AP1201-0061

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Abstract—In-body localization implies identifying 3D positions

of thermometer pills, smart pills, and other autonomous small

objects within the human body. The use of far-field scanning

arrays operating at frequencies above 900 MHz is generally

prohibitive due to severe multipath caused by different electric

properties of body organs. On the other hand, the magnetic

properties of the body are constant. Therefore, the standard

method is that of (quasi) magnetostatics. An intermediate region

between the two extremes is the Fresnel region, which

approximately corresponds to the center frequency of 400MHz

and the wavelength of ~10cm within the body. In this study, we

describe the new concept of a directional receiving antenna array

intended for localization purposes within a human body in the

Fresnel region. The individual array element is composed of two

small orthogonal coils (magnetic dipoles). The coils are to be

acquired/driven in quadrature, for both CW and pulse signals.

The individual array element possesses a highly-directional

single-lobe beam into the body directed at 45 degrees from the

broadside. An array of such radiators makes it possible to

develop a simple yet effective localization algorithm within a

realistic body using direct RSS estimates for every individual

receiver.

Index Terms— Antenna arrays, Beam steering, Biomedical

communication, Biomedical electromagnetic imaging

I. INTRODUCTION

N-BODY localization implies identifying 3D positions of

thermometer pills, smart pills, and other autonomous small

objects within the human body. The use of far-field scanning

arrays operating at frequencies above 900 MHz is generally

prohibitive due to severe multipath caused by different

permittivities and electric conductivities of body organs, skin,

Manuscript received January 20, 2012.

S. N. Makarov is with the Department of Electrical and Computer

Engineering at Worcester Polytechnic Institute, Worcester, MA 01609 USA (phone: 508-831-5017; fax: 508-831-5491; e-mail: makarov@wpi.edu).

G. M. Noetscher is with the Department of Electrical and Computer

Engineering at Worcester Polytechnic Institute, Worcester, MA 01609 USA. He is also with the Natick Soldier Research, Development and Engineering

Center, Natick, MA 01760 USA (e-mail: gregn@wpi.edu).

L. C. Kempel is with the College of Engineering, Michigan State University, East Lansing, MI 48824 USA (e-mail: kempel@egr.msu.edu).

muscles, and fat. On the other hand, the permeability and the

magnetic loss tangent of the body are constant. Therefore, the

standard method is that of (quasi) magnetostatics where the

direction of the imposed 3D magnetic field is acquired by a

sensor, which results in encoding the sensor location.

Commercial magnetic surgical navigation systems include the

Medtronic Axiem, Northern Digital's Aurora, Ascension

Technology (Flock of birds, microBird), Biosense Webster,

Calypso, Polhemus, Praxim's Surgetics, GE Medical, etc. The

magnetostatic systems are bulky and hardly wearable; the

sensor must be cable- or battery-powered.

An intermediate region between the two extremes is the

Fresnel region, or the radiating near field, which

approximately corresponds to the center frequency of 400MHz

and the wavelength of ~10cm within the body. In this study,

we will describe the new concept of a directional receiving

antenna array intended for localization purposes of a small

radiating source within a human body in the Fresnel region.

A. Magnetic (electric) dipoles on the air-dielectric interface

in the quasi-static limit

In the quasi-static limit, an extensive study of magnetic

dipoles (electrically small loop/coil antennas) radiating into or

immersed within a lossy dielectric has been performed by J.

Wait and co-workers [1]-[4] and A. Baños [5]. The quasistatic

limit implies that the conduction current in a lossy medium

dominates the displacement current, i.e.

(1)

where is the medium conductivity, is the dielectric

constant, and is the angular frequency. No significant

directive properties of magnetic (and electric) dipoles

radiating close to an air-dielectric interface have been

established [5]. Average human body properties might be

characterized by 050,S/m5.0 . Eq. (1) is then satisfied

(assuming 10 ) only at frequencies below approximately

20MHz.

B. Magnetic (electric) dipoles on the air-dielectric interface

in the far field

Using a 2D spatial Fourier transform to solve Maxwell’s

Directional In-Quadrature Orthogonal-Coil

Antenna and an Array Thereof for Localization

Purposes within a Human Body in the Fresnel

Region. Numerical Simulations

Sergey N. Makarov, Senior Member, IEEE, Gregory M. Noetscher, Student Member, IEEE and Leo C.

Kempel, Fellow, IEEE

I

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equations, G. Smith [6] established radiation patterns for

horizontal magnetic(electric) dipoles at the air-dielectric

interface. He found that the horizontal dipoles may create

highly-directive patterns into a dielectric, with off-broadside

main lobes. This effect occurs when the dipole is close to the

interface and when the dielectric contrast of two media is

reasonably large ( 4/12 ). This effect is weakly influenced

by conductivity of the medium. Using a similar approach, W.

Lukosz and R. E. Kunz [7], [8] have derived analytical

radiation patterns for vertical magnetic(electric) dipoles, and

arrived at a similar conclusion. Electric dipole patterns were

investigated in [9] and [10] (including finite wire dipoles).

Results for finite (resonant) loops are given in [11] and [12].

Near-field electric-dipole radiation dynamics through Finite

Difference Time Domain (FDTD) modeling have been

quantified in [13].

C. Frequency band under study

We will consider wideband pulse propagation with a center

frequency of around 400 MHz, which is within the UHF band.

Thus, the pulse spectrum will include a band newly

established by the FCC Medical Device Radiocommunication

Service used for diagnostic and therapeutic purposes in

humans at 401-406 MHz. If average human body properties of

050,S/m5.0 are used, the fields within the human

body medium at 400 MHz do not exactly correspond to the far

field. Instead, the bulk of the body volume in any direction

belongs to the Fresnel region of operation (the radiating near

field). Nevertheless, some general facts established with the

help of the far-field models [6], [8], [12] will be quite helpful

in providing theoretical background of our model.

D. Model of orthogonal magnetic dipoles

In order to create a highly-directive one-lobe beam into the

body medium in the Fresnel region, we suggest using two

orthogonal magnetic dipoles (small coil antennas) with

coincident phase centers. The problem geometry is shown in

Fig. 1. The upper half-space is free space while the lower half-

space is a dielectric. Both dipoles have the same magnetic

moment, m; they are oriented as shown in Fig. 1.

II. PATTERN COMBINATION OF TWO ORTHOGONAL DIPOLES IN

THE FAR FIELD

A. CW radiation patterns in a lossless medium 2

With reference to Fig. 1, the radiated far-field electric-field

component 2E of the horizontal magnetic dipole in a lossless

medium has the form

r

nrjk

nhjk

nn

nnmkE

4

exp

sin1exp

sin1cos

sin1cossin2,

2

22

122

22

102

(2a)

Here, 12/ n is the relative refractive index, 2,12,1

/ ck , and

m is the magnetic dipole moment. Equation (2a) follows from

Eq. (24b) and Eq. (47d) of Ref. [6]. When 1n , it is reduced to

the isolated magnetic-dipole pattern in the lower half-space ( coscos ).

Similarly, the radiated far-field electric-field component

2E of the vertical magnetic dipole (the original Sommerfeld

asymptotic) has the form

r

nrjk

nhjk

nn

nnmkE

4

exp

sin1exp

sin1cos

cossin2,

2

22

122

102

(2b)

in a lossless medium. Equation (2b) follows from Eqs. (16a, d,

e) of Ref. [12]. When 1n , it is reduced to the isolated

vertical magnetic-dipole pattern in the lower halfspace ( coscos ).

B. Case 0,1 hn

In this particular and most interesting case, we restrict

ourselves to H-plane patterns ( 2/3,2/ ). In the H-plane,

which is the yz-plane in Fig. 1, we use the Cartesian field

component EysignE

x)( . Equations (2), which represent the

horizontal and vertical dipole moments of m, respectively, are

asymptotically reduced to

r

nrjk

jnmkjE

x

4

exp

sincos

2sin2

102

(3a)

r

nrjk

j

ysignnmkE

x

4

exp

sincos

2sin)(2

102

(3b)

The present asymptotic predicts that either dipole generates

two equal main lobes into the dielectric. Both lobes originate

from the function 2sin in Eqs. (3); they are centered at

90,45 and 270,45 , respectively. This result is

clearly expected for the vertical magnetic dipole, but is less

obvious for the horizontal magnetic dipole. It is explained by

the contribution of the evanescent spectrum of the isolated

antenna [6], [14]. The present asymptotic ignores a cusp

confined by critical angles, )/1arcsin( nc , for the horizontal

Fig. 1. Problem geometry and definition of the H-plane for two orthogonal

magnetic dipoles where the radiation patterns will be computed and

combined. ]2,0[],,0[ .

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magnetic dipole [6]. Such cusps will become visible in the

further study.

C. CW radiation patterns in a lossless medium 2

The key observation is that Eqs. (3a) and (3b) become

identical to within: (i) a phase factor of )2/exp( j

corresponding to a quadrature phase delay between two

dipoles of the quarter wave period, 1

T , in free space 1 and (ii)

a space factor, )( ysign . This space factor obviously indicates

that the two main lobes of the vertical dipole are out of phase.

Therefore, two orthogonal magnetic dipoles in quadrature

should produce a highly directional beam with only one main

lobe: either along 45 and 90 ( 0y ) or along 45

and 270 ( 0y ), while exactly cancelling out the other

lobe. This concept is shown in Fig. 2 where the radiation

pattern into lower half space is depicted. The dashed curve is

the normalized linear pattern, xEE

22

, of either (horizontal

or vertical) dipole from Eqs. (3). The solid curve is the pattern

combination from Eqs. (3) when the horizontal dipole has a

time delay, 4/Ttt . Equations (3) predict a perfect

cancellation of one lobe and a creation of a highly-directive

beam into the dielectric at 45 degrees from broadside. In order

to re-direct the main beam into the third quadrant, either the

horizontal dipole should be subject to a negative time delay

4/Ttt or the vertical dipole should obey a positive time

delay, 4/Ttt .

III. PATTERN COMBINATION OF TWO ORTHOGONAL DIPOLES IN

THE FRESNEL REGION

A. Wideband pulse signal

We intend to show that the theoretical prediction of the

previous sections also holds in a Fresnel zone within a (highly

lossy) human body for wideband pulses with the center

frequency of 400 MHz. In this and following sections, a

bipolar Gaussian (Rayleigh) excitation current pulse is used

for a TX antenna in the form

A1,5,)2(

)(exp

)()(

002

2

00

0

It

ttttIti

(4a)

Its center frequency and a 3dB-power bandwidth are given by

16.0

cf (4b)

cf15.1BW (4c)

We employ 460MHzBWMHz,400ns4.0 c

f in

all examples given in the following text. Other pulse forms

have been checked with similar results. The in-quadrature CW

condition may be transformed to the pulse delay of 2 to

achieve the proper phase synchronization for two pulses. This

pulse delay is within 10% of the expected time delay of one

quarter wave period for a CW signal with frequency, c

f .

B. Numerical simulations and their results

Numerical simulations are carried out using the standard 3D

FDTD method (cubic Yee cells with cell size, D, of 5mm or

2.5mm) for antennas just above a dielectric brick with the

average properties of the human body given as

050,S/m5.0 . An accurate source model with

coincident phase centers has been employed [15]-[17]. Three

examples (individual horizontal TX magnetic dipole,

individual vertical TX magnetic dipole, orthogonal-coil

radiator) have been considered with parameters from Table 1.

The corresponding geometry including the H-field probes is

shown in Fig. 3. Figure 4 shows the snapshots of the radiated

electric field, xE . To the right, sampled magnetic fields at

probe locations are plotted. Figure 4 demonstrates that the

beamforming effect clearly takes place.

Table 2 quantifies the beamforming effect from Fig. 4. The

table is obtained on the base of three examples reported above.

The array of two orthogonal coils with the time delay

performs almost ideal signal addition in the desired direction

(0.73A/m versus the ideal result of 0.8A/m). The signal in the

undesired direction is about 18 dB weaker than the main

signal (powerwise). Similar results have been observed for

harmonic excitation. Table 2 may be rewritten in terms of the

radiating E-field, xE , too.

Fig. 2. Normalized dipole radiation patterns into the lower half-space. The

dashed curve is the normalized linear pattern, 2E , of either (horizontal or

vertical) dipole from Eqs. (3). The solid curve is the pattern combination

from Eqs. (3) when the horizontal dipole has a time delay, 4/Ttt .

Arrows indicate magnetic field directions.

Fig. 3. Geometry assembly for individual coils and for the orthogonal-coil

quadrupole antenna

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IV. CONCEPT OF A RECEIVING ARRAY OF WIDEBAND

ORTHOGONAL-COIL ANTENNAS ON A HUMAN BODY SURFACE

A. Array concept – RSS array

The concept of a scanning receiving array utilizes pattern

reciprocity; it is shown in Fig. 5. The dark circle represents a

transmitting antenna within the body (e.g., a “smart pill”).

With a positive set of time delays, the maximum RSS will be

received by antenna #3. If a negative set of time delays is

used, the maximum RSS signal will be received by antenna

#1. A simple triangulation allows us to find the TX target

location in the yz-plane. A similar concept applies to 2D

scanning.

The array in Fig. 5 is not the phased far-field array in the

classical sense: we do not really combine the received voltages

from individual radiators with different phase shifts. Instead,

we estimate the RSS for every individual radiator and make a

decision based on this data. This circumstance might enable a

great stability of results with respect to significant random

variations of the human-body dielectric medium. The

operating volume of the array is restricted to the Fresnel

region; it is on the order of the array size. Large circles in Fig.

5 represent a “safe” detection region (region 1) whereas the

small circles correspond to a “conditional” detection (region

2). Probes are located 100mm below the surface of the

dielectric region (i.e.,

100mmz ).

B. Proof of array concept using numerical simulations for a

body phantom

Emphasize that, irrespective of a possible rotation of any

two-coil combination in Fig. 5 about its axis of symmetry, the

main beam will always be directed at 45 degrees from the

vertical axis into the dielectric material. This remarkable

property follows from the expansion of any quadrupole into

two axes-aligned dipoles; it was verified numerically.

Figure 6 shows how the four-element array from Fig. 5 is

applied to a localization problem within a human body

phantom. A custom torso phantom manufactured by The

Phantom Laboratory, NY was scanned using a Model WB4

TABLE I PARAMETERS FOR THREE ANTENNAS USED FOR NUMERICAL VALIDATION OF

THE BEAMFORMING EFFECT

Excitation Port Receiver/probe ports

One TX coil (+D/2 offset from the

interface) located parallel to the dielectric/air interface and oriented

along the y-axis, with the magnetic

moment 23m10

per one ampere

Two field probes (copolar H-field

sampling) within the dielectric at the distances 100mm and

mm1002 from the radiator, respectively.

One TX coil (+D/2 offset from the

interface) located perpendicular to the dielectric/air interface and

oriented along the z-axis, with the

magnetic moment 23m10

per one

ampere

Two field probes (copolar H-field

sampling) within the dielectric at the distances 100mm and

mm1002 from the radiator,

respectively.

Two TX coils (+D/2 offset from the

interface) located parallel and

perpendicular to the dielectric/air interface, with the same magnetic

moment 23m10

per one ampere

Two field probes (copolar H-field

sampling) within the dielectric at

the distance mm1002 from the

radiator (45 degrees offset),

respectively.

Fig. 4. Field snapshots (electric field) at 5ns and sampled magnetic fields at

probe locations

TABLE II

MAXIMUM SIGNAL STRENGTH WITHIN THE DIELECTRIC (ABSOLUTE VALUES)

Configuration Magnitude of Magnetic Field (A/m)

y = -100 mm y = 100 mm

Horizontal coil alone 0.40 0.40

Vertical coil alone 0.40 0.40 Array of two coils with delay 0.09 0.73 0.73

Fig. 5. A 1D scanning array of orthogonal-coil antennas. The output signal

of every receiver is the in-quadrature combination of two coil signals. A 1D

array enables 2D localization in the yz-plane.

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whole body color scanner manufactured by Cyberware, Inc.,

CA. A transmitting coil antenna to be localized is located

inside the body, at a 100mm normal distance from the back –

see Fig. 6a. Its position corresponds to a movement through

the oesophagus. Received open-circuit voltages are recorded

for every orthogonal-coil receiver. The receiver separation

distance is 80mm. The Rayleigh pulse described by Eqs. (4) is

used.

In Fig. 6a, the homogeneous phantom medium with

050,S/m5.0 was used for the simulations. In Fig. 6b,

an artificial composition of generic human body organs within

the phantom has been created using appropriately scaled and

positioned organs and bones (over 47 individual manifolds).

The dielectric properties of organs at 400MHz have been

acquired from [19], [20]. Furthermore, using a Constructive

Volume Geometry (CVG) algorithm, we created two layers of

uniform normal thickness on the body surface: a 2mm thick

skin layer ( 047,S/m7.0 ), and a 6mm thick fat layer (

012,S/m1.0 ).

To the right of Fig. 6a and Fig. 6b, the received voltages for

every orthogonal-coil antenna are given, after direct or reverse

in-quadrature combination, respectively. Note that every coil

pair is rotated by 45 degrees in Fig.6. According to Fig. 6, the

array operates as expected for either phantom: the positive set

of time delays gives the maximum RSS at antenna #3 of the

array whereas the negative set of time delays gives the

maximum RSS at antenna #1. This is exactly the scheme of

Fig. 5.

Note that the array functions despite a rather sophisticated

environment in Fig. 6b. This is a critical observation from the

viewpoint of practical applications. Table 3 gives the L2-norm

for every received pulse in both cases. The multipath effect

decreases the pulse strength at antenna #1 for the negative set

of time delays as compared to the homogeneous solution.

C. Superior performance of the orthogonal-coil array

compared to an ordinary array

Figure 7 replaces the array of orthogonal-coil antennas in

Fig. 6 by an array of ordinary coil antennas (conventional

magnetic dipoles) with the same polarization as the original

source. All other problem parameters remain the same. One

can see that the RSS test barely points toward the closest array

element (#2) given the complicated body shape and

composition. Thus, the orthogonal-coil array quite

significantly outperforms the ordinary receiving array.

V. DISCUSSION AND CONCLUSIONS

We described and justified, both theoretically and

numerically, the new concept of a small directional receiving

antenna array intended for localization purposes within a

human body in the Fresnel region. The array element is

composed of two small orthogonal coils (magnetic dipoles).

These coils are to be driven/acquired in quadrature, for both

CW and pulse signals. An array of such radiators makes it

possible to develop a simple yet effective localization

algorithm within the body using RSS (Received Signal

Strength) estimates for every individual radiator.

The observed array performance in a complicated dielectric

environment is explained as follows. To a certain degree, the

array still utilizes near-field behavior of magnetic antennas,

which is weakly affected by variable dielectric properties. On

the other hand, every individual orthogonal-coil antenna forms

a directional beam already in the Fresnel region, which

significantly improves RSS estimates as compared to ordinary

coil antennas (magnetic dipoles). Numerical simulations have

shown that the directional beam is formed at distances greater

than quarter wavelength in the body (~2.5cm at 400MHz)

from the orthogonal-coil radiator.

Fig. 6. Left – RX array of orthogonal-coil antennas; right – received open-

circuit voltages. The in-body TX coil has the magnetic moment ×25

Am10

;

array coils have the moment ×24

Am10

.

TABLE III

L2-NORM FOR EVERY RECEIVED PULSE IN FIG. 6

Phase Body Type

L2-norm (V2×ns)

Receiver #1

Receiver #2

Receiver #3

Receiver #4

Positive Homogeneous 6.9×10-5 2.2×10-4 7.8×10-4 2.7×10-5

Negative Homogeneous 8.6×10-4 1.4×10-4 8.7×10-5 2.7×10-6

Positive Inhomogeneous 2.6×10-5 1.4×10-4 8.0×10-4 5.1×10-5 Negative Inhomogeneous 2.0×10-4 2.3×10-5 7.1×10-5 3.1×10-6 0.73

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ACKNOWLEDGMENT

The authors would like to thank Dr. Bryan McLaughlin of

Draper Laboratory, MA for useful discussion and opinions on

this subject.

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Fig. 7. Left – RX array of orthogonal-coil antennas; right – received open-

circuit voltages. The in-body TX coil has the magnetic moment ×25

Am10

;

array coils have the moment ×24

Am10

.