Bioelectromagnetics 13:313-316 (1992)
Electric Fields Induced in Rat and Human Models by 6 0 4 2 Magnetic Fields: Comparison of Calculated and Measured Values Francis X. Hart Department of Physics, University of the South, Sewanee, Tennessee The calculated distribution of electric fields induced in homogeneous human and rat models by a 60-Hz magnetic field is compared with values measured in instrumented mannequins. The calculated values agree well with measured values. 8 1992 Wiley-Liss, Inc.
Key words: ELF, magnetic, electric
Determination of the current-density and electric-field distributions produced by time-varying magnetic fields is a topic of considerable interest in bioelectromagnetic dosimetry. The impedance-network method developed by Gandhi and co-workers [Gandhi et al., 1984; DeFord and Gandhi, 1985; Orcutt and Gandhi, 19881has been implemented successfully on a microcomputer [Hart and Wood, 19911 with a commercially available spreadsheet program that predicts the induced electricfield distribution in square and circular dishes filled with a saline solution. The numerical spreadsheet predictions agreed well with the results of analytical calculations and also with measured values. This method has recently been extended to homogeneous rat and human models [Hart, 19911. Validation of this technique for such models must be obtained by a comparison with measured values. Miller [ 19911has published the results of measurements made on instrumented rat and human mannequins. Although the shapes of his models differ somewhat from those used in the numerical calculations [Hart, 19911, a general comparison can be made between the two sets of values. Figures 1 and 2 are, respectively, sections of the rat and human models used in those calculations. The details of the implementation of the finite-difference method for calculating the induced-current-density distribution with a spreadsheet are provided elsewhere [Hart and Wood, 19911. Each spreadsheet cell represents a physical length of 1 mm in the rat model and 1 cm in the human model. The cells are not actually displayed in Figures 1 and 2 because of their relatively small size. A total of 5,040 cells was used for the rat model. Received for review July 15, 1991; revision received November 22, 1991. Address reprint requests to Francis X. Hart, Department of Physics, University of the South, Sewanee, TN 37375.
0 1992 Wiley-Liss, Inc.
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Hart
Fig. I . Lateral cross section of a rat model. Scan lines are shown for the head (H), neck (N), chest (C), diaphragm (D), and abdomen (A). The positions of the scan lines are ttaken from the text of Miller [ 19911. The y coordinate locates the position of the body surface along the scan line.
Fig. 2. Frontal cross section of a human model. Scan lines are shown for the head (H), neck (N), chest (C), diaphragm (D) abdomen (A) and knee (K). The positions of the scan lines are taken from the text of Miller [1991].The y coordinate locates the position of the body surface along the scan line.
Symmetry about the midline allowed the human model to be represented by 5,400 cells. The solid line in the human model indicates the, separation of the arms from the trunk for the flow of current. Because the applied magnetic field was spatially uniform in both the experimental and theoretical models, the induced current was
Magnetically Induced Electric Fields
315
confined to a plane perpendicular to the field. Hence, a two-dimensional model may be used for the calculation. The calculated current density values [Hart, 19911, which correspond to an applied 0.1-mT magnetic field and a medium of conductivity 0.005 S/m, can be converted to induced electric field values in a 1-mT field for ready comparison with the measured values [Miller, 19911. The theoretical cross-sections correspond to the lateral (rat) and frontal (human) experimental exposures. Tables 1 and 2 compare the measured and calculated values of the gradient (slope) of the induced electric field along a scan line and the electric field at a point on the scan line for several positions in the rat and human models. The scan lines and positions are those presented by Miller [1991]. The calculated values for the rat and human models generally agree well with the measured values. Probe placement uncertainty was about +2 mm in both the rat and human mannequins [Miller, 19911. The rat mannequin was similar in size to an adult rat; hence, this uncertainty corresponded to a range of +2 cells of the spreadsheet. The variation in the calculated values over this range of cells was on the order of 10%. Comparison of the outlines of the theoretical rat model in Figure 1 and the experimental mannequin [Miller, 1991;Fig. 21 also reveals differences in shape. Disagreement between the measured and calculated values in Table 1 thus reflects an uncertainty in the assignment of which spreadsheet cells correspond to a particular set of experimental measurements. The human mannequin was one-fourth the size of an adult human. The uncertainty in the probe placement corresponded to a range of f l cell of the spreadsheet model. The variation in the calculated values over this range of cells depended on the body’s position, being on the order of 20% at the knee but less than 5 % in
TABLE 1. Comparison of Measured and Calculated Values for the Electric Field Gradient and the Electric Field in a Rat Model Exposed to a 1 mT, 60 Hz Magnetic Field Slope(V/m’) Location Abdomen Diaphragm Chest Neck Head
Meas 0.26 0.28 0.33 0.39 0.30
Calc 0.33 0.32 0.35 0.37 0.37
E(mV/m) Y(m) ,043 .043 .033 .023 ,020
Meas 10.9 12.0 10.7 8.8 6.0
Calc 14.1 13.8 11.5 8.4 7.4
TABLE 2. Comparison of Measured and Calculated Values for the Electric Field Gradient and the Electric Field in a Human Model Exposed to a 1 mT, 60 Hz Magnetic Field
Location Knee Abdomen Diaphragm Chest Neck Head
Slope(V/m*) Meas Calc 0.35 0.61 0.29 0.28 0.42 0.32 0.17 0.1-0.26 0.74 0.89 0.27 0.32
E(mV/m) Y(m) .060 . I 80 .168 ,264 .064 ,096
Meas 21.7 49.1 69.9 44.9 47.1 26.1
Calc 36.7 49.8 54.3 26-68 56.9 30.8
316
Hart
the abdomen. Comparison of the outlines of the stylized human model in Figure 2 and the experimental mannequin [Miller, 1991; Fig. 31 revealed a noticeable difference in shape, particularly at the knee of the stylized model, which has sharp corners. The wide variation in the calculated values in the human chest region reflects the changing pattern of currents in the vicinity of the armpit. In the chest some of the current flows down into the arm. The remainder of the current circulates back toward the center of the body and is joined by current flowing up the outer arm. A similar pattern occurs in the groin region in which some current flows down into the legs. The remainder of the current flows directly toward the side of the body and joins the current flowing back up the outer side of the leg. The complicated current flow pattern in the human model leads to a considerable variation of internal fields with position and introduces errors beyond those due to probe-placement uncertainty and differences in model shape. The better agreement obtained for the rat model is due to a simpler flow pattern and closer similarity in model shapes for that case. More realistic, less-stylized models should give even better agreement. The impedance network method thus provides results that are consistent with measured values for homogeneous objects of highly irregular shape. One can then scale among culture dish, rat, and human models [Hart, 19911 with confidence in the results. At the present, this technique is being validated for inhomogeneous models. ACKNOWLEDGMENTS
This research is supported by the Electric Power Research Institute. REFERENCES Deford JF, Gandhi OP (1 985): An impedance method to calculate currents induced in biological bodies exposed to quasistatic electromagnetic fields. IEEE Trans Electromagn Compat 27: 168-1 73. Gandhi OP, DeFord JF, Kanai H (1984): Impedance method for the calculation of power deposition patterns in magnetically induced hyperthermia. IEEE Trans Biomed Eng :I 1 :644-65 1. Hart FX: Numerical and analytical methods to determine the current density distributions produced i n human and rat models by electric and magnetic fields. Bioelectromagnetics (Special Dosimetry Issue, In press). Hart FX, Wood KW (1991): Eddy current distributions: Their calculation with a spreadsheet and their measurement with a dual dipole antenna probe. Am J Phys 59:461-467. Miller DL (1991): Miniature-probe measurements of electric fields and currents induced by a 60-Hz magnetic field in rat and human models. Bioelectromagnetics 12: 157-171. Orcutt N, Gandhi OP (1988): A 3-D impedance method to calculate power deposition in biological bodies subjected to time varying magnetic fields. IEEE Trans Biomed Eng. 35:577-583.
Electric Fields Induced in Rat and Human Models by 6 0 4 2 Magnetic Fields: Comparison of Calculated and Measured Values Francis X. Hart Department of Physics, University of the South, Sewanee, Tennessee The calculated distribution of electric fields induced in homogeneous human and rat models by a 60-Hz magnetic field is compared with values measured in instrumented mannequins. The calculated values agree well with measured values. 8 1992 Wiley-Liss, Inc.
Key words: ELF, magnetic, electric
Determination of the current-density and electric-field distributions produced by time-varying magnetic fields is a topic of considerable interest in bioelectromagnetic dosimetry. The impedance-network method developed by Gandhi and co-workers [Gandhi et al., 1984; DeFord and Gandhi, 1985; Orcutt and Gandhi, 19881has been implemented successfully on a microcomputer [Hart and Wood, 19911 with a commercially available spreadsheet program that predicts the induced electricfield distribution in square and circular dishes filled with a saline solution. The numerical spreadsheet predictions agreed well with the results of analytical calculations and also with measured values. This method has recently been extended to homogeneous rat and human models [Hart, 19911. Validation of this technique for such models must be obtained by a comparison with measured values. Miller [ 19911has published the results of measurements made on instrumented rat and human mannequins. Although the shapes of his models differ somewhat from those used in the numerical calculations [Hart, 19911, a general comparison can be made between the two sets of values. Figures 1 and 2 are, respectively, sections of the rat and human models used in those calculations. The details of the implementation of the finite-difference method for calculating the induced-current-density distribution with a spreadsheet are provided elsewhere [Hart and Wood, 19911. Each spreadsheet cell represents a physical length of 1 mm in the rat model and 1 cm in the human model. The cells are not actually displayed in Figures 1 and 2 because of their relatively small size. A total of 5,040 cells was used for the rat model. Received for review July 15, 1991; revision received November 22, 1991. Address reprint requests to Francis X. Hart, Department of Physics, University of the South, Sewanee, TN 37375.
0 1992 Wiley-Liss, Inc.
314
Hart
Fig. I . Lateral cross section of a rat model. Scan lines are shown for the head (H), neck (N), chest (C), diaphragm (D), and abdomen (A). The positions of the scan lines are ttaken from the text of Miller [ 19911. The y coordinate locates the position of the body surface along the scan line.
Fig. 2. Frontal cross section of a human model. Scan lines are shown for the head (H), neck (N), chest (C), diaphragm (D) abdomen (A) and knee (K). The positions of the scan lines are taken from the text of Miller [1991].The y coordinate locates the position of the body surface along the scan line.
Symmetry about the midline allowed the human model to be represented by 5,400 cells. The solid line in the human model indicates the, separation of the arms from the trunk for the flow of current. Because the applied magnetic field was spatially uniform in both the experimental and theoretical models, the induced current was
Magnetically Induced Electric Fields
315
confined to a plane perpendicular to the field. Hence, a two-dimensional model may be used for the calculation. The calculated current density values [Hart, 19911, which correspond to an applied 0.1-mT magnetic field and a medium of conductivity 0.005 S/m, can be converted to induced electric field values in a 1-mT field for ready comparison with the measured values [Miller, 19911. The theoretical cross-sections correspond to the lateral (rat) and frontal (human) experimental exposures. Tables 1 and 2 compare the measured and calculated values of the gradient (slope) of the induced electric field along a scan line and the electric field at a point on the scan line for several positions in the rat and human models. The scan lines and positions are those presented by Miller [1991]. The calculated values for the rat and human models generally agree well with the measured values. Probe placement uncertainty was about +2 mm in both the rat and human mannequins [Miller, 19911. The rat mannequin was similar in size to an adult rat; hence, this uncertainty corresponded to a range of +2 cells of the spreadsheet. The variation in the calculated values over this range of cells was on the order of 10%. Comparison of the outlines of the theoretical rat model in Figure 1 and the experimental mannequin [Miller, 1991;Fig. 21 also reveals differences in shape. Disagreement between the measured and calculated values in Table 1 thus reflects an uncertainty in the assignment of which spreadsheet cells correspond to a particular set of experimental measurements. The human mannequin was one-fourth the size of an adult human. The uncertainty in the probe placement corresponded to a range of f l cell of the spreadsheet model. The variation in the calculated values over this range of cells depended on the body’s position, being on the order of 20% at the knee but less than 5 % in
TABLE 1. Comparison of Measured and Calculated Values for the Electric Field Gradient and the Electric Field in a Rat Model Exposed to a 1 mT, 60 Hz Magnetic Field Slope(V/m’) Location Abdomen Diaphragm Chest Neck Head
Meas 0.26 0.28 0.33 0.39 0.30
Calc 0.33 0.32 0.35 0.37 0.37
E(mV/m) Y(m) ,043 .043 .033 .023 ,020
Meas 10.9 12.0 10.7 8.8 6.0
Calc 14.1 13.8 11.5 8.4 7.4
TABLE 2. Comparison of Measured and Calculated Values for the Electric Field Gradient and the Electric Field in a Human Model Exposed to a 1 mT, 60 Hz Magnetic Field
Location Knee Abdomen Diaphragm Chest Neck Head
Slope(V/m*) Meas Calc 0.35 0.61 0.29 0.28 0.42 0.32 0.17 0.1-0.26 0.74 0.89 0.27 0.32
E(mV/m) Y(m) .060 . I 80 .168 ,264 .064 ,096
Meas 21.7 49.1 69.9 44.9 47.1 26.1
Calc 36.7 49.8 54.3 26-68 56.9 30.8
316
Hart
the abdomen. Comparison of the outlines of the stylized human model in Figure 2 and the experimental mannequin [Miller, 1991; Fig. 31 revealed a noticeable difference in shape, particularly at the knee of the stylized model, which has sharp corners. The wide variation in the calculated values in the human chest region reflects the changing pattern of currents in the vicinity of the armpit. In the chest some of the current flows down into the arm. The remainder of the current circulates back toward the center of the body and is joined by current flowing up the outer arm. A similar pattern occurs in the groin region in which some current flows down into the legs. The remainder of the current flows directly toward the side of the body and joins the current flowing back up the outer side of the leg. The complicated current flow pattern in the human model leads to a considerable variation of internal fields with position and introduces errors beyond those due to probe-placement uncertainty and differences in model shape. The better agreement obtained for the rat model is due to a simpler flow pattern and closer similarity in model shapes for that case. More realistic, less-stylized models should give even better agreement. The impedance network method thus provides results that are consistent with measured values for homogeneous objects of highly irregular shape. One can then scale among culture dish, rat, and human models [Hart, 19911 with confidence in the results. At the present, this technique is being validated for inhomogeneous models. ACKNOWLEDGMENTS
This research is supported by the Electric Power Research Institute. REFERENCES Deford JF, Gandhi OP (1 985): An impedance method to calculate currents induced in biological bodies exposed to quasistatic electromagnetic fields. IEEE Trans Electromagn Compat 27: 168-1 73. Gandhi OP, DeFord JF, Kanai H (1984): Impedance method for the calculation of power deposition patterns in magnetically induced hyperthermia. IEEE Trans Biomed Eng :I 1 :644-65 1. Hart FX: Numerical and analytical methods to determine the current density distributions produced i n human and rat models by electric and magnetic fields. Bioelectromagnetics (Special Dosimetry Issue, In press). Hart FX, Wood KW (1991): Eddy current distributions: Their calculation with a spreadsheet and their measurement with a dual dipole antenna probe. Am J Phys 59:461-467. Miller DL (1991): Miniature-probe measurements of electric fields and currents induced by a 60-Hz magnetic field in rat and human models. Bioelectromagnetics 12: 157-171. Orcutt N, Gandhi OP (1988): A 3-D impedance method to calculate power deposition in biological bodies subjected to time varying magnetic fields. IEEE Trans Biomed Eng. 35:577-583.
