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MODELING OF PROPAGATION LOSSES FOR HUMAN BEING BEHIND A BRICK WALL

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MODELING OF PROPAGATION

LOSSES FOR HUMAN BEING BEHIND

A BRICK WALL

KEDAR NATH SAHU

Professor, Department of Electronics and Communication Engineering Stanley College of Engineering and Technology for Women, Hyderabad, India

knsahu72@gmail.com DR.C. DHANUNJAYA NAIDU

Principal

VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, India cdnaidu@yahoo.com

DR.M. SATYAM

Professor, Department of Electronics and Communication Engineering Vasavi College of Engineering, Hyderabad, India

satyam_mandavilli@yahoo.com DR.K. JAYA SANKAR

Professor and Head, Department of Electronics and Communication Engineering Vasavi College of Engineering, Hyderabad, India

kottareddyjs@gmail.com

Abstract:

In this paper, ultra-wideband propagation modeling and analysis of a human being behind a brick wall is presented. First, the propagation modeling of a brick wall and the propagation losses predicted by this model are obtained. Then, the modeling of a human being behind a brick wall is developed. The reflection coefficient, transmission coefficient and signal attenuation for such a through-the-wall (TTW) propagation are computed from the composite model consisting of a brick wall and a human being behind it using the method of impedance transformation. The variation of heart dimension with respect to time during a cardiac cycle is incorporated and the performance of the cardiac activity is studied from the change of signal attenuation. This estimation will enable in the design of an ultra wideband through-the wall radar which can be used as a non-invasive diagnostic system.

Keywords: brick; dielectric properties; through-the-wall (TTW); ultra-wideband; signal attenuation.

1. Introduction

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frequencies ranging over L- and S-bands are recommended for better penetration into a wall [9], the modeling and analysis is carried out over the ultra-wideband of 1 to 5 GHz.

2. The Impedance Transformation Method for Multilayer Multi-interface Models

Considering that a plane wave is incident normally on the interface between medium-1 and medium-2 (i.e. normal incidence of a plane wave) then it becomes interesting to compute the reflected, transmitted components of the wave energy. This problem can be analyzed using the analytical technique known as the impedance transformation method as described in [6]. The underlying principle of dealing with multiple interfaces in layered models is identical to that in case of the impedance matching of transmission lines. In this method, every layer is considered as a transmission line equivalent and the complete layered medium is considered as a cascaded transmission line. Considering the three-interface four layered configuration [Fig.1], medium-1 is analogous to a transmission line of characteristic impedance z1 and is terminated at the load i.e. medium-4 by

means of transmission lines viz. medium-2 and medium-3 of characteristic impedance z2 and z3.respectively.

The wave equations are identical to transmission line equations and the electromagnetic boundary conditions here are equivalent to those for the continuity of voltage and current at a line termination.

In this method, the effective input impedance as seen from the transmission line to the load is calculated.

The input impedance is calculated at interface-1 whereas the input impedance at interface-3 is equal to the impedance seen at this interface towards medium-4 and is equal to the intrinsic impedance of medium-4. The effective input impedance at all interfaces as obtained in [6] are mentioned below.

At interface-3, the effective input impedance, (1)

At interface-2, the effective input impedance, (2)

At interface-1, the effective input impedance, (3)

and the effective reflection coefficient,

1 1 , 1 1 ,

η

η

η

η

+

=

Γ

in in

eff (4)

Reflected power coefficient in layer-1 = (5)

Transmitted power coefficient in layer-4 = (6)

Fig. 1. Three-interface, four-layer configuration.

3 3 3 , 3 3 3 3 3 , 3 2 ,

tan

tan

l

j

l

j

in in

in

η

η

β

β

η

η

η

η

+

+

=

2 2 2 , 2 2 2 2 2 , 2 1 ,

tan

tan

l

j

l

j

in in

in

η

η

β

β

η

η

η

η

+

+

=

2

1

Γ

eff

4 3

,

η

η

in

=

2

eff

(3)

2.1. Dielectric Properties of Brick

In this paper, brick is modeled as a simple dielectric material having an effective permittivity,

ε

constant and equal to 5-j0.45 over the entire frequency range from 1 to 5 GHz as obtained from the empirical measurements carried out at Office National d’Etudes et de Recherches Aerospatiales (ONERA), a French aerospace research agency and a public scientific and technical establishment with both industrial and commercial responsibilities. Using this permittivity value the attenuation constant, phase-shift constant and

Fig.2. Variation of (a) attenuation constant vs. phase-shift constant (b) conductivity of brick with frequency.

conductivity are calculated and their variations are plotted as a function of frequency as shown in Fig.2. It is seen that as frequency increases, these quantities increase almost linearly. In general, wall transmission coefficient depends much more on conductivity than on permittivity [2].

2.2. Brick Wall Modeling and Propagation Results

RF attenuation analysis is carried out for a 20 cm thick brick wall. As brick is a lossy medium from an electromagnetic point of view, it is characterized in terms of the frequency dependent propagation parameters and is modeled as a two-interface three layered composite medium [Fig.3] for the determination of propagation losses using the impedance transformation technique. Assuming normal incidence of a plane wave on 1 (air-brick interface), the input impedance is calculated at 1 whereas the input impedance at interface-2 (brick-air interface) is equal to the input seen at this interface towards medium-3 and is equal to the intrinsic impedance of medium-3 (i.e. air).

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(a) (b)

Fig.4. Propagation behavior of brick wall (a) transmission (b) reflection

It is obtained that the transmission coefficient decreases from -2 dB to -10 dB and thus shows a transmission loss of about 8 dB [Fig.4(a)]. This implies that the wall attenuation is lesser at lower values of frequency. The frequency dependent reflection coefficient is shown in Fig.4(b) and the average reflection coefficient is around -4.24 dB over the entire band of frequencies. The impedance transformation approach was then used for study of through-the-wall (TTW) RF propagation of human being behind a brick wall as discussed below.

3. The Planar Model of TTW Propagation for Human Being behind a Brick Wall

In order to evaluate the propagation characteristics for varied heart dimensions the time dependence of heart motion was studied and described in the following section with a brief description about the constitution of human heart.

3.1. Structure of Human Heart

This is a muscular structure located between the lungs and behind the sternum; two-third of which is located to the left of the midline of the body and the rest is placed to the right. According to the medical illustrations, right and left correspond to the person’s right and left assuming that the person is looking at us.

The transverse cross-sectional view of heart structure as shown in Fig.5 consists of left ventricle wall, left ventricle cavity, inter ventricular septum, right ventricle cavity and right ventricle wall. The ventricles (LV and RV) are the longer cavities in the human heart and the left ventricle has thicker wall than the right ventricle.

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3.1.1. Diastole and Systole in a Cardiac Cycle

A cardiac cycle comprises of contraction and relaxation, both followed by each other in a concerted pattern known as the cardiac cycle. One cardiac cycle consists of one complete diastole and one complete systole. Diastole is the phase of the cardiac cycle during which the chambers of the heart relax and the ventricles dilate allowing the blood to flow in. Systole is the phase of the cardiac cycle during which the ventricles contract pumping the blood into the aorta and pulmonary artery. At the start of the diastole, the heart muscle is relaxed and blood flows into the atria. At the end of diastole both atria contract simultaneously and this helps to fill the ventricles with blood immediately prior to the systole. One cardiac cycle is completed in 0.8 second (i.e. in less than 1 second). Systole is one complete contraction phase and diastole is one complete relaxation phase of the same cardiac cycle.

3.1.2. Variation of Heart Dimension in a Cardiac Cycle

The heart and its performance are commonly measured in terms of one-dimensional distances. The left ventricle end diastole (LVED) is the length measured at the end of diastole (i.e. when heart is fully relaxed) and normally corresponds to the largest cardiac dimension. Similarly, the left ventricle end systole (LVES) is the length measured at the end of systole (i.e. when heart is fully contracted) and corresponds to the smallest cardiac dimension. Ventricular cavity, inter ventricular septum, ventricular free wall thickness and their changes with respect to time during the cardiac cycle have been measured using various methods such as echocardiography, angiography, cine MRI etc. The time of dimensions and the rate of changes in wall thickness, cavity area and transverse dimension during isovolumic relaxation (end-diastole) and contraction (end-systole) for normal human subjects are estimated and reported in [5]. Results of the normal diameters of the cardiac cavities and ventricular, inter ventricular wall thickness values as reported in literature are mentioned as below.

The end-diastolic LV cavity wall thickness is 0.9+/-0.2cm which is almost close to the value 0.8+/-0.2 cm as reported in [12] increasing to 2.0+/-0.5 at end systole [5].The LVED cavity diameter, 4.9+/-0.4 cm [5] is close to 50 mm [12]. At end-systole the LV cavity gets a reduction of 2.2+/-0.4 cm [5] and thus the cavity diameter becomes about 2.7cm. This value is in the normal range 2.78 to 5.4 cm as reported in [7]. The thickness value of inter ventricular septum is 8.3mm which satisfies the normal range of 7 to 11 mm and is in consistent with 10.3+/-0.5 mm as reported in [8]. The RV cavity diameter at end of diastole is 37.1+/-5.9mm i.e. 3.7 cm+/-0.59 cm and at end of systole is equal to 2.8 cm as mentioned in the web [http://www.ncbi.nlm.nih.gov/pubmed (as downloaded on January 2010)] and its adjacent wall (the posterior wall) thickness at end diastole is 0.8+/-0.2 cm as found in [12] which is close to the value 10.2+/-0.5 reported in [8] and corresponding end systolic value of this is 1.3+/- 0.2 cm as given in [12]. So far as the rate of change of dimension (dD/dt) is concerned, the peak systolic dD/dt is 13+/-5 cm/s and the peak diastolic dD/dt is 16+/-4 cm/s as mentioned in [5]. The total thickness of heart at end of diastole, end of systole and during the interval from end of diastole to end of systole is the sum of the instantaneous thickness values of left ventricle wall (anterior wall), left ventricle (LV) cavity, septum thickness, right ventricle (RV) cavity, and the right ventricle wall (posterior wall). Based on the facts about the changes of cavity dimension, wall thickness with time as well as their peak rates of change as discussed above, the total heart size (in millimeter) during systole and diastole are chosen over one complete cardiac cycle of 0.8s as shown in Table 1and are used in the propagation model as discussed in section 3.2.

Table 1. Instantaneous dimensions of human heart.

Time (s) Heart size (mm)

Heart activity

0 111.4 End-diastole and start of systole 0.1 103.7

SYSTOLE 0.2 102.3

0.3 100.4 End-systole and start of diastole 0.4 102.8

DIASTOLE 0.5 106.3

0.6 107.8 0.7 108.8

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3.2 The Planar Multilayered Model of Human Thorax

The propagation analysis is done by including significant tissues right from chest skin surface (anterior side) up to the skin surface of human back (posterior side) through the heart as shown in Fig.7.The Visible Human Project based anatomical thickness values of the tissue layers as used in [10-11] are considered for this model. The thickness of dry skin as 1.5 mm, average infiltrated fat as 9.6 mm, muscle as 13.5 mm, cartilage of 11.6 mm, deflated lung of 5.78 mm and different heart thickness values corresponding to different instants of time of the cardiac cycle have been considered. From the dispersive behavior of human tissues given in Gabriel’s data book of dielectric properties of tissues [4] and also reported on the Web [http://niremf.ifac.cnr.it/tissprop] it is seen that the relative permittivity decreases, but conductivity, attenuation constant, phase-shift constant, wave velocity and magnitude of intrinsic impedance increase with increase in frequency.

Fig.7.Tissue structure for EM modeling of human thorax

Then, a composite model consisting of a human being behind a brick wall was developed as shown in Fig.8 considering a distance of one meter between the brick wall and the position of the human subject. The equivalent multilayered model is shown in Fig.9 (a) and (b) for forward and backward propagation of the plane wave respectively.

Fig.6.Variation of end-diastolic and end-systolic transverse dimension of normal human heart.

SKIN FAT

MUSCLE CARTILAGE LUNG (Deflated, Inflated)

HEART

CARTILAGE

MUSCLE FAT SKIN

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Fig.9. Composite multilayered model of human being behind a brick wall (a) forward propagation (b) backward propagation

4. Modeling Results and Discussion

In this section, the transmitted and reflected electric field magnitudes computed in the frequency domain from 1 to 5 GHz using MATLAB are presented. Considering the completely relaxed state of heart at the end of diastole, the variation of magnitude of reflection coefficient with frequency is plotted and shown in Fig. 10(a). It is observed that the average reflection coefficient is as close as -2.5 dB (approx.) over the whole band of frequencies. This means that more than half of the incident electromagnetic power is reflected back and the remaining is transmitted through the human body. Moreover the reflected pulse amplitudes show an inversion with respect to the incident pulses caused by a negative value of the reflection coefficient. This is due to the lower value of the impedance of the human body with respect to the free space impedance. Similarly, the transmission coefficient values shown in Fig. 10(b) have almost an increasing trend.

Fig.10. Through-the- brick wall propagation behavior at the end of diastole (a) Reflection (b) Transmission

Depending on the wavelength and frequency when the heart is in its active state the points of maximum and minimum attenuation shift. This can be attributed to the variation in the attenuation constant because of dimensional changes with respect to wavelength. At 1 GHz, the minimum attenuation occurs at heart dimension equal to 106.3 mm corresponding to 0.5 seconds and maximum attenuation takes place at 111.4 mm at the end of diastole as depicted in Fig.11 (a). This similar behavior is also observed at other frequencies e.g. 2 GHz, 3 GHz, 3.5 GHz etc. as shown in Fig.11(b), (c) and (d) respectively. Also it is observed that the amount of attenuation reduces when the heart motion changes from maximum diastole (111.4 mm) to systolic mode. This is due to the reduced propagation path as heart dimension reduces during systole (contraction). Then, the attenuation again starts to increase when the heart motion enters into a diastolic form (dilation).

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Fig.11.Variation of signal attenuation with time at (a) 1 GHz (b) 2 GHz (c) 3 GHz (d) 3.5 GHz respectively.

This model predicted attenuation is obtained separately for every instantaneously changing dimensions of heart during the cardiac cycle. It is found that there is a maximum and a minimum value of attenuation corresponding to every frequency. The 5- point moving average regression line plots representing the variations of maximum and minimum signal attenuation over all frequencies from 1 to 5 GHz are shown in Fig.12 (a) and (b) respectively.

Fig.12. Variations of (a) maximum and (b) minimum signal attenuation with frequency (5- point moving average regression lines)

(a) (b)

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Thus, there is periodic variation in attenuation of an active heart at a given frequency. The periodicity of attenuation characteristics (period between maximum attenuation or minimum attenuation) refers to the heartbeat period. Knowing the period of maximum attenuation or minimum attenuation one will be able to decide the health of the heart. Lack of periodicity might indicate the problem of an unhealthy heart. This attenuation measurement can be carried out on persons in cases when they are not accessible for other methods using stethoscope, electrocardiograph (ECG) etc.

5. Conclusions

Electromagnetic response of the human tissue is highly frequency dependent. Of all body tissues that encounter in the path of propagation, heart is the only moving element that can have a noticeable displacement and all others are static. Therefore, in the wake of the study of propagation characteristics i.e. signal attenuation and reflection coefficient, we focused computation of these parameters with changing dimensions of heart during a complete cardiac cycle. Then, the change of attenuation and reflection coefficient corresponding to the change of heart size during relaxation-contraction-relaxation (one cardiac cycle) at different instants of time during the cardiac period was studied. This can provide good information about the state of a person’s heart whether healthy or unhealthy. Any noticeable change of attenuation shall indicate that the person is live while no change of attenuation found in this way might lead to an unusual guess that the person might be dead.

In this paper, we have presented a simple one-dimensional electromagnetic model of human being behind a brick wall incorporating the electromagnetic properties of significant body tissues beyond heart over an ultra-wideband of frequencies ranging from 1 to 5 GHz. Moreover, the analysis is performed for changes with time of heart dimension, not for a fixed heart dimension as in earlier thoracic models found in the literature. A study of variation of signal attenuation due to instantaneous change of heart dimensions during cardiac cycle can provide reliable information about the health of heart. This feature of change of signal attenuation may also be used to study the performance of cardiac activity of persons buried under the rubbles of the debris of a collapsed building by including various types of building construction materials in a model.

References

[1] Cavagnaro, M., Pittella, E., and Pisa, S. (2013): UWB pulse propagation into human tissues. Physics in Medicine and Biology, 58, pp.8689-8707

[2] Cuinas I, et al. (2001): Frequency dependence of dielectric constant of construction materials in microwave and millimeter-wave bands. Microwave and Optical Technology Lett., vol.30, No.2, pp.123-124.

[3] Cuinas, I. and Sanchez, M.G. (2002): Permittivity and conductivity measurements of building materials at 5.8 GHz and 41.5 GHz. Wireless and Personal Communications, No.20, pp.93-100.

[4] Gabriel, C., (1996):Compilation of the dielectric properties of body tissues at RF and microwave frequencies. Report N.AL/OE-TR-1996-0037, Occupational and environmental health directorate, Radio frequency radiation division, Brooks Air Force Base, Texas, USA.

[5] Gibson, D. G., Traill, T.A., and Brown, D. J. (1977). Changes in left ventricular free wall thickness in patients with ischaemic heart disease. British Heart Journal, 39, 1312-1318

[6] Hayt, W. H. and Buck, J. A. (2006). Engineering Electromagnetics. (7th ed.). India: Tata McGraw-Hill.

[7] Hudsmith Lucy E., et al. (2005): Normal human left and right ventricular and left atrial dimension using steady state free precession magnetic resonance imaging”, J. Cardiovasc. Mag. Reso, vol.7, pp.775-782.

[8] Kaul Sanjiv, et al. (1986): Measurement of normal left heart dimensions using optimally oriented MR images. American Roentgen Ray Society, AJR 146:75-79

[9] Muqaibel, et al. (2005): Ultra wideband through-the-wall propagation”, in Proc. Inst. Elect. Eng.-Microw., Antennas, Propag., vol.152, pp.581-588.

[10] Sahu, K. N., Naidu, C. D., and Jaya Sankar, K.( 2014):“Frequency dependent planar electromagnetic modeling of human body and theoretical study on attenuation for budget estimation of UWB radar”, Global J. of Res. in Engg.: F, Vol.14, No.3, Version 1.0, pp. 35-44.

[11] Staderini, E. M., (2002): UWB radars in medicine.IEEE Aerospace and Electronic System Magazine, Vol.17, No.1, pp. 13-18. [12] Traill, T.A., Gibson, D. G., and Brown, D. J. (1978). Study of left ventricular wall thickness and dimension changes using

echocardiography. British Heart Journal, 40, 162-169.

Figure

Fig. 1.  Three-interface, four-layer configuration.

References

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