Research ArticleBreast Cancer Nodes Detection Using Ultrasonic MicroscaleSubarrayed MIMO RADAR

Attaphongse Taparugssanagorn1 Siwaruk Siwamogsatham1 and Carlos Pomalaza-Raacuteez2

1 Wireless Information Security and Eco-Electronics Research Unit National Electronics and Computer Technology Center112 Phahon Yothin Road Klong 1 Klong Luang PathumThani 12120 Thailand

2 College of Engineering Technology and Computer Science Department of Engineering Purdue UniversityFort Wayne IN 46805 USA

Correspondence should be addressed to Attaphongse Taparugssanagorn attaphongsetaparugssanagornnectecorth

Received 28 May 2014 Revised 3 September 2014 Accepted 4 September 2014 Published 15 September 2014

Academic Editor Alexander Zelikovsky

Copyright copy 2014 Attaphongse Taparugssanagorn et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

This paper proposes the use of ultrasonic microscale subarrayed MIMO RADARs to estimate the position of breast cancer nodesThe transmit and receive antenna arrays are divided into subarrays In order to increase the signal diversity each subarray is assigneda different waveform from an orthogonal set High-frequency ultrasonic transducers are used since a breast is considered to bea superficial structure Closed form expressions for the optimal Neyman-Pearson detector are derived The combination of thewaveform diversity present in the subarrayed deployment and traditional phased-array RADAR techniques provides promisingresults

1 Introduction

Breast cancer is the most common cancer among women inmany countries in the world Early detection of this type ofcancer increases the likelihood of a successful treatment X-Ray mammography is considered the most effective imagingtechnology to detect early-stage breast cancer [1] In spiteof its wide use mammography does not provide accurateresults On average 20 of false-negative results occur whenmammograms appear normal even though cancer is presentThese results are due mainly to high breast density [2]When mammograms are used over a period of time forexample once a year for ten years the percentage of havinga false-positive result can be as high as 50 When a false-positive result occurs additional tests are needed for examplea biopsy to determine whether a cancer is present False-positive results can also lead to anxiety and other formsof psychological distress in the affected women [3] As analternative technology microwave imaging has been pro-posed since at microwave frequencies there is a significantdifference in the dielectric properties of normal and malig-nant breast tissue [4ndash6] Furthermore the attenuation of

microwave signals in a normal breast tissue is low enough tofacilitate their propagation through even a large breast vol-ume Microwave technology provides high contrast but itlacks potential for high spatial resolution Electromagneticwaves at lower frequencies thanmicrowaves suffer from poorpropagation within body tissues leading to high attenuationlevels Another factor to take into account is the in-bodytransmissions which have to be low-power constrained toprevent overheating of tissues and the consequent death ofcells

Magnetic resonance imaging (MRI) scans use pulses ofradio waves and strongmagnets to provide detailed images ofbody parts [7 8] However forMRI to be effective in detectingbreast cancer a contrast liquid called gadolinium needs to beinjected into a vein so the scan can show good details Thisprocess takes a long time up to an hour and it is expensive

Another option to consider is the use of echoes fromultrasound waves impinging on parts of the breast In [9] thefeasibility of using ultrasound waves for communications inintrabody area networks was discussed That study includedthe fundamentals of ultrasonic propagation in human tissuesand explored the choices proper transmission frequency

Hindawi Publishing CorporationAdvances in BioinformaticsVolume 2014 Article ID 797013 8 pageshttpdxdoiorg1011552014797013

2 Advances in Bioinformatics

transmission power bandwidth and transducer size Animportant advantage of using ultrasound waves is that thetests are painless and do not expose the body to radiationsBased on the medical experience of several decades ultra-sound is safe with no dangerous bioeffects being observed aslong as the energy delivered to the tissues is less than 50 Jcm2[10] Also ultrasound technology might be the most helpfulfor those women with high density breasts

For the general problem of target position detection andestimation multiple input multiple output (MIMO) RADARis an attractive option to increase the quality of the resultsUnlike a standard phased-array RADAR which transmitsscaled versions of a singlewaveform [11 12] aMIMORADARsystem can use multiple different probing signals that can bechosen quite freely [13] This diversity in the type of signalscan provide better results when compared with a standardphased array RADAR A MIMO RADAR system consists ofcollocated transmit and receive antennas forwhich it has beenshown to offer high resolution [14] and high sensitivity todetect slowly moving targets [15] MIMO RADAR also offerthe ability to have waveform optimization

Due to the advantages of ultrasound andMIMORADARsystems this paper proposes a noninvasivemethod comprisedof an ultrasonic microscaled collocated and subarrayedMIMO RADAR for the high resolution detection of multiplebreast cancer nodes of less than 1 centimeter in size Theresults show that a subarrayed deployment in combinationwith traditional phased-array RADAR and optimal Neyman-Pearson detection provides very promising results

The rest of the paper is organized as follows Section 2formulates the problem including a signal model that is themicroscaled subarrayedMIMORADAR and the propagationmodel Section 3 describes the analytical solution of the mul-tiple target detection problem Section 4 has the simulationresults The conclusions are given in Section 5

2 System ModelAn ultrasound is a mechanical wave similar in nature toan audible sound but at frequencies greater than 20 kHzMedical ultrasounddevices use ultrasoundwaves in the rangeof 1ndash20MHz The selection of a proper transducer frequencyis a very important factor to obtain an optimal image reso-lution High-frequency ultrasound waves (short wavelength)generate images of high axial resolution However for agiven distance high-frequency waves are more attenuatedthan lower frequency waves thus they are more suitable forimaging of superficial structures Conversely low-frequencywaves (long wavelength) provide images of lower resolutionbut can penetrate into deeper structures due to a lower degreeof attenuation For this reason it is preferred to use high-frequency transducers (up to 10ndash15MHz range) to imagesuperficial structures and to use low-frequency transducers(typically 2ndash5MHz) for imaging deep structures for examplelumbar neuraxial ultrasound A breast is considered to be asuperficial structure and therefore high-frequency waves arethe preferred choice

A microscaled subarrayed MIMO RADAR system with119873119905transmit antennas and119873

119903receive antennas is considered

Subarray 1 Subarray 2 Subarray

dt

Ns

middot middot middot middot middot middot middot middot middot middot middot middot

Figure 1 Subarrayed MIMO RADAR transmit architecture

Skin

1205822

1205822

Transmit ULA

Chest wallReceive ULA

Clutter of fat and muscleMalignant tumor or cancer

Figure 2 Breast model and MIMO RADAR placement

Both transmit and receive antenna arrays are assumed tobe a uniform linear array (ULA) with antenna spacing of119889119905and 119889

119903 respectively Both 119889

119905and 119889

119903are small enough

so that each individual antenna sees the target at about thesame orientation Typically 119889

119905and 119889

119903are set to 1205822 where

120582 is the carrier wavelength [16] Each array is divided into119873119904subarrays each of which uses a different orthogonal

narrowband signal from a set of waveforms S = [s1198791 s119879

119873119904

]where each s in S is a vector of119871 time-samples of the basebandequivalent signals transmitted from each transmit subarrayThe number of elements 119873

119904in each subarray need not be

identical although it is assumed to be equal for this analysisIn principle a subarray can overlap another one [16] but notfor the case shown in Figure 1 The transmit antenna arrayand the receive antenna array are placed on the skin (whichis often first lubricated with a special gel) as illustrated inFigure 2 and their positions are close to each other or evenon the same location The 119873

119904waveforms are extracted by a

set of matched filters which gives an output signal vector oflength119873

119904119873119903 Two distinct characteristics can be observed for

this type of system First different transmit subarrays eachwith different orthogonal waveforms result in that the targetRADAR cross sections (RCS) become independent randomvariables Consequently a better detection performance canbe obtained from the multiple independent measurementsSecond a better spatial resolution can be obtained In thisscenario the transmit antennas are collocated such that theRCS observed by each transmitting path are identical Thecomponents extracted by thematched filters in each receivingantenna contain information of the transmitting path fromone of the transmitting antenna elements to one of thereceiving antenna elements By using the information aboutall the transmitting paths a better spatial resolution can beobtained

A breast or a mammary gland is a highly efficient organmainly tasked to produce milk and consists of a mass of

Advances in Bioinformatics 3

glandular chest wall pectoralis muscles lobules nippleareola milk duct fatty tissue and skin To simplify the breaststructure for wave propagation study we model it as depictedin Figure 2 As in [17] the Debyemodel is used to describe theelectromagnetic characteristics of the breast tissue

120598119903= 120598infin

+Δ120598

1 + 120596120591+

120590119904

1198951205961205980

(1)

where 120598infin Δ120598 120591 and 120590

119904are tissue-dependent parameters A

simpler dielectric model can be used to describe breast tissuesuch as

120598119903= 1205981015840minus 11989512059810158401015840= 1205981015840minus 119895

120590

1205961205980

(2)

It is assumed that the breast is immersed in a dielectricmatching medium and the skin can be ignored Normaltissue and tumor tissue are assumed to have the followingrelative permittivities

120598119873

119903= 10 (1 + 01119894) (3)

120598119879

119903= 50 (1 + 01119894) (4)

respectively [18]The human body is composed of different organs and

tissues eachwith different sizes densities and correspondingsound velocities it can then be modeled as an environmentwith a rich presence of reflectors and scatterers Conse-quently an ultrasonic signal that travels through the breastand is received at the receive ULA can be represented asthe sum of numerous attenuated and delayed versions ofthe transmitted signal that is a multipath fading propaga-tion scenario To characterize the statistical behavior of thereceived signal the phase shift of the received signal 120601 canbe assumed to be uniformly distributed over [0 2120587] and themagnitude of the received signal 120588 can be modeled as aNakagami-distributed random variable [19] Therefore theprobability density functions of these random variables canbe expressed as

119891 (120601) =1

2120587rect2120587

(120601)

119891 (120588) =21198981198981205882119898minus1

Γ (119898)Ω119898

119890(minus(119898Ω)120588

2

)119880 (120588)

(5)

where119898 is the Nakagami parameterΩ is a scaling parameter119880(sdot) is the unit-step function Γ(sdot) is the gamma function andrect2120587(sdot) is the rectangular function of duration 2120587

Suppose that there are119870 target points (cancer cells) in thefar field at angles 120579

119896 119896 = 1 2 119870 then the corresponding

119873119905times 119870 transmit steering matrix is expressed as A(120579) =

[a(1205791) sdot sdot sdot a(120579

119870)] where

a (120579119896) = [1 119890

(minus1198952120587119889119905sin(120579119896)120582)

sdot sdot sdot 119890(minus1198952120587(119873

119905minus1)119889119905sin(120579119896)120582)

]

(6)

and the119873119903times119870 receive steeringmatrixB is defined in a similar

way to A The signal at the receive array can be written as

R =

119870

sum

119896=1

B (120579) ΓA119879 (120579)TlowastS +W (7)

where Γ is a 119870 times 119870 diagonal matrix of the target complexamplitudes and lowast denotes the complex conjugate operationThe matrix of size 119873

119905times 119873119904 T has in the 119894th column ones

for the elements belonging to subarray 119894 and zero otherwiseW is the noise component due to sensing error thermalnoise and clutter returns which is assumed to be a complexcircular symmetric white Gaussian noise with zero mean andcovariance matrixQ

After applying a matched filter bank at the receiver thefollowing output signal vector is obtained

z = Y (120579) 120574 + vec (W) (8)

where Y(120579) is the combined transmit and receive arrayresponses matrix 120574 is a 119870 times 1 vector of the target complexamplitudes and W = WS119867 is the noise component of thesignal after the match filtering with a covariance matrix Q =

E[vec(W) vec(W)119867] where E[sdot] is the expectation operator

119867 is the Hermitian transpose operation and vec(sdot) is thecolumn-wise stacking operation

3 RADAR Detection Problem

The likelihood function describing the statistical distributionof the received signal after the match filter bank z can beexpressed as

119891z|120579 =1

(2120587)119873119911210038161003816100381610038161003816Q10038161003816100381610038161003816

12119890minus(12)(zminusY(120579)120574)119867Qminus1(zminusY(120579)120574)

(9)

The radar detection problem is then reduced to the followingbinary hypothesis test

H0 z = vec (W) (a cancer cell is not present)

H1 Y (120579) 120574 + vec (W) (a cancer is present)

(10)

The MAP decision rule can be written as

119891z|H1

(z | H1) 1199011

H=1

⋛

H=0

119891z|H0

(z | H0) 1199010 (11)

where each hypothesis is equally likely that is 1199011

= 1199012

=

12 Therefore the Neyman-Pearson optimal detection rulefor this problem is given by the following log-likelihood ratio

119871 (z) = log119891z|H

1

(z | H1)

119891z|H0

(z | H0)

H=1

⋛

H=0

0 (12)

After some algebraic manipulation the log-likelihood ration119871(z) becomes

119871 (z) = minus(z minus Y(120579)120574)119867Qminus1 (z minus Y (120579) 120574) (13)

Since the targetsrsquo amplitudes and directions (or angles) areunknown their maximum likelihood estimates are estimatedas

120579ML = argmax120579

z119867Qminus1Y (120579) (Y(120579)119867Qminus1Y (120579))minus1

Y(120579)119867Qminus1z(14)

120574ML = (Y(120579)119867Qminus1Y(120579))minus1

Y(120579)119867Qminus1z (15)

4 Advances in Bioinformatics

Table 1 Simulation parameters

Parameters Values (units)Monte-Carlo run 1000 (runs)Carrier frequency 15 (MHz)Transmit power intensity 700 (mWcm2)Speed of the ultrasonic signal in breast 1500 (ms)Time samples of the baseband equivalent signals 119871 10

6 (samples)[119873119905119873119903119873119904] [2 2 2] [4 4 2] [6 6 3] [8 8 4] [8 8 2] [10 10 5] [10 10 2]

Number of the targets 119870 1 2 3 (points)Direction of the targets for 119870 = 1 10 (degree)Direction of the targets for 119870 = 2 [0 10] [0 20] (degree)Direction of the targets for 119870 = 3 [0 10 20] [0 20 40] (degree)

The result from (14) is substituted into (15) to find 120574ML Thenumber of targets (cancer cells)119870 is unknown but they can beestimated using a Bayesian information criterion (BIC) [20]119870 is estimated minimizing the following BIC cost function

BIC (119870) = 2119891 (120579 120574) + 3119870 ln 119871 (16)

where 120579 and 120574 are the estimates of 120579 and 120574 which are obtainedfrom (14) and (15) respectively 119891 is given by

119891 (120579 120574) = 119871 ln 10038161003816100381610038161003816(z minus Y (120579) 120574) (z minus Y (120579) 120574)

11986710038161003816100381610038161003816 (17)

4 Simulation and Results

The performance of the proposed system is evaluatedusing Monte-Carlo simulations with 10

6 runs All simula-tion parameters are summarized in Table 1 Current limitsimposed by ultrasound safety regulations dictated by theFood and Drug Administration (FDA) an agency of theUS federal government allow for power intensities of up to720mWcm2 [21] Within this limit a power normalizationis carried out so that the target power is fixed to 0 dB Firstit is assumed that there is only one cancer cell position thatis 119870 = 1 in the breast Using the above mentioned BIC thenumber of targets (cancer cells) 119870 is estimated to be 124and it is then rounded to 1 The actual target direction withrespect to the receive ULA 120579 is set to 10 degrees Since thecarrier frequency applied in the simulations is 15MHz andthe speed of the signal in the breast is assumed to be 1500ms[22] the wavelength 120582 becomes 1500(15 times 10

6) = 100 120583m

The number of antennas in both transmit and receive ULAs119873119905times 119873119903is varied as follows 2 times 2 4 times 4 6 times 6 8 times 8

and 10 times 10 The number of subarrays 119873119904for each case is

shown in the same table The overall beampatterns or powerspectrums versus angles (which can provide the position ofthe target using the standard trigonometry expressions) foreach case are shown in Figures 3 4 5 6 and 7 It can beobserved that the estimation performances of the proposedsystem are better than the ones from the traditional phased-array RADAR technique since the central lobe is smallerThebeamwidths are reduced when the number of antennas in

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

Figure 3 The overall beampattern for [119873119905 119873119903 119873119904] = [2 2 2]

the ULAs increases meaning that the accuracy of the targetposition estimate becomes better In addition the larger 119873

119904

is the higher the accuracy of the target position estimate isIn practice the number of antennas in both ULAs cannot betoo large 119873

119905and 119873

119903 when more than 10 do not give much

different results than when they are 10 Therefore119873119905= 119873119903=

10 is deemed to provide sufficiently good estimates and itis more practical for an actual implementation The absolutemean error in degree is summarized in Table 2

The evaluation is extended for the multiple-target casethat is 119870 = 2 and 3 The case of using 119873

119905= 119873119903

= 8

and 119873119904= 4 is first considered With the above mentioned

BIC the number of targets (cancer cells) 119870 is estimatedto be 205 and 310 and rounded to 2 and 3 respectivelyThe simulation results for 119870 = 2 at 0 and 20 degrees andfor 119870 = 3 at 0 20 and 40 degrees are shown in Figures8 and 9 Due to the smaller central lobe of the overallbeampatterns the estimation performances of the proposed

Advances in Bioinformatics 5

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

Figure 4 The overall beampattern for [119873119905 119873119903 119873119904] = [4 4 2]

0 20 40 60 80

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 5 The overall beampattern for [119873119905 119873119903 119873119904] = [6 6 3]

system are considered to be better than the ones from thetraditional phased-array RADAR technique As it can be seenin Figure 9 it is still possible to use 119873

119905= 119873119903= 8 and 119873

119904= 4

to successfully detect three targets when they are located 20degrees apart However it is not possible when the targets arelocated closer for example 10 degrees For this case moreantennas are requiredThe number of antennas was increaseduntil119873

119905= 119873119903= 16 and119873

119904= 4were found to be able to detect

the targets located 10 degrees apart as shown in Figures 10 and11 The closer the locations of multiple targets are the moreantennas are needed The average absolute mean error overfor case investigated is summarized in Table 3

In addition to the system evaluation presented above acommon technique that used for early breast cancer detectionis expressed in terms of sensitivity and specificity

0 20 40 60 80

0

20

Pow

er sp

ectr

um (d

B)

Phased-array RADAR

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

MIMO subarrayed RADAR [8 8 2]

MIMO subarrayed RADAR [8 8 4]

Figure 6 The overall beampattern for [119873119905 119873119903 119873119904] = [8 8 2] and

[8 8 4]

Phased-array RADARMIMO subarrayed RADAR [10 10 2]

MIMO subarrayed RADAR [10 10 5]

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 7The overall beampattern for [119873119905 119873119903 119873119904] = [10 10 2] and

[10 10 5]

(1) Sensitivity is the probability of detecting a cancer ifit is actually present in the breast For example if5 women who have cancer are tested and cancer isdetected in 4 of them then the sensitivity is 45 or80

(2) Specificity is the probability of determining that thereis no cancer when in fact no cancer is presentthereby avoiding a false-positive finding If 200women without cancer are examined and 190 arecorrectly told that they do not have cancer (while

6 Advances in Bioinformatics

Table 2 Estimation errors for the case of one target 119870 = 1

[119873119905119873119903119873119904]

Absolute mean error(degrees)

[2 2 2] 55[4 4 2] 211[6 6 3] 053[8 8 2] 043[8 8 4] 035[10 10 2] 027[10 10 5] 023[gt10 gt10 any number] about 02

0 20 40 60 80

0

20

Phased-array RADARMIMO subarrayed RADAR

Pow

er sp

ectr

um (d

B)

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 8Theoverall beampattern for two targets at 0 and 20 degreesusing119873

119905= 119873119903= 8 and119873

119904= 4

the other 10 have further examination) then thespecificity is 190200 or 95

Most medical tests do not have a single sensitivity orspecificity Instead these can be varied according to howthe test is performed or interpreted One graphic way ofdescribing the performance characteristics of a test is throughwhat is known as its receiver operating characteristic (ROC)where the sensitivity versus 1-specificity of a test is plottedA perfect test represented by the dot in the upper left handcorner of the plot would find all cancers (100 sensitivity)and create no false positives (100 specificity) To be ableto evaluate such a performance due to lacking of real dataand real testbeds an additional simulation experiment hasbeen carried out One hundred different types of testbeds arerandomly generated with uniform distribution to representone hundred different testbeds with one target (119870 = 1)(cancer cell) or without cancer The breasts of each testbedhave different sizes and densities which can be modeledwith different Nakagami parameter 119898 varying from 119898 =

Table 3 Estimation errors for the case of multiple targets 119870 = 2 3

Number of targets 119870 Average absolutemean error (degrees)

2 at [0 10] degree119873119905= 16119873

119903= 16 and119873

119904= 4

033

2 at [0 20] degree119873119905= 8119873

119903= 8 and119873

119904= 4

034

3 at [0 10 20] degree119873119905= 16119873

119903= 16 and119873

119904= 4

036

3 at [0 20 40] degree119873119905= 8119873

119903= 8 and119873

119904= 4

035

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 9 The overall beampattern for three targets at 0 20 and 40degrees119873

119905= 119873119903= 8 and119873

119904= 4

05 to 119898 = 1 [23] All one hundred cases are randomlyassigned to each testbed The simulation is run one hundredtimes (realizations) The result is shown in the ROC curvein Figure 12 The results from another one hundred differenttestbeds with multiple targets (119870 = 2 and 3) and also withoutcancer are compared to the one target case As it can beseen the ROC performances for the multiple target cases areslightly worse than the ones for the one target cases Similar tothe results of the previously presented detection performancethe ROC performance improves as the number of antennasincreases

5 Conclusion and Future Work

In this paper a subarrayed MIMO RADAR to detect breastcancer position was proposed The ultrasound frequencyband was selected for the proposed system because it issafe and commonly used for medical applications Since abreast is a superficial structure high-frequency ultrasonictransducers were used The transmit and receive antenna

Advances in Bioinformatics 7

minus80 minus60 minus40 minus20 0 20 40 60 80

minus100

minus80

minus60

minus40

minus20

0

20

Pow

er sp

ectr

um (d

B)

minus120

Phased-array RADARMIMO subarrayed RADAR

Angle (deg)

Figure 10 The overall beampattern for two targets at 0 and 10degrees119873

119905= 119873119903= 16 and119873

119904= 4

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 11 The overall beampattern for three targets at 0 10 and 20degrees119873

119905= 119873119903= 16 and119873

119904= 4

arrays were divided into subarrays Each subarray usesdifferent orthogonal waveforms providing the signal diver-sity that enables an improved performance Closed formexpressions for the optimal Neyman-Pearson detector werederived The proposed system combines waveform diversitymade possible by the subarrayed deployment and traditionalphased-array RADAR together with an optimal Neyman-Pearson detection The system shows promising results forthe detection of breast cancer position not only in the caseof one target node but also in the case of multiple targetnodes

0 02 04 06 08 1

01

02

03

04

05

06

07

08

09

1

Sens

itivi

ty

0

One target [8 8 4]Multiple targets [8 8 4]One target [8 8 2]Multiple targets [8 8 2]

One target [6 6 3]Multiple targets [6 6 3]One target [4 4 2]Multiple targets [4 4 2]

1 minus specificity

Figure 12 The ROC curve for both one target and multiple targetcases

The system described in this paper determines the direc-tion or angle with respect to the ULA where the targets arelocated As future work we intend to use a two-dimensionaldeployment of ULAs so that by properly combining theestimated angles the 3D locations of the targets are esti-mated

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] E C Fear S C Hagness P M Meaney M Okoniewski andMA Stuchly ldquoEnhancing breast tumor detection with near-fieldimagingrdquo IEEE Microwave Magazine vol 3 no 1 pp 48ndash562002

[2] P T Huynh A M Jarolimek and S Daye ldquoThe false-negativemammogramrdquo Radiographics vol 18 no 5 pp 1137ndash1154 1998

[3] J G Elmore M B Barton V M Moceri S Polk P J Arenaand S W Fletcher ldquoTen-year risk of false positive screeningmammograms and clinical breast examinationsrdquo The NewEngland Journal of Medicine vol 338 no 16 pp 1089ndash10961998

[4] A J Surowiec S S Stuchly J R Barr andA Swarup ldquoDielectricproperties of breast carcinoma and the surrounding tissuesrdquoIEEE Transactions on Biomedical Engineering vol 35 no 4 pp257ndash263 1988

[5] W T Joines Y Zhang C Li and R L Jirtle ldquoThe measuredelectrical properties of normal and malignant human tissuesfrom 50 to 900 MHzrdquo Medical Physics vol 21 no 4 pp 547ndash550 1994

[6] S S Chaudhary R K Mishra A Swarup and J M ThomasldquoDielectric properties of normal amp malignant human breast

8 Advances in Bioinformatics

tissues at radiowave amp microwave frequenciesrdquo Indian Journalof Biochemistry and Biophysics vol 21 no 1 pp 76ndash79 1984

[7] E Brookner ldquoPhase arrays around the world progress andfuture trendsrdquo in Proceedings of the IEEE International Sympo-sium Phased Array Systems and Technology pp 1ndash8 October2008

[8] J Y Lee and E A Morris ldquoBreast MRI historical overviewrdquoin Breast MRI diagnosis and intervention E A Morris and LLiberman Eds pp 3ndash6 Springer New York NY USA 2005

[9] L Galluccio T Melodia S Palazzo and G E SantagatildquoChallenges and implications of using ultrasonic communica-tions in intra-body area networksrdquo in Proceedings of the 9thAnnual Conference on Wireless On-Demand Network Systemsand Services (WONS rsquo12) pp 182ndash189 January 2012

[10] S G Orel and M D Schnall ldquoMR imaging of the breast for thedetection diagnosis and staging of breast cancerrdquo Radiologyvol 220 no 1 pp 13ndash30 2001

[11] M Fink G Montaldo and M Tanter ldquoTime-reversal acousticsin biomedical engineeringrdquo Annual Review of Biomedical Engi-neering vol 5 pp 465ndash497 2003

[12] L Swindlehurst and P Stoica ldquoMaximum likelihood methodsin radar array signal processingrdquo Proceedings of the IEEE vol86 no 2 pp 421ndash441 1998

[13] D W Bliss and K W Forsythe ldquoMultiple-input multiple-output (MIMO) radar and imaging degrees of freedom andresolutionrdquo in Proceedings of the 37th Asilomar Conference onSignals Systems and Computers pp 54ndash59 November 2003

[14] E Fishler A Haimovich R Blum L Cimini D Chizhik andR Valenzuela ldquoMIMO radar an idea whose time has comerdquo inProceedings of the IEEE Radar Conference pp 71ndash78 April 2004

[15] A de Maio and M Lops ldquoDesign principles of MIMO radardetectorsrdquo IEEE Transactions on Aerospace and Electronic Sys-tems vol 43 no 3 pp 886ndash898 2007

[16] J Li and P Stoica ldquoMIMO radar with colocated antennasrdquo IEEESignal Processing Magazine vol 24 no 5 pp 106ndash114 2007

[17] G Zhu B Oreshkin E Porter M Coates and M PopovicldquoNumerical breast models for commercial FDTD simulatorsrdquoin Proceedings of the 3rd European Conference on Antennas andPropagation pp 263ndash267 March 2009

[18] S K Davis H Tandradinata S C Hagness and B D vanVeen ldquoUltrawideband microwave breast cancer detection adetection-theoretic approach using the generalized likelihoodratio testrdquo IEEE Transactions on Biomedical Engineering vol 52no 7 pp 1237ndash1250 2005

[19] N Bahbah H Djelouah and A Bouakaz ldquoUse of Nakagamistatistical model in ultrasonic tissuemimicking phantoms char-acterizationrdquo in Proceedings of the 24th International Conferenceon Microelectronics (ICM rsquo12) December 2012

[20] L Xu P Stoica and J Li ldquoParameter estimation and numberdetection of MIMO radar targetsrdquo in Proceedings of the 41stAsilomar Conference on Signals Systems andComputers (ACSSCrsquo07) pp 177ndash181 Pacific Grove Calif USA November 2007

[21] T R Nelson J B Fowlkes J S Abramowicz and C CChurch ldquoUltrasound biosafety considerations for the practicingsonographer and sonologistrdquo Journal of Ultrasound inMedicinevol 28 no 2 pp 139ndash150 2009

[22] HMadjarThePractice of Breast Ul Trasound Techniques Find-ings Differential Diagnosis Georg Thieme Stuttgart Germany2000

[23] J Mamou A Coron M L Oelze et al ldquoThree-dimensionalhigh-frequency backscatter and envelope quantification ofcancerous human lymph nodesrdquo Ultrasound in Medicine andBiology vol 37 no 3 pp 345ndash357 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal of

Microbiology

2 Advances in Bioinformatics

transmission power bandwidth and transducer size Animportant advantage of using ultrasound waves is that thetests are painless and do not expose the body to radiationsBased on the medical experience of several decades ultra-sound is safe with no dangerous bioeffects being observed aslong as the energy delivered to the tissues is less than 50 Jcm2[10] Also ultrasound technology might be the most helpfulfor those women with high density breasts

For the general problem of target position detection andestimation multiple input multiple output (MIMO) RADARis an attractive option to increase the quality of the resultsUnlike a standard phased-array RADAR which transmitsscaled versions of a singlewaveform [11 12] aMIMORADARsystem can use multiple different probing signals that can bechosen quite freely [13] This diversity in the type of signalscan provide better results when compared with a standardphased array RADAR A MIMO RADAR system consists ofcollocated transmit and receive antennas forwhich it has beenshown to offer high resolution [14] and high sensitivity todetect slowly moving targets [15] MIMO RADAR also offerthe ability to have waveform optimization

Due to the advantages of ultrasound andMIMORADARsystems this paper proposes a noninvasivemethod comprisedof an ultrasonic microscaled collocated and subarrayedMIMO RADAR for the high resolution detection of multiplebreast cancer nodes of less than 1 centimeter in size Theresults show that a subarrayed deployment in combinationwith traditional phased-array RADAR and optimal Neyman-Pearson detection provides very promising results

The rest of the paper is organized as follows Section 2formulates the problem including a signal model that is themicroscaled subarrayedMIMORADAR and the propagationmodel Section 3 describes the analytical solution of the mul-tiple target detection problem Section 4 has the simulationresults The conclusions are given in Section 5

2 System ModelAn ultrasound is a mechanical wave similar in nature toan audible sound but at frequencies greater than 20 kHzMedical ultrasounddevices use ultrasoundwaves in the rangeof 1ndash20MHz The selection of a proper transducer frequencyis a very important factor to obtain an optimal image reso-lution High-frequency ultrasound waves (short wavelength)generate images of high axial resolution However for agiven distance high-frequency waves are more attenuatedthan lower frequency waves thus they are more suitable forimaging of superficial structures Conversely low-frequencywaves (long wavelength) provide images of lower resolutionbut can penetrate into deeper structures due to a lower degreeof attenuation For this reason it is preferred to use high-frequency transducers (up to 10ndash15MHz range) to imagesuperficial structures and to use low-frequency transducers(typically 2ndash5MHz) for imaging deep structures for examplelumbar neuraxial ultrasound A breast is considered to be asuperficial structure and therefore high-frequency waves arethe preferred choice

A microscaled subarrayed MIMO RADAR system with119873119905transmit antennas and119873

119903receive antennas is considered

Subarray 1 Subarray 2 Subarray

dt

Ns

middot middot middot middot middot middot middot middot middot middot middot middot

Figure 1 Subarrayed MIMO RADAR transmit architecture

Skin

1205822

1205822

Transmit ULA

Chest wallReceive ULA

Clutter of fat and muscleMalignant tumor or cancer

Figure 2 Breast model and MIMO RADAR placement

Both transmit and receive antenna arrays are assumed tobe a uniform linear array (ULA) with antenna spacing of119889119905and 119889

119903 respectively Both 119889

119905and 119889

119903are small enough

so that each individual antenna sees the target at about thesame orientation Typically 119889

119905and 119889

119903are set to 1205822 where

120582 is the carrier wavelength [16] Each array is divided into119873119904subarrays each of which uses a different orthogonal

narrowband signal from a set of waveforms S = [s1198791 s119879

119873119904

]where each s in S is a vector of119871 time-samples of the basebandequivalent signals transmitted from each transmit subarrayThe number of elements 119873

119904in each subarray need not be

identical although it is assumed to be equal for this analysisIn principle a subarray can overlap another one [16] but notfor the case shown in Figure 1 The transmit antenna arrayand the receive antenna array are placed on the skin (whichis often first lubricated with a special gel) as illustrated inFigure 2 and their positions are close to each other or evenon the same location The 119873

119904waveforms are extracted by a

set of matched filters which gives an output signal vector oflength119873

119904119873119903 Two distinct characteristics can be observed for

this type of system First different transmit subarrays eachwith different orthogonal waveforms result in that the targetRADAR cross sections (RCS) become independent randomvariables Consequently a better detection performance canbe obtained from the multiple independent measurementsSecond a better spatial resolution can be obtained In thisscenario the transmit antennas are collocated such that theRCS observed by each transmitting path are identical Thecomponents extracted by thematched filters in each receivingantenna contain information of the transmitting path fromone of the transmitting antenna elements to one of thereceiving antenna elements By using the information aboutall the transmitting paths a better spatial resolution can beobtained

A breast or a mammary gland is a highly efficient organmainly tasked to produce milk and consists of a mass of

Advances in Bioinformatics 3

glandular chest wall pectoralis muscles lobules nippleareola milk duct fatty tissue and skin To simplify the breaststructure for wave propagation study we model it as depictedin Figure 2 As in [17] the Debyemodel is used to describe theelectromagnetic characteristics of the breast tissue

120598119903= 120598infin

+Δ120598

1 + 120596120591+

120590119904

1198951205961205980

(1)

where 120598infin Δ120598 120591 and 120590

119904are tissue-dependent parameters A

simpler dielectric model can be used to describe breast tissuesuch as

120598119903= 1205981015840minus 11989512059810158401015840= 1205981015840minus 119895

120590

1205961205980

(2)

It is assumed that the breast is immersed in a dielectricmatching medium and the skin can be ignored Normaltissue and tumor tissue are assumed to have the followingrelative permittivities

120598119873

119903= 10 (1 + 01119894) (3)

120598119879

119903= 50 (1 + 01119894) (4)

respectively [18]The human body is composed of different organs and

tissues eachwith different sizes densities and correspondingsound velocities it can then be modeled as an environmentwith a rich presence of reflectors and scatterers Conse-quently an ultrasonic signal that travels through the breastand is received at the receive ULA can be represented asthe sum of numerous attenuated and delayed versions ofthe transmitted signal that is a multipath fading propaga-tion scenario To characterize the statistical behavior of thereceived signal the phase shift of the received signal 120601 canbe assumed to be uniformly distributed over [0 2120587] and themagnitude of the received signal 120588 can be modeled as aNakagami-distributed random variable [19] Therefore theprobability density functions of these random variables canbe expressed as

119891 (120601) =1

2120587rect2120587

(120601)

119891 (120588) =21198981198981205882119898minus1

Γ (119898)Ω119898

119890(minus(119898Ω)120588

2

)119880 (120588)

(5)

where119898 is the Nakagami parameterΩ is a scaling parameter119880(sdot) is the unit-step function Γ(sdot) is the gamma function andrect2120587(sdot) is the rectangular function of duration 2120587

Suppose that there are119870 target points (cancer cells) in thefar field at angles 120579

119896 119896 = 1 2 119870 then the corresponding

119873119905times 119870 transmit steering matrix is expressed as A(120579) =

[a(1205791) sdot sdot sdot a(120579

119870)] where

a (120579119896) = [1 119890

(minus1198952120587119889119905sin(120579119896)120582)

sdot sdot sdot 119890(minus1198952120587(119873

119905minus1)119889119905sin(120579119896)120582)

]

(6)

and the119873119903times119870 receive steeringmatrixB is defined in a similar

way to A The signal at the receive array can be written as

R =

119870

sum

119896=1

B (120579) ΓA119879 (120579)TlowastS +W (7)

where Γ is a 119870 times 119870 diagonal matrix of the target complexamplitudes and lowast denotes the complex conjugate operationThe matrix of size 119873

119905times 119873119904 T has in the 119894th column ones

for the elements belonging to subarray 119894 and zero otherwiseW is the noise component due to sensing error thermalnoise and clutter returns which is assumed to be a complexcircular symmetric white Gaussian noise with zero mean andcovariance matrixQ

After applying a matched filter bank at the receiver thefollowing output signal vector is obtained

z = Y (120579) 120574 + vec (W) (8)

where Y(120579) is the combined transmit and receive arrayresponses matrix 120574 is a 119870 times 1 vector of the target complexamplitudes and W = WS119867 is the noise component of thesignal after the match filtering with a covariance matrix Q =

E[vec(W) vec(W)119867] where E[sdot] is the expectation operator

119867 is the Hermitian transpose operation and vec(sdot) is thecolumn-wise stacking operation

3 RADAR Detection Problem

The likelihood function describing the statistical distributionof the received signal after the match filter bank z can beexpressed as

119891z|120579 =1

(2120587)119873119911210038161003816100381610038161003816Q10038161003816100381610038161003816

12119890minus(12)(zminusY(120579)120574)119867Qminus1(zminusY(120579)120574)

(9)

The radar detection problem is then reduced to the followingbinary hypothesis test

H0 z = vec (W) (a cancer cell is not present)

H1 Y (120579) 120574 + vec (W) (a cancer is present)

(10)

The MAP decision rule can be written as

119891z|H1

(z | H1) 1199011

H=1

⋛

H=0

119891z|H0

(z | H0) 1199010 (11)

where each hypothesis is equally likely that is 1199011

= 1199012

=

12 Therefore the Neyman-Pearson optimal detection rulefor this problem is given by the following log-likelihood ratio

119871 (z) = log119891z|H

1

(z | H1)

119891z|H0

(z | H0)

H=1

⋛

H=0

0 (12)

After some algebraic manipulation the log-likelihood ration119871(z) becomes

119871 (z) = minus(z minus Y(120579)120574)119867Qminus1 (z minus Y (120579) 120574) (13)

Since the targetsrsquo amplitudes and directions (or angles) areunknown their maximum likelihood estimates are estimatedas

120579ML = argmax120579

z119867Qminus1Y (120579) (Y(120579)119867Qminus1Y (120579))minus1

Y(120579)119867Qminus1z(14)

120574ML = (Y(120579)119867Qminus1Y(120579))minus1

Y(120579)119867Qminus1z (15)

4 Advances in Bioinformatics

Table 1 Simulation parameters

Parameters Values (units)Monte-Carlo run 1000 (runs)Carrier frequency 15 (MHz)Transmit power intensity 700 (mWcm2)Speed of the ultrasonic signal in breast 1500 (ms)Time samples of the baseband equivalent signals 119871 10

6 (samples)[119873119905119873119903119873119904] [2 2 2] [4 4 2] [6 6 3] [8 8 4] [8 8 2] [10 10 5] [10 10 2]

Number of the targets 119870 1 2 3 (points)Direction of the targets for 119870 = 1 10 (degree)Direction of the targets for 119870 = 2 [0 10] [0 20] (degree)Direction of the targets for 119870 = 3 [0 10 20] [0 20 40] (degree)

The result from (14) is substituted into (15) to find 120574ML Thenumber of targets (cancer cells)119870 is unknown but they can beestimated using a Bayesian information criterion (BIC) [20]119870 is estimated minimizing the following BIC cost function

BIC (119870) = 2119891 (120579 120574) + 3119870 ln 119871 (16)

where 120579 and 120574 are the estimates of 120579 and 120574 which are obtainedfrom (14) and (15) respectively 119891 is given by

119891 (120579 120574) = 119871 ln 10038161003816100381610038161003816(z minus Y (120579) 120574) (z minus Y (120579) 120574)

11986710038161003816100381610038161003816 (17)

4 Simulation and Results

The performance of the proposed system is evaluatedusing Monte-Carlo simulations with 10

6 runs All simula-tion parameters are summarized in Table 1 Current limitsimposed by ultrasound safety regulations dictated by theFood and Drug Administration (FDA) an agency of theUS federal government allow for power intensities of up to720mWcm2 [21] Within this limit a power normalizationis carried out so that the target power is fixed to 0 dB Firstit is assumed that there is only one cancer cell position thatis 119870 = 1 in the breast Using the above mentioned BIC thenumber of targets (cancer cells) 119870 is estimated to be 124and it is then rounded to 1 The actual target direction withrespect to the receive ULA 120579 is set to 10 degrees Since thecarrier frequency applied in the simulations is 15MHz andthe speed of the signal in the breast is assumed to be 1500ms[22] the wavelength 120582 becomes 1500(15 times 10

6) = 100 120583m

The number of antennas in both transmit and receive ULAs119873119905times 119873119903is varied as follows 2 times 2 4 times 4 6 times 6 8 times 8

and 10 times 10 The number of subarrays 119873119904for each case is

shown in the same table The overall beampatterns or powerspectrums versus angles (which can provide the position ofthe target using the standard trigonometry expressions) foreach case are shown in Figures 3 4 5 6 and 7 It can beobserved that the estimation performances of the proposedsystem are better than the ones from the traditional phased-array RADAR technique since the central lobe is smallerThebeamwidths are reduced when the number of antennas in

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

Figure 3 The overall beampattern for [119873119905 119873119903 119873119904] = [2 2 2]

the ULAs increases meaning that the accuracy of the targetposition estimate becomes better In addition the larger 119873

119904

is the higher the accuracy of the target position estimate isIn practice the number of antennas in both ULAs cannot betoo large 119873

119905and 119873

119903 when more than 10 do not give much

different results than when they are 10 Therefore119873119905= 119873119903=

10 is deemed to provide sufficiently good estimates and itis more practical for an actual implementation The absolutemean error in degree is summarized in Table 2

The evaluation is extended for the multiple-target casethat is 119870 = 2 and 3 The case of using 119873

119905= 119873119903

= 8

and 119873119904= 4 is first considered With the above mentioned

BIC the number of targets (cancer cells) 119870 is estimatedto be 205 and 310 and rounded to 2 and 3 respectivelyThe simulation results for 119870 = 2 at 0 and 20 degrees andfor 119870 = 3 at 0 20 and 40 degrees are shown in Figures8 and 9 Due to the smaller central lobe of the overallbeampatterns the estimation performances of the proposed

Advances in Bioinformatics 5

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

Figure 4 The overall beampattern for [119873119905 119873119903 119873119904] = [4 4 2]

0 20 40 60 80

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 5 The overall beampattern for [119873119905 119873119903 119873119904] = [6 6 3]

system are considered to be better than the ones from thetraditional phased-array RADAR technique As it can be seenin Figure 9 it is still possible to use 119873

119905= 119873119903= 8 and 119873

119904= 4

to successfully detect three targets when they are located 20degrees apart However it is not possible when the targets arelocated closer for example 10 degrees For this case moreantennas are requiredThe number of antennas was increaseduntil119873

119905= 119873119903= 16 and119873

119904= 4were found to be able to detect

the targets located 10 degrees apart as shown in Figures 10 and11 The closer the locations of multiple targets are the moreantennas are needed The average absolute mean error overfor case investigated is summarized in Table 3

In addition to the system evaluation presented above acommon technique that used for early breast cancer detectionis expressed in terms of sensitivity and specificity

0 20 40 60 80

0

20

Pow

er sp

ectr

um (d

B)

Phased-array RADAR

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

MIMO subarrayed RADAR [8 8 2]

MIMO subarrayed RADAR [8 8 4]

Figure 6 The overall beampattern for [119873119905 119873119903 119873119904] = [8 8 2] and

[8 8 4]

Phased-array RADARMIMO subarrayed RADAR [10 10 2]

MIMO subarrayed RADAR [10 10 5]

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 7The overall beampattern for [119873119905 119873119903 119873119904] = [10 10 2] and

[10 10 5]

(1) Sensitivity is the probability of detecting a cancer ifit is actually present in the breast For example if5 women who have cancer are tested and cancer isdetected in 4 of them then the sensitivity is 45 or80

(2) Specificity is the probability of determining that thereis no cancer when in fact no cancer is presentthereby avoiding a false-positive finding If 200women without cancer are examined and 190 arecorrectly told that they do not have cancer (while

6 Advances in Bioinformatics

Table 2 Estimation errors for the case of one target 119870 = 1

[119873119905119873119903119873119904]

Absolute mean error(degrees)

[2 2 2] 55[4 4 2] 211[6 6 3] 053[8 8 2] 043[8 8 4] 035[10 10 2] 027[10 10 5] 023[gt10 gt10 any number] about 02

0 20 40 60 80

0

20

Phased-array RADARMIMO subarrayed RADAR

Pow

er sp

ectr

um (d

B)

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 8Theoverall beampattern for two targets at 0 and 20 degreesusing119873

119905= 119873119903= 8 and119873

119904= 4

the other 10 have further examination) then thespecificity is 190200 or 95

Most medical tests do not have a single sensitivity orspecificity Instead these can be varied according to howthe test is performed or interpreted One graphic way ofdescribing the performance characteristics of a test is throughwhat is known as its receiver operating characteristic (ROC)where the sensitivity versus 1-specificity of a test is plottedA perfect test represented by the dot in the upper left handcorner of the plot would find all cancers (100 sensitivity)and create no false positives (100 specificity) To be ableto evaluate such a performance due to lacking of real dataand real testbeds an additional simulation experiment hasbeen carried out One hundred different types of testbeds arerandomly generated with uniform distribution to representone hundred different testbeds with one target (119870 = 1)(cancer cell) or without cancer The breasts of each testbedhave different sizes and densities which can be modeledwith different Nakagami parameter 119898 varying from 119898 =

Table 3 Estimation errors for the case of multiple targets 119870 = 2 3

Number of targets 119870 Average absolutemean error (degrees)

2 at [0 10] degree119873119905= 16119873

119903= 16 and119873

119904= 4

033

2 at [0 20] degree119873119905= 8119873

119903= 8 and119873

119904= 4

034

3 at [0 10 20] degree119873119905= 16119873

119903= 16 and119873

119904= 4

036

3 at [0 20 40] degree119873119905= 8119873

119903= 8 and119873

119904= 4

035

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 9 The overall beampattern for three targets at 0 20 and 40degrees119873

119905= 119873119903= 8 and119873

119904= 4

05 to 119898 = 1 [23] All one hundred cases are randomlyassigned to each testbed The simulation is run one hundredtimes (realizations) The result is shown in the ROC curvein Figure 12 The results from another one hundred differenttestbeds with multiple targets (119870 = 2 and 3) and also withoutcancer are compared to the one target case As it can beseen the ROC performances for the multiple target cases areslightly worse than the ones for the one target cases Similar tothe results of the previously presented detection performancethe ROC performance improves as the number of antennasincreases

5 Conclusion and Future Work

In this paper a subarrayed MIMO RADAR to detect breastcancer position was proposed The ultrasound frequencyband was selected for the proposed system because it issafe and commonly used for medical applications Since abreast is a superficial structure high-frequency ultrasonictransducers were used The transmit and receive antenna

Advances in Bioinformatics 7

minus80 minus60 minus40 minus20 0 20 40 60 80

minus100

minus80

minus60

minus40

minus20

0

20

Pow

er sp

ectr

um (d

B)

minus120

Phased-array RADARMIMO subarrayed RADAR

Angle (deg)

Figure 10 The overall beampattern for two targets at 0 and 10degrees119873

119905= 119873119903= 16 and119873

119904= 4

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 11 The overall beampattern for three targets at 0 10 and 20degrees119873

119905= 119873119903= 16 and119873

119904= 4

arrays were divided into subarrays Each subarray usesdifferent orthogonal waveforms providing the signal diver-sity that enables an improved performance Closed formexpressions for the optimal Neyman-Pearson detector werederived The proposed system combines waveform diversitymade possible by the subarrayed deployment and traditionalphased-array RADAR together with an optimal Neyman-Pearson detection The system shows promising results forthe detection of breast cancer position not only in the caseof one target node but also in the case of multiple targetnodes

0 02 04 06 08 1

01

02

03

04

05

06

07

08

09

1

Sens

itivi

ty

0

One target [8 8 4]Multiple targets [8 8 4]One target [8 8 2]Multiple targets [8 8 2]

One target [6 6 3]Multiple targets [6 6 3]One target [4 4 2]Multiple targets [4 4 2]

1 minus specificity

Figure 12 The ROC curve for both one target and multiple targetcases

The system described in this paper determines the direc-tion or angle with respect to the ULA where the targets arelocated As future work we intend to use a two-dimensionaldeployment of ULAs so that by properly combining theestimated angles the 3D locations of the targets are esti-mated

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] E C Fear S C Hagness P M Meaney M Okoniewski andMA Stuchly ldquoEnhancing breast tumor detection with near-fieldimagingrdquo IEEE Microwave Magazine vol 3 no 1 pp 48ndash562002

[2] P T Huynh A M Jarolimek and S Daye ldquoThe false-negativemammogramrdquo Radiographics vol 18 no 5 pp 1137ndash1154 1998

[3] J G Elmore M B Barton V M Moceri S Polk P J Arenaand S W Fletcher ldquoTen-year risk of false positive screeningmammograms and clinical breast examinationsrdquo The NewEngland Journal of Medicine vol 338 no 16 pp 1089ndash10961998

[4] A J Surowiec S S Stuchly J R Barr andA Swarup ldquoDielectricproperties of breast carcinoma and the surrounding tissuesrdquoIEEE Transactions on Biomedical Engineering vol 35 no 4 pp257ndash263 1988

[5] W T Joines Y Zhang C Li and R L Jirtle ldquoThe measuredelectrical properties of normal and malignant human tissuesfrom 50 to 900 MHzrdquo Medical Physics vol 21 no 4 pp 547ndash550 1994

[6] S S Chaudhary R K Mishra A Swarup and J M ThomasldquoDielectric properties of normal amp malignant human breast

8 Advances in Bioinformatics

tissues at radiowave amp microwave frequenciesrdquo Indian Journalof Biochemistry and Biophysics vol 21 no 1 pp 76ndash79 1984

[7] E Brookner ldquoPhase arrays around the world progress andfuture trendsrdquo in Proceedings of the IEEE International Sympo-sium Phased Array Systems and Technology pp 1ndash8 October2008

[8] J Y Lee and E A Morris ldquoBreast MRI historical overviewrdquoin Breast MRI diagnosis and intervention E A Morris and LLiberman Eds pp 3ndash6 Springer New York NY USA 2005

[9] L Galluccio T Melodia S Palazzo and G E SantagatildquoChallenges and implications of using ultrasonic communica-tions in intra-body area networksrdquo in Proceedings of the 9thAnnual Conference on Wireless On-Demand Network Systemsand Services (WONS rsquo12) pp 182ndash189 January 2012

[10] S G Orel and M D Schnall ldquoMR imaging of the breast for thedetection diagnosis and staging of breast cancerrdquo Radiologyvol 220 no 1 pp 13ndash30 2001

[11] M Fink G Montaldo and M Tanter ldquoTime-reversal acousticsin biomedical engineeringrdquo Annual Review of Biomedical Engi-neering vol 5 pp 465ndash497 2003

[12] L Swindlehurst and P Stoica ldquoMaximum likelihood methodsin radar array signal processingrdquo Proceedings of the IEEE vol86 no 2 pp 421ndash441 1998

[13] D W Bliss and K W Forsythe ldquoMultiple-input multiple-output (MIMO) radar and imaging degrees of freedom andresolutionrdquo in Proceedings of the 37th Asilomar Conference onSignals Systems and Computers pp 54ndash59 November 2003

[14] E Fishler A Haimovich R Blum L Cimini D Chizhik andR Valenzuela ldquoMIMO radar an idea whose time has comerdquo inProceedings of the IEEE Radar Conference pp 71ndash78 April 2004

[15] A de Maio and M Lops ldquoDesign principles of MIMO radardetectorsrdquo IEEE Transactions on Aerospace and Electronic Sys-tems vol 43 no 3 pp 886ndash898 2007

[16] J Li and P Stoica ldquoMIMO radar with colocated antennasrdquo IEEESignal Processing Magazine vol 24 no 5 pp 106ndash114 2007

[17] G Zhu B Oreshkin E Porter M Coates and M PopovicldquoNumerical breast models for commercial FDTD simulatorsrdquoin Proceedings of the 3rd European Conference on Antennas andPropagation pp 263ndash267 March 2009

[18] S K Davis H Tandradinata S C Hagness and B D vanVeen ldquoUltrawideband microwave breast cancer detection adetection-theoretic approach using the generalized likelihoodratio testrdquo IEEE Transactions on Biomedical Engineering vol 52no 7 pp 1237ndash1250 2005

[19] N Bahbah H Djelouah and A Bouakaz ldquoUse of Nakagamistatistical model in ultrasonic tissuemimicking phantoms char-acterizationrdquo in Proceedings of the 24th International Conferenceon Microelectronics (ICM rsquo12) December 2012

[20] L Xu P Stoica and J Li ldquoParameter estimation and numberdetection of MIMO radar targetsrdquo in Proceedings of the 41stAsilomar Conference on Signals Systems andComputers (ACSSCrsquo07) pp 177ndash181 Pacific Grove Calif USA November 2007

[21] T R Nelson J B Fowlkes J S Abramowicz and C CChurch ldquoUltrasound biosafety considerations for the practicingsonographer and sonologistrdquo Journal of Ultrasound inMedicinevol 28 no 2 pp 139ndash150 2009

[22] HMadjarThePractice of Breast Ul Trasound Techniques Find-ings Differential Diagnosis Georg Thieme Stuttgart Germany2000

[23] J Mamou A Coron M L Oelze et al ldquoThree-dimensionalhigh-frequency backscatter and envelope quantification ofcancerous human lymph nodesrdquo Ultrasound in Medicine andBiology vol 37 no 3 pp 345ndash357 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

Advances in Bioinformatics 3

glandular chest wall pectoralis muscles lobules nippleareola milk duct fatty tissue and skin To simplify the breaststructure for wave propagation study we model it as depictedin Figure 2 As in [17] the Debyemodel is used to describe theelectromagnetic characteristics of the breast tissue

120598119903= 120598infin

+Δ120598

1 + 120596120591+

120590119904

1198951205961205980

(1)

where 120598infin Δ120598 120591 and 120590

119904are tissue-dependent parameters A

simpler dielectric model can be used to describe breast tissuesuch as

120598119903= 1205981015840minus 11989512059810158401015840= 1205981015840minus 119895

120590

1205961205980

(2)

It is assumed that the breast is immersed in a dielectricmatching medium and the skin can be ignored Normaltissue and tumor tissue are assumed to have the followingrelative permittivities

120598119873

119903= 10 (1 + 01119894) (3)

120598119879

119903= 50 (1 + 01119894) (4)

respectively [18]The human body is composed of different organs and

tissues eachwith different sizes densities and correspondingsound velocities it can then be modeled as an environmentwith a rich presence of reflectors and scatterers Conse-quently an ultrasonic signal that travels through the breastand is received at the receive ULA can be represented asthe sum of numerous attenuated and delayed versions ofthe transmitted signal that is a multipath fading propaga-tion scenario To characterize the statistical behavior of thereceived signal the phase shift of the received signal 120601 canbe assumed to be uniformly distributed over [0 2120587] and themagnitude of the received signal 120588 can be modeled as aNakagami-distributed random variable [19] Therefore theprobability density functions of these random variables canbe expressed as

119891 (120601) =1

2120587rect2120587

(120601)

119891 (120588) =21198981198981205882119898minus1

Γ (119898)Ω119898

119890(minus(119898Ω)120588

2

)119880 (120588)

(5)

where119898 is the Nakagami parameterΩ is a scaling parameter119880(sdot) is the unit-step function Γ(sdot) is the gamma function andrect2120587(sdot) is the rectangular function of duration 2120587

Suppose that there are119870 target points (cancer cells) in thefar field at angles 120579

119896 119896 = 1 2 119870 then the corresponding

119873119905times 119870 transmit steering matrix is expressed as A(120579) =

[a(1205791) sdot sdot sdot a(120579

119870)] where

a (120579119896) = [1 119890

(minus1198952120587119889119905sin(120579119896)120582)

sdot sdot sdot 119890(minus1198952120587(119873

119905minus1)119889119905sin(120579119896)120582)

]

(6)

and the119873119903times119870 receive steeringmatrixB is defined in a similar

way to A The signal at the receive array can be written as

R =

119870

sum

119896=1

B (120579) ΓA119879 (120579)TlowastS +W (7)

where Γ is a 119870 times 119870 diagonal matrix of the target complexamplitudes and lowast denotes the complex conjugate operationThe matrix of size 119873

119905times 119873119904 T has in the 119894th column ones

for the elements belonging to subarray 119894 and zero otherwiseW is the noise component due to sensing error thermalnoise and clutter returns which is assumed to be a complexcircular symmetric white Gaussian noise with zero mean andcovariance matrixQ

After applying a matched filter bank at the receiver thefollowing output signal vector is obtained

z = Y (120579) 120574 + vec (W) (8)

where Y(120579) is the combined transmit and receive arrayresponses matrix 120574 is a 119870 times 1 vector of the target complexamplitudes and W = WS119867 is the noise component of thesignal after the match filtering with a covariance matrix Q =

E[vec(W) vec(W)119867] where E[sdot] is the expectation operator

119867 is the Hermitian transpose operation and vec(sdot) is thecolumn-wise stacking operation

3 RADAR Detection Problem

The likelihood function describing the statistical distributionof the received signal after the match filter bank z can beexpressed as

119891z|120579 =1

(2120587)119873119911210038161003816100381610038161003816Q10038161003816100381610038161003816

12119890minus(12)(zminusY(120579)120574)119867Qminus1(zminusY(120579)120574)

(9)

The radar detection problem is then reduced to the followingbinary hypothesis test

H0 z = vec (W) (a cancer cell is not present)

H1 Y (120579) 120574 + vec (W) (a cancer is present)

(10)

The MAP decision rule can be written as

119891z|H1

(z | H1) 1199011

H=1

⋛

H=0

119891z|H0

(z | H0) 1199010 (11)

where each hypothesis is equally likely that is 1199011

= 1199012

=

12 Therefore the Neyman-Pearson optimal detection rulefor this problem is given by the following log-likelihood ratio

119871 (z) = log119891z|H

1

(z | H1)

119891z|H0

(z | H0)

H=1

⋛

H=0

0 (12)

After some algebraic manipulation the log-likelihood ration119871(z) becomes

119871 (z) = minus(z minus Y(120579)120574)119867Qminus1 (z minus Y (120579) 120574) (13)

Since the targetsrsquo amplitudes and directions (or angles) areunknown their maximum likelihood estimates are estimatedas

120579ML = argmax120579

z119867Qminus1Y (120579) (Y(120579)119867Qminus1Y (120579))minus1

Y(120579)119867Qminus1z(14)

120574ML = (Y(120579)119867Qminus1Y(120579))minus1

Y(120579)119867Qminus1z (15)

4 Advances in Bioinformatics

Table 1 Simulation parameters

Parameters Values (units)Monte-Carlo run 1000 (runs)Carrier frequency 15 (MHz)Transmit power intensity 700 (mWcm2)Speed of the ultrasonic signal in breast 1500 (ms)Time samples of the baseband equivalent signals 119871 10

6 (samples)[119873119905119873119903119873119904] [2 2 2] [4 4 2] [6 6 3] [8 8 4] [8 8 2] [10 10 5] [10 10 2]

Number of the targets 119870 1 2 3 (points)Direction of the targets for 119870 = 1 10 (degree)Direction of the targets for 119870 = 2 [0 10] [0 20] (degree)Direction of the targets for 119870 = 3 [0 10 20] [0 20 40] (degree)

The result from (14) is substituted into (15) to find 120574ML Thenumber of targets (cancer cells)119870 is unknown but they can beestimated using a Bayesian information criterion (BIC) [20]119870 is estimated minimizing the following BIC cost function

BIC (119870) = 2119891 (120579 120574) + 3119870 ln 119871 (16)

where 120579 and 120574 are the estimates of 120579 and 120574 which are obtainedfrom (14) and (15) respectively 119891 is given by

119891 (120579 120574) = 119871 ln 10038161003816100381610038161003816(z minus Y (120579) 120574) (z minus Y (120579) 120574)

11986710038161003816100381610038161003816 (17)

4 Simulation and Results

The performance of the proposed system is evaluatedusing Monte-Carlo simulations with 10

6 runs All simula-tion parameters are summarized in Table 1 Current limitsimposed by ultrasound safety regulations dictated by theFood and Drug Administration (FDA) an agency of theUS federal government allow for power intensities of up to720mWcm2 [21] Within this limit a power normalizationis carried out so that the target power is fixed to 0 dB Firstit is assumed that there is only one cancer cell position thatis 119870 = 1 in the breast Using the above mentioned BIC thenumber of targets (cancer cells) 119870 is estimated to be 124and it is then rounded to 1 The actual target direction withrespect to the receive ULA 120579 is set to 10 degrees Since thecarrier frequency applied in the simulations is 15MHz andthe speed of the signal in the breast is assumed to be 1500ms[22] the wavelength 120582 becomes 1500(15 times 10

6) = 100 120583m

The number of antennas in both transmit and receive ULAs119873119905times 119873119903is varied as follows 2 times 2 4 times 4 6 times 6 8 times 8

and 10 times 10 The number of subarrays 119873119904for each case is

shown in the same table The overall beampatterns or powerspectrums versus angles (which can provide the position ofthe target using the standard trigonometry expressions) foreach case are shown in Figures 3 4 5 6 and 7 It can beobserved that the estimation performances of the proposedsystem are better than the ones from the traditional phased-array RADAR technique since the central lobe is smallerThebeamwidths are reduced when the number of antennas in

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

Figure 3 The overall beampattern for [119873119905 119873119903 119873119904] = [2 2 2]

the ULAs increases meaning that the accuracy of the targetposition estimate becomes better In addition the larger 119873

119904

is the higher the accuracy of the target position estimate isIn practice the number of antennas in both ULAs cannot betoo large 119873

119905and 119873

119903 when more than 10 do not give much

different results than when they are 10 Therefore119873119905= 119873119903=

10 is deemed to provide sufficiently good estimates and itis more practical for an actual implementation The absolutemean error in degree is summarized in Table 2

The evaluation is extended for the multiple-target casethat is 119870 = 2 and 3 The case of using 119873

119905= 119873119903

= 8

and 119873119904= 4 is first considered With the above mentioned

BIC the number of targets (cancer cells) 119870 is estimatedto be 205 and 310 and rounded to 2 and 3 respectivelyThe simulation results for 119870 = 2 at 0 and 20 degrees andfor 119870 = 3 at 0 20 and 40 degrees are shown in Figures8 and 9 Due to the smaller central lobe of the overallbeampatterns the estimation performances of the proposed

Advances in Bioinformatics 5

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

Figure 4 The overall beampattern for [119873119905 119873119903 119873119904] = [4 4 2]

0 20 40 60 80

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 5 The overall beampattern for [119873119905 119873119903 119873119904] = [6 6 3]

system are considered to be better than the ones from thetraditional phased-array RADAR technique As it can be seenin Figure 9 it is still possible to use 119873

119905= 119873119903= 8 and 119873

119904= 4

to successfully detect three targets when they are located 20degrees apart However it is not possible when the targets arelocated closer for example 10 degrees For this case moreantennas are requiredThe number of antennas was increaseduntil119873

119905= 119873119903= 16 and119873

119904= 4were found to be able to detect

the targets located 10 degrees apart as shown in Figures 10 and11 The closer the locations of multiple targets are the moreantennas are needed The average absolute mean error overfor case investigated is summarized in Table 3

In addition to the system evaluation presented above acommon technique that used for early breast cancer detectionis expressed in terms of sensitivity and specificity

0 20 40 60 80

0

20

Pow

er sp

ectr

um (d

B)

Phased-array RADAR

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

MIMO subarrayed RADAR [8 8 2]

MIMO subarrayed RADAR [8 8 4]

Figure 6 The overall beampattern for [119873119905 119873119903 119873119904] = [8 8 2] and

[8 8 4]

Phased-array RADARMIMO subarrayed RADAR [10 10 2]

MIMO subarrayed RADAR [10 10 5]

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 7The overall beampattern for [119873119905 119873119903 119873119904] = [10 10 2] and

[10 10 5]

(1) Sensitivity is the probability of detecting a cancer ifit is actually present in the breast For example if5 women who have cancer are tested and cancer isdetected in 4 of them then the sensitivity is 45 or80

(2) Specificity is the probability of determining that thereis no cancer when in fact no cancer is presentthereby avoiding a false-positive finding If 200women without cancer are examined and 190 arecorrectly told that they do not have cancer (while

6 Advances in Bioinformatics

Table 2 Estimation errors for the case of one target 119870 = 1

[119873119905119873119903119873119904]

Absolute mean error(degrees)

[2 2 2] 55[4 4 2] 211[6 6 3] 053[8 8 2] 043[8 8 4] 035[10 10 2] 027[10 10 5] 023[gt10 gt10 any number] about 02

0 20 40 60 80

0

20

Phased-array RADARMIMO subarrayed RADAR

Pow

er sp

ectr

um (d

B)

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 8Theoverall beampattern for two targets at 0 and 20 degreesusing119873

119905= 119873119903= 8 and119873

119904= 4

the other 10 have further examination) then thespecificity is 190200 or 95

Most medical tests do not have a single sensitivity orspecificity Instead these can be varied according to howthe test is performed or interpreted One graphic way ofdescribing the performance characteristics of a test is throughwhat is known as its receiver operating characteristic (ROC)where the sensitivity versus 1-specificity of a test is plottedA perfect test represented by the dot in the upper left handcorner of the plot would find all cancers (100 sensitivity)and create no false positives (100 specificity) To be ableto evaluate such a performance due to lacking of real dataand real testbeds an additional simulation experiment hasbeen carried out One hundred different types of testbeds arerandomly generated with uniform distribution to representone hundred different testbeds with one target (119870 = 1)(cancer cell) or without cancer The breasts of each testbedhave different sizes and densities which can be modeledwith different Nakagami parameter 119898 varying from 119898 =

Table 3 Estimation errors for the case of multiple targets 119870 = 2 3

Number of targets 119870 Average absolutemean error (degrees)

2 at [0 10] degree119873119905= 16119873

119903= 16 and119873

119904= 4

033

2 at [0 20] degree119873119905= 8119873

119903= 8 and119873

119904= 4

034

3 at [0 10 20] degree119873119905= 16119873

119903= 16 and119873

119904= 4

036

3 at [0 20 40] degree119873119905= 8119873

119903= 8 and119873

119904= 4

035

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 9 The overall beampattern for three targets at 0 20 and 40degrees119873

119905= 119873119903= 8 and119873

119904= 4

05 to 119898 = 1 [23] All one hundred cases are randomlyassigned to each testbed The simulation is run one hundredtimes (realizations) The result is shown in the ROC curvein Figure 12 The results from another one hundred differenttestbeds with multiple targets (119870 = 2 and 3) and also withoutcancer are compared to the one target case As it can beseen the ROC performances for the multiple target cases areslightly worse than the ones for the one target cases Similar tothe results of the previously presented detection performancethe ROC performance improves as the number of antennasincreases

5 Conclusion and Future Work

In this paper a subarrayed MIMO RADAR to detect breastcancer position was proposed The ultrasound frequencyband was selected for the proposed system because it issafe and commonly used for medical applications Since abreast is a superficial structure high-frequency ultrasonictransducers were used The transmit and receive antenna

Advances in Bioinformatics 7

minus80 minus60 minus40 minus20 0 20 40 60 80

minus100

minus80

minus60

minus40

minus20

0

20

Pow

er sp

ectr

um (d

B)

minus120

Phased-array RADARMIMO subarrayed RADAR

Angle (deg)

Figure 10 The overall beampattern for two targets at 0 and 10degrees119873

119905= 119873119903= 16 and119873

119904= 4

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 11 The overall beampattern for three targets at 0 10 and 20degrees119873

119905= 119873119903= 16 and119873

119904= 4

arrays were divided into subarrays Each subarray usesdifferent orthogonal waveforms providing the signal diver-sity that enables an improved performance Closed formexpressions for the optimal Neyman-Pearson detector werederived The proposed system combines waveform diversitymade possible by the subarrayed deployment and traditionalphased-array RADAR together with an optimal Neyman-Pearson detection The system shows promising results forthe detection of breast cancer position not only in the caseof one target node but also in the case of multiple targetnodes

0 02 04 06 08 1

01

02

03

04

05

06

07

08

09

1

Sens

itivi

ty

0

One target [8 8 4]Multiple targets [8 8 4]One target [8 8 2]Multiple targets [8 8 2]

One target [6 6 3]Multiple targets [6 6 3]One target [4 4 2]Multiple targets [4 4 2]

1 minus specificity

Figure 12 The ROC curve for both one target and multiple targetcases

The system described in this paper determines the direc-tion or angle with respect to the ULA where the targets arelocated As future work we intend to use a two-dimensionaldeployment of ULAs so that by properly combining theestimated angles the 3D locations of the targets are esti-mated

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] E C Fear S C Hagness P M Meaney M Okoniewski andMA Stuchly ldquoEnhancing breast tumor detection with near-fieldimagingrdquo IEEE Microwave Magazine vol 3 no 1 pp 48ndash562002

[2] P T Huynh A M Jarolimek and S Daye ldquoThe false-negativemammogramrdquo Radiographics vol 18 no 5 pp 1137ndash1154 1998

[3] J G Elmore M B Barton V M Moceri S Polk P J Arenaand S W Fletcher ldquoTen-year risk of false positive screeningmammograms and clinical breast examinationsrdquo The NewEngland Journal of Medicine vol 338 no 16 pp 1089ndash10961998

[4] A J Surowiec S S Stuchly J R Barr andA Swarup ldquoDielectricproperties of breast carcinoma and the surrounding tissuesrdquoIEEE Transactions on Biomedical Engineering vol 35 no 4 pp257ndash263 1988

[5] W T Joines Y Zhang C Li and R L Jirtle ldquoThe measuredelectrical properties of normal and malignant human tissuesfrom 50 to 900 MHzrdquo Medical Physics vol 21 no 4 pp 547ndash550 1994

[6] S S Chaudhary R K Mishra A Swarup and J M ThomasldquoDielectric properties of normal amp malignant human breast

8 Advances in Bioinformatics

tissues at radiowave amp microwave frequenciesrdquo Indian Journalof Biochemistry and Biophysics vol 21 no 1 pp 76ndash79 1984

[7] E Brookner ldquoPhase arrays around the world progress andfuture trendsrdquo in Proceedings of the IEEE International Sympo-sium Phased Array Systems and Technology pp 1ndash8 October2008

[8] J Y Lee and E A Morris ldquoBreast MRI historical overviewrdquoin Breast MRI diagnosis and intervention E A Morris and LLiberman Eds pp 3ndash6 Springer New York NY USA 2005

[9] L Galluccio T Melodia S Palazzo and G E SantagatildquoChallenges and implications of using ultrasonic communica-tions in intra-body area networksrdquo in Proceedings of the 9thAnnual Conference on Wireless On-Demand Network Systemsand Services (WONS rsquo12) pp 182ndash189 January 2012

[10] S G Orel and M D Schnall ldquoMR imaging of the breast for thedetection diagnosis and staging of breast cancerrdquo Radiologyvol 220 no 1 pp 13ndash30 2001

[11] M Fink G Montaldo and M Tanter ldquoTime-reversal acousticsin biomedical engineeringrdquo Annual Review of Biomedical Engi-neering vol 5 pp 465ndash497 2003

[12] L Swindlehurst and P Stoica ldquoMaximum likelihood methodsin radar array signal processingrdquo Proceedings of the IEEE vol86 no 2 pp 421ndash441 1998

[13] D W Bliss and K W Forsythe ldquoMultiple-input multiple-output (MIMO) radar and imaging degrees of freedom andresolutionrdquo in Proceedings of the 37th Asilomar Conference onSignals Systems and Computers pp 54ndash59 November 2003

[14] E Fishler A Haimovich R Blum L Cimini D Chizhik andR Valenzuela ldquoMIMO radar an idea whose time has comerdquo inProceedings of the IEEE Radar Conference pp 71ndash78 April 2004

[15] A de Maio and M Lops ldquoDesign principles of MIMO radardetectorsrdquo IEEE Transactions on Aerospace and Electronic Sys-tems vol 43 no 3 pp 886ndash898 2007

[16] J Li and P Stoica ldquoMIMO radar with colocated antennasrdquo IEEESignal Processing Magazine vol 24 no 5 pp 106ndash114 2007

[17] G Zhu B Oreshkin E Porter M Coates and M PopovicldquoNumerical breast models for commercial FDTD simulatorsrdquoin Proceedings of the 3rd European Conference on Antennas andPropagation pp 263ndash267 March 2009

[18] S K Davis H Tandradinata S C Hagness and B D vanVeen ldquoUltrawideband microwave breast cancer detection adetection-theoretic approach using the generalized likelihoodratio testrdquo IEEE Transactions on Biomedical Engineering vol 52no 7 pp 1237ndash1250 2005

[19] N Bahbah H Djelouah and A Bouakaz ldquoUse of Nakagamistatistical model in ultrasonic tissuemimicking phantoms char-acterizationrdquo in Proceedings of the 24th International Conferenceon Microelectronics (ICM rsquo12) December 2012

[20] L Xu P Stoica and J Li ldquoParameter estimation and numberdetection of MIMO radar targetsrdquo in Proceedings of the 41stAsilomar Conference on Signals Systems andComputers (ACSSCrsquo07) pp 177ndash181 Pacific Grove Calif USA November 2007

[21] T R Nelson J B Fowlkes J S Abramowicz and C CChurch ldquoUltrasound biosafety considerations for the practicingsonographer and sonologistrdquo Journal of Ultrasound inMedicinevol 28 no 2 pp 139ndash150 2009

[22] HMadjarThePractice of Breast Ul Trasound Techniques Find-ings Differential Diagnosis Georg Thieme Stuttgart Germany2000

[23] J Mamou A Coron M L Oelze et al ldquoThree-dimensionalhigh-frequency backscatter and envelope quantification ofcancerous human lymph nodesrdquo Ultrasound in Medicine andBiology vol 37 no 3 pp 345ndash357 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

4 Advances in Bioinformatics

Table 1 Simulation parameters

Parameters Values (units)Monte-Carlo run 1000 (runs)Carrier frequency 15 (MHz)Transmit power intensity 700 (mWcm2)Speed of the ultrasonic signal in breast 1500 (ms)Time samples of the baseband equivalent signals 119871 10

6 (samples)[119873119905119873119903119873119904] [2 2 2] [4 4 2] [6 6 3] [8 8 4] [8 8 2] [10 10 5] [10 10 2]

Number of the targets 119870 1 2 3 (points)Direction of the targets for 119870 = 1 10 (degree)Direction of the targets for 119870 = 2 [0 10] [0 20] (degree)Direction of the targets for 119870 = 3 [0 10 20] [0 20 40] (degree)

The result from (14) is substituted into (15) to find 120574ML Thenumber of targets (cancer cells)119870 is unknown but they can beestimated using a Bayesian information criterion (BIC) [20]119870 is estimated minimizing the following BIC cost function

BIC (119870) = 2119891 (120579 120574) + 3119870 ln 119871 (16)

where 120579 and 120574 are the estimates of 120579 and 120574 which are obtainedfrom (14) and (15) respectively 119891 is given by

119891 (120579 120574) = 119871 ln 10038161003816100381610038161003816(z minus Y (120579) 120574) (z minus Y (120579) 120574)

11986710038161003816100381610038161003816 (17)

4 Simulation and Results

The performance of the proposed system is evaluatedusing Monte-Carlo simulations with 10

6 runs All simula-tion parameters are summarized in Table 1 Current limitsimposed by ultrasound safety regulations dictated by theFood and Drug Administration (FDA) an agency of theUS federal government allow for power intensities of up to720mWcm2 [21] Within this limit a power normalizationis carried out so that the target power is fixed to 0 dB Firstit is assumed that there is only one cancer cell position thatis 119870 = 1 in the breast Using the above mentioned BIC thenumber of targets (cancer cells) 119870 is estimated to be 124and it is then rounded to 1 The actual target direction withrespect to the receive ULA 120579 is set to 10 degrees Since thecarrier frequency applied in the simulations is 15MHz andthe speed of the signal in the breast is assumed to be 1500ms[22] the wavelength 120582 becomes 1500(15 times 10

6) = 100 120583m

The number of antennas in both transmit and receive ULAs119873119905times 119873119903is varied as follows 2 times 2 4 times 4 6 times 6 8 times 8

and 10 times 10 The number of subarrays 119873119904for each case is

shown in the same table The overall beampatterns or powerspectrums versus angles (which can provide the position ofthe target using the standard trigonometry expressions) foreach case are shown in Figures 3 4 5 6 and 7 It can beobserved that the estimation performances of the proposedsystem are better than the ones from the traditional phased-array RADAR technique since the central lobe is smallerThebeamwidths are reduced when the number of antennas in

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

Figure 3 The overall beampattern for [119873119905 119873119903 119873119904] = [2 2 2]

the ULAs increases meaning that the accuracy of the targetposition estimate becomes better In addition the larger 119873

119904

is the higher the accuracy of the target position estimate isIn practice the number of antennas in both ULAs cannot betoo large 119873

119905and 119873

119903 when more than 10 do not give much

different results than when they are 10 Therefore119873119905= 119873119903=

10 is deemed to provide sufficiently good estimates and itis more practical for an actual implementation The absolutemean error in degree is summarized in Table 2

The evaluation is extended for the multiple-target casethat is 119870 = 2 and 3 The case of using 119873

119905= 119873119903

= 8

and 119873119904= 4 is first considered With the above mentioned

BIC the number of targets (cancer cells) 119870 is estimatedto be 205 and 310 and rounded to 2 and 3 respectivelyThe simulation results for 119870 = 2 at 0 and 20 degrees andfor 119870 = 3 at 0 20 and 40 degrees are shown in Figures8 and 9 Due to the smaller central lobe of the overallbeampatterns the estimation performances of the proposed

Advances in Bioinformatics 5

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

Figure 4 The overall beampattern for [119873119905 119873119903 119873119904] = [4 4 2]

0 20 40 60 80

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 5 The overall beampattern for [119873119905 119873119903 119873119904] = [6 6 3]

system are considered to be better than the ones from thetraditional phased-array RADAR technique As it can be seenin Figure 9 it is still possible to use 119873

119905= 119873119903= 8 and 119873

119904= 4

to successfully detect three targets when they are located 20degrees apart However it is not possible when the targets arelocated closer for example 10 degrees For this case moreantennas are requiredThe number of antennas was increaseduntil119873

119905= 119873119903= 16 and119873

119904= 4were found to be able to detect

the targets located 10 degrees apart as shown in Figures 10 and11 The closer the locations of multiple targets are the moreantennas are needed The average absolute mean error overfor case investigated is summarized in Table 3

In addition to the system evaluation presented above acommon technique that used for early breast cancer detectionis expressed in terms of sensitivity and specificity

0 20 40 60 80

0

20

Pow

er sp

ectr

um (d

B)

Phased-array RADAR

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

MIMO subarrayed RADAR [8 8 2]

MIMO subarrayed RADAR [8 8 4]

Figure 6 The overall beampattern for [119873119905 119873119903 119873119904] = [8 8 2] and

[8 8 4]

Phased-array RADARMIMO subarrayed RADAR [10 10 2]

MIMO subarrayed RADAR [10 10 5]

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 7The overall beampattern for [119873119905 119873119903 119873119904] = [10 10 2] and

[10 10 5]

(1) Sensitivity is the probability of detecting a cancer ifit is actually present in the breast For example if5 women who have cancer are tested and cancer isdetected in 4 of them then the sensitivity is 45 or80

(2) Specificity is the probability of determining that thereis no cancer when in fact no cancer is presentthereby avoiding a false-positive finding If 200women without cancer are examined and 190 arecorrectly told that they do not have cancer (while

6 Advances in Bioinformatics

Table 2 Estimation errors for the case of one target 119870 = 1

[119873119905119873119903119873119904]

Absolute mean error(degrees)

[2 2 2] 55[4 4 2] 211[6 6 3] 053[8 8 2] 043[8 8 4] 035[10 10 2] 027[10 10 5] 023[gt10 gt10 any number] about 02

0 20 40 60 80

0

20

Phased-array RADARMIMO subarrayed RADAR

Pow

er sp

ectr

um (d

B)

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 8Theoverall beampattern for two targets at 0 and 20 degreesusing119873

119905= 119873119903= 8 and119873

119904= 4

the other 10 have further examination) then thespecificity is 190200 or 95

Most medical tests do not have a single sensitivity orspecificity Instead these can be varied according to howthe test is performed or interpreted One graphic way ofdescribing the performance characteristics of a test is throughwhat is known as its receiver operating characteristic (ROC)where the sensitivity versus 1-specificity of a test is plottedA perfect test represented by the dot in the upper left handcorner of the plot would find all cancers (100 sensitivity)and create no false positives (100 specificity) To be ableto evaluate such a performance due to lacking of real dataand real testbeds an additional simulation experiment hasbeen carried out One hundred different types of testbeds arerandomly generated with uniform distribution to representone hundred different testbeds with one target (119870 = 1)(cancer cell) or without cancer The breasts of each testbedhave different sizes and densities which can be modeledwith different Nakagami parameter 119898 varying from 119898 =

Table 3 Estimation errors for the case of multiple targets 119870 = 2 3

Number of targets 119870 Average absolutemean error (degrees)

2 at [0 10] degree119873119905= 16119873

119903= 16 and119873

119904= 4

033

2 at [0 20] degree119873119905= 8119873

119903= 8 and119873

119904= 4

034

3 at [0 10 20] degree119873119905= 16119873

119903= 16 and119873

119904= 4

036

3 at [0 20 40] degree119873119905= 8119873

119903= 8 and119873

119904= 4

035

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 9 The overall beampattern for three targets at 0 20 and 40degrees119873

119905= 119873119903= 8 and119873

119904= 4

05 to 119898 = 1 [23] All one hundred cases are randomlyassigned to each testbed The simulation is run one hundredtimes (realizations) The result is shown in the ROC curvein Figure 12 The results from another one hundred differenttestbeds with multiple targets (119870 = 2 and 3) and also withoutcancer are compared to the one target case As it can beseen the ROC performances for the multiple target cases areslightly worse than the ones for the one target cases Similar tothe results of the previously presented detection performancethe ROC performance improves as the number of antennasincreases

5 Conclusion and Future Work

In this paper a subarrayed MIMO RADAR to detect breastcancer position was proposed The ultrasound frequencyband was selected for the proposed system because it issafe and commonly used for medical applications Since abreast is a superficial structure high-frequency ultrasonictransducers were used The transmit and receive antenna

Advances in Bioinformatics 7

minus80 minus60 minus40 minus20 0 20 40 60 80

minus100

minus80

minus60

minus40

minus20

0

20

Pow

er sp

ectr

um (d

B)

minus120

Phased-array RADARMIMO subarrayed RADAR

Angle (deg)

Figure 10 The overall beampattern for two targets at 0 and 10degrees119873

119905= 119873119903= 16 and119873

119904= 4

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 11 The overall beampattern for three targets at 0 10 and 20degrees119873

119905= 119873119903= 16 and119873

119904= 4

arrays were divided into subarrays Each subarray usesdifferent orthogonal waveforms providing the signal diver-sity that enables an improved performance Closed formexpressions for the optimal Neyman-Pearson detector werederived The proposed system combines waveform diversitymade possible by the subarrayed deployment and traditionalphased-array RADAR together with an optimal Neyman-Pearson detection The system shows promising results forthe detection of breast cancer position not only in the caseof one target node but also in the case of multiple targetnodes

0 02 04 06 08 1

01

02

03

04

05

06

07

08

09

1

Sens

itivi

ty

0

One target [8 8 4]Multiple targets [8 8 4]One target [8 8 2]Multiple targets [8 8 2]

One target [6 6 3]Multiple targets [6 6 3]One target [4 4 2]Multiple targets [4 4 2]

1 minus specificity

Figure 12 The ROC curve for both one target and multiple targetcases

The system described in this paper determines the direc-tion or angle with respect to the ULA where the targets arelocated As future work we intend to use a two-dimensionaldeployment of ULAs so that by properly combining theestimated angles the 3D locations of the targets are esti-mated

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] E C Fear S C Hagness P M Meaney M Okoniewski andMA Stuchly ldquoEnhancing breast tumor detection with near-fieldimagingrdquo IEEE Microwave Magazine vol 3 no 1 pp 48ndash562002

[2] P T Huynh A M Jarolimek and S Daye ldquoThe false-negativemammogramrdquo Radiographics vol 18 no 5 pp 1137ndash1154 1998

[3] J G Elmore M B Barton V M Moceri S Polk P J Arenaand S W Fletcher ldquoTen-year risk of false positive screeningmammograms and clinical breast examinationsrdquo The NewEngland Journal of Medicine vol 338 no 16 pp 1089ndash10961998

[4] A J Surowiec S S Stuchly J R Barr andA Swarup ldquoDielectricproperties of breast carcinoma and the surrounding tissuesrdquoIEEE Transactions on Biomedical Engineering vol 35 no 4 pp257ndash263 1988

[5] W T Joines Y Zhang C Li and R L Jirtle ldquoThe measuredelectrical properties of normal and malignant human tissuesfrom 50 to 900 MHzrdquo Medical Physics vol 21 no 4 pp 547ndash550 1994

[6] S S Chaudhary R K Mishra A Swarup and J M ThomasldquoDielectric properties of normal amp malignant human breast

8 Advances in Bioinformatics

tissues at radiowave amp microwave frequenciesrdquo Indian Journalof Biochemistry and Biophysics vol 21 no 1 pp 76ndash79 1984

[7] E Brookner ldquoPhase arrays around the world progress andfuture trendsrdquo in Proceedings of the IEEE International Sympo-sium Phased Array Systems and Technology pp 1ndash8 October2008

[8] J Y Lee and E A Morris ldquoBreast MRI historical overviewrdquoin Breast MRI diagnosis and intervention E A Morris and LLiberman Eds pp 3ndash6 Springer New York NY USA 2005

[9] L Galluccio T Melodia S Palazzo and G E SantagatildquoChallenges and implications of using ultrasonic communica-tions in intra-body area networksrdquo in Proceedings of the 9thAnnual Conference on Wireless On-Demand Network Systemsand Services (WONS rsquo12) pp 182ndash189 January 2012

[10] S G Orel and M D Schnall ldquoMR imaging of the breast for thedetection diagnosis and staging of breast cancerrdquo Radiologyvol 220 no 1 pp 13ndash30 2001

[11] M Fink G Montaldo and M Tanter ldquoTime-reversal acousticsin biomedical engineeringrdquo Annual Review of Biomedical Engi-neering vol 5 pp 465ndash497 2003

[12] L Swindlehurst and P Stoica ldquoMaximum likelihood methodsin radar array signal processingrdquo Proceedings of the IEEE vol86 no 2 pp 421ndash441 1998

[13] D W Bliss and K W Forsythe ldquoMultiple-input multiple-output (MIMO) radar and imaging degrees of freedom andresolutionrdquo in Proceedings of the 37th Asilomar Conference onSignals Systems and Computers pp 54ndash59 November 2003

[14] E Fishler A Haimovich R Blum L Cimini D Chizhik andR Valenzuela ldquoMIMO radar an idea whose time has comerdquo inProceedings of the IEEE Radar Conference pp 71ndash78 April 2004

[15] A de Maio and M Lops ldquoDesign principles of MIMO radardetectorsrdquo IEEE Transactions on Aerospace and Electronic Sys-tems vol 43 no 3 pp 886ndash898 2007

[16] J Li and P Stoica ldquoMIMO radar with colocated antennasrdquo IEEESignal Processing Magazine vol 24 no 5 pp 106ndash114 2007

[17] G Zhu B Oreshkin E Porter M Coates and M PopovicldquoNumerical breast models for commercial FDTD simulatorsrdquoin Proceedings of the 3rd European Conference on Antennas andPropagation pp 263ndash267 March 2009

[18] S K Davis H Tandradinata S C Hagness and B D vanVeen ldquoUltrawideband microwave breast cancer detection adetection-theoretic approach using the generalized likelihoodratio testrdquo IEEE Transactions on Biomedical Engineering vol 52no 7 pp 1237ndash1250 2005

[19] N Bahbah H Djelouah and A Bouakaz ldquoUse of Nakagamistatistical model in ultrasonic tissuemimicking phantoms char-acterizationrdquo in Proceedings of the 24th International Conferenceon Microelectronics (ICM rsquo12) December 2012

[20] L Xu P Stoica and J Li ldquoParameter estimation and numberdetection of MIMO radar targetsrdquo in Proceedings of the 41stAsilomar Conference on Signals Systems andComputers (ACSSCrsquo07) pp 177ndash181 Pacific Grove Calif USA November 2007

[21] T R Nelson J B Fowlkes J S Abramowicz and C CChurch ldquoUltrasound biosafety considerations for the practicingsonographer and sonologistrdquo Journal of Ultrasound inMedicinevol 28 no 2 pp 139ndash150 2009

[22] HMadjarThePractice of Breast Ul Trasound Techniques Find-ings Differential Diagnosis Georg Thieme Stuttgart Germany2000

[23] J Mamou A Coron M L Oelze et al ldquoThree-dimensionalhigh-frequency backscatter and envelope quantification ofcancerous human lymph nodesrdquo Ultrasound in Medicine andBiology vol 37 no 3 pp 345ndash357 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

Advances in Bioinformatics 5

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

Figure 4 The overall beampattern for [119873119905 119873119903 119873119904] = [4 4 2]

0 20 40 60 80

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Phased-array RADARMIMO subarrayed RADAR

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 5 The overall beampattern for [119873119905 119873119903 119873119904] = [6 6 3]

system are considered to be better than the ones from thetraditional phased-array RADAR technique As it can be seenin Figure 9 it is still possible to use 119873

119905= 119873119903= 8 and 119873

119904= 4

to successfully detect three targets when they are located 20degrees apart However it is not possible when the targets arelocated closer for example 10 degrees For this case moreantennas are requiredThe number of antennas was increaseduntil119873

119905= 119873119903= 16 and119873

119904= 4were found to be able to detect

the targets located 10 degrees apart as shown in Figures 10 and11 The closer the locations of multiple targets are the moreantennas are needed The average absolute mean error overfor case investigated is summarized in Table 3

In addition to the system evaluation presented above acommon technique that used for early breast cancer detectionis expressed in terms of sensitivity and specificity

0 20 40 60 80

0

20

Pow

er sp

ectr

um (d

B)

Phased-array RADAR

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

MIMO subarrayed RADAR [8 8 2]

MIMO subarrayed RADAR [8 8 4]

Figure 6 The overall beampattern for [119873119905 119873119903 119873119904] = [8 8 2] and

[8 8 4]

Phased-array RADARMIMO subarrayed RADAR [10 10 2]

MIMO subarrayed RADAR [10 10 5]

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 7The overall beampattern for [119873119905 119873119903 119873119904] = [10 10 2] and

[10 10 5]

(1) Sensitivity is the probability of detecting a cancer ifit is actually present in the breast For example if5 women who have cancer are tested and cancer isdetected in 4 of them then the sensitivity is 45 or80

(2) Specificity is the probability of determining that thereis no cancer when in fact no cancer is presentthereby avoiding a false-positive finding If 200women without cancer are examined and 190 arecorrectly told that they do not have cancer (while

6 Advances in Bioinformatics

Table 2 Estimation errors for the case of one target 119870 = 1

[119873119905119873119903119873119904]

Absolute mean error(degrees)

[2 2 2] 55[4 4 2] 211[6 6 3] 053[8 8 2] 043[8 8 4] 035[10 10 2] 027[10 10 5] 023[gt10 gt10 any number] about 02

0 20 40 60 80

0

20

Phased-array RADARMIMO subarrayed RADAR

Pow

er sp

ectr

um (d

B)

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 8Theoverall beampattern for two targets at 0 and 20 degreesusing119873

119905= 119873119903= 8 and119873

119904= 4

the other 10 have further examination) then thespecificity is 190200 or 95

Most medical tests do not have a single sensitivity orspecificity Instead these can be varied according to howthe test is performed or interpreted One graphic way ofdescribing the performance characteristics of a test is throughwhat is known as its receiver operating characteristic (ROC)where the sensitivity versus 1-specificity of a test is plottedA perfect test represented by the dot in the upper left handcorner of the plot would find all cancers (100 sensitivity)and create no false positives (100 specificity) To be ableto evaluate such a performance due to lacking of real dataand real testbeds an additional simulation experiment hasbeen carried out One hundred different types of testbeds arerandomly generated with uniform distribution to representone hundred different testbeds with one target (119870 = 1)(cancer cell) or without cancer The breasts of each testbedhave different sizes and densities which can be modeledwith different Nakagami parameter 119898 varying from 119898 =

Table 3 Estimation errors for the case of multiple targets 119870 = 2 3

Number of targets 119870 Average absolutemean error (degrees)

2 at [0 10] degree119873119905= 16119873

119903= 16 and119873

119904= 4

033

2 at [0 20] degree119873119905= 8119873

119903= 8 and119873

119904= 4

034

3 at [0 10 20] degree119873119905= 16119873

119903= 16 and119873

119904= 4

036

3 at [0 20 40] degree119873119905= 8119873

119903= 8 and119873

119904= 4

035

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 9 The overall beampattern for three targets at 0 20 and 40degrees119873

119905= 119873119903= 8 and119873

119904= 4

05 to 119898 = 1 [23] All one hundred cases are randomlyassigned to each testbed The simulation is run one hundredtimes (realizations) The result is shown in the ROC curvein Figure 12 The results from another one hundred differenttestbeds with multiple targets (119870 = 2 and 3) and also withoutcancer are compared to the one target case As it can beseen the ROC performances for the multiple target cases areslightly worse than the ones for the one target cases Similar tothe results of the previously presented detection performancethe ROC performance improves as the number of antennasincreases

5 Conclusion and Future Work

In this paper a subarrayed MIMO RADAR to detect breastcancer position was proposed The ultrasound frequencyband was selected for the proposed system because it issafe and commonly used for medical applications Since abreast is a superficial structure high-frequency ultrasonictransducers were used The transmit and receive antenna

Advances in Bioinformatics 7

minus80 minus60 minus40 minus20 0 20 40 60 80

minus100

minus80

minus60

minus40

minus20

0

20

Pow

er sp

ectr

um (d

B)

minus120

Phased-array RADARMIMO subarrayed RADAR

Angle (deg)

Figure 10 The overall beampattern for two targets at 0 and 10degrees119873

119905= 119873119903= 16 and119873

119904= 4

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 11 The overall beampattern for three targets at 0 10 and 20degrees119873

119905= 119873119903= 16 and119873

119904= 4

arrays were divided into subarrays Each subarray usesdifferent orthogonal waveforms providing the signal diver-sity that enables an improved performance Closed formexpressions for the optimal Neyman-Pearson detector werederived The proposed system combines waveform diversitymade possible by the subarrayed deployment and traditionalphased-array RADAR together with an optimal Neyman-Pearson detection The system shows promising results forthe detection of breast cancer position not only in the caseof one target node but also in the case of multiple targetnodes

0 02 04 06 08 1

01

02

03

04

05

06

07

08

09

1

Sens

itivi

ty

0

One target [8 8 4]Multiple targets [8 8 4]One target [8 8 2]Multiple targets [8 8 2]

One target [6 6 3]Multiple targets [6 6 3]One target [4 4 2]Multiple targets [4 4 2]

1 minus specificity

Figure 12 The ROC curve for both one target and multiple targetcases

The system described in this paper determines the direc-tion or angle with respect to the ULA where the targets arelocated As future work we intend to use a two-dimensionaldeployment of ULAs so that by properly combining theestimated angles the 3D locations of the targets are esti-mated

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] E C Fear S C Hagness P M Meaney M Okoniewski andMA Stuchly ldquoEnhancing breast tumor detection with near-fieldimagingrdquo IEEE Microwave Magazine vol 3 no 1 pp 48ndash562002

[2] P T Huynh A M Jarolimek and S Daye ldquoThe false-negativemammogramrdquo Radiographics vol 18 no 5 pp 1137ndash1154 1998

[3] J G Elmore M B Barton V M Moceri S Polk P J Arenaand S W Fletcher ldquoTen-year risk of false positive screeningmammograms and clinical breast examinationsrdquo The NewEngland Journal of Medicine vol 338 no 16 pp 1089ndash10961998

[4] A J Surowiec S S Stuchly J R Barr andA Swarup ldquoDielectricproperties of breast carcinoma and the surrounding tissuesrdquoIEEE Transactions on Biomedical Engineering vol 35 no 4 pp257ndash263 1988

[5] W T Joines Y Zhang C Li and R L Jirtle ldquoThe measuredelectrical properties of normal and malignant human tissuesfrom 50 to 900 MHzrdquo Medical Physics vol 21 no 4 pp 547ndash550 1994

[6] S S Chaudhary R K Mishra A Swarup and J M ThomasldquoDielectric properties of normal amp malignant human breast

8 Advances in Bioinformatics

tissues at radiowave amp microwave frequenciesrdquo Indian Journalof Biochemistry and Biophysics vol 21 no 1 pp 76ndash79 1984

[7] E Brookner ldquoPhase arrays around the world progress andfuture trendsrdquo in Proceedings of the IEEE International Sympo-sium Phased Array Systems and Technology pp 1ndash8 October2008

[8] J Y Lee and E A Morris ldquoBreast MRI historical overviewrdquoin Breast MRI diagnosis and intervention E A Morris and LLiberman Eds pp 3ndash6 Springer New York NY USA 2005

[9] L Galluccio T Melodia S Palazzo and G E SantagatildquoChallenges and implications of using ultrasonic communica-tions in intra-body area networksrdquo in Proceedings of the 9thAnnual Conference on Wireless On-Demand Network Systemsand Services (WONS rsquo12) pp 182ndash189 January 2012

[10] S G Orel and M D Schnall ldquoMR imaging of the breast for thedetection diagnosis and staging of breast cancerrdquo Radiologyvol 220 no 1 pp 13ndash30 2001

[11] M Fink G Montaldo and M Tanter ldquoTime-reversal acousticsin biomedical engineeringrdquo Annual Review of Biomedical Engi-neering vol 5 pp 465ndash497 2003

[12] L Swindlehurst and P Stoica ldquoMaximum likelihood methodsin radar array signal processingrdquo Proceedings of the IEEE vol86 no 2 pp 421ndash441 1998

[13] D W Bliss and K W Forsythe ldquoMultiple-input multiple-output (MIMO) radar and imaging degrees of freedom andresolutionrdquo in Proceedings of the 37th Asilomar Conference onSignals Systems and Computers pp 54ndash59 November 2003

[14] E Fishler A Haimovich R Blum L Cimini D Chizhik andR Valenzuela ldquoMIMO radar an idea whose time has comerdquo inProceedings of the IEEE Radar Conference pp 71ndash78 April 2004

[15] A de Maio and M Lops ldquoDesign principles of MIMO radardetectorsrdquo IEEE Transactions on Aerospace and Electronic Sys-tems vol 43 no 3 pp 886ndash898 2007

[16] J Li and P Stoica ldquoMIMO radar with colocated antennasrdquo IEEESignal Processing Magazine vol 24 no 5 pp 106ndash114 2007

[17] G Zhu B Oreshkin E Porter M Coates and M PopovicldquoNumerical breast models for commercial FDTD simulatorsrdquoin Proceedings of the 3rd European Conference on Antennas andPropagation pp 263ndash267 March 2009

[18] S K Davis H Tandradinata S C Hagness and B D vanVeen ldquoUltrawideband microwave breast cancer detection adetection-theoretic approach using the generalized likelihoodratio testrdquo IEEE Transactions on Biomedical Engineering vol 52no 7 pp 1237ndash1250 2005

[19] N Bahbah H Djelouah and A Bouakaz ldquoUse of Nakagamistatistical model in ultrasonic tissuemimicking phantoms char-acterizationrdquo in Proceedings of the 24th International Conferenceon Microelectronics (ICM rsquo12) December 2012

[20] L Xu P Stoica and J Li ldquoParameter estimation and numberdetection of MIMO radar targetsrdquo in Proceedings of the 41stAsilomar Conference on Signals Systems andComputers (ACSSCrsquo07) pp 177ndash181 Pacific Grove Calif USA November 2007

[21] T R Nelson J B Fowlkes J S Abramowicz and C CChurch ldquoUltrasound biosafety considerations for the practicingsonographer and sonologistrdquo Journal of Ultrasound inMedicinevol 28 no 2 pp 139ndash150 2009

[22] HMadjarThePractice of Breast Ul Trasound Techniques Find-ings Differential Diagnosis Georg Thieme Stuttgart Germany2000

[23] J Mamou A Coron M L Oelze et al ldquoThree-dimensionalhigh-frequency backscatter and envelope quantification ofcancerous human lymph nodesrdquo Ultrasound in Medicine andBiology vol 37 no 3 pp 345ndash357 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

6 Advances in Bioinformatics

Table 2 Estimation errors for the case of one target 119870 = 1

[119873119905119873119903119873119904]

Absolute mean error(degrees)

[2 2 2] 55[4 4 2] 211[6 6 3] 053[8 8 2] 043[8 8 4] 035[10 10 2] 027[10 10 5] 023[gt10 gt10 any number] about 02

0 20 40 60 80

0

20

Phased-array RADARMIMO subarrayed RADAR

Pow

er sp

ectr

um (d

B)

Angle (deg)

minus20

minus40

minus60

minus80

minus20minus40minus60minus80

minus100

minus120

Figure 8Theoverall beampattern for two targets at 0 and 20 degreesusing119873

119905= 119873119903= 8 and119873

119904= 4

the other 10 have further examination) then thespecificity is 190200 or 95

Most medical tests do not have a single sensitivity orspecificity Instead these can be varied according to howthe test is performed or interpreted One graphic way ofdescribing the performance characteristics of a test is throughwhat is known as its receiver operating characteristic (ROC)where the sensitivity versus 1-specificity of a test is plottedA perfect test represented by the dot in the upper left handcorner of the plot would find all cancers (100 sensitivity)and create no false positives (100 specificity) To be ableto evaluate such a performance due to lacking of real dataand real testbeds an additional simulation experiment hasbeen carried out One hundred different types of testbeds arerandomly generated with uniform distribution to representone hundred different testbeds with one target (119870 = 1)(cancer cell) or without cancer The breasts of each testbedhave different sizes and densities which can be modeledwith different Nakagami parameter 119898 varying from 119898 =

Table 3 Estimation errors for the case of multiple targets 119870 = 2 3

Number of targets 119870 Average absolutemean error (degrees)

2 at [0 10] degree119873119905= 16119873

119903= 16 and119873

119904= 4

033

2 at [0 20] degree119873119905= 8119873

119903= 8 and119873

119904= 4

034

3 at [0 10 20] degree119873119905= 16119873

119903= 16 and119873

119904= 4

036

3 at [0 20 40] degree119873119905= 8119873

119903= 8 and119873

119904= 4

035

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 9 The overall beampattern for three targets at 0 20 and 40degrees119873

119905= 119873119903= 8 and119873

119904= 4

05 to 119898 = 1 [23] All one hundred cases are randomlyassigned to each testbed The simulation is run one hundredtimes (realizations) The result is shown in the ROC curvein Figure 12 The results from another one hundred differenttestbeds with multiple targets (119870 = 2 and 3) and also withoutcancer are compared to the one target case As it can beseen the ROC performances for the multiple target cases areslightly worse than the ones for the one target cases Similar tothe results of the previously presented detection performancethe ROC performance improves as the number of antennasincreases

5 Conclusion and Future Work

In this paper a subarrayed MIMO RADAR to detect breastcancer position was proposed The ultrasound frequencyband was selected for the proposed system because it issafe and commonly used for medical applications Since abreast is a superficial structure high-frequency ultrasonictransducers were used The transmit and receive antenna

Advances in Bioinformatics 7

minus80 minus60 minus40 minus20 0 20 40 60 80

minus100

minus80

minus60

minus40

minus20

0

20

Pow

er sp

ectr

um (d

B)

minus120

Phased-array RADARMIMO subarrayed RADAR

Angle (deg)

Figure 10 The overall beampattern for two targets at 0 and 10degrees119873

119905= 119873119903= 16 and119873

119904= 4

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 11 The overall beampattern for three targets at 0 10 and 20degrees119873

119905= 119873119903= 16 and119873

119904= 4

arrays were divided into subarrays Each subarray usesdifferent orthogonal waveforms providing the signal diver-sity that enables an improved performance Closed formexpressions for the optimal Neyman-Pearson detector werederived The proposed system combines waveform diversitymade possible by the subarrayed deployment and traditionalphased-array RADAR together with an optimal Neyman-Pearson detection The system shows promising results forthe detection of breast cancer position not only in the caseof one target node but also in the case of multiple targetnodes

0 02 04 06 08 1

01

02

03

04

05

06

07

08

09

1

Sens

itivi

ty

0

One target [8 8 4]Multiple targets [8 8 4]One target [8 8 2]Multiple targets [8 8 2]

One target [6 6 3]Multiple targets [6 6 3]One target [4 4 2]Multiple targets [4 4 2]

1 minus specificity

Figure 12 The ROC curve for both one target and multiple targetcases

The system described in this paper determines the direc-tion or angle with respect to the ULA where the targets arelocated As future work we intend to use a two-dimensionaldeployment of ULAs so that by properly combining theestimated angles the 3D locations of the targets are esti-mated

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] E C Fear S C Hagness P M Meaney M Okoniewski andMA Stuchly ldquoEnhancing breast tumor detection with near-fieldimagingrdquo IEEE Microwave Magazine vol 3 no 1 pp 48ndash562002

[2] P T Huynh A M Jarolimek and S Daye ldquoThe false-negativemammogramrdquo Radiographics vol 18 no 5 pp 1137ndash1154 1998

[3] J G Elmore M B Barton V M Moceri S Polk P J Arenaand S W Fletcher ldquoTen-year risk of false positive screeningmammograms and clinical breast examinationsrdquo The NewEngland Journal of Medicine vol 338 no 16 pp 1089ndash10961998

[4] A J Surowiec S S Stuchly J R Barr andA Swarup ldquoDielectricproperties of breast carcinoma and the surrounding tissuesrdquoIEEE Transactions on Biomedical Engineering vol 35 no 4 pp257ndash263 1988

[5] W T Joines Y Zhang C Li and R L Jirtle ldquoThe measuredelectrical properties of normal and malignant human tissuesfrom 50 to 900 MHzrdquo Medical Physics vol 21 no 4 pp 547ndash550 1994

[6] S S Chaudhary R K Mishra A Swarup and J M ThomasldquoDielectric properties of normal amp malignant human breast

8 Advances in Bioinformatics

tissues at radiowave amp microwave frequenciesrdquo Indian Journalof Biochemistry and Biophysics vol 21 no 1 pp 76ndash79 1984

[7] E Brookner ldquoPhase arrays around the world progress andfuture trendsrdquo in Proceedings of the IEEE International Sympo-sium Phased Array Systems and Technology pp 1ndash8 October2008

[8] J Y Lee and E A Morris ldquoBreast MRI historical overviewrdquoin Breast MRI diagnosis and intervention E A Morris and LLiberman Eds pp 3ndash6 Springer New York NY USA 2005

[9] L Galluccio T Melodia S Palazzo and G E SantagatildquoChallenges and implications of using ultrasonic communica-tions in intra-body area networksrdquo in Proceedings of the 9thAnnual Conference on Wireless On-Demand Network Systemsand Services (WONS rsquo12) pp 182ndash189 January 2012

[10] S G Orel and M D Schnall ldquoMR imaging of the breast for thedetection diagnosis and staging of breast cancerrdquo Radiologyvol 220 no 1 pp 13ndash30 2001

[11] M Fink G Montaldo and M Tanter ldquoTime-reversal acousticsin biomedical engineeringrdquo Annual Review of Biomedical Engi-neering vol 5 pp 465ndash497 2003

[12] L Swindlehurst and P Stoica ldquoMaximum likelihood methodsin radar array signal processingrdquo Proceedings of the IEEE vol86 no 2 pp 421ndash441 1998

[13] D W Bliss and K W Forsythe ldquoMultiple-input multiple-output (MIMO) radar and imaging degrees of freedom andresolutionrdquo in Proceedings of the 37th Asilomar Conference onSignals Systems and Computers pp 54ndash59 November 2003

[14] E Fishler A Haimovich R Blum L Cimini D Chizhik andR Valenzuela ldquoMIMO radar an idea whose time has comerdquo inProceedings of the IEEE Radar Conference pp 71ndash78 April 2004

[15] A de Maio and M Lops ldquoDesign principles of MIMO radardetectorsrdquo IEEE Transactions on Aerospace and Electronic Sys-tems vol 43 no 3 pp 886ndash898 2007

[16] J Li and P Stoica ldquoMIMO radar with colocated antennasrdquo IEEESignal Processing Magazine vol 24 no 5 pp 106ndash114 2007

[17] G Zhu B Oreshkin E Porter M Coates and M PopovicldquoNumerical breast models for commercial FDTD simulatorsrdquoin Proceedings of the 3rd European Conference on Antennas andPropagation pp 263ndash267 March 2009

[18] S K Davis H Tandradinata S C Hagness and B D vanVeen ldquoUltrawideband microwave breast cancer detection adetection-theoretic approach using the generalized likelihoodratio testrdquo IEEE Transactions on Biomedical Engineering vol 52no 7 pp 1237ndash1250 2005

[19] N Bahbah H Djelouah and A Bouakaz ldquoUse of Nakagamistatistical model in ultrasonic tissuemimicking phantoms char-acterizationrdquo in Proceedings of the 24th International Conferenceon Microelectronics (ICM rsquo12) December 2012

[20] L Xu P Stoica and J Li ldquoParameter estimation and numberdetection of MIMO radar targetsrdquo in Proceedings of the 41stAsilomar Conference on Signals Systems andComputers (ACSSCrsquo07) pp 177ndash181 Pacific Grove Calif USA November 2007

[21] T R Nelson J B Fowlkes J S Abramowicz and C CChurch ldquoUltrasound biosafety considerations for the practicingsonographer and sonologistrdquo Journal of Ultrasound inMedicinevol 28 no 2 pp 139ndash150 2009

[22] HMadjarThePractice of Breast Ul Trasound Techniques Find-ings Differential Diagnosis Georg Thieme Stuttgart Germany2000

[23] J Mamou A Coron M L Oelze et al ldquoThree-dimensionalhigh-frequency backscatter and envelope quantification ofcancerous human lymph nodesrdquo Ultrasound in Medicine andBiology vol 37 no 3 pp 345ndash357 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

Advances in Bioinformatics 7

minus80 minus60 minus40 minus20 0 20 40 60 80

minus100

minus80

minus60

minus40

minus20

0

20

Pow

er sp

ectr

um (d

B)

minus120

Phased-array RADARMIMO subarrayed RADAR

Angle (deg)

Figure 10 The overall beampattern for two targets at 0 and 10degrees119873

119905= 119873119903= 16 and119873

119904= 4

Phased-array RADARMIMO subarrayed RADAR

minus80 minus60 minus40 minus20 0 20 40 60 80minus120

minus100

minus80

minus60

minus40

minus20

0

20

Angle (deg)

Pow

er sp

ectr

um (d

B)

Figure 11 The overall beampattern for three targets at 0 10 and 20degrees119873

119905= 119873119903= 16 and119873

119904= 4

arrays were divided into subarrays Each subarray usesdifferent orthogonal waveforms providing the signal diver-sity that enables an improved performance Closed formexpressions for the optimal Neyman-Pearson detector werederived The proposed system combines waveform diversitymade possible by the subarrayed deployment and traditionalphased-array RADAR together with an optimal Neyman-Pearson detection The system shows promising results forthe detection of breast cancer position not only in the caseof one target node but also in the case of multiple targetnodes

0 02 04 06 08 1

01

02

03

04

05

06

07

08

09

1

Sens

itivi

ty

0

One target [8 8 4]Multiple targets [8 8 4]One target [8 8 2]Multiple targets [8 8 2]

One target [6 6 3]Multiple targets [6 6 3]One target [4 4 2]Multiple targets [4 4 2]

1 minus specificity

Figure 12 The ROC curve for both one target and multiple targetcases

The system described in this paper determines the direc-tion or angle with respect to the ULA where the targets arelocated As future work we intend to use a two-dimensionaldeployment of ULAs so that by properly combining theestimated angles the 3D locations of the targets are esti-mated

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] E C Fear S C Hagness P M Meaney M Okoniewski andMA Stuchly ldquoEnhancing breast tumor detection with near-fieldimagingrdquo IEEE Microwave Magazine vol 3 no 1 pp 48ndash562002

[2] P T Huynh A M Jarolimek and S Daye ldquoThe false-negativemammogramrdquo Radiographics vol 18 no 5 pp 1137ndash1154 1998

[3] J G Elmore M B Barton V M Moceri S Polk P J Arenaand S W Fletcher ldquoTen-year risk of false positive screeningmammograms and clinical breast examinationsrdquo The NewEngland Journal of Medicine vol 338 no 16 pp 1089ndash10961998

[4] A J Surowiec S S Stuchly J R Barr andA Swarup ldquoDielectricproperties of breast carcinoma and the surrounding tissuesrdquoIEEE Transactions on Biomedical Engineering vol 35 no 4 pp257ndash263 1988

[5] W T Joines Y Zhang C Li and R L Jirtle ldquoThe measuredelectrical properties of normal and malignant human tissuesfrom 50 to 900 MHzrdquo Medical Physics vol 21 no 4 pp 547ndash550 1994

[6] S S Chaudhary R K Mishra A Swarup and J M ThomasldquoDielectric properties of normal amp malignant human breast

8 Advances in Bioinformatics

tissues at radiowave amp microwave frequenciesrdquo Indian Journalof Biochemistry and Biophysics vol 21 no 1 pp 76ndash79 1984

[7] E Brookner ldquoPhase arrays around the world progress andfuture trendsrdquo in Proceedings of the IEEE International Sympo-sium Phased Array Systems and Technology pp 1ndash8 October2008

[8] J Y Lee and E A Morris ldquoBreast MRI historical overviewrdquoin Breast MRI diagnosis and intervention E A Morris and LLiberman Eds pp 3ndash6 Springer New York NY USA 2005

[9] L Galluccio T Melodia S Palazzo and G E SantagatildquoChallenges and implications of using ultrasonic communica-tions in intra-body area networksrdquo in Proceedings of the 9thAnnual Conference on Wireless On-Demand Network Systemsand Services (WONS rsquo12) pp 182ndash189 January 2012

[10] S G Orel and M D Schnall ldquoMR imaging of the breast for thedetection diagnosis and staging of breast cancerrdquo Radiologyvol 220 no 1 pp 13ndash30 2001

[11] M Fink G Montaldo and M Tanter ldquoTime-reversal acousticsin biomedical engineeringrdquo Annual Review of Biomedical Engi-neering vol 5 pp 465ndash497 2003

[12] L Swindlehurst and P Stoica ldquoMaximum likelihood methodsin radar array signal processingrdquo Proceedings of the IEEE vol86 no 2 pp 421ndash441 1998

[13] D W Bliss and K W Forsythe ldquoMultiple-input multiple-output (MIMO) radar and imaging degrees of freedom andresolutionrdquo in Proceedings of the 37th Asilomar Conference onSignals Systems and Computers pp 54ndash59 November 2003

[14] E Fishler A Haimovich R Blum L Cimini D Chizhik andR Valenzuela ldquoMIMO radar an idea whose time has comerdquo inProceedings of the IEEE Radar Conference pp 71ndash78 April 2004

[15] A de Maio and M Lops ldquoDesign principles of MIMO radardetectorsrdquo IEEE Transactions on Aerospace and Electronic Sys-tems vol 43 no 3 pp 886ndash898 2007

[16] J Li and P Stoica ldquoMIMO radar with colocated antennasrdquo IEEESignal Processing Magazine vol 24 no 5 pp 106ndash114 2007

[17] G Zhu B Oreshkin E Porter M Coates and M PopovicldquoNumerical breast models for commercial FDTD simulatorsrdquoin Proceedings of the 3rd European Conference on Antennas andPropagation pp 263ndash267 March 2009

[18] S K Davis H Tandradinata S C Hagness and B D vanVeen ldquoUltrawideband microwave breast cancer detection adetection-theoretic approach using the generalized likelihoodratio testrdquo IEEE Transactions on Biomedical Engineering vol 52no 7 pp 1237ndash1250 2005

[19] N Bahbah H Djelouah and A Bouakaz ldquoUse of Nakagamistatistical model in ultrasonic tissuemimicking phantoms char-acterizationrdquo in Proceedings of the 24th International Conferenceon Microelectronics (ICM rsquo12) December 2012

[20] L Xu P Stoica and J Li ldquoParameter estimation and numberdetection of MIMO radar targetsrdquo in Proceedings of the 41stAsilomar Conference on Signals Systems andComputers (ACSSCrsquo07) pp 177ndash181 Pacific Grove Calif USA November 2007

[21] T R Nelson J B Fowlkes J S Abramowicz and C CChurch ldquoUltrasound biosafety considerations for the practicingsonographer and sonologistrdquo Journal of Ultrasound inMedicinevol 28 no 2 pp 139ndash150 2009

[22] HMadjarThePractice of Breast Ul Trasound Techniques Find-ings Differential Diagnosis Georg Thieme Stuttgart Germany2000

[23] J Mamou A Coron M L Oelze et al ldquoThree-dimensionalhigh-frequency backscatter and envelope quantification ofcancerous human lymph nodesrdquo Ultrasound in Medicine andBiology vol 37 no 3 pp 345ndash357 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

8 Advances in Bioinformatics

tissues at radiowave amp microwave frequenciesrdquo Indian Journalof Biochemistry and Biophysics vol 21 no 1 pp 76ndash79 1984

[7] E Brookner ldquoPhase arrays around the world progress andfuture trendsrdquo in Proceedings of the IEEE International Sympo-sium Phased Array Systems and Technology pp 1ndash8 October2008

[8] J Y Lee and E A Morris ldquoBreast MRI historical overviewrdquoin Breast MRI diagnosis and intervention E A Morris and LLiberman Eds pp 3ndash6 Springer New York NY USA 2005

[9] L Galluccio T Melodia S Palazzo and G E SantagatildquoChallenges and implications of using ultrasonic communica-tions in intra-body area networksrdquo in Proceedings of the 9thAnnual Conference on Wireless On-Demand Network Systemsand Services (WONS rsquo12) pp 182ndash189 January 2012

[10] S G Orel and M D Schnall ldquoMR imaging of the breast for thedetection diagnosis and staging of breast cancerrdquo Radiologyvol 220 no 1 pp 13ndash30 2001

[11] M Fink G Montaldo and M Tanter ldquoTime-reversal acousticsin biomedical engineeringrdquo Annual Review of Biomedical Engi-neering vol 5 pp 465ndash497 2003

[12] L Swindlehurst and P Stoica ldquoMaximum likelihood methodsin radar array signal processingrdquo Proceedings of the IEEE vol86 no 2 pp 421ndash441 1998

[13] D W Bliss and K W Forsythe ldquoMultiple-input multiple-output (MIMO) radar and imaging degrees of freedom andresolutionrdquo in Proceedings of the 37th Asilomar Conference onSignals Systems and Computers pp 54ndash59 November 2003

[14] E Fishler A Haimovich R Blum L Cimini D Chizhik andR Valenzuela ldquoMIMO radar an idea whose time has comerdquo inProceedings of the IEEE Radar Conference pp 71ndash78 April 2004

[15] A de Maio and M Lops ldquoDesign principles of MIMO radardetectorsrdquo IEEE Transactions on Aerospace and Electronic Sys-tems vol 43 no 3 pp 886ndash898 2007

[16] J Li and P Stoica ldquoMIMO radar with colocated antennasrdquo IEEESignal Processing Magazine vol 24 no 5 pp 106ndash114 2007

[17] G Zhu B Oreshkin E Porter M Coates and M PopovicldquoNumerical breast models for commercial FDTD simulatorsrdquoin Proceedings of the 3rd European Conference on Antennas andPropagation pp 263ndash267 March 2009

[18] S K Davis H Tandradinata S C Hagness and B D vanVeen ldquoUltrawideband microwave breast cancer detection adetection-theoretic approach using the generalized likelihoodratio testrdquo IEEE Transactions on Biomedical Engineering vol 52no 7 pp 1237ndash1250 2005

[19] N Bahbah H Djelouah and A Bouakaz ldquoUse of Nakagamistatistical model in ultrasonic tissuemimicking phantoms char-acterizationrdquo in Proceedings of the 24th International Conferenceon Microelectronics (ICM rsquo12) December 2012

[20] L Xu P Stoica and J Li ldquoParameter estimation and numberdetection of MIMO radar targetsrdquo in Proceedings of the 41stAsilomar Conference on Signals Systems andComputers (ACSSCrsquo07) pp 177ndash181 Pacific Grove Calif USA November 2007

[21] T R Nelson J B Fowlkes J S Abramowicz and C CChurch ldquoUltrasound biosafety considerations for the practicingsonographer and sonologistrdquo Journal of Ultrasound inMedicinevol 28 no 2 pp 139ndash150 2009

[22] HMadjarThePractice of Breast Ul Trasound Techniques Find-ings Differential Diagnosis Georg Thieme Stuttgart Germany2000

[23] J Mamou A Coron M L Oelze et al ldquoThree-dimensionalhigh-frequency backscatter and envelope quantification ofcancerous human lymph nodesrdquo Ultrasound in Medicine andBiology vol 37 no 3 pp 345ndash357 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology