Chapter 2

Electromagnetic Characteristics of the Human Body

2.1 Human Body Composition

The elements of the human body can be classified into different levels such as the atom, molecule, cell, tissue, and internal organs. When the human body is exposed to an external electromagnetic field, its electromagnetic characteristics are generally treated at the celluar or tissue level.

At the cellular level, electrical properties of the human body are characterized by the cell membrane and the conductive intracellular fluid and extracellular fluid. The cell membrane consists of a phospholipid bilayer with embedded proteins, and separates the interior of the cell from the outside environment. Although the membrane thickness is 10 nm at most, both its resistance and capacitance are large. Since life originated from the sea, the extracellular fluid has a composition similar to that of seawater. The composition of the intracellular fluid is about 20% protein and this is where metabolic activity occurs. The electrical properties change according to the intracellular fluid composition.

On the other hand, the resistance of the extracellular fluid is considered to be smaller than that of the intracellular liquid. The cells unite in the extracellular fluid to compose tissue. The tissue is therefore roughly distinguishable according to the method of uniting so that the electrical properties of the human body can also be characterized by the different moisture content and composition at the tissue level. One kind of tissue is known as low water content tissue which includes skin and bone. The cells unite closely, and there is little intracellular fluid and extracellular liquid. Another kind of tissue is known as high water content tissue, such as blood and muscle, in which there is more extracellular fluid. As for fat, the moisture content varies. The fat in the abdomen is similar to muscle, whereas in other parts of the body it may be similar to bone. Since each tissue is fundamentally the same structure, an equivalent circuit of the electrical properties at the tissue level can be shown as in Figure 2.1 (IEE of Japan, 1995), where the subscripts m, e and i denote the membrane, the extracellular fluid and the intracellular fluid, respectively.

At low frequencies, the equivalent circuit in Figure 2.1 only needs to consider R_e and C_e, because the impedance of the cell membrane is very high and the current will flow in the extracellular fluid. As the frequency increases, the impedance of the cell membrane becomes small so that the membrane can be disregarded by a short-circuit and the current then flows in the cell. In this case, the equivalent circuit should consist of the parallel circuit of R_i, C_i and R_e, C_e. However, C_i and C_e can be disregarded, as long as it is not in a very high frequency band, for example in the microwave band. In the intermediate frequency band, it is necessary to consider both the current which flows in the extracellular fluid and the current which flows in the cell. This means that the equivalent circuit is Figure 2.1 itself in the intermediate frequency band. In short, the equivalent circuit shows a strong frequency dependency.

2.2 Frequency-Dependent Dielectric Properties

Polarization is the most important effect arising from the interaction of an electromagnetic field with the human body. It occurs when internal charge moves in response to an external electromagnetic field. This yields both displacement and conduction currents. For this reason, the human body is classified as a lossy dielectric material. In general, dielectric properties of the human body are expressed as complex permittivity with relative permittivity and conductivity

(2.1)

where ε₀ is the permittivity of free space, and ω is the angular frequency. In Equation 2.1, is a loss factor associated with the conductivity . The conductivity is given by

(2.2)

where is the displacement conductivity and is the ionic conductivity. This frequency dependence is determined mainly by three interaction mechanisms, each governed by its own characteristic. When we systematically illustrate the complex permittivity as a function of frequency for human tissue, we can observe three main dispersion regions from the dielectric spectrum, as shown in Figure 2.2 (Schwan, 1957). These dispersions are identified experimentally in the hertz, MHz and GHz frequency regions, and are known as the , and dispersions, respectively.

The low frequency dispersion is associated with an ionic diffusion process at the cell membrane. The dispersion is mainly due to the polarization of cell membranes which act as barriers to ionic flow between the interior and exterior of the cell. Other contributions to the dispersion come from the polarization of protein and other organic macromolecules. With respect to the dispersion in the GHz region, the polarization of water molecules, which are the main constituent of the human body, plays a major role.

To characterize the human body at tissue level, dielectric properties are usually used. The dielectric properties are expressed as and values, or and values, as shown in Equation 2.1, as a function of frequency.

2.3 Tissue Property Modeling

Human body modeling should be anatomically accurate at the tissue and organ levels in body area communications. Current high resolution computer models of the human body are based on medical imaging data. The level of detail is such that over 30 tissue types are used, and the resolution is of the order of several millimeters. The application of such models requires the dielectric properties to be allocated to various tissues and organs at the considered frequencies so that the electromagnetic fields can be analyzed with Maxwell's equations. An analytic expression for the dielectric properties, that is, the complex permittivity as a function of frequency, is therefore highly useful in body area communications.

The database on the dielectric properties of biological tissue is mainly based on Gabriel's measurement data (Gabriel, 1996). The dielectric measurements were performed in the frequency range from 1 MHz to 20 GHz for over 20 tissue types. The tissue samples came from animals (mostly ovine from freshly killed sheep), human autopsy materials, and human skin and tongue. All animal tissues used were as fresh as possible, mostly obtained within 2 h of death, and human tissues were obtained 24–48 h after death. The principle is based on scattering parameter or S-parameter measurement with a two-port swept frequency network analyzer or an impedance analyzer. An open-ended coaxial probe is used to interface the input port of the measurement equipment with the tissue samples. At first, the reflection coefficient S₁₁ at the input port is obtained. Then, under the assumption that the tissue sample has a sufficiently large cross-section, the complex permittivity is derived from the reflection coefficient as a function of frequency (Misra, 1987). Gabriel carried out a comprehensive survey of past published dielectric data, and found that her data fell well within them and bridge the gaps between them.

The basis used to model the frequency dependence of dielectric properties is the dispersion phenomena in the dielectric spectrum of tissue. The dielectric spectrum is characterized by several dispersion regions. Each one can be characterized by a single relaxation time constant τ with the following frequency dependence

(2.3)

This is known as the Debye expression. The magnitude of the dispersion is described by , and is the permittivity when the frequency approaches infinity.

The dielectric properties of the human body can be therefore expressed as a summation of terms corresponding to various dispersion mechanisms. For a frequency range of Hz up to 10 GHz, four Debye-type dispersion region expressions provide good modeling for most tissues. The corresponding expression, named a 4-Cole-Cole expression, is

(2.4)

where each term is described in terms of a modified Debye expression because is introduced to describe the deviation from Debye behavior. It should be noted that the 4-Cole-Cole expression corresponds to the α, β and γ dispersions fundamentally but adds a new dispersion term in higher frequencies. It is actually a semi-empirical multiple Cole-Cole expression. An ionic conductivity term is also added to the expression for modeling a conduction current at zero frequency. In each dispersion region, is the relaxation time constant, and is the magnitude of dispersion. With an appropriate choice of parameters for each tissue, Equation 2.4 can give the dielectric properties as a function of frequency over a desired frequency range. The parameters in the 4-Cole-Cole expression are determined to closely fit the measurement data for each tissue. However, due to the difficulty in measurement at lower frequencies, the determined parameters in the 4-Cole-Cole expression only have confidence for frequencies above 1 MHz.

Table 2.1 gives the corresponding parameters in Equation 2.4 for obtaining the complex permittivity at any frequencies of interest below 10 GHz (Gabriel, 1996). Higher permittivity corresponds to more water content. Such tissues are called high water content tissues. Conversely, lower permittivity corresponds to less water content. Such tissues are called low water content tissues. Figure 2.3 shows the frequency dependence calculated from Equation 2.4 for typical high water content tissue of muscle and low water content tissue of fat. The relative permittivity decreases and the conductivity increases with the frequency. Significantly higher permittivity and conductivity are shown in the high water content tissues compared with the low water content tissues. Tables 2.2–2.5 give the conductivity , relative permittivity and loss tangent (defined as ) at 10 MHz, 400 MHz, 2.45 GHz and 5 GHz, respectively, for some main tissues and organs of the human body. The chosen frequencies cover main candidate bands for body area communications, and the dielectric properties play a dominant role in characterizing the body area channels. A comprehensive database for the dielectric properties of various tissues can be found from the FCC website http://transition.fcc.gov/oet/rfsafety/dielectric.html or the Italian National Research Council website http://niremf.ifac.cnr.it/tissprop/htmlclie/htmlclie.htm.

Table 2.1 Parameters in Equation 2.4 for obtaining the complex permittivity at frequencies of interest below 10 GHz.

Table 2.2 Dielectric properties of some main tissues and organs at 10 MHz.

Table 2.3 Dielectric properties of some main tissues and organs at 400 MHz.

Table 2.4 Dielectric properties of some main tissues and organs at 2.45 GHz.

Table 2.5 Dielectric properties of some main tissues and organs at 5 GHz.

Although Equation 2.4 gives a good expression for the dielectric properties of tissue, it is sufficiently complicated so as not to be easily incorporated into actual electromagnetic analysis. As shown in Figure 2.2, however, the dielectric properties are dominated by different dispersions in different frequency bands. For example in Figure 2.3, the variations of conductivity and relative permittivity from 100 MHz to 1 GHz are relatively small, which suggests that only one Cole-Cole term, that is, a simpler expression for Equation 2.4 may be sufficient in a specific frequency band. In these cases, the parameter is nearly zero and the complex relative permittivity can be approximated by the Debye expression. The first-order Debye expression is given by

(2.5)

or

(2.6)

with an ionic conductivity term in the human body. At high frequencies, however, the third term in Equation 2.6 is omissible. Figure 2.4 shows an example of the first-order Debye expression to approximate the dielectric properties of muscle for frequencies from 3.4 to 4.8 GHz, that is, in the UWB low band. The symbols are the actual values and the lines are the Debye approximated values with = 4.0, = 48.5, = 7.6 ps and = 1.0 S/m. A reasonable accuracy with the maximum difference smaller than 5% demonstrates the usefulness of the first-order Debye approximation.

2.4 Aging Dependence of Tissue Properties

For the complex relative permittivity expression of a biological tissue, we can rewrite Equation 2.1 as

(2.7)

where . There is a useful expression, known as a Cole-Cole plot, for . A Cole-Cole plot is a plot of on the y (or imaginary) axis versus on the x (or real) axis. Figure 2.5 gives such a plot for measured complex relative permittivity data for aging rat tissues (Peyman, Rezazadeh, and Gabriel, 2001). It is found that all five tissues, that is, the skin, muscle, skull, brain, and salivary gland, have an almost constant ratio of to or an almost constant τ_A. This finding suggests that τ_A is nearly independent of age.

On the other hand, a biological tissue can be considered as a composition of water and organic material. The amount of water inside the biological tissue should change with age, while the organic material depends only on the tissue type. Therefore, ε_r in Equation 2.7 should dominate the change in dielectric properties with age. In addition, it is known that Lichtenecker's exponential law holds for ε_r in composite dielectric materials (Lichtenecker, 1926). We can thus express ε_r for any tissue as

(2.8)

where is the relative permittivity of water (ranging from 74.3 at 10 MHz to 71.6 at 5 GHz at 37 °C), is the relative permittivity of organic material, and α is the hydrated rate which is related to the mass density ρ and the total body water (TBW) by . It should be noted that depends only on the tissue type and is not a function of age. Substituting Equation 2.8 into 2.7 for adult tissue, we can represent using the relative permittivity , relaxation time constant τ_A, and hydrated rate for adult tissue. After a primary operation to eliminate in Equation 2.7, we have

(2.9)

.

Equation 2.9 gives an empirical representation of the complex relative permittivity for a tissue with a hydrated rate α. It is therefore possible to derive the dielectric properties at different ages from Equation 2.9 as long as the hydrated rate α is known as a function of age and the dielectric properties are known for an adult.

Actually, the hydrated rate α is related to the TBW by . Figure 2.6 shows the TBW as a function of age based on the data in Altman and Dittmer (1974). As can be seen, the TBW varies greatly under 3 years old, but becomes insignificant over 3 years old. In a total trend, the TBW may be fitted with the following equation (Wang, Fujiwara, and Watanabe, 2006)

(2.10)

and then the hydrated rate α can be obtained for Equation 2.9. It should be noted that the TBW is not guaranteed to be the same in various human tissues because the developmental change of tissues may be quite different. However, as a first step for approximating the aging dependence of dielectric properties of various tissues, Equation 2.10 is a reasonable approximation to determine the hydrated rate α. Moreover, as for the tissue density ρ, there is not enough data to take into account its change with the amount of water. We thus also assume a direct link between α and TBW for a fixed tissue density.

We can check the validity of Equation 2.9 using measured data. Figure 2.7 shows the derived ε_r and σ, respectively, for the skin, muscle, skull, and brain at 900 MHz. Also shown by symbols are measured data for rats in Peyman, Rezazadeh, and Gabriel (2001). The differences between the calculated and measured data are ±20% for all the tissues. The empirical formula of Equation 2.9 is therefore a reasonable representation of the complex relative permittivity for various aged tissues.

Based on the above result, we can obtain the relative permittivity and conductivity at various ages and various frequencies. The calculation steps are as follows:

Figures 2.8–2.10 show the calculated relative permittivity and conductivity as a function of age at 400 MHz, 2.45 GHz and 5 GHz, respectively. A decreasing tendency with age can be observed in both the relative permittivity and the conductivity, which is attributed to the decrease in water content in the human body with increase in age. It can also be found that the obvious aging dependence of dielectric properties mainly occurs below 10 years old.

The approximation formula of Equation 2.9 is very useful when we have to consider the aging effect of human tissue. However, it suffers from a limitation that its validity is only confirmed when the relative permittivity of the tissue is below that of water. In reality, especially at lower frequencies such as 10 MHz, the relative permittivity of human tissue may be much larger than that of water. Whether Equation 2.9 is still valid in that case needs further validation.

2.5 Penetration Depth versus Frequency

Since the human body is a lossy medium, the wavelength is shortened mainly due to the real part of the frequency-dependent dielectric properties. This makes the attenuation inside the human body also change with frequency. With the notation in Equation 2.1, the wavenumber

(2.11)

is complex where μ₀ denotes the permeability of free space. Let us consider a semi-infinite large plane medium of homogeneous human body tissue with a plane wave with normal incidence to it, as shown in Figure 2.11. The electric field intensity in human body tissue can be described as a function of the propagation distance d along the x axis by

(2.12)

where E_z0 is the electric field at the air–body boundary, and depicts the attenuation term in the direction of propagation with

(2.13)

where because the speed of light . The wavelength in human body tissue is thus

(2.14)

This wavelength shortening effect yields a propagation speed slower than light in the human body as . Moreover, if which implies a good conductor, we have . It can be concluded from Equation 2.12 that the electric field thus attenuates exponentially with inside the human body. The exponential attenuation characteristic differs from the wave propagation in free space. It is a main propagation mechanism in in-body communication.

In Equation 2.12, the distance where the field E_z is attenuated to 1/e (0.368 or −8.68 dB) of its initial value E_z0 is called the skin depth or penetration depth, expressed by δ. This is defined as or

(2.15)

Table 2.6 gives the penetration depth for some main tissues and organs at typical body area communication frequencies. The higher the frequency, the smaller the penetration depth. For the high water content tissue such as muscle, the penetration depth is of the order of 20 cm at 10 MHz and 1 cm at 5 GHz. However,for the low water content tissue such as fat, the penetration depth is of the order of 100 cm at 10 MHz and 5 cm at 5 GHz. The significant difference in the penetration depth must be considered especially in in-body communication.

Table 2.6 Penetration depth (cm) for some main tissues and organs.

Let us go back to Figure 2.11 to consider the path loss. We assume the lossy medium to be a typical body tissue of muscle. The path loss is defined as . From we obtain the path loss versus frequency at two typical distances of d (10 and 5 cm) from the internal digestive organs to the body surface (Figure 2.12). As can be seen from Figure 2.12, at 10 cm depth, to allow a 50 dB path loss for the in-body transmission, a frequency below 3 GHz should be chosen. If a 100 dB path loss is acceptable in the receiver, the frequency can be increased to 5 GHz. On the other hand, at 5 cm depth, the path loss may be lower than 50 dB up to 6 GHz. These results suggest that in-body communication is more appropriate at lower frequencies from the point of view of penetration depth. The penetration depth is therefore an important index for choosing an appropriate frequency band, especially in in-body communication.

2.6 In-Body Absorption Characteristic

The attenuation of transmitting power in the human body is due to absorption by body tissue. The absorption characteristic of body tissue is frequency-dependent. At low frequencies, the penetration depth is large and therefore the electromagnetic wave can go into the depths of the human body. At high frequencies, however, the penetration depth becomes shallow and therefore the electric field concentrates on the body surface. Although the conductivity σ is larger at higher frequencies than that at lower frequencies, the SAR in the depths of the human body is often smaller at higher frequencies because of the weaker electric field intensity penetration in the deep tissue.

This characteristic is easy to understand when we consider a plane wave incident to a semi-infinite slab of tissues. In this case an analytical expression is available which can provide a physical insight into the result. As a primary step for the physical insight, we consider a plane wave incident normal to the semi-infinite slab with a thickness l, as shown in Figure 2.13(a). The semi-infinite slab structure is assumed to be a layer of muscle, terminated by air. A transmission line model is given in Figure 2.13(b). Then we can apply the transmission line theory to obtain a SAR profile inside the slab structure.

Let us first consider the basic concept of a transmission line structure as in Figure 2.14. The transmission line is terminated at x = l in a complex impedance Z_L, and the source is a phasor source with output voltage V_s. Let us define a complex voltage reflection coefficient Γ(x) at a particular point x on the transmission line as the ratio of the phasor voltage of the backward and forward traveling waves. In terms of the reflection coefficient Γ(x), the voltage and current expressions on the transmission line can be written as

(2.16a)

(2.16b)

where V⁺ represents the forward traveling wave, and γ and Z₀ are the propagation constant and characteristic impedance of the transmission line, respectively. Then the input impedance at any point x on the transmission line is

(2.17)

The reflection coefficient at the load is

(2.18)

and the reflection coefficient at any x is related to the reflection coefficient at the load Z_L by

(2.19)

Submitting Equation 2.19 into Equation (2.16a) we can get the voltage at any x as

(2.20)

With the above basic knowledge of transmission line theory, now let us consider the equivalent transmission line model in Figure 2.13(b). Inside the muscle tissue, the propagation constant is given by

(2.21)

and the characteristic impedance is given by

(2.22)

In addition, with Z_L equal to the air's intrinsic impedance , we have the voltage at any x as

(2.23)

The power absorption in the human body is proportional to the squared electric field and the tissue conductivity. In the above transmission line model, therefore, the power absorption should be proportional to the squared voltage and the tissue conductivity. Assuming l = 20 cm, we show the power absorption as a function of the depth x in Figure 2.15 at frequencies of 10 MHz, 400 MHz and 4 GHz (nearly the center frequency of the UWB low band), respectively. The power absorptions are normalized to that at x = 0 for 10 MHz for comparison. As can be seen, the higher frequencies yield obviously significant power absorption at the tissue surface, which actually results in shallower penetration into the tissue. As the frequency decreases, however, the power concentration at the tissue surface becomes not so obvious so that the electromagnetic wave can go deeper into the human body.

The quantization of power absorption usually uses the SAR. SAR is defined as power absorbed by unit mass

(2.24)

in units of W/kg, where ρ is the mass density and E is the root mean squared electric field intensity in the human body. The SAR is a quantity often used for safety evaluation of electromagnetic interaction with the human body because it acts as a means to cause a temperature rise in the human body. In short, the larger the power absorbed by the human body, the larger the path loss. From the point of view of in-body communication, we have to pay attention to the path loss because it is needed in the system design such as the link budget evaluation. However, from the point of view of safety evaluation, we should pay attention to the SAR because it is related to a temperature rise in the human body where a rise exceeding 1 °C is considered to be unsafe.

When a human body in thermal equilibrium is exposed to electromagnetic fields, the resultant temperature rise can be calculated from a bio-heat equation which takes into account heat exchange mechanisms such as heat conduction, blood flow, and electromagnetic heating. The bio-heat equation is given by (Pennes, 1948)

(2.25)

with the boundary condition

(2.26)

where T is temperature, C_P is specific heat, K is thermal conductivity, b is a constant related to the blood flow, T_b is blood temperature, T_a is ambient temperature, h is the convective heat transfer coefficient, n is unit vector normal to the body surface, and SAR is the input electromagnetic heating source. It should be noted that there are two kinds of convective heat transfer coefficient h. One is h_a, the convective heat transfer coefficient from the human body surface to the ambient temperature, and the other is h_b, the convective heat transfer coefficient from the internal surface to the internal cavity, which is generally larger than h_a. These thermal parameters can be found in some physiological textbooks (Guyton and Hall, 1996), but a comprehensive database for the thermal parameters does not exist. By solving Equation 2.25 with the SAR as excitation, the temperature distribution inside the human body as a function of time can be obtained. As for the steady-state temperature rise, it can be calculated from the difference between the temperature T and T₀ where T₀ is the normal temperature in the unexposed body (with SAR = 0) at the thermal equilibrium state.

2.7 On-Body Propagation Mechanism

The on-body propagation mechanism is not as simple as the in-body propagation mechanism. The on-body propagation mechanism may depend on working frequency so that different propagation mechanisms may be involved.

Here we attempt to derive a general explanation for the propagation mechanism in various frequency bands based on electromagnetic theory. Let us first consider the electric field from a vertical dipole in free space (Figure 2.16). In a spherical coordinate system , the electric field at r is given by

(2.27)

where I is the wire current in amperes, Δz is the dipole length in meters, is the intrinsic impedance of free space, and k₀ is the wavenumber of free space. Equation 2.27 contains terms in 1/r, 1/r², and 1/r³. In the near field, the 1/r³ term is dominant. This term is called the electrostatic field component. As the distance r increases, the 1/r³ and 1/r² terms attenuate rapidly so that the far field is dominated by the 1/r term which is known as the radiation field. That is to say, the 1/r, 1/r², and 1/r³ terms correspond to the electric fields in the far-field, induction-field, and near-field region of the dipole, respectively. This basic concept is helpful to understand the propagation mechanism of on-body communication.

To derive the propagation mechanism from a theoretical approach, we simplify the human body to be a semi-infinitely large lossy dielectric medium with relative permittivity and conductivity . When a unit vertical dipole is placed on the boundary plane as shown in Figure 2.17, the electric field from the dipole is given by (Norton, 1937)

(2.28)

where II is the wave potential which has only a single component

(2.29)

where is the first kind Bessel function with order zero, and

(2.30)

(2.31)

(2.32)

(2.33)

Under the cylindrical coordinate system , we have

(2.34)

(2.35)

(2.36)

So the problem of determining the electric field intensity on the lossy dielectric plane can be reduced to calculate . After some complex mathematics operations, we may obtain the z-directed electric field on the lossy dielectric surface as (Bae et al., 2012)

(2.37)

where

(2.38)

(2.39)

(2.40)

and

(2.41)

.

In Equation 2.37, the first term proportional to the inverse of the surface distance, that is, the 1/r term, contains an additional gain factor . Since is related to the dielectric properties of the lossy dielectric medium, the first term in Equation 2.37 can be approximately regarded as a wave propagating along the surface of the medium. Strictly speaking, a surface wave is a signal that propagates along a boundary of two kinds of different media without radiation to the outside. In this sense the first term in Equation 2.37 is not a strict surface wave because it also radiates towards the outside of the boundary. However, in view of the fact that this field component decreases with an increase in the surface distance r, we refer to it as a “surface propagation component”. In addition, the other two terms (1/r² and 1/r³ terms) in Equation 2.37 correspond to the induction and electrostatic field components of the dipole, respectively. The surface propagation component should predominate at larger transmission distances, whereas the transmission in shorter distances may be dominated only by the electrostatic field and the induction field.

The propagation mechanism of on-body communication can be therefore divided into three parts: the surface propagation of the 1/r term, the reactive induction of the 1/r² term, and the electrostatic coupling of the 1/r³ term. Which term is dominant is not dependent on the actual propagation distance r but the distance normalized to the wavelength. That is to say, at a specified distance r, the size of contribution from the three different mechanisms depends on the frequency. At low frequencies, the wavelength is large and the normalized distance is consequently small. This makes the electrostatic coupling contribute more to the on-body propagation. On the other hand, as the frequency increases, the shorter wavelength yields a larger normalized distance. This makes the 1/r term or the surface propagation term begin to have a significant contribution whereas the electrostatic coupling term becomes negligible. It should be noted that, however, since the surface propagation term consists of a gain factor , the larger the gain factor, the larger the field component of surface propagation.

Let us see the frequency dependence of the gain factor . We assume the semi-infinitely large lossy dielectric medium to be muscle. With Equations 2.33 and 2.38–(2.41), we can obtain the gain factor as a function of frequency. In the calculation of Equation 2.41 for the complementary error function with a complex argument, we employ the following Taylor series expression for complex argument z

(2.42)

Figure 2.18 shows the calculation result at the unit propagation distance (1 m). Another representation is to plot it as a function of also at the unit propagation distance, as shown in Figure 2.19. As can be seen, the gain factor decreases with frequency or , which means that the surface propagation component attenuates more rapidly at higher frequencies. When the frequency is below 100 MHz, the degradation in the gain factor of the surface propagation component is relatively smooth with frequency and is always larger than 0.85. Above 100 MHz, however, the gain factor degrades rapidly with frequency and reaches 0.27 at 5 GHz. Similarly, from Figure 2.19, the corresponding is about 2.0 for a gain factor of the surface propagation component larger than 0.85.

In order to distinguish the size of contribution from each mechanism to the received field component, the percentage of the surface propagation component, the induction field component, and the electrostatic field component, that is, the three components in Equation 2.37, are calculated. Figure 2.20 shows the percentage of contribution as a function of frequency, and Figure 2.21 shows it as a function of . From Figure 2.20, the three field components are found to be equal at 50 MHz. The corresponding value is 1.0 in Figure 2.21. Therefore, at frequencies below 50 MHz, the electrostatic field component is dominant and electrostatic coupling is the main on-body propagation mechanism. On the other hand, when the frequency exceeds 50 MHz, the surface propagation term becomes dominant. In particular, at frequencies larger than 100 MHz, the surface propagation component is larger than the sum of the other two components and acts as the main on-body propagation mechanism. The corresponding value of is about 2.0.

Based on the above observations, we now summarize the on-body propagation mechanism for typical candidate frequencies of body area communications, that is, 10 MHz, 400 MHz and the UWB band.

• At 10 MHz, almost 80% of the received field component is contributed by the electrostatic field term at a unit on-body communication distance. The signal transmission is thus realized mainly by electrostatic coupling in this frequency band.
• At 400 MHz, almost 80% of the received field component is contributed by the surface propagation term, which acts as a main on-body propagation mechanism.
• In the UWB band, more than 95% of the received field component is contributed by the surface propagation term. It completely dominates the on-body propagation.

Although the findings are derived from a semi-infinite large plane medium with the dielectric properties of muscle, they are useful in understanding the basic on-body propagation mechanism. Of course, the actual body tissue and shape may result in some deviations for the values in Figures 2.20 and 2.21.

In addition, we can rewrite Equation 2.37 as

(2.43)

with (where c is the speed of light) to derive an expression for the received electric field as a function of frequency. It is evident that the third term of electrostatic coupling at low frequencies exhibits a low-pass filter feature, whereas the first term of surface propagation at high frequencies exhibits a high-pass filter feature. In total the on-body propagation has a band-stop filter feature. The stop-band is dependent on the body tissue properties and propagation distance. This characteristic makes the choice of whether the lower HBC band or the higher UWB band become more reasonable for on-body communication. Moreover, the electrostatic coupling is little affected by propagation distance, whereas the gain factor decreases rapidly in the UWB band. This feature further suggests that the HBC band may be more suitable than the UWB band for on-body communication.

2.8 Diffraction Characteristic

Since the human body has a complicated surface shape, the actual propagation on it may differ from the propagation along a smooth plane. If the direct propagation path between the transmitter and receiver is obstructed by an obstacle, electromagnetic waves may travel into the shadow zone behind the obstacle. The apparent bending of waves around small obstacles is known as diffraction. Diffraction occurs when the dimensions of the obstacle are not greater than dozens of times of the wavelength. This is generally fulfilled in body area communications where the wavelengths are above several centimeters. In on-body communication the obstacle may be a part of the body or the curved body surface, whereas in in-body communication the obstacle may be the organs. Since the diffracted wave propagates on the body surface with the speed of light, it is also called a creeping wave. This wave can actually be considered as the surface propagation component as in the previous section. The difference is that it propagates along a curved surface. In this sense the diffraction may act as a propagation mechanism at higher frequencies on the curved part of the human body.

Let us consider an infinitely long circular cylinder with radius a as shown in Figure 2.22. A z-directed magnetic line source of unit strength is located at (x, y) = (a, 0) as the transmitter and excites a transverse electric (TE) field. The corresponding magnetic field on the cylinder surface is z-directed and is given by (Paknys, 1993)

(2.44)

where k denotes the wavenumber, and and are the second kind Hankel function and its derivative, respectively. In order to calculate the magnetic field numerically, the Hankel functions in the numerator and denominator of Equation 2.44 are replaced with the Watson approximation. This yields

(2.45)

where

(2.46)

is known as the Fock-type Airy function in which is the Airy function and is the second kind Airy function,

(2.47)

(2.48)

and d is the distance between the line-source-type transmitter and the receiving point on the cylinder surface. Hence the diffracted field for TE polarization can be calculated from Equation 2.45 as a function of the angle ϕ between the transmitter and the receiving point. In the calculation of the diffracted fields, MATLAB® provides a conventional tool to treat the Airy functions in Equation 2.45.

Figure 2.23 shows the diffracted fields calculated on the cylinder surface as a function of ϕ at 10 MHz and 5 GHz, respectively. The circular cylinder is assumed to be muscle tissue and the radius a = 15 cm. The diffracted field is normalized to that in the vicinity of the excitation source. As expected, the diffracted field attenuates with increasing angle. The attenuation is larger at higher frequencies. For ϕ = 180°, which corresponds to the case where the transmitter and the receiving point are located on opposite sides of the cylinder, the diffracted field attenuates around 40 dB at 10 MHz and 50 dB at 5 GHz. The attenuation at 400 MHz band is between the two curves in Figure 2.23 but closer to that at 5 GHz. Such a level attenuation or path loss is of an acceptable order for on-body transmission. The diffraction phenomenon is thus a useful mechanism and provides the possibility for on-body communication along the curved body surface.

On the other hand, for the infinitely long circular cylinder in Figure 2.22, if we assume a ϕ-directed magnetic line source located at (r, ϕ) = (a, 0) in a cylindrical coordinate system, it will excite a transverse magnetic (TM) field with both r component and ϕ component. That is to say, the excited magnetic field is given by

(2.49)

However, at the body surface, that is, when , will vanish so that we only need to consider the component. is given by

(2.50)

for a unit strength line source. In order to derive an easy approximation solution for Equation 2.50, again, the Fock-type Airy function w₂(τ) in Equation 2.46 can be used. Then Equation 2.50 becomes

(2.51)

where ξ and τ can be found from Equations 2.47 and 2.48, respectively.

Figure 2.24 shows the diffracted fields for TM polarization, which are calculated using Equation 2.51 on the cylinder surface as a function of ϕ at 10 MHz and 5 GHz, respectively. The circular cylinder is assumed to be muscle tissue and the radius a = 15 cm. The diffracted fields are normalized to that in the vicinity of the excitation source. As can be seen, the diffracted field attenuates larger than that in TE polarization. It attenuates around 80 dB at 10 MHz and 90 dB at 5 GHz for ϕ = 180°. Theses field characteristics reasonably suggest that a diffracted wave should propagate easier when it has an electric field component normal to the curved surface.

Although the diffraction characteristics are derived from a circular cylinder in this section, they are basically applicable to a human body. In view of the acceptable attenuation or path loss level especially in the TE polarization, the diffraction phenomenon should be considered as a valid mechanism in on-body transmission. It should be noted that, however, at low frequencies, the larger penetration depth may make the wave penetrate the human body so that a direct path exists between the transmitter and receiver in addition to the path of the diffracted wave. In this case, the received field signal should be the sum of the direct wave and the diffracted wave.

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