Radiofrequency Radiation
Dosimetry Handbook

(Fourth Edition)

Chapter 9. Dosimetry In The Very-Low-Frequency And Medium-Frequency Ranges

In the frequency range from 10 kHz to 3 MHz, which includes the very low-frequency (VLF) and medium-frequency (MF) bands, other dosimetric data may be more important than the SARs given in Chapters 6 and 8. Exposure fields (even relatively intense ones) at the low frequencies produce relatively inconsequential amounts of absorbed energy but may cause electric shocks and RF burns. Since the shocks and burns are more directly related to current density and total current, these quantities are probably more useful dosimetric data than SARs in the VLF-MF ranges.

Dosimetry in the VLF-MF bands thus consists primarily of relating current densities in the exposed bodies to the exposure fields. Important factors in this relationship are the presence of nearby objects, especially conducting objects such as automobiles, and the exposed person's contact with the objects. The impedance between the exposed person and ground is useful in relating the current densities to the exposure field. This section contains information about methods of calculating and measuring impedances and current densities, and summaries of such data. Most of the information was obtained from work reported under USAFSAM contracts with Guy and Chou (1982) and Gandhi and Chatterjee (1982).

9.1. METHODS

Most objects of interest are small compared to a wavelength in the VLF-MF ranges, so quasi-static analyses are useful for obtaining dosimetric information. In the quasi-static approximation, the calculated results at one frequency are directly applicable to all frequencies for which the approximation is valid. Fortunately this includes the 60-Hz range, where a great deal of theoretical and experimental dosimetry has been done. All of these 60-Hz results can be applied to the VLF-MF bands. The basic reason is explained by Kaune and Gillis (1981), among many others. They showed, from the quasistatic approximation to Maxwell's equations, that the field internal to a living subject is very small compared to the external field, which means that the perturbed external field and the induced surface-charge density are independent of the permittivity of the body tissues. The induced surface charge causes internal currents that depend directly on the electrical properties of the body tissue, but the total conduction current passing through any section of the body is independent of the tissue characteristics (Kaune and Gillis, 1981; Deno, 1977). This also means that the total induced volume charge in the body is negligible compared to the total induced surface charge. The induced current in the body is directly proportional to frequency.

Several approaches have been used to calculate induced currents and energy absorption, but experimental measurements have proved to be more accurate. The methods described here consist of calculating currents, current densities, potential distributions, resistances, and local and average SARs from measured impedances and fields. The only polarization considered here is the one that causes the greatest absorption; as indicated in Chapters 6 and 8, that is the polarization in which E is parallel to the long dimension of the body.

9.1.1. Calculation of Current

In the quasi-static approximation, the total charge, q, on an object close to ground is given by

(Equation 9.1)

where E is the E-field magnitude in the absence of the object, h is the effective height of the object, and is the capacitance between the object and ground. The current, induced on the object by E when the object is short-circuited to ground is given by

(Equation 9.2)

where corresponds to the time derivative in the sinusoidal steady-state case, and is the radian frequency of E. Writing as

(Equation 9.3)

where S is an effective surface area and is the permittivity of free space,and combining Equations 9.1, 9.2, and 9.3 gives for the magnitude of ,

(Equation 9.4)

An approximate value for S may be obtained from the geometrical relation shown in Figure 9.1. Using this calculated value for S gives

(Equation 9.5)

where h is the height in meters, E is the E-field magnitude in kilovolts per meter, f is the frequency in kilohertz, and is in milliamperes.

Deno (1977) measured the short-circuit current and the distribution of current at 60 Hz in a metallized mannequin consisting of insulated material covered with copper foil. Breaks in the copper foil were used to measure current distribution. By measuring short-circuit currents near powerful VLF-MF transmitting stations, Guy and Chou (1982) showed that the determination of currents at 60 Hz is applicable to the VLF-MF band.
Gandhi and Chatterjee (1982) used a Norton's equivalent circuit to represent the body and from it calculated the total current in the human body to be

(Equation 9.6)

where is leakage resistance of the body to ground, and and are equivalent body resistance and capacitance respectively. Combining Equations 9.6 and 9.4 gives the current in a person exposed to an electric field, E.

Figure 9.1.
Relationship between effective area and short-circuit current () for exposed human figure (Guy and Chou, 1982).

9.1.2. Measurement of Body Potential and Dimensions

In baboons the equipotential planes occur perpendicular to the long axis of the body when the incident E-field is parallel to the long axis (Frazier et al. , 1978; Bridges and Frazier, 1979), so the potential distribution inside the body can be predicted from the surface potential. While applying a harmless low-level VLF current through volunteers' bodies, Guy and Chou (1982) measured the surface potential distribution. They measured the circumference and maximum dimensions of the subject's body and limbs as a function of position every 5 cm from the feet to the head, and then assumed an elliptical cross section to determine the cross-sectional area. The sum of the volumes of those elliptical cylinders was compared to the body volume to check the accuracy of the measurements. The body volume was calculated from body weight by assuming a specific gravity of 1.06.

9.1.3. Calculation of Body Resistance and SAR

From the information obtained in the body potential measurements described above, Guy and Chou (1982) calculated the electrical conductivity and the resistance per unit length for various regions of the body. The resistance between two equipotential planes perpendicular to the axis of the body or body member is given by

(Equation 9.7)

where is the measured potential difference, I is the applied current, is the incremental distance, and R(i) is the resistance per unit length of the length. The conductivity of a particular region of the body is related to R(i) by

(Equation 9.8)

where A(i) is the cross-sectional area of the ith section. Combining Equations 9.8 and 9.7 and solving for gives

(Equation 9.9)

where is the effective conductivity in the region between the equipotential planes where Vnm is measured. Once a has been determined, the potential distribution [V(k)], the current density [J(i)], and the local SAR [SAR(i)] may be obtained for any known current distribution [I(i)] from the following equations:

(Equation 9.10)

J(i)=I(i)/A(i) (Equaiton 9.11)

(Equation 9.12)

where is the density of the tissue (usually assumed to be equal to unity). Regional and whole-body power absorption can be found from

(Equation 9.13)

9.2. CALCULATED AND MEASURED DATA

Figures 9.2-9.4 show Guy and Chou's (1982) plots of Deno's measured distributions of surface currents on copper-foil-covered mannequins. In the data shown in Figures 9.2 and 9.3, Deno had not measured the current distribution in the arm but reported it as 14% of the short-circuit current. Guy and Chou assumed a cosine distribution for their plots. In Figure 9.2, the maximum current occurs at the feet, with a value given by Equation 9.5. From Figure 9.3, the maximum current for a man exposed in free space is given by

(Equation 9.14)

(same units as Equation 9.5), and from Figure 9.4, with feet insulated but a hand grounded, by

(Equation 9.15)

Figure 9.2.
Relative surface-current distribution in grounded man exposed to VLF-MF fields [after Deno, 1977 (Guy and Chou, 1982)].

Figure 9.3.
Relative surface-current distribution in man exposed in free space to VLF-MF electric fields [after Deno, 1977 (Guy and Chou, 1982)].

Figure 9.4.
Relative surface-current distribution in man exposed to VLF-MF electric fields with feet insulated and hand grounded [after Deno, 1977 (Guy and Chou, 1982)].

Tables 9.1 and 9.2 summarize, respectively, the effects of currents on humans and some values specified in safety standards. Table 9.3 gives currents in various parts of the body, based on 60-Hz work by Kaune (1980). Table 9.4 gives short-circuit currents for various objects exposed to VLF-MF fields, based on 60-Hz work. Tables 9.5-9.7 show data measured in VLF-MF fields. The plot of these data in Figure 9.5 compares very well with values calculated from Equation 9.5

Table 9.1.
Summary Of Electric-Current Effects On Humans (Guy and Chou, 1982)

Table 9.2.
Maximum 60-Hz Currents Allowed To Human Body By National Electrical Code (mA) And Equivalent Levels At Other Frequencies (Guy and Chou, 1982)

Table 9.3.
Current And Current Density In Man Exposed To VLF-MF [f(kHz)] 1-kV/m Electric Fields (based on Kaune, 1980) (Guy and Ghou, 1982)

Table 9.4.
Short-Circuit Currents For Objects Exposed To VLF-MF [f(kHz)] 1-kV/m Electric Fields (Guy and Chou, 1982)

Table 9.5.
Comparison Of Measured And Theoretical Short-Circuit Body Current For Man Exposed To VLF-MF Electric Fields With Feet Grounded (Guy and Chou, 1982)

Table 9.6.
Measured Body Currents [mA/(kv/m)] To Ground For Subjects Exposed Under Different Conditions To 24.8-kHz VLF Electric Fields [Washington VLF (Guy and Chou, 1982)]

Table 9.7.
Comparison Of Measured And Theoretical Person-To-VehicleCurrent Resulting From VLF-MF Electric-Field Exposure (Guy and Chou, 1982)

Figure 9.5.
Comparison of theoretical and measured short-circuit body current of grounded man exposed to VLF-IAF electric field that is parallel to body axis (Guy and Chou,1982).

Figures 9.6-9.8 show results by Gandhi and Chatterjee (1982) of human body resistance, threshold perception and let-go currents and corresponding unperturbed incident E-fields that would produce these threshold currents for various conditions. Perception current is defined as the smallest current at which a person feels a tingling or pricking sensation due to nerve stimulation. Let-go current is defined as the maximum current at which a human is still capable of releasing an energized conductor using muscles directly stimulated by that current. Tables 9.8-9.10 show values of threshold perception measured with an experimental setup like the one illustrated in Figure 9.9. Either a copper-disk or a brass-rod electrode was used in the measurements. Table 9.11 gives calculated values of currents through the wrist and finger for a maximum SAR of 8 W/kg.

Table 9.12 shows the body dimensions calculated by Guy and Chou for one person. Figures 9.10-9.17 show their calculated current distributions for the current distributions of Figures 9.2-9.4. The data in Figures 9.10-9.17 are for exposure of a subject with feet electrically grounded, in free space, with feet insulated but hands grounded, and with feet grounded but one hand contacting a large object such as a vehicle. To calculate values of current, current density, and potential in a subject contacting one of the specific objects in Table 9.4, multiply the values in Figures 9.10-9.17 by the shortcircuit object currents in Table 9.4. Calculations for objects not given in Table 9.4 can be made by looking up methods for calculating the effective surface area, S, in the literature (for example, Deno, 1977; Transmission-Line Reference Book, 1979) using Equation 9.5 to calculate , and proceeding as described above.

Figure 9.6.
Average values of the human body resistance, Rh, (see Equation 9.6) assumed for the range 10 kHz to 20 MHz (Gandhi and Chatterjee, 1982).

Figure 9.7.
Perception and let-go currents for finger contact for a 50th percentile human as a function of frequency assumed for the calculations (Gandhi and Chatterjee, 1982). [These were obtained as a composite of the experimental data of Dalziel and Mansfield (1950), Dalziel and Lee (1969), and Rogers (1981).]

Figure 9.8.
Unperturbed incident E-field required to create threshold perception and let-go currents in a human for conductive finger contact with various metallic objects, as a function of frequency (Gandhi and Chatterjee, 1982)

Table 9.8.
Threshold Currents For Perception When In Contact With The Copper-Plate Electrode And Threshold Incident Electric Fields For Perception When In Contact With Various Metal Objects (Gandhi et al., 1984)

Table 9.9.
Statistical Analysis Of Measured Data On Threshold Currents For Perception With Subjects Barefoot And With The Wristband (Gandhi et al., 1984)

Table 9.10.
Threshold Currents For Perception When In Grasping Contact With The Brass-Rod Electrode And Threshold External Electric Fields For Perception When In Contact With A Compact Car (Cg = 800 pF) (Gandhi et al., 1984)

Figure 9.9.
Experimental arrangement for measuring threshold currents for perception and let-go (Gandhi and Chatterjee, 1982).

Table 9.11.
Currents Through The Wrist And Finger For Maximum SAR = 8 W/kg. (Cross-sectional areas are for nonbony regions of respective parts of the body.) (Gandhi et al., 1984)

Table 9.12.
Dimensions Of Body Used For VLF-MF Exposure Model (Guy and Chou, 1982)

Figure 9.10.
Calculated current distributions as a function of a position in man exposed to 1-kV/m VLF-MF fields with feet grounded (Guy and Chou, 1982)

Figure 9.11.
Calculated current density flowing through one arm. The exposure is the same as that of Figure 9.10 (Guy and Chou, 1982).

Figure 9.12.
Calculated current distribution as a function of position in man exposed to 1-kv/m VLF-MF fields in free space (Guy and Chou, 1982).

Figure 9.13.
Calculated current density flowing through one arm. The exposure condition is the same as for Figure 9.12 (Guy and Chou, 1982).

Figure 9.14.
Calculated current distribution as a function of position in man exposed to 1-kv/m VLF-MF fields with feet insulated but hands grounded (Guy and Chou, 1982).

Figure 9.15.
Calculated current density flowing through one arm. The exposure condition is the same as for Figure 9.14 (Guy and Chou, 1982).

Figure 9.16.
Calculated current distribution as a function of position in man with hand contacting a large object and with feet grounded. A 1-mA current is assumed to floating throughb the arm, thorax, and legs of the subject to the ground, F=60 Hz (Guy and Chou, 1982).

Figure 9.17.
Calculated current density flowing through one arm. The exposure condition is the same as for Figure 9.16 (Guy and Chou, 1982).

Table 9.13 gives regional and average SARs for various exposure conditions. Figure 9.18 shows measured values of the imaginary component of the permittivity (Tables 9.14 and 9.15; see Section 3.2.6 for the relationships of permittivity, conductivity, and loss factor) along with values of the real and imaginary components given in the first edition of this handbook. Figures 9.19 and 9.20 show average SARs of Table 9.13 compared with theoretical values. Further power absorption calculations are given in Table 9.16.
Figure 9.21 shows the maximum electric-field strength below levels of 1000 V/m that would violate any of the following conditions:
  1. The maximum current through any body member contacting ground or an object should not exceed levels equivalent to those allowed by the National Electric Safety Code in the frequency range where shock hazards may occur.
  2. Total possible current entering the body should not exceed 200 mA, for prevention of RF burns.
  3. The 0.4-W/kg average and 8-W/kg maximum SAR recommended by the ANSI C95.1-1982 Standard shall not be exceeded.
According to the calculated data of Guy and Chou (1982), none of the conditions would be violated for exposure of persons isolated in free space at E-field strengths of 1 kV/m or below. Other conditions are shown in Figure 9.21.

Table 9.13.
Distribution Of Power Absorption (Watts)In Man Exposed To VLF-MF Fields: 1-kV/m Exposure, E-Field Parallel Long Axis, 1-mACurrent Assumed For Contact With Object (Guy and Chou, 1982)

Figure 9.18.
Real part, ', and imaginary part,", of the dielectric constant for high-water-content tissue. The dashed line is measured values (Guy and Chou, 1982) The other lines are values given in the first edition of this handbook

Table 9.14.
Average Apparent Conductivity Of Man Based On Whole-Body In Vivo Measurements(S/m) (Guy and Chou, 1982)

Table 9.15.
Average Apparent Loss Factor Of Man Based On Whole-Body In Vivo Measurements (Guy and Chou, 1982)

Figure 9.19.
Comparison of calculated average SAR (obtained from VLF analysis) with average SAR (reported in the first edition of this handbook) of average absorbed power in an ellipsoidal model of an average man (Guy and Chou, 1982).

Figure 9.20.
Comparison of theoretical and experimentally measured whole-body average SAR for realistic man models exposed at various frequencies. The experimental curve is measured results in scaled human-shaped models at simulated VLF frequencies (Guy and Chou, 1982).

Table 9.16.
Distribution Of Power Absorption (Watts) In Man, With Feet Grounded, Exposed To 1-kV/m VLF-MF Fields While In Contact With Vehicle (Guy and Chou, 1982)

Figure 9.21.
Required restrictions of VLF-MF electric-field strength to prevent biological hazards related to shock, RF burns, and SAR exceeding ANSI C95.1 criteria (Guy and Chou, 1982).


Go to Chapter 10.

Return to Table of Contents.

Last modified: June 14, 1997
October 1986, USAF School of Aerospace Medicine, Aerospace Medical Division (AFSC), Brooks Air Force Base, TX 78235-5301