDLAY
frequency. The dielectric properties for the eye tissues have been taken from the study by Dimbylow(10). NUMERICAL METHODS The quasi-static potential equation(6) was solved to calculate the interaction of low frequency fields with the human body. The solution is divided into two parts. First, the coupling between the externally applied field and the human body, defined as a conductor at low frequencies, is calculated to provide the surface charge. This charge is then used as a boundary condition to calculate the internal potential and hence induced fields and current densities in the body. The outer region must extend sufficiently so the perturbation of the applied field due to the phantom is small at the periphery. However, the resolution of the calculation must be sufficiently fine so as to adequately represent the internal structure of the anatomical model. To do this, a nested grid technique was used(7). The outermost grid resolution was 32 mm. The field values from this initial run were used to set the outer boundary conditions at a closer boundary for the next iteration at 16 mm resolution. Successive calculations were then performed at 8 mm, 4 mm and finally either a 2, 1 or 0.5 mm resolution. The electrical properties of the composite cells were volume-weighted averages of the non-air voxels. Once the external potential had been calculated, the internal potentials and therefore the induced internal electric fields could be computed. The quasi-static approximation is approaching the limit of its validity at 10 MHz; however, induced electric field values are presented at this frequency for comparison with the Dimbylow(7) results. A check on the numerical method used to calculate induced fields and currents from exposure to external electric fields can be made by calculating the short-
circuit current ISC. ISC can be defined as the current flowing through the cross section of the feet when the phantom is grounded and can be calculated by performing the integral (Equation 1) over the base of the grounded feet. ð ð1Þ ISC ¼ Ji dS S
where dS is the unit vector normal to the section, S, and Ji is the induced current density in the body and dependent on the conductivity of the tissues and the induced electric fields within the phantom. ISC can also be related to the total surface charge and therefore the external field. ð ð2Þ ISC ¼ v 10 ðn Eo ÞdS S
where v is the angular frequency, 10 is the permittivity of free space, n is the normal vector to the surface, E0 is the external field and S is taken over the entire surface of the phantom. Figure 4 displays how the ISC value obtained from the current flowing through the base of the feet (Equation 1) converges to the identity (Equation 2) calculated from the external field values as the number of steps in the internal region simulation progresses. This is for the MAXWEL phantom grounded at 50 Hz and 2 mm resolution. This figure shows that the discrepancy between the two values is 1.05 % after 477 iterations and 0.07 % after 8000 iterations. ISC can also be used to indicate the correct distance to place the boundaries of the outermost grid away from the phantom for the 32 mm computational run. The outer domain must be sufficiently far away from the numerical phantom so that the perturbation due to the presence of the phantom is small. If the
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Figure 3. Surface-based representations of the (a) bone, (b) subcutaneous fat, (c) muscle and (d) cerebro-spinal fluid (csf ) tissue types in the head and shoulder region of the MAXWEL phantom.
INDUCED ELECTRIC FIELDS IN MAXWEL
domain is truncated too close to the phantom, a conservative estimation of ISC (and hence the induced current density and electric field) will be produced. Figure 5 displays the way in which the short-circuit current converges as the separation distance between the phantom and the boundary of the outermost region is increased. From these results, a boundary separation of 150 cells (4.8 m) was chosen for the initial 32 mm computational run. The potentials from this run are then used for the 16 mm computational run, and so on. As described previously, this process is continued using successively finer resolution grids until the calculations at the final desired resolution have been completed. To compare calculated ISC values for grounded phantoms when exposed to an external electric field, ISC for MAXWEL at 50 Hz was 15.2 mA per kV m21 using the SPFD method. For NORMAN, from the study by Dimbylow(7) at 50 Hz, this value was 14.8 mA per kV m21 using the SPFD method and 14.0 mA per kV m21 using the FDTD method. For the Gandhi phantom (1.76 m, 71 kg) in the Furse and Gandhi work(4), the short-circuit current was 14.3 mA per kV m21, linearly scaled from 17.2 mA per kV m21 at 60 Hz. Also in this paper, Furse and Gandhi calculated induced current densities in the brain from exposure to external electric fields. Conversion of their results to 50 Hz yields minimum, average and maximum values of 0.059, 0.157 and 0.694 mA m22 per kV m21, respectively, compared with average values of 0.201 mA m22 for MAXWEL, 0.184 mA m22 for NAOMI and 0.178 mA m22 for NORMAN. For the University of Victoria phantom (1.77 m, 76 kg) in Dawson et al.(2) the short-circuit current was 14.7 mA per kV m21, linearly scaled from 17.6 mA per kV m21 at 60 Hz. Dimbylow and Findlay(9)
Figure 5. The percentage difference between the shortcircuit current calculated at a particular separation distance (solid line with symbols) with the short-circuit current calculated at the highest separation value (line without symbols).
calculated the short-circuit current for NORMAN in different postures for an applied electric field at 50 Hz under grounded conditions. The values varied from11.6 mA per kV m21 (sitting) to 19.2 mA per kV m21 (arms out to the side). RESULTS Table 2 shows the calculated maximum 99th percentile induced electric field values (E99), i.e. the value exceeded in 1 % of the voxels of that organ, in the CNS of the MAXWEL model for exposure to an external electric field under grounded (denoted as GRO) and isolated (denoted as ISO) conditions. The first entries are for the standard tissue conductivity values at 50 Hz from Gabriel et al.(19 – 22) The suffixes in the remainder in the table refer to modified conductivity values used for the same calculations. For GROa, the conductivities of brain, spinal cord and retina were multiplied by 2.0. For GROb, the conductivities of the brain, spinal cord and retina were multiplied by 0.5. For GROc, the conductivity of the spinal cord was set to the averaged brain value, 0.08 S m21. The highest induced electric field values usually occurred in the lower conductivity tissues. The brain and spinal cord have a lower conductivity than the retina. Therefore, in contrast to the induced current density, it is unusual for the retina to represent the maximum E99 value in the CNS. The highest E99 value for calculations performed in this study always occurred in the spinal cord. The values for MAXWEL were 3.49 mV m21 per kV m21 for grounded conditions and 1.54 mV m21 per kV m21 for isolated conditions. These values were 2 % higher
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Figure 4. The convergence of the short-circuit current calculated by using Equation (1) (solid line) as the internal region calculation progresses. The short-circuit current calculated by using Equation (2) is shown as a line without symbols.
R. P. FINDLAY Table 2. Maximum 99th percentile electric field (E99) voxel values in mV m21 per kV m21 for an applied electric field at 50 Hz and 2 mm resolution. Phantom and geometry
Maximum electric field (mV m21) per kV m21 for 99th percentile
External field (kV m21)
Brain Spinal cord Retina Maximum brain/spinal cord/retina Maximum brain/spinal cord/retina MAXWEL, GRO MAXWEL, ISO MAXWEL, GROa MAXWEL, GROb MAXWEL, GROc
1.87 0.884 1.36 2.53 1.87
3.49 1.54 3.03 3.85 2.86
0.604 0.287 0.398 0.950 0.605
3.49 sc 1.54 sc 3.03 sc 3.85 sc 2.86 sc
28.7 (5.73) 64.9 (13.0) 33.0 (6.60) 30.0 (5.19) 35.0 (6.99)
Table 3. Maximum E99 voxel values in mV m21 per kV m21 for MAXWEL as a function of frequency from exposure to an applied electric field at 2 mm resolution under grounded conditions. Frequency
1 kHz 10 kHz 100 kHz 1 MHz 10 MHz
Maximum electric field (mV m21) per kV m21 for 99th percentile
NORMAN
Brain
Spinal cord
Retina
Maximum brain/spinal cord/retina
Maximum brain/spinal cord/retina
0.0350 0.322 2.92 28.4 227
0.0610 0.535 4.51 40.8 253
0.0117 0.110 1.03 9.51 86.6
0.061 sc 0.535 sc 4.51 sc 40.8 sc 253 sc
0.0621 0.562 4.81 35.3 223
The corresponding values for NORMAN calculated by Dimbylow(7) are presented for comparison. sc denotes spinal cord.
and 6 % lower than the corresponding values for NORMAN(7) under grounded and isolated conditions, respectively. Table 3 lists the maximum E99 values, as a function of frequency for an applied electric field in MAXWEL and NORMAN. The values for NORMAN were derived from external magnetic flux densities required to produce ICNIRP(1) basic restrictions on induced electric field in the study by Dimbylow(7). The maximum E99 values in MAXWEL under grounded conditions occurred in the spinal cord for all frequencies considered in this work. These E99 values compared well with corresponding values calculated by Dimbylow(7) for NORMAN. The percentage differences between the two values were 2, 5, 6, 15 and 13 for 1, 10, 100 kHz, 1 and 10 MHz values, respectively. In Table 4, the E99 and maximum electric field (Emax) values for selected tissues within the eye and the spinal cord for different voxel resolutions for applied electric fields at 50 Hz under grounded and isolated conditions are presented. The resolutions used were 2, 1 and 0.5 mm. The E99 values for 2 and
1 mm resolutions were within 30 % of the 0.5 mm resolution values for tissues within the eye. It can be seen that similar differences in E99 and Emax values exist regardless of the resolution. This may be due to the presence of sharp corners in the voxelised models, even at higher resolution, resulting in staircasing errors. The values for the spinal cord were considerably higher than the induced electric fields in the eye due to its relatively low conductivity. The values in the spinal cord were also relatively insensitive to voxel resolution as this organ is larger than the small components making up the eye. Table 5 gives the maximum E99 values and conductivities at 50 Hz for the different tissue types in MAXWEL when exposed to an external electric field under grounded and isolated conditions. The highest E99 value for MAXWEL from Table 5 was 15.7 mV m21 per kV m21 in bone for exposure under grounded conditions. Dimbylow’s calculations of the maximum E99 value in all tissues using the female model NAOMI form the basis of the ICNIRP reference levels for peripheral nerve stimulation. The
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The external field value (in kV m21) required to produce a maximum induced electric field in the brain, retina or spinal cord of 100 (20) mV m21 is shown. The values in brackets refer to public exposure. Suffixes refer to different conductivities. a—the conductivities of brain, spinal cord and retina are multiplied by 2.0. b—the conductivities of the brain, spinal cord and retina are multiplied by 0.5. c—the conductivity of the spinal cord is set to brain, 0.08 S m21. sc denotes spinal cord.
INDUCED ELECTRIC FIELDS IN MAXWEL Table 4. The maximum (Emax) and 99th percentile (E99) induced electric fields in mV m21 per kV m21 at 50 Hz for selected tissues in the MAXWEL eye when exposed to an applied electric field under grounded and isolated conditions at 2, 1 and 0.5 mm resolution.
Table 5. Maximum E99 and conductivity values in selected MAXWEL tissue types at 50 Hz and 2 mm resolution for an applied electric field under grounded and isolated conditions.
s (S m21)
Maximum E99 values (mV m21 per kV m21)
Resolution 2 mm
1 mm
Grounded
Isolated
15.7 15.5 14.9 14.8 14.4 7.27 7.11 5.66 5.36 4.03 3.49 2.50 2.43 2.43 2.00 1.87 1.77 1.55 1.54 1.52 1.47 1.45 1.34 1.29 1.26 1.03 1.01 0.967 0.955 0.929 0.807 0.730 0.727 0.605 0.596 0.547 0.333 0.307
2.57 2.41 2.29 2.08 2.22 1.51 1.60 1.25 1.29 1.03 1.54 1.06 1.05 1.19 0.884 0.992 0.816 0.708 0.440 0.697 0.721 0.745 0.593 0.633 0.561 0.531 0.397 0.405 0.363 0.433 0.347 0.197 0.297 0.296 0.329 0.238 0.179 0.173
0.5 mm
Emax
E99
Emax
E99
Emax
Grounded Retina Optic nerve Sclera Lens Humour Spinal cord
0.605 1.31 0.596 0.333 0.307 3.49
0.646 1.43 0.625 0.625 0.333 6.74
0.750 1.32 0.619 0.446 0.292 3.42
0.791 1.65 0.654 0.549 0.311 7.58
0.718 1.15 0.625 0.453 0.264 3.45
0.817 1.83 0.687 0.627 0.273 9.26
Isolated Retina Optic nerve Sclera Lens Humour Spinal cord
0.296 0.611 0.329 0.179 0.173 1.54
0.350 0.695 0.502 0.212 0.173 2.68
0.313 0.594 0.447 0.220 0.143 1.58
0.324 0.715 0.522 0.324 0.158 3.12
0.370 0.568 0.375 0.210 0.165 1.60
0.541 0.684 0.649 0.378 0.238 3.92
maximum 99th percentile value for NAOMI, calculated by in bone, was 49.4 mV m21 per kV m21 at 50 Hz under grounded conditions. This is considerably higher than the corresponding value calculated in the MAXWEL male phantom. The large difference is due to anatomical differences between male and female models. It is intended in future work to investigate the location and nature of the differences in maximum tissue E99 values between various human models, to determine why such large variations exist. Figure 6 shows the induced electric fields in the MAXWEL model for exposure to an external electric field at 50 Hz under grounded and isolated conditions. The map is a greyscale spectrum, with the highest values in white and the lowest values in black. The values have been normalised to the highest value in the whole phantom. The map was then stretched to enhance the higher part of the spectrum. This colour map is intended to give a general view of the field patterns for comparison. Figure 6 demonstrates the difference in the induced electric fields in the sections of low cross-sectional area such as the knees and ankles for the grounded and isolated cases. The layer current will increase as one goes down the body to the grounded feet. It will then be further enhanced by narrow cross sections, and so the induced electric field also depends inversely of the cross-sectional areas of the section. Therefore, higher electric field values are to be expected in these ankle and knee sections and also to a lesser extent in the neck. The joints of the knees and ankles are
Bone Tendon Trabec bone Skin Fat Muscle Cartilage Blood Bladder Prostate Spinal cord Liver Spleen Heart muscle Lung White matter Stomach Oesophagus Lower LI Kidney Grey matter Thyroid Pancreas Thymus Adrenals Csf Small intestine Gall bladder Upper LI Breast Duodenum Testis Bile Retina Sclera Urine Lens Humour
0.02 0.27 0.07 0.1 0.04 0.35 0.18 0.70 0.21 0.42 0.03 0.07 0.09 0.08 0.07 0.06 0.52 0.52 1.20 0.09 0.1 0.52 0.21 0.52 0.09 2.00 1.09 0.90 1.28 0.06 1.09 0.42 1.40 0.50 0.50 3.30 0.26 1.50
The table is sorted in descending order of the grounded E99 value. Csf, cerebro-spinal fluid.
mainly made up of low conductivity bone and connective tissue with little high conductivity tissue, so there is a further enhancement of the induced electric field. The enhanced absorption in these low conductivity sections as the current flows through the feet in the grounded case demonstrates why, in Table 4 for the grounded exposure of MAXWEL to an external electric field, the induced electric field value in bone was higher than for the corresponding isolated exposure case.
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E99
R. P. FINDLAY
CONCLUSIONS This article presents simulations of the induced electric field in the body of the male surface-based phantom, MAXWEL, from exposure to external low frequency electric fields. It investigates how the use of a different human model changes the calculated internal electric fields when exposed to external electric fields, by comparing the results from MAXWEL simulations with corresponding calculations using the NORMAN and NAOMI phantoms. The work also studies the effect of voxel resolution on the induced electric fields in small organs from exposure to
external electric fields by calculating internal fields in 2, 1 and 0.5 mm resolution voxel models of the eye produced from the surface-based version present in the MAXWEL phantom. The maximum 99th percentile induced electric fields calculated in the MAXWEL CNS were 3.49 (grounded) and 1.54 (isolated) mV m21 per kV m21 at 50 Hz. These calculations compared well with corresponding simulations performed by Dimbylow in the male NORMAN model of 3.42 (grounded) and 1.63 (isolated) mV m21 per kV m21. The 2 and 1 mm resolution maximum 99th percentile induced electric field values calculated in selected tissues of the eye at 50 Hz were within
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Figure 6. The induced electric field in (a) whole-body, (b) coronal and (c) sagittal views of the MAXWEL phantom for exposure to an applied electric field under isolated conditions at 50 Hz. The map is a greyscale spectrum, with the highest values in white and the lowest values in black.
INDUCED ELECTRIC FIELDS IN MAXWEL
30 % of those calculated at 0.5 mm resolution. Calculations of induced electric field values for the female model NAOMI in all tissues form the basis of the ICNIRP Reference Levels for peripheral nerve stimulation. The maximum 99th percentile value for NAOMI, calculated by Dimbylow in bone, was 49.4 mV m21 per kV m21 at 50 Hz under grounded conditions. The corresponding value calculated in bone tissue using the MAXWEL phantom was 15.7 mV m21 per kV m21, considerably lower due to anatomical differences between the male and female models.
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The author thanks Dr Peter Dimbylow for his kind support and comments made on the methods used in this article. 13.
FUNDING This work was partially supported by National Grid. 14.
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ACKNOWLEDGEMENTS
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