**2. Dielectric parameters of human biological tissues derived from their correlation with animal biological tissues**

For ethical reasons and due to the complexity of *in vivo* research with human biological tissues, especially for children, few researchers have conducted experiments with animal biological tissues tending to confirm the age-dependence of dielectric parameters of biological tissues.

One of the most systematic and cited studies dealing with dielectric properties of biological tissues remains report [5] based on which the database and software applet is developed presenting the values of permittivity , conductivity and the other dielectric characteristics, for main biological tissues at microwave frequencies.

The presented results of permittivity and conductivity of human biological tissues have been obtained by experimental techniques on three types of materials: excised animal tissues, human autopsy materials and in vivo human skin and tongue, whose details are given in [5].

The comparison between dielectric characteristics of human and animal biological tissues and between animal species is given on Figures 2, 3 and 4.

**Figure 2.** Comparison between the dielectric properties of tongue muscle from animal and human samples [5]

The difference between dielectric parameters of animal and human is not systematic, thus it has to be noted that the difference between dielectric parameters of the same specie may sometimes exceed the difference between the different species.

These differences make the method of extrapolation of dielectric parameters from one specie to the other not sustainable at desired extent.

Nevertheless, from the above figures, the similarity of dielectric parameters variation trend between the animals and human biological tissues can be observed.

**Figure 3.** Comparison between the dielectric properties of tendon from two animal species [5]

**Figure 4.** Comparison between the dielectric properties of small intestine tissue from animal and human samples [5]

Even the study gives detailed results and deep description of research methodologies, providing broad based consensus results on the subject, the age-dependency of dielectric characteristics of biological tissues is not included in software application and the user can not obtain the values of permittivity and conductivity as a function of age.

144 Microwave Materials Characterization

human samples [5]

The difference between dielectric parameters of animal and human is not systematic, thus it has to be noted that the difference between dielectric parameters of the same specie may

These differences make the method of extrapolation of dielectric parameters from one specie

Nevertheless, from the above figures, the similarity of dielectric parameters variation trend

**Figure 3.** Comparison between the dielectric properties of tendon from two animal species [5]

**Figure 4.** Comparison between the dielectric properties of small intestine tissue from animal and

sometimes exceed the difference between the different species.

between the animals and human biological tissues can be observed.

to the other not sustainable at desired extent.

Few studies have reported variation of dielectric parameters with age mostly for animal biological tissues.

*Thurai et al. 1984*[6] *and 1985*[7] reported a change on values of dielectric parameters as a function of age for brain of animal tissue.

*Peyman et al*. [8,9] presented the values of experimental measurements of dielectric parameters of rats aged 10-70 days, thus confirming the age-dependence of permittivity and conductivity of the animal biological tissues. In the study, the dielectric properties of ten rat tissues at six different ages were measured at 37 degrees celzius in the frequency range between 130 MHz and 10 GHz, using an open-ended coaxial probe and a computer controlled network analyser. The results showed a general decrease of the dielectric properties with age, with a trend being more apparent for skull, skin and brain tissues and less noticeable for abdominal tissues. The variation in the dielectric properties with age reported in the study is due to the changes in the water content and the organic composition of tissues. The results presented in study have given some insight to research community for possible differences and comparative assessment of exposure between children and adults.

In the review article [10], experimental results are presented on the dielectric properties of tissue samples of 10, 30, and 70 days-old Wistar strain rats in the frequency range 300 KHz– 300 MHz. The study concluded that at frequencies higher than 100 MHz, where the γ dispersion is dominant, the permittivity and the conductivity increase monotonically with decreasing age. At lower frequencies, the site of the β dispersion, a change in the frequency dependence of the dielectric parameters is observed and is mostly evident in the spectra for brain and skin. According to this research, it is attributed to changes in the tissue structure.

In the same study [10] age-related dielectric data were incorporated in a numerical plane wave exposure dosimetry applied on anatomically heterogeneous rat models with body sizes corresponding to the ages of 10, 30, and 70 days at a number of spot frequencies from 27 to 2000 MHz. The obtained results showed that the variation in the dielectric properties affect the whole body SAR by less than 5% with the most conservative value (highest SAR) obtained when 70 day properties were used.

*Schmid and Uberbacher* [11] have presented the results of experimental measurements confirming that conductivity and permittivity of younger animal tissues were for 15-22 %, respectively 12-15 % , higher than the ones of older animal tissues.

Peyman et. al. [12, 13] also conducted measurements of dielectric parameters of pig biological tissues at different ages, re-confirming the age- dependence of dielectric characteristics of animal tissues, and in the same study the correlation between the animal dielectric parameters and human dielectric parameters is given.

The dielectric properties of pig cerebrospinal tissues were measured *in vivo* and *in vitro*, in the frequency range of 50 MHz–20 GHz. The total combined measurement uncertainty was calculated at each frequency point and is reported over representative frequency regions. Comparisons were made for each tissue between the two sets of data and with the literature of the past decade. The *in vitro* study was extended to include tissue from pigs weighing approximately 10, 50 and 250 kg to confirm the issue of the variation of dielectric properties with age.

**Figure 5.** The measured permittivity of the long bone for different age pigs [4]

**Figure 6.** The measured permittivity of the skull for different age pigs [4]

As reported on [4] the age related effects were more noted for some tissues types. Results of porcine study showed that at tissues: white matter, dura, fat, skin, skull and spinal cord the age related effects were noticed, while at tissues as: tongue, cornea and grey matter no age related effects were noticed.

For some tissues at microwave frequencies there was no significant change between results obtained from *in vitro* and *in vivo* measurements.

**Figure 7.** The measured permittivity of the skin for different age pigs [4]

146 Microwave Materials Characterization

with age.

The dielectric properties of pig cerebrospinal tissues were measured *in vivo* and *in vitro*, in the frequency range of 50 MHz–20 GHz. The total combined measurement uncertainty was calculated at each frequency point and is reported over representative frequency regions. Comparisons were made for each tissue between the two sets of data and with the literature of the past decade. The *in vitro* study was extended to include tissue from pigs weighing approximately 10, 50 and 250 kg to confirm the issue of the variation of dielectric properties

**Figure 5.** The measured permittivity of the long bone for different age pigs [4]

**Figure 6.** The measured permittivity of the skull for different age pigs [4]

As reported on [4] the age related effects were more noted for some tissues types. Results of porcine study showed that at tissues: white matter, dura, fat, skin, skull and spinal cord the Recalling the study of Peyman at al . [13], based on discussions with numbers of vets, the studies on pig and human growth curves with markers along curves (e.g., sexual maturity etc.), a partial extrapolation of results to humans is reported.

The study concluded that it was more straightforward to correlate the end points, i.e., the piglets to be equivalent to very small children and mature pigs equivalent to adults, whereas the ages in between are more difficult to correlate.

The study reports : 10 kg pigs, which are less than 30 days old, are very young animals and far from puberty age; - it may be assumed that dielectric properties of these piglets correspond to those of human children of age between 1-4 years. The 50 kg pigs , which are about 100 days old , are not still fully matured in terms of sexual activity, and therefore are assumed to be equivalent to 11-13 years old human. Finally, at 250 kg, pigs are fully matured animals and are therefore considered equivalent to human adults.

The results obtained with extrapolation were then used to calculate the SAR values in children of age 3 and 7 years when they are exposed to microwave induced by walkie–talkie devices.

Even though a first steps were made to find a correlation between dielectric parameters of animal and human at different age, still there is no systematic scientific-based general correlation formula or extrapolation methodology that would propose the extrapolation of obtained results of animal dielectric parameters to humans.

## **3. Age-dependent dielectric parameters of human biological tissues derived with analytical formula**

The complex permittivity of any tissue, including here the biological tissues, the parameter that contains both: tissues relative permittivity and conductivity, is given by the formula:

$$\underline{\boldsymbol{\varepsilon}}\_{r} = \boldsymbol{\varepsilon}\_{r}^{\top} - \boldsymbol{j} \,\boldsymbol{\varepsilon}\_{r}^{\top} = \boldsymbol{\varepsilon}\_{r} - \boldsymbol{j} \,\frac{\boldsymbol{\sigma}}{\cos \varepsilon\_{0}}\tag{2}$$

where:

*j* 1


If on relation is added


$$
\pi = \frac{\varepsilon\_0}{\sigma} \varepsilon\_r \tag{3}
$$

By substituting the relaxation constant into the complex permittivity formula (2), the following expression is obtained:

$$\underline{\varepsilon}\_r = \varepsilon\_r \left( 1 - j \frac{1}{\alpha \tau} \right) \tag{4}$$

The plot of the relation between the imaginary and the real part of permittivity at frequency 900 MHz, for few aging rats biological tissues as: the brain, the muscle, the salivary gland, the skin and the skull, based on results presented on [8], confirms that ratio between the imaginary and real part of permittivity is almost constant for different biological tissues as described on [14].

Therefore, it may be concluded that the relaxation constant is almost independent from age and its value can be taken statistically as a mean derived from different ages.

Under the above mentioned assumption, either relative permittivity or conductivity of biological tissue has to be known and the other can be calculated using relation (3).

Referring to mathematical expression (4) the only parameter that may change with age is tissue relative permittivity *<sup>r</sup>* .

The dielectric parameters of tissue depend on tissue composition.

It is known that human biological tissues are dominantly constituted by water content, therefore if water content changes with age it is to be expected that dielectric parameters change with age as a result of TBW change, and this has to be put in a formula expressing the function of relative permittivity from age of tissue, respectively TBW, approach proposed by Wang at al. [14] on 2006.

**Figure 8.** Ratio between real and imaginary part of permittivity of biological tissues [14]

### **3.1. Empirical derivation of dielectric parameters of human tissues as a function of age**

The relative permittivity based on Leichtencker's logarithmic mixture law [15] for medium consisted from N composites may be expressed as:

$$\varepsilon = \prod\_{n=1}^{N} \varepsilon\_n^{\alpha} \tag{5}$$

*n* - relative permittivity of n composite

*<sup>n</sup>* - hydration rate of n composite

with sum of all α equal to one.

148 Microwave Materials Characterization

where:

*j* 1


following expression is obtained:

described on [14].

tissue relative permittivity *<sup>r</sup>*

.

The dielectric parameters of tissue depend on tissue composition.

**derived with analytical formula** 

**3. Age-dependent dielectric parameters of human biological tissues** 

' ''


 *j*

and its value can be taken statistically as a mean derived from different ages.

biological tissue has to be known and the other can be calculated using relation (3).

0 *r*

By substituting the relaxation constant into the complex permittivity formula (2), the

<sup>1</sup> <sup>1</sup> *<sup>r</sup> <sup>r</sup>*

The plot of the relation between the imaginary and the real part of permittivity at frequency 900 MHz, for few aging rats biological tissues as: the brain, the muscle, the salivary gland, the skin and the skull, based on results presented on [8], confirms that ratio between the imaginary and real part of permittivity is almost constant for different biological tissues as

Therefore, it may be concluded that the relaxation constant is almost independent from age

Under the above mentioned assumption, either relative permittivity or conductivity of

Referring to mathematical expression (4) the only parameter that may change with age is

It is known that human biological tissues are dominantly constituted by water content, therefore if water content changes with age it is to be expected that dielectric parameters change with age as a result of TBW change, and this has to be put in a formula expressing

 

*j j <sup>r</sup> r rr*

 

The complex permittivity of any tissue, including here the biological tissues, the parameter that contains both: tissues relative permittivity and conductivity, is given by the formula:

0

(2)

(3)

(4)

For medium consisted from two composites the relative permittivity is given as:

$$
\varepsilon = \varepsilon\_1^{\alpha\_{-\bullet}} \varepsilon\_2^{1-\alpha} \tag{6}
$$

As noted on [15] Leichtencker mixture formula is symmetric with respect to its constitutes thus:

$$\frac{\mathcal{E}}{\mathcal{E}\_2} = (\frac{\mathcal{E}\_1}{\mathcal{E}\_2})^{1-\alpha} \text{ can be written as } \frac{\mathcal{E}}{\mathcal{E}\_1} = (\frac{\mathcal{E}\_2}{\mathcal{E}\_1})^{\alpha} \tag{7}$$

Even though formula (6) served as a starting point to Wang et al. [14], 2006, it has been regarded for a long time as semi-empirical formula without theoretical justification. Recently, a 2010 study [16] has confirmed that formula (6) can be derived by applying Maxwell's equations and the principle of charge conservation to a mixture for which the spatial distribution of shapes and orientations of the components is randomly distributed.

According to Wang [14] the biological tissues may be considered as given by two composites: water and organ specific material, therefore the relative permittivity of human biological tissues may be given as:

$$
\varepsilon\_r = \varepsilon\_r^a{}\_w \cdot \varepsilon\_r^{1-a}{}\_{rt} \tag{8}
$$

*r w* - relative permittivity of water, *rt* - organ specific relative permittivity – tissue hydration rate.

The tissue hydration rate, as a function of TBW and mass density ρ, is expressed by the relation:

$$
\Box \alpha = \rho \cdot T \text{BW} \tag{9}
$$

Even though the other compounds, organ specific ones, vary with age, for simplification is considered that only hydration rate is age dependent.

The mass density is not considered as a function of age, therefore the only parameter that reflects change with age is TBW, while TBW variation with age has to be quantified in order to derive expression/formula that gives permittivity as a function of age.

Wang at al.[14] has proposed the fitting function for TBW which tends to fit values of TBW as a function of human age, values published by Altman and Dittmer on 1974 [17].

**Figure 9.** Fitting function for TBW [14]

After few mathematical operations the formula for calculating complex tissue permittivity is extracted, as a function of tissue hydration rate, adult tissue permittivity and adult tissue hydration rate:

The Age-Dependence of Microwave Dielectric Parameters of Biological Tissues 151

$$\frac{^{a-a}A}{^{1-a}A}\_{r\;\;r} \frac{1-a}{^{1-a}A}\_{\cdot\;\;r} \frac{1-a}{^{1-a}A}\_{A} \left(1-j\frac{1}{^{1-a}\tau}\right) \tag{10}$$


150 Microwave Materials Characterization

biological tissues may be given as:

– tissue hydration rate.


.

**Figure 9.** Fitting function for TBW [14]

hydration rate:

considered that only hydration rate is age dependent.


*r w* 

*rt* 

Maxwell's equations and the principle of charge conservation to a mixture for which the spatial distribution of shapes and orientations of the components is randomly distributed.

According to Wang [14] the biological tissues may be considered as given by two composites: water and organ specific material, therefore the relative permittivity of human

> *r rw rt*

The tissue hydration rate, as a function of TBW and mass density ρ, is expressed by the relation:

Even though the other compounds, organ specific ones, vary with age, for simplification is

The mass density is not considered as a function of age, therefore the only parameter that reflects change with age is TBW, while TBW variation with age has to be quantified in order

Wang at al.[14] has proposed the fitting function for TBW which tends to fit values of TBW

After few mathematical operations the formula for calculating complex tissue permittivity is extracted, as a function of tissue hydration rate, adult tissue permittivity and adult tissue

as a function of human age, values published by Altman and Dittmer on 1974 [17].

 

to derive expression/formula that gives permittivity as a function of age.

1

  (8)

*TBW* (9)

*<sup>A</sup>* - adult biological tissue hydration rate

*rA* - relative permittivity of adult biological tissue

Even though it is a very good approach on finding dielectric parameters of humans at different ages, the following remarks need to be raised up: Fitting function values deviate considerably from experimental measurements for some ages and according to figure the TBW varies at great extent under 3 years old but becomes insignificant for ages over 3 years old.

The very important aspect is the formula validation. Wang at al. [14] report validation of formula by checking validity using Peyman at al. [8] measured data for rats. The difference of results obtained with formula and measure data for rats were within 20% for all the tissues in the young rats, thus empirical formula proposed by Wang is therefore the reasonable representation of age-dependent tissue dielectric properties.

### **3.2. Dielectric parameters of 3 months-13 year's old boys biological tissues**

Wang et al. [14], as described on previous paragraph, derived an empirical formula for the calculation of age dependency of permittivity and conductivity of human biological tissues as a function of the total body water content (TBW), where TBW values were taken from Altman and Dittmer [17] measurements of year 1974.

As reported in [18], secular trends in the nutritional status of infants and children alter the relation between age or weight and TBW, thus equations proposed in previous decades overestimated TBW in all age groups, including children.

TBW at humans has changed from year 1974 and especially in children. There are lately revised formulas that give relation of TBW as a function of child height and weight.

Therefore, in [19] we propose the formulas for calculation of permittivity and conductivity of children biological tissues as a function of children weight and height, respectively age, whereas child TBW values are calculated with formula presented on [18].

Children biological tissues are composed mainly of water, thus for simplification reason they may be considered as given by two composites, water and organ specific tissue. Even though concentration of other compounds, organ specific ones, may also vary with age, for simplification purpose we assume that organ specific part is not age dependent, while main part of biological tissue TBW changes as a function of age.

For the child biological tissues, permittivity can be expressed as:

$$
\boldsymbol{\varepsilon}\_{r\,ch} = \boldsymbol{\varepsilon}\_{r\,ch}^{a\_{ch}} \cdot \boldsymbol{\varepsilon}\_{r\,0}^{1-a\_{ch}} \tag{11}
$$

#### *ch* - Child biological tissue hydration rate

Following mathematical operations, as described at Wang et al. [14], permittivity as a function of hydration rates, respectively child and adult TBW, can be formulated as:

$$
\varepsilon\_{rch} = \varepsilon\_{rw}^{\frac{a\_{ch} - a\_A}{1 - a\_A}} \cdot \varepsilon\_{rA}^{\frac{1 - a\_{ch}}{1 - a\_A}} \tag{12}
$$

Lately, the Mellits and Cheeks formula for the determination of child TBW has been reformulated. According to [18], child TBW in liters for age 3-month-old to 13-year-old boys can be expressed as:

$$TBW = 0.0846 \left(Height \cdot Weight \right)^{0.65} \tag{13}$$

For girls for age 3-month-old to 13-year-old the TBW is expressed as:

$$TBW = 0.0846 \, ^\circ 0.95 \left( \, Height \cdot Weight \right) \, ^\circ 0.65$$

When replacing TBW for boys on above equations and after few approximations we derived formulas (15) and (18) that were presented in [19].

In order to derive formulas we made some approximations. For tissues, we considered mass density 1,071 g/ml that might be taken as an average of mass density for most tissues, but not all of them. Some organs, such as lungs, do have mass density that differs significantly, up to 3 times, from the taken average value. For such tissues the proposed formula needs to be adopted.

In order to find approximate adult hydration rate, and take it as a constant in formula, we assume adult weight as 75 kg and TBW as 41.9 liters. Based on measurements conducted on [20], 41.9 liters corresponds to a man who is 20-29 years old.

For relative permittivity of water the value of 74.3 at 37 Celsius is taken [21].

Presented formulas express the relative permittivity of child biological tissue as a function of child height and weight and a function of an adult relative permittivity.

The formulas are considered valid if we refer other values of adult TBW and weight that do not reflect significant change of adult hydration rate.

$$
\mathfrak{s}\_{r\_{ch}}(X) = 2.616 \, ^{(X-6.63)} \ast \mathfrak{s}\_{r\_A} \, ^{2.4813(1-0.09X)}\tag{15}
$$

The variable X is introduced to simplify the formula in terms of its dependence on child height and weight:

The Age-Dependence of Microwave Dielectric Parameters of Biological Tissues 153

$$X = Height^{0.65} \* Weight^{-0.35} \tag{16}$$

Referring to relation (3) , the conductivity of tissue as function of relative permittivity may be expressed as:

$$
\sigma\_{ch}(X) = \frac{10^{-9}}{36\,\pi\,\pi} \varepsilon\_{r\_{ch}}(X) \tag{17}
$$

Replacing relation (15) on (17) the following relation for conductivity is obtained:

152 Microwave Materials Characterization

can be expressed as:

be adopted.

height and weight:

*ch* - Child biological tissue hydration rate

1 0 *c h c h*

 

1

 

> 

(11)

(12)

0.65 *TBW Height Weight* 0.0846 (13)

0.65 *TBW* 0.0846 \*0.95 *Height Weight* (14)

*rch rw r* 

Following mathematical operations, as described at Wang et al. [14], permittivity as a

1 1 *ch A c h A A*

 

*rch rw rA*

Lately, the Mellits and Cheeks formula for the determination of child TBW has been reformulated. According to [18], child TBW in liters for age 3-month-old to 13-year-old boys

When replacing TBW for boys on above equations and after few approximations we derived

In order to derive formulas we made some approximations. For tissues, we considered mass density 1,071 g/ml that might be taken as an average of mass density for most tissues, but not all of them. Some organs, such as lungs, do have mass density that differs significantly, up to 3 times, from the taken average value. For such tissues the proposed formula needs to

In order to find approximate adult hydration rate, and take it as a constant in formula, we assume adult weight as 75 kg and TBW as 41.9 liters. Based on measurements conducted on

Presented formulas express the relative permittivity of child biological tissue as a function of

The formulas are considered valid if we refer other values of adult TBW and weight that do

( 6.63) 2.4813(1 0.09 ) ( ) 2.616 \* *ch <sup>A</sup>*

The variable X is introduced to simplify the formula in terms of its dependence on child

 

*X X*

*r r <sup>X</sup>* (15)

 

function of hydration rates, respectively child and adult TBW, can be formulated as:

For girls for age 3-month-old to 13-year-old the TBW is expressed as:

formulas (15) and (18) that were presented in [19].

[20], 41.9 liters corresponds to a man who is 20-29 years old.

not reflect significant change of adult hydration rate.

For relative permittivity of water the value of 74.3 at 37 Celsius is taken [21].

child height and weight and a function of an adult relative permittivity.

$$
\sigma\_{ch}(\mathbf{X}) = \frac{10^{-9}}{36\,\pi\,\tau} \varepsilon\_{r\_{ch}}(\mathbf{X}) = 2.616^{\,(\text{X} - 6.63)} \ast\_{r\_A} \,\, ^{2.4813(1 - 0.09X)}\tag{18}
$$

With the formula (15) and (16) the values of permittivity of child bio tissues are calculated and presented in Figures 10-11.

Adult tissue relative permittivity values were taken from [5] while child height and weight were taken from World Health Organization growing charts, as 50th growing percentiles [22].

The advantage of the proposed approach is the calculation of dielectric parameters, conductivity and permittivity, for biological tissues of children of specific height and weight.

**Figure 10.** Children's relative permittivity at 900 MHz

The results are presented for brain, muscle and skin for children aged 1-10 years old, boys, for frequencies 900 MHz, 1800 MHz and 2.4 GHz.

From Figures 8-10, it can be easily extrapolated the difference between biological tissue dielectric parameters of end ages, 1-year-old and 10-year-old children, but it can be also made a comparative analysis between the permittivity of the same child age but different biological tissue.

Even though the values at different frequencies change, the similar variation trend of tissue permittivity as a function of age is noticed for all microwave frequencies

If we compare obtained permittivity values among different tissues, we notice that highest values are obtained for the muscle and the lowest ones for the skin.

It should be mentioned that height and weight were taken as 50th growing percentiles in relation age- (height and weight) while the methodology for extracting values for other growing percentiles remains unchanged.

**Figure 11.** Children's relative permittivity at 1800 MHz

**Figure 12.** Children's relative permittivity at 2400 MHz

After obtaining results for children biological tissues dielectric parameters, the comparison between obtained values and adult bio tissues dielectric parameters can be conducted.

In Figure 13 is presented only one example of comparative analysis, namely the differences on muscle permittivity for frequency 900 MHz.

**Figure 13.** Child vs. adult relative permittivity at 900 MHz

154 Microwave Materials Characterization

growing percentiles remains unchanged.

**Figure 11.** Children's relative permittivity at 1800 MHz

**Figure 12.** Children's relative permittivity at 2400 MHz

Even though the values at different frequencies change, the similar variation trend of tissue

If we compare obtained permittivity values among different tissues, we notice that highest

It should be mentioned that height and weight were taken as 50th growing percentiles in relation age- (height and weight) while the methodology for extracting values for other

After obtaining results for children biological tissues dielectric parameters, the comparison between obtained values and adult bio tissues dielectric parameters can be conducted.

permittivity as a function of age is noticed for all microwave frequencies

values are obtained for the muscle and the lowest ones for the skin.

It should be pointed out that all obtained values of children dielectric parameters are results of proposed theoretical approach which needs experimental validation; therefore the proposed formulas need experimental validation.

The aim of the study was to confirm age-dependence of dielectric parameters and to verify that child dielectric parameters differ from adults and they should not be taken as the same in the dosimetric research, as many research studies have done so far.

The knowledge of dielectric properties for humans at different age is important as well to create body-simulant materials that will be used for electromagnetic measurement applications. These materials should have dielectric properties that mimic those of human tissues [23].

The human body is composed by multilayered tissues, dielectric parameters of each of them vary with age, some more some less. For simplification purpose multilayered tissues can be simulated by one homogenous liquid whose dielectric properties match those of the tissue that is of most interest [24].

Beside comparative analysis between children and adult dielectric parameters of biological tissues, the very limited comparative analysis between child tissues permittivity obtained by different studies was conducted.

As noticed in the Figures 14-15, there is a good agreement between values obtained by different studies.

Nevertheless the comparative research should be more inclusive conducted for more tissue in order to come to exhaustive conclusions.

**Figure 14.** The child permittivity obtained by two studies


**Figure 15.** The 3-year old child permittivity obtained by three studies

### **4. Conclusions**

The confirmation of age-dependence of dielectric parameters of human biological tissues potentially may contribute on issue whether children should be considered a sensitive group in comparison to adults regarding exposure to microwave electromagnetic fields, issue that still remains debatable at scientific forums.

Experimental measurement *in vivo* at most human biological tissues is impossible, thus alternative methodologies have to be considered, few of them mentioned on this chapter.

Extrapolation of obtained experimental results of dielectric parameters of animal bio tissues to humans is considered debatable since animal tissues differ significantly from human tissues, and a detailed and all –inclusive study of animal and human growing curves along with markers along curves should be performed to propose correlation between animal and human dielectric parameters.

Thus, presenting the empiric formulas for estimating permittivity and conductivity of human biological tissues as a function of age is to be considered as a reasonable solution for the issue even though the each proposed theoretical approach needs experimental validation, which is very limited due to available measuring techniques.

Since biological tissues are dominantly composed of water content, their dielectric characterization is a function of TBW- a parameter that changes with age. This has triggered researchers to propose formulas for estimating permittivity and conductivity of human biological tissues as a function of age, respectively TBW.

The results presented in the chapter, with all covered methods, confirm that permittivity and conductivity of human tissues are age-dependent, presenting also change trend over age.

The limited comparative analysis shows a satisfactory agreement between results obtained with different approaches.

Nevertheless it should be pointed that results presented with theoretical approach are not experimentally validated, so they should be taken with reserve by the scientific community. As a matter of fact, the aim was to confirm the variation trend of permittivity and conductivity with age and not to present precise values of microwave dielectric parameters of human tissues for each human age.

Experimental validation of theoretical approaches for derivation of dielectric parameters of human tissues as a function of age, detailed comparative analysis of obtained results by different studies, assessment of difference between dielectric parameters of males and females at each age, are just a few of issues that remain open for further research.
