Ultrasonic spectrum analysis for tissue evaluation

Frederic L. Lizzi *, Ernest J. Feleppa, S. Kaisar Alam, Cheri X. Deng

Biomedical Engineering Laboratories, Riverside Research Institute, 156 William Street, New York, NY 10038, USA

Abstract

Spectrum analysis procedures have been developed to improve upon the diagnostic capabilities afforded by con-

ventional ultrasonic images. These procedures analyze the frequency content of broadband, coherent echo signals re-

turned from the body. They include calibration procedures to remove system artifacts and thereby provide quantitative

measurements of tissue backscatter. Several independent spectral parameters have been used to establish databases for

various organs; several investigations have shown that these parameters can be used with statistical classifiers to identify

tissue type. Locally computed spectra have been used to generate sets of images displaying independent spectral pa-

rameters. Stained images have been derived by analyzing these parameter images with statistical classifiers and using

color to denote tissue type (e.g., cancer). This report describes spectrum analysis procedures, discusses how measured

parameters are related to physical tissue properties, and summarizes results describing estimator precision. It also

presents illustrative clinical results showing how such procedures are being adapted to address specific clinical problems

for a number of organs. This report indicates where further developments are needed and suggests how these techniques

may improve image segmentation for three-dimensional displays and volumetric assays.

� 2002 Elsevier Science B.V. All rights reserved.

Keywords: Ultrasonic imaging; Ultrasonic spectrum analysis; Prostate ultrasonography; Ocular ultrasonography; Ultrasonic

parameter images

1. Introduction

Over the past three decades, ultrasonic imaging

has emerged as a standard diagnostic technique

within a broad range of medical specialities

(Kremkau, 1990). Pulse-echo ultrasound systems

are routinely used to obtain cross-sectional images

of the abdomen, heart, breast, prostate, and eye,

and they have become the international standard

for imaging the fetus. The use of ultrasound is

motivated by its proven clinical utility as well asseveral other factors including its safety record,

real-time visualization, ease of use, and the avail-

ability of economic systems. Ultrasonography is

likely to become even more useful because of on-

going developments (Goldberg et al., 1994; Sherar

and Foster, 1989) that include advanced ultrasonic

arrays and digital processing (for improved imag-

ing), contrast agents (to enhance imaging andquantification of blood flow), probe miniaturiza-

tion (for incorporation in catheters to examine

blood-vessel disease), and very-high-frequency

transducers (for improved spatial resolution).

Pattern Recognition Letters 24 (2003) 637–658

www.elsevier.com/locate/patrec

*Corresponding author. Tel.: +1-212-502-1774; fax: +1-212-

502-1729.

E-mail address: lizzi@rrinyc.org (F.L. Lizzi).

0167-8655/03/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S0167-8655 (02 )00172-1

While conventional ultrasonic images (termed

B-mode images) convey key diagnostic informa-

tion, these images are degraded by phenomena

that are not usually encountered with other

imaging modalities, such as magnetic resonance

and computed tomography, used in radiology. Asdescribed in this report, image degradations occur

because of the coherent nature of ultrasound, the

complex interaction of tissues and ultrasonic

waves, and the fact that reflections (echoes) are

employed for imaging. These factors lead to ran-

dom speckles, artifactual specular-reflection drop-

outs, and spatially varying resolution in ultrasonic

images. The extent of these degradations is affectedby the instrument and the instrument settings

which are used in examinations.

The image degradations impede the direct ap-

plication of conventional pattern recognition

procedures to ultrasonic images. They also hinder

attempts to quantify tissue features for objective

diagnostic schemes.

These considerations have prompted many in-vestigations that seek to improve ultrasonic imag-

ing and to provide a framework for quantitative

tissue evaluation. This report describes frequency-

domain approaches that have been developed to

analyze ultrasonic echoes and to generate alterna-

tive types of ultrasonic images. Frequency-domain

techniques offer fundamental advantages for ad-

dressing a number of constituent problems inultrasonography. First, they permit a systems

perspective that clarifies and separates the effects of

system components and tissue properties on image

features. Second, they afford a convenient means

of incorporating well-established frequency-do-

main results describing ultrasonic beam propaga-

tion and tissue scattering. Third, averaged power

spectra provide a cogent means of addressing thestochastic nature of tissue microstructure.

Spectral techniques are designed to analyze

coherent radio frequency (RF) echo signals, digi-

tally acquired at the outputs of ultrasonic trans-

ducers, as opposed to the RF-signal envelope

(video signals) that are displayed in conventional

B-mode ultrasonic images (Lizzi et al., 1983; Fel-

eppa et al., 1986). This is an important distinctionbecause calibration and corrective procedures that

can be applied to RF spectra are usually not ap-

plicable following the non-linear process of

envelope detection. Video detection also obliter-

ates subtle RF-signal features that can convey

important information regarding tissue micro-

structure.

The spectral techniques described in this reportcan evaluate two independent parameters that

characterize ultrasonic scattering by tissues: one

parameter provides a measure of overall scattering

strength, while the other measures the frequency

dependence of scattering. Under certain conditions

(e.g., known or negligible acoustic attenuation),

these spectral parameters can be used to estimate

two independent physical properties of tissueconstituents (related to their size and concentra-

tion) (Lizzi et al., 1987). Thus, unlike conventional

ultrasonography, which provides a single qualita-

tive image, spectral procedures can yield a pair of

images depicting independent, quantitative tissue

parameters.

Spectral techniques have been clinically de-

ployed in two complementary modes. The firstcomputes average spectral parameters within a

demarcated spatial region: this mode is often em-

ployed in database studies that elucidate para-

meter values indicative of specific diseases. The

second mode generates spectral parameter images

that have been linked to quantitative clinical

databases to assist disease detection and diagnosis

(Feleppa et al., 1986). Spectral parameter imagesoffer new opportunities for pattern recognition

based on conjoint, independent parameters. They

may become particularly valuable for automated

boundary determination and segmentation of dif-

ferent tissue structures. These opportunities are

just beginning to be explored and promise to

become key elements for automated tissue biom-

etry and three-dimensional (3-D) imaging.This report first summarizes the operation of

ultrasonic systems and describes image artifacts

associated with different types of tissues. It then

describes spectrum analysis and calibration pro-

cedures, and presents illustrative averaged spectra

for different types of tissue. The report next de-

scribes how local spectral features are computed

and displayed to form sets of cross-sectionalspectral parameter images. Next, the report sum-

marizes how spectral parameters are related to

638 F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658

physical scatterer properties including the effective

sizes, concentrations, and mechanical properties of

subresolution tissue constituents. The statistics of

spectral parameters are described in terms of sys-

tem and analysis parameters, and explicit rela-

tionships are presented regarding the trade-offsbetween, e.g., spatial resolution and statistical

variability in spectral parameter images.

The last section of the report summarizes clin-

ical spectral results for several organs and illus-

trates how spectral techniques can be adapted to

meet particular medical needs. Because calibrated

spectrum analysis provides quantitative outputs,

images of spectral parameters can be compared toorgan-specific databases that characterize sets of

spectral parameters indicative of particular dis-

eases. In examinations of the eye, where biopsies

are precluded, database information is being used

to identify and subclassify ocular tumors (Feleppa

et al., 1986; Feleppa and Lizzi, 1993), using col-

ored ‘‘stains’’ superimposed on two-dimensional

(2-D) and 3-D images. Non-invasive treatmentmonitoring is also being implemented by staining

tumor segments whose spectral parameters have

changed due to microstructural alterations in-

duced by radiotherapy or intense-ultrasonic ther-

apy (Lizzi et al., 1997a). In prostate examinations,

database information combining spectral param-

eters and blood levels of prostate specific antigen

(PSA) are being used to detect prostate cancer(Feleppa et al., 1996, 1997); ‘‘suspicious’’ regions

are being color coded to guide biopsy placement.

In breast examinations, spectral parameters and

morphological descriptors of tumor shapes are

being used with the goal of differentiating benign

and malignant tumors to avoid the risks, expense,

and anxiety associated with unneeded biopsies

(Alam et al., 2000, 2002a,b).Cardiac examinations have employed a spectral

parameter (integrated backscatter (IB)) to detect

aberrant cyclic variations associated with myo-

cardial infarction (O’Donnell et al., 1981; Vered

et al., 1987). Studies of the kidney have shown how

spectral parameters and derived estimates can

elucidate kidney microstructure and characterize

kidney disease (Insana et al., 1991; Garra et al.,1994). Several studies have shown how spectral

techniques may help diagnose local and diffuse

liver disease (Oosterveld et al., 1991; King et al.,

1985). Other promising results have been obtained

for characterizing threats posed by vascular plaque

(Lee et al., 1999) and for identifying cancerous

metastases in lymph nodes (Tateishi et al., 1998).

Recent in vitro studies have shown that spectraltechniques may sense cell division and death

(Kolios et al., 1999), thereby providing an im-

portant non-invasive potential for monitoring the

efficacy of emerging tumor-therapy agents.

In addition to tissue applications, the theoreti-

cal framework for spectrum analysis has been

modified to treat ultrasonic contrast agents, so

that spectra can be used to help improve ultrasonicevaluation of blood flow and tissue perfusion

(Deng et al., 1998).

This report cites our own research results to

explain key points involved in spectral procedures

and to provide a unified framework for describing

the relations between theory, implementation, and

clinical results. Using this framework, the report

also cites relevant reports of the many other in-vestigators who have made important contribu-

tions to developing frequency-domain approaches

for ultrasonic examinations.

2. Conventional ultrasonic imaging

A discussion of frequency-domain techniquesrequires a systems perspective identifying instru-

ment and tissue components that influence con-

ventional ultrasonic imaging. Ultrasonic systems

employ piezoelectric transducers that act as fo-

cused transmitters and receivers in a pulse-echo

mode (Kremkau, 1990). Along a single ‘‘look di-

rection’’, the transducer is excited with a short

voltage pulse and launches a brief ultrasonicpressure pulse. Each pulse comprises a series of

alternating compressions and rarefactions that

propagates through the body, via a coupling bath

or gel.

As the ultrasonic pulse propagates, its pressure

amplitude is progressively diminished by absorp-

tion, and it is partially scattered by changes

occurring in tissue density and/or acoustic prop-agation velocity. Tissues typically produce weak

scattering so that most of the ultrasonic energy

F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658 639

continues propagating to deeper sites in the body.

Portions of the backscattered pressure pulses

propagate back to the transducer; the transducer

coherently integrates these bipolar echo pulses over

its receive aperture and generates a corresponding

RF voltage pulse. As described above, the videoenvelope of the returned echo signals is used to

generate image signals along a line corresponding

to the transducer orientation.

A cross-sectional image is synthesized by re-

peating the pulse-echo imaging operations along a

series of scan directions offset by lateral beam

displacements (linear scans) or angled beam dis-

placements (sector scans). Simple systems utilizemechanically scanned transducers, typically with

1–2 cm radiating diameters, which are focused by

acoustic lenses. Many modern systems employ

piezoelectric arrays whose beams are scanned and

focused under electronic control.

The axial (depth) resolution of an ultrasonic

system is equal to cT=2 where c is the tissue’s

acoustic propagation velocity and T is the dura-tion of the echo signal received from a single re-

flector. (The factor 2 accounts for two-way travel.)

T depends primarily on the bandwidth of the

transducer, which is usually near 30–40% of its

resonant frequency fr. Lateral resolution is de-termined by the focused beamwidth, typically

equal to 1.2F k=D where F is focal length, D is

aperture diameter and k ¼ c=fr is the wavelengthat the center frequency. It is useful to define a

resolution volume whose axial length is cT=2 andwhose cross-sectional area is equal to the beam-

width; this volume encompasses the tissue volume

contributing to received echoes at a single instant

of time.

These relationships show that both axial and

lateral resolution improve as frequency increases.However, tissue attenuation increases with fre-

quency, typically at a rate of 0.5 dB/MHz cm,

limiting the useful depth of penetration at high

frequencies. Because of this, organs that require

deep penetration, such as the liver, are examined

at relatively low center frequencies (e.g., 2 MHz)

and relatively coarse resolution (near 1 mm) is

achieved. At the other extreme, superficial sectionsof the eye can be examined using 50 MHz to

achieve resolution finer than 50 lm. Most clinical

examinations employ center frequencies between 5

and 7.5 MHz providing a resolution near 0.3 mm.

The following section discusses frequency-

domain relationships governing echo signals from

realistic tissue and system models. Corresponding

time-domain expressions are complex, involvingnumerous spatially dependent convolutions and

factors, such as attenuation and backscatter

functions, that have only been well characterized

over finite frequency bands. These considerations

make it difficult to calibrate conventional images

and to remove system-dependent artifacts.

The summary descriptions presented above can

help elucidate factors that affect ultrasonic imagesand complicate efforts at employing standard

pattern recognition and image segmentation pro-

cedures. It is useful to consider two types of tissue

structures, characterized as deterministic and sto-

chastic. First, we consider simple ‘‘deterministic’’

or coherent reflectors, which comprise smooth

tissue surfaces that are broader than the beam-

width. Such surfaces may be found at the bound-aries of organs, encapsulated tumors, and large

blood vessels. In general, such surfaces are well

imaged, but they constitute specular ultrasonic

reflectors and their echo amplitudes depend upon

the angle of incidence of the ultrasound beam.

When viewed obliquely, reflections from these

surfaces are not captured by the transducer, lead-

ing to ‘‘specular drop-out’’. If the surfaces alsoexhibit a degree of roughness commensurate with

the incident wavelength, then, various elements

within the beamwidth can produce coherent in-

terference phenomena, leading to a speckled

brightness pattern as described below.

Stochastic tissues are more complex and con-

tain many closely spaced, independent scatterers

within a resolution volume. This situation is fre-quently encountered in normal organs (liver,

breast, prostate, etc.), in blood masses, and in

many, if not most, types of tumors. The RF echo

signals received from these tissues involve the co-

herent summation of pressure components from

many constituent scatterers; the resultant RF sig-

nal is affected by the exact number and position of

each scatterer in the system’s resolution volume.The stochastic natures of scatterer density and

location lead to a randomness in the RF signal

640 F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658

and result in a corresponding random modulation

(‘‘speckling’’) in B-mode image brightness. Ultra-

sonic speckling is similar to that found with co-

herent laser illumination, and it can obscure fine

tissue details, as discussed in (Abbott and Thur-

stone, 1979; Wagner et al., 1983).Speckling is evident in Fig. 1, which shows a B-

mode image of the prostate obtained with a

transrectal ultrasonic probe (located at the bottom

of the image). The prostate is centrally located

within the displayed 6-cm depth. Fig. 2 plots RF

echo signals from adjacent scan lines within the

rectangle that is superimposed on the prostate

image.The statistics of echo signals and speckle from

stochastic scatterers is of prime importance in

signal and image analysis, and it has been studied

by several investigators (Wagner et al., 1983;

Tuthill et al., 1988). In simple situations where

more than 5 or 10 independent scatterers are pre-

sent in the resolution volume, the RF echo am-

plitudes exhibit a Gaussian probability densityfunction (pdf) and corresponding video signals

manifest a Rayleigh pdf.

Speckling complicates boundary detection and

segmentation operations. Several techniques to

suppress speckle involve averaging B-mode images

that exhibit independent speckle patterns. Inde-

pendent speckle can be obtained by using B-mode

images obtained at sequential time instants (where

small transducer or tissue motion decorrelates

speckle patterns) or images obtained using differ-

ent frequency bands (since speckle is frequencydependent) (Magnin et al., 1982). Adaptive spatial

filtering has also been employed (Bamber and

Cook-Marten, 1987). We have developed a tech-

nique that filters received RF echo signals into M,

ideally, non-overlapping frequency bands (Lizzi

et al., 1986; Lizzi and Feleppa, 2000), the corre-

sponding B-mode images (with independent

speckle) are then averaged to reduce the standarddeviation of speckle by

ffiffiffiffiffiM

p. (As described in

(Lizzi et al., 1986), pre-whitening is included to

partially offset the concomitant loss in axial reso-

lution.)

3. Ultrasonic spectrum analysis

In the late 1960s, several investigators realized

that the frequency dependence of tissue backscat-

ter might convey useful information. Initially, such

information was gathered by simply imaging tis-

sues with transducers that had different center

frequencies (Coleman et al., 1977). In the early

1970s, frequency characteristics were analyzed

digitally or by applying RF echo signals to analogFig. 1. B-mode image of prostate.

Fig. 2. RF echo signals from prostate.

F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658 641

spectrum analyzers (Namery and Lele, 1972; Lizzi

et al., 1976). One innovative system generated

color images depicting backscatter frequency

characteristics by applying RF signals to a bank of

three analog bandpass filters with different center

frequencies: filter outputs were color coded andcombined so that the resultant color indicated the

spectral characteristics of echo signals (Purnell

et al., 1975).

In the latter 1970s, more quantitative ap-

proaches (Lizzi and Laviola, 1975) were designed

to compute the calibrated average power spectrum

obtained from a demarcated region of interest

(ROI) in examined tissue. We will first describe theROI approach and subsequently developed spec-

tral imaging techniques. In many clinical applica-

tions, the ROI approach is used first in order to

establish databases that delineate the spectral fea-

tures of particular diseases; this information is then

applied in spectral images to identify diseased tis-

sues. We will then consider the theoretical rela-

tionships among derived spectral parameters andphysical properties of tissue microstructure. Lastly,

we will examine the statistics of spectral estimates

and spectral parameter images.

3.1. Spectrum analysis procedures

ROI spectrum analysis involves a sequence of

operations applied to digitized RF echo signalsdigitally acquired directly at the transducer (Lizzi

et al., 1983; Feleppa et al., 1986). In our investi-

gations, acquired signals from an entire scan are

first used to compute and display a B-mode image,

which serves to identify overall anatomic rela-

tionships. A mouse is then used to demarcate an

ROI on the image, as shown for the prostate in

Fig. 1. The ROI defines the range-segment length(L) and the number of adjacent scan lines to be

used in the analysis. Note that the B-mode image

serves only as a map to define the ROI; the actual

analysis is applied to acquired RF data.

Along each bracketed scan line, stored RF echo

data (as shown in Fig. 2) are multiplied by a

Hamming window of length L, and a fast Fourier

transform (FFT) algorithm calculates the RF echospectrum. An average power spectrum is then

computed as the mean of the squared spectral

magnitudes from the ensemble of bracketed scan

lines in the ROI. A calibrated power spectrum is

next calculated by dividing the echo power spec-

trum by the power spectrum of RF echoes from a

planar calibration target; the target is placed in a

water-bath and located in the transducer’s focalplane. For ROIs within the transducer’s focal

zone, this calibration removes artifacts associated

with the composite transfer function of the elec-

tronic transmitter/receiver and the transducer

(Lizzi et al., 1983); in addition, spectra are cor-

rected for the recorded system gain setting in order

to provide a common spectral level for all tissue

measurements.When ROIs are not located in the transducer

focal zone or when arrays with different transmit

and receive foci are employed, compensation for

range-dependent diffraction effects is required.

This compensation uses data from targets (e.g., gel

blocks) that contain diffuse suspensions of small

scatterers (e.g., glass beads). Diffraction compen-

sation is achieved by dividing tissue spectra by thediffraction-target power spectrum measured at

the same range as that of the ROI.

Fig. 3 shows relevant prostate and calibration

spectra for the ROI of Fig. 1. The single-element

focused transducer used to obtain these data had a

nominal 7-MHz center frequency, and RF data

were acquired (8 bits) using a 50-MHz sampling

frequency (Feleppa et al., 1997).

Fig. 3. RF tissue spectrum and calibration spectrum.

642 F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658

The figure shows plots of power spectra (dB) vs.

frequency. The uncalibrated average tissue spec-

trum has a shape that is heavily influenced by the

system transfer function, as evidenced in the cali-

bration (glass-plate) spectrum. In this illustration,

useful signal-to-noise ratios occur within the 3–8-MHz frequency band. Fig. 4 shows the calibrated

power spectrum, obtained by dividing the RF tis-

sue spectrum by the calibration spectrum. By re-

moving the system transfer function, this process

extends the bandwidth available for analysis. The

calibrated spectrum is seen to exhibit a quasi-linear

shape over its bandwidth, and the figure also plots

the corresponding linear fit calculated from lin-ear regression analysis (Feleppa et al., 1986; Lizzi

et al., 1987).

Many investigators have described alternative

approaches to the procedures described above.

For example, Wear et al. (1994) have shown that

ARMA spectral estimation procedures may reduce

the required gated signal length and thereby im-

prove spatial resolution for spectral techniques.Calibration procedures, to remove extraneous

system factors, have been treated by Waag and

Astheimer (1993), Insana et al. (1994) and Boote

et al. (1988). In addition, a number of investiga-

tors, including Kuc and Schwartz (1979), have

described related methods that compute acoustic

attenuation coefficients by analyzing spectra over

a range of depths in tissue.

3.2. Representative tissue spectra

Early studies showed that it was useful to in-

terpret spectra in terms of deterministic and sto-

chastic tissue structures, as described above forconventional ultrasonic images.

Many deterministic structures produce a ‘‘scal-

loped’’ pattern of periodic spectral peaks. This

shape is most evident in tissues (e.g., detached

retinas) with two well-defined boundaries, as

shown in (Lizzi et al., 1983). This spectral shape

arises because the RF echo complex has the form

q1eðtÞ þ q2eðt � 2w=cÞ where eðtÞ is the echo froma single surface, w is the thickness of the tissue, and

q1 and q2 represent the reflection coefficients of thefirst and second surfaces, respectively. If these re-

flection coefficients are equal, the power-spectral

magnitude of the RF echo will be proportional to

j cosð2pfw=cÞj2 and successive spectral peaks willoccur at frequencies separated by an interval of

c=2w.As noted above, stochastic tissue structures

(e.g., many tumors) contain numerous small scat-

terers with randomly distributed positions. The

ROI spectra for such tissues exhibits relatively

smooth monotonic shapes without prominent

peaks. As shown for the prostate, in Fig. 4, these

spectra (in dB) often exhibit quasi-linear shapes

over the limits of the measurement bandwidth sothat linear regression analysis is useful in summa-

rizing key spectral features.

Mixed tissue segments combine deterministic

and stochastic elements. For example, normal liver

has been reported to contain stochastic elements

that are situated within a quasi-periodic matrix

with a periodicity near 1 mm (Fellingham and

Sommer, 1984). In this case, ROI spectra showsmall periodic peaks which can be used to estimate

the periodic spacing interval within the tissue.

Several methods have been employed to estimate

this spacing; these can involve power spectra (as

described above for detached retinas), autocorre-

lation functions (ACFs) (computed as the inverse

FFT of the power spectrum), and cepstra (com-

puted as the inverse FFT of the logarithm of thepower spectrum) (Lizzi et al., 1981).

The spectral parameters described above have

been used with ROI procedures to establishFig. 4. Calibrated power spectrum.

F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658 643

clinical databases for a number of organs, as de-

scribed in subsequent sections. Database studies

typically involve the measurement of ROI spectra

and correlation of spectral parameters with tissue

type following definitive diagnosis of the examined

tissue. Definitive diagnosis is usually obtainedfrom histological examination of biopsied speci-

mens. Statistical procedures including linear dis-

criminant analysis, cluster analysis, or neural

networks (NNs) have been used to identify con-

joint values of spectral parameters (e.g., slope and

intercept) that are correlated with specific diseases.

3.3. Spectral parameter images

Sets of quantitative descriptors have been de-

fined to summarize the key features of tissue

spectra so that comprehensive database studies

can be conducted for tissue identification. These

descriptors are also used for spectral images, which

display the spatial patterns of tissue properties.

For deterministic structures, tissue thickness orspatial periodicity is the most important parame-

ter. For stochastic tissues, usually of most interest,

linear regression analysis (Fig. 4) has been applied

to spectra expressed in dB in order to determine

two basic parameters: spectral intercept (dB; ex-

trapolation to zero frequency) and spectral slope

(dB/MHz) (Lizzi et al., 1987, 1997a; Feleppa et al.,

1996). An additional parameter which is oftenemployed is the midband fit (dB), defined as the

value of the regression line at the center frequency

fc of the spectral band. The midband fit is nu-merically equal to the average value of the spec-

trum over the measurement bandwidth. Thus, the

midband fit is directly related to a widely em-

ployed parameter termed integrated backscatter orIB (O’Donnell et al., 1979) which is also calculated

from the average value of spectral levels (in dB).

(While only two linear regression parameters are

independent, it is useful to consider all three as

illustrated in following sections.)

Spectral parameter images display local values

of spectral slope, intercept, or midband fit in tis-

sue cross-sections (Feleppa et al., 1997). Theimages are formed using a sliding Hamming win-

dow to progressively analyze RF data along each

scan line. At each window site, all of the spectral,

calibration, and linear-regression procedures de-

scribed above are employed to compute unaver-

aged calibrated spectra and corresponding local

values of spectral parameters. These values are

then encoded in gray scale or color, and a set ofimages is displayed using a common cross-sec-

tional format. Fig. 5 shows midband fit (Fig. 5a)

and intercept (Fig. 5b) images of the prostate.

Spectral parameter images of, e.g., slope and

midband fit are often analyzed in conjunction with

database classifiers from ROI spectral studies. The

images are analyzed on a pixel-by-pixel basis to

determine whether spectral properties are consis-tent with those of a particular disease. ‘‘Stained’’

Fig. 5. Spectral parameter images of prostate: (a) midband fit; (b) intercept.

644 F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658

images, using color-coded presentations, are then

synthesized to depict classifier outputs indicating

tissue type (Lizzi et al., 1986; Feleppa et al., 1997).

Fig. 6 presents a stained image of the prostate,

which was generated by analyzing the images of

Fig. 5 with a NN classifier trained using an ROI

database, as described in a subsequent section.

Areas of suspected cancer are presented as redoverlays, which appear as bright areas in this

black-and-white reproduction.

Staining procedures may be considered a form

of image segmentation that spatially separates

normal and abnormal regions. Because they con-

vey independent information, pairs of spectral

parameter images should also be useful in more

general segmentation and boundary detectionprocedures that delineate different organs and tis-

sue surfaces. These applications have not yet been

systematically explored, although relevant theo-

retical treatments of parameter statistics are now

available, as described subsequently.

3.4. Theoretical relationships between spectral pa-

rameters and tissue microstructure

Empirical clinical studies, described below, have

demonstrated that linear-regression spectral pa-

rameters are correlated with tissue type in several

organs. We have developed a theoretical model in

order to elucidate this correlation (Lizzi et al.,

1983, 1987). The analysis treats the relationships

between physical properties of tissue microstruc-

ture and corresponding values of spectral slope,

intercept, and midband fit.

Our model treats weak scattering (Born ap-

proximation) from tissue segments in the focal zoneof a typical (weakly focused) ultrasonic transducer,

where quasi-plane wave conditions exist. The sto-

chastic tissue microstructure is specified in terms of

an ACF that describes the spatial disposition of

acoustic impedance within the examined tissue.

(Acoustic impedance is the product of tissue den-

sity and acoustic propagation velocity.)

The model assumes that tissue microstructure isstatistically homogeneous in the examined region

and that its statistics exhibit wide-sense stationa-

rity. A number of acoustic-impedance ACFs have

been examined with emphasis on isotropic 3-D

Gaussian functions (Lizzi et al., 1987; Lizzi, 1998).

This ACF applies to a continuous spatial variation

of acoustic impedance, which is appropriate for

most tissues. However, it has proven useful to in-terpret theoretical results in terms of a spatial

distribution of effective, discrete scatterers char-

acterized by three physical parameters: d, scatterer

diameter (determined by the width or correlation

dimension of the tissue ACF); C, the spatial con-

centration of scatterers; and Q, the fractional

difference between the acoustic impedance of scat-

terers and that of the surround. (The peak, zero-lag, value of the tissue ACF is proportional

to CQ2.)Mathematically, the model shows that cali-

brated power spectra are determined by the tissue

ACF, the ACF of the beam-pattern cross-section,

and the ACF of the gating function (taken to be a

Hamming function). We will first consider results

in the absence of intervening ultrasonic attenua-tion. As shown in (Lizzi et al., 1987), when d is

much smaller than the wavelengths in the spectral

frequency band, spectral amplitudes increase dra-

matically with increasing frequency. This situation

corresponds to Rayleigh scattering where spectra

vary as the fourth power of frequency. For larger

scatterers, spectra increase more slowly with fre-

quency; for scatterer sizes commensurate with orlarger than constituent wavelengths, spectra de-

crease as a function of frequency.

Fig. 6. Stained image highlighting suspected prostate cancer.

F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658 645

Linear regression was applied to theoretical

spectra in order to relate these analytical results to

the summary spectral parameters used in clinical

studies. Fig. 7 plots the resulting spectral slope as a

function of scatterer size for conditions relevant to

prostate examinations (5.75-MHz center frequency

and 4.5-MHz bandwidth). For small scatterers

(d < 0:05 mm), spectral slope is relatively constantat a value corresponding to f 4 Rayleigh scattering;the slope progressively decreases from this value as

scatterer size increases. Fig. 7 also plots the spec-

tral intercept value for these scatterer sizes with

CQ2 set to unity. For small scatterers, interceptincreases rapidly with size, since power spectral

amplitudes increase as d6 for Rayleigh scatterers.A recent report (Lizzi, 1998) presents closed-

form general expressions that relate spectral in-

tercept, slope, and midband fit to d and CQ2. Theseexpressions involve a number of parameters which

depend on the transducer dimensions, center fre-

quency, and bandwidth. They permit d and CQ2 tobe evaluated when ultrasonic attenuation is negli-

gible in intervening tissue (interposed between the

transducer and examination site). In general,bandwidth is particularly important for estimation

of small scatterer sizes and, as shown below, it is

also a critical factor in the precision of spectral

parameter measurements.

Insana et al. have described a useful alternate

theoretical scattering model, which analyzes spec-

tral shapes in terms of form factors associated with

the dimensions and morphology of tissue constit-

uents (Insana and Brown, 1993).

Intervening attenuation can be neglected in su-

perficial organs (e.g., in 10-MHz ocular examina-

tions), but it becomes a factor in examinations of

deeper organs. In tissue, attenuation (dB) usually

increases in an approximately linear fashion with

frequency, and attenuation coefficients are speci-fied in dB/cmMHz. To consider the effects of at-

tenuation, we treat an intervening tissue of depth

X and average attenuation coefficient a. We denotethe ideal (a ¼ 0) value of spectral intercept as I,ideal spectral slope as m, and ideal midband fit as

M. The values of these parameters that are mea-

sured in the presence of intervening attenuation

are indicated with a prime. The measured spec-trum (dB) is equal to the ideal spectrum (dB)

minus 2aXf , where the factor of 2 accounts fortwo-way beam transit. From this relation it fol-

lows (Lizzi et al., 1997a) that:

I 0 ¼ I ð1aÞ

m0 ¼ m� 2aX ð1bÞ

M 0 ¼ M � 2aXfc ð1cÞ

where fc is the center frequency of the spectrum.These results demonstrate that spectral inter-

cept values are not affected by intervening atten-

uation. Slope and midband fit are affected in ways

that can be easily accounted for, provided a and X

Fig. 7. Plots of spectral slope and intercept vs. scatterer size for typical prostate examinations.

646 F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658

are known. Many clinical studies correct m0 andM 0

based on tabulated values of a for the organ beingstudied together with measurements of X from

B-mode images (Feleppa et al., 1997). These cor-

rections are used in both database studies and

parameter images to remove the effects associatedwith tissue depth. The corrections also permit d

and CQ2 to be estimated from spectral data using

the relations in (Lizzi, 1998).

3.5. Statistics of spectral estimates and images

The statistics of spectral estimates are impor-

tant considerations in planning ROI spectral pro-cedures and in analyzing spectral parameter

images. The variance levels associated with ROI

spectral estimates affect the degree of confidence

that can be realized in diagnostic applications. The

variance associated with spectral images directly

affects image quality. In both cases, trade-offs exist

between spatial resolution and statistical stability.

We have analyzed the statistical quantities that arerelated to the spectral parameters employed in our

investigations (Lizzi and Laviola, 1975; Lizzi et al.,

1997b,c). Other investigators have also described

relevant statistical models (Huisman and Thijssen,

1996; Chaturvedi and Insana, 1996).

Our analysis of spectral statistics applies to the

same situation that was used in discussing the

statistics of conventional ultrasonic images (Lizziet al., 1997b,c). We consider statistically homoge-

neous stochastic tissue segments whose RF signal

amplitudes exhibit Gaussian statistics. The cali-

brated RF spectrum is computed with a Hamming

window of length L along a set of adjacent inde-

pendent scan lines. Along each line, the spectrum

extends over a total bandwidth B, and it includes n

spectral resolution cells, each of which has a sub-bandwidth b. The value of b is determined by the

�3 dB width of the gating function’s Fourier

transform. For a Hamming window of temporal

duration TH, b ¼ 1:33=TH where the correspondingspatial extent of the gate is L ¼ cTH=2. The valueof c is typically near 1.5 mm/ls, so that b 1=Lwhere b is specified in MHz and L in mm. Thus,

the number of spectral resolution cells is n ¼ BLwhere B is that total spectral bandwidth (MHz)

being analyzed.

The conditions stated above are the same as

those treated in spectrum analysis of Gaussian

white noise. As described in (Lizzi et al., 1997c), the

n spectral resolution cells constitute independent

random variables whose magnitude exhibits a

Rayleigh pdf, and the corresponding power spec-tral values exhibit v2 (negative exponential) statis-tics.

We now consider the statistics—most impor-

tantly the standard deviations—that apply to

spectral slope, intercept, and midband fit. As dis-

cussed in (Lizzi et al., 1997c), the pdfs of these

parameters are affected by the non-linear conver-

sion to dB and the linear-regression operators. Theresults are somewhat different for ROI and pa-

rameter-image values.

For ROI analysis, power spectra (with v2 sta-tistics) from N independent scan lines are aver-

aged, and the result is converted to dB; the

resulting n independent average-spectra cells are

then analyzed with linear-regression techniques.

We denote the mean values of ROI estimates formidband fit, slope, and intercept as M , m, and I ,respectively. If N is greater than about 10, the

standard deviations of midband fit (rM ), slope (rm)

and intercept (rI ) are:

rM ¼ kffiffiffin

p ð2aÞ

rm ¼ kffiffiffiffiffi12

p

Bn

n2 � 1

� �1=2ð2bÞ

rI ¼ r2M�

þ f 2c r2m

�1=2 ð2cÞ

where k ¼ 4:34/ffiffiffiffiN

pdB.

For spectral parameter images, individual

(unaveraged) power spectra with v2 statistics areconverted to dB and analyzed with linear-regres-

sion techniques. We designate means and standarddeviations using a prime together with the corre-

sponding ROI symbols. The means of midband fit,

slope, and intercept, respectively, are:

M0 ¼ M � 2:5 ðdBÞ; m0 ¼ m;

I0 ¼ I � 2:5 ðdBÞ ð3Þ

The standard deviations for each unaveraged

spectral parameter have the same forms as Eqs.

(2a), (2b) and (2c) with k ¼ 5:6 dB.

F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658 647

Eq. (3) shows that the mean values of midband

fit and intercept for parameter images are 2.5 dB

lower than ROI values; this is due to the fact that

ROI averages are computed prior to dB conver-

sion while parameter-image averaging occurs after

conversion to dB. Mean slope values are the samefor both approaches. The standard-deviation re-

sults for ROI and parameter images have similar

forms and demonstrate the importance of the

factor n ¼ BL in determining estimator precision.The spectral bandwidth B is particularly important

for slope estimation because, for typical cases

(n2 1), the standard deviations for slope are

inversely proportional to B1:5. Overall, estimates ofmidband fit exhibit smaller standard deviations

than other parameters.

The pdfs for parameter images are derived in

(Lizzi et al., 1997c). Midband fit results are plotted

for various values of n ¼ BL in Fig. 8 where theabscissa is midband fit (dB) minus its mean value.

The figure shows several interesting characteristics.

The pdfs for small values of n are asymmetric; as nincreases, the curves become more symmetric, ap-

proaching Gaussian curves for values of n near 10.

Furthermore, the shape of the pdf curve does not

depend on the mean midband-fit value. Slope pdf

results are symmetric about their mean value and

approach Gaussian shapes for values of n near 5.

Intercept pdf results depend upon slope and mid-

band fit pdfs together with the values of fc and B.The theoretical pdf results have been confirmed

by deriving corresponding histograms of clinical

spectral parameter images. Homogeneous tissue

regions have been examined in several organs

(Lizzi et al., 1997c), and excellent agreement has

been found with theoretical results. As expected,

departures from theory occur when heterogeneous

tissue regions are examined, violating the as-sumption of homogeneity. We are now examining

whether these departures can be used to form

quantitative measures of tissue heterogeneity.

The statistical results described above have

proven valuable for evaluating the merits of vari-

ous ultrasonic systems (in terms of B and fc) andfor designing appropriate ROI and sliding-window

parameters (L and N). The results explicitly de-scribe the trade-offs that must be made between

statistical stability and spatial resolution. Specifi-

cally, Eqs. (2a), (2b) and (2c) shows how the

standard deviations of each parameter estimator is

related to spatial resolution, which is determined

by the window length L and the number of aver-

aged scan-line segments N.

The pdf results for spectral parameter imagesare relevant to tissue segmentation and boundary

detection. These applications could also benefit

from the fact that two independent parameters are

imaged. Additionally, segmentation should be ex-

pedited since the shapes of the pdf curves do not

vary with the mean value of each parameter.

Studies in these applications are still in their early

stages and are largely motivated by the need forautomated 3-D imaging and biometry, as de-

scribed in subsequent sections.

4. Illustrative clinical results

The spectrum analysis procedures described in

preceding sections have been applied to clinicaldata obtained from a number of organs. The

procedures have been adapted to address specific

needs germane to the organ being studied. The

objectives include the detection, diagnosis, and

staging of both focal and diffuse diseases. Infor-

mation from spectral procedures has also been

used for treatment planning and treatment moni-

toring in several organs.Most clinical applications of spectrum analysis

involve two phases. First, database studies, usingFig. 8. Probability density functions for midband fit.

648 F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658

ROI procedures, are performed with statistical

classifiers to identify conjoint values of spectral

parameters that are associated with specific dis-

eases, as identified in subsequent biopsy proce-

dures. In studies of superficial tissues (e.g., the

eye), intervening attenuation can often be ne-glected so that measured values of spectral slope

and midband fit can be used directly in databases.

In other organs, spectral intercept, which is not

affected by attenuation, can be used together with

slope or midband fit after they are be compensated

for estimated attenuation, as described in a pre-

ceding section. Several specialized parameters do

not require attenuation compensation: these in-clude measurements of tissue periodicity (from

analysis of spectral peaks) or assays of heteroge-

neity (using standard deviations of spectral pa-

rameters). In addition, attenuation does not affect

measurements of cyclic temporal changes in car-

diac parameters. Some database studies have in-

cluded auxiliary quantities, such as the measured

blood level of PSA, to complement spectral data.The second phase in clinical applications typi-

cally involves the synthesis of spectral parameter

images. The particular parameters to be imaged

and the inclusion of attenuation compensation are

planned using database results for the organ under

study. Classification procedures developed in dat-

abase studies can be used to process sets of pa-

rameter images and delineate tissue regions likelyto contain specific diseases. Some clinical studies

have incorporated theoretical results to generate

images of effective scatterer size and CQ2.The following sections illustrate how these

procedures have been applied to a number of

organs.

4.1. Ocular examinations

Ultrasonic spectrum analysis was initially ap-

plied in ophthalmology in order to identify tumors

developing in the posterior section of the eye

(Feleppa et al., 1986). These studies were con-

ducted using focused transducers with center fre-

quencies of 10 MHz. More recently, spectrum

analysis has been employed using focused PVDFtransducers with center frequencies near 50 MHz

(Silverman et al., 1995). These very-high-frequency

examinations have been used to evaluate small (1–

2 mm) tumors in the anterior ocular segment, to

examine traumatic injury, and to study micro-

structural changes associated with glaucoma.

Clinical database studies (10 MHz) showed that

ocular tumors could be classified using spectralslope and intercept; classification was improved

to a modest extent by also including the residual

uncertainty of the linear fit. Classification was

accomplished using linear discriminant analysis

incorporating two discriminant functions (linear

combinations of these three spectral parameters)

(Feleppa and Lizzi, 1993). Discriminant maps de-

lineated regions associated with malignant mela-nomas, metastatic carcinomas, and choroidal

hemangiomas (Coleman et al., 1983). Melanomas

could be further subclassified into two groups

(types B and E) that were correlated with con-

ventional histologic subclassifications. These clas-

sification capabilities are clinically important

because biopsies cannot be conducted within the

eye and because these tumors can require differenttreatments, ranging from continued observation

to enucleation (surgical removal of the globe).

Ocular tumor spectra were also analyzed using

the theoretical model described above (Lizzi et al.,

1983; Feleppa et al., 1986, 1988). Fig. 9 shows how

the different tumor types characteristically exhibit

different values of effective scatterer size and CQ2

(termed ‘‘acoustic concentration’’). Melanomasexhibit the smallest scatterer sizes, thought to be

associated with small vessels as well as aggrega-

tions of specialized cells (melanocytes) that ingest

the dense melanin pigment from these tumors.

Metastatic carcinomas exhibit larger scatterer

sizes, possibly associated with aggregations of cells

within the tumor stroma. Hemangiomas exhibit

large scatterer sizes, associated with internalblood-filled cavities. The results in Fig. 9 demon-

strate the importance of measuring two comple-

mentary features: size or CQ2 values by themselveswould not produce reliable classification of these

tumors.

Long-term clinical studies of melanoma pa-

tients showed that spectral parameters and derived

estimates of scatterer properties can directly ben-efit treatment planning (Coleman et al., 1990,

1991). These ROI studies found that such

F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658 649

parameters in combination with tumor location in

the globe can be used as predictors of survival

times following alternative procedures (enucle-

ation and radiation therapy). Additional clinical

studies have shown that spectral estimates of

scatterer properties can help identify small anom-alous blood vessels that are associated with in-

creased lethality potential in melanomas

(Silverman et al., 1997).

Animal and clinical ROI studies have also

shown that tissue changes induced by both radio-

therapy and ultrasonic hyperthermia cause signif-

icant elevations in intercept and CQ2 (Silvermanet al., 1986). This finding is now being used todevelop non-invasive treatment monitoring pro-

cedures.

The ocular ROI studies described in the pre-

ceding paragraphs have been used to develop a

number of special types of spectral parameter im-

ages. Ocular-tumor databases have been employed

to synthesize stained images that use color to en-

code tumor type (Lizzi et al., 1986). These imagesare generated from a pair of images of spectral

slope and intercept, respectively. Slope and inter-

cept values at corresponding locations in each

image were compared with database results to

determine whether their conjoint values were

indicative of a specific tumor type. The stained

image was then generated: locations whose pa-

rameters were indicative of malignant melanomas

were displayed in, e.g., red; metastatic carcinoma

was indicated in blue; the anechoic vitreous humor

was indicated with black; other tissues were indi-cated with green (see cover illustration of Optics

and Photonics News, Vol. 5 (1), 1994).

The stained image of Fig. 10 displays a segment

of a posterior tumor (2-mm thickness) whose

shape conforms to the curved posterior sclera. In

this gray-scale reproduction, metastatic carcinoma

is represented in bright white, normal tissue in

gray, and vitreous humor in black. The predomi-nant color (bright white) of this tumor correctly

classified it as a metastatic carcinoma.

A second type of parameter image has been

developed to delineate ocular-tumor regions whose

microstructure has been altered by radiotherapy or

ultrasonic heating. These images were developed

based on ROI studies showing that such altera-

tions produce substantial changes in intercept and

Fig. 10. Stained image highlighting metastatic carcinoma in

rear segment of eye.

Fig. 9. Scatter plot of CQ2 (acoustic concentration) and scat-terer size for ocular tumors.

650 F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658

CQ2. Parallel-plane scan data has been used todisplay color-coded intercept in 3-D tissue blocks

for this purpose. As shown in (Lizzi et al., 1997a),

post-treatment results can be ‘‘sliced’’ and com-

pared with corresponding pre-treatment results to

identify responsive tissue segments. An alternative‘‘differential stain’’ approach (Feleppa and Lizzi,

1993) can be employed to identify these segments.

In this approach, pre-treatment slope and inter-

cept values are computed from multiplane spectral

parameter images and their joint distribution is

computed. Following treatment, scan planes are

again examined, and regions whose conjoint slope

and intercept values lie outside of the pre-treat-ment range are highlighted. This method has

identified internal tissue responses occurring be-

fore changes in tumor volume, and it is being used

in long-term patient follow-ups.

A third type of parameter image displays local

computations of effective scatterer size and CQ2.Fig. 11 shows clinical results obtained with a very-

high-frequency ultrasound (VHFU) transducer(40-MHz center frequency), which affords a large

(50 MHz) spectral bandwidth (Lizzi et al., 1992).

The figure shows scatterer size and CQ2 within theregion of a blood mass (hyphema, labelled H) in

the anterior chamber, posterior to the cornea (la-

belled C), which has a 0.5-mm thickness. Regions

where blood organization (clotting) is occurring

demonstrate larger sizes and higher CQ2 levels, as

seen in the center of the hyphema. Such informa-

tion may help in planning optimal treatments to

restore visual acuity.

VHFU spectral parameter images are startingto be employed with 3-D images of the anterior eye

(Silverman et al., 1995). Fig. 12 shows a clinical

example in which a simulated excision has been

made through sections of the cornea (dark gray)

and sclera (white) to reveal an underlying ciliary-

body malignant melanoma. Midband-fit images

(from parallel scan planes) are especially useful in

these applications because large VHFU band-widths provide very stable (low rM ) gray-scale

images that facilitate image segmentation. Thus

far, computer-assisted segmentation has been em-

ployed to identify ocular structures and assign

relevant optical properties (color, transparency,

etc.) for 3-D rendering. An operator brackets each

structure with coarse lines, and a threshold search

algorithm is used for fine boundary delineation.Efforts are underway to totally automate this

process, so that such detailed 3-D images can be

used in applications that include diagnosis as well

as realistic tumor-treatment simulations to help

design optimal ultrasonic therapy beams (Lizzi

et al., 2001).

4.2. Prostate examinations

Ultrasonic spectrum analysis is being investi-

gated for diagnosing and staging prostate cancer

(Feleppa et al., 1996, 2001). As in ocular-tumorFig. 11. Images of effective size and CQ2 for anterior-chamberhyphema in eye.

Fig. 12. 3-D excised image showing anterior ocular melanoma.

F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658 651

studies, a clinical database has been established

using ROI approaches to identify spectral pa-

rameters that can distinguish cancerous from non-

cancerous prostatic tissue. However, the spectral

procedures have been modified to address specific

clinical problems associated with prostate exam-inations.

Conventional ultrasound, using transrectal

probes, is commonly used for biopsy guidance in

patients with elevated serum levels of PSA. Un-

fortunately, cancerous regions do not exhibit dis-

tinctive features in prostate B-mode images, and

biopsy placement in the prostate is essentially

random. Consequently, many prostate cancers (atleast 30%) are missed by the, typically, six biopsy

samples obtained from subjects. Thus, a first goal

has been to determine whether stained spectral

images could be employed to highlight prostate

regions likely to contain cancer. If successful, cli-

nicians could biopsy these suspicious sites, reduc-

ing false-negative rates and permitting prompt

treatment.To investigate this application, ROI spectral

studies have been conducted using a B&K Medical

Systems Model 3535 which employs a mechanical

sector-scan transrectal probe (Feleppa et al., 1996,

1997). RF data are acquired from an entire scan

plane immediately preceding the insertion of the

biopsy needle. Calibrated power spectra are sub-

sequently computed using an ROI that encom-passes the biopsy site, which is spatially registered

with the ultrasonic image. Database correlations

with subsequent biopsy reports employ the spec-

tral intercept and midband fit as well as the pa-

tient’s PSA level.

Classification studies have employed nearest-

neighbor and NN techniques, using ‘‘jack-knife’’statistical procedures (Feleppa et al., 2000, 2001).

Results are documented in terms of receiver op-

erator characteristics (ROC). As shown in Fig. 13,

ROC curves plot the true positive fraction, TPF

(correctly identified cancers) vs. the false positive

fraction, FPF (non-cancers incorrectly classified as

cancer); these fractions are plotted as the classifi-

cation threshold is varied. For an ideal classifier,the true positive fraction would always be unity,

and the area under the ROC curve would equal

one. For a totally random classifier, the ROC

curve would lie along the diagonal of the axes, and

the ROC area would be 0.5.

The results plotted in Fig. 13 were obtained

from 1019 biopsies. The upper curve was obtained

using spectral procedures with a NN classifier.Several different NN models were evaluated; the

best performance was obtained with a multi-layer

perceptron model using off-the-shelf NConnect

software. The inputs to the NN were spectral, in-

tercept, and midband values along with PSA level;

the gold standard for training and evaluating the

classifier was biopsy histology. The lower curve

was derived from numerical levels of suspicion(LOS) that were independently assigned by clini-

cians based on conventional B-mode images and

ancillary clinical data such as PSA levels. (The

LOS increases from 1 to 5 with increasing suspi-

cion of cancer.) The plotted results show that the

spectral classification, which has an ROC area

of 0:85� 0:05, is significantly superior to the

clinicians’ classification, which has an area of0:66� 0:03.As in ocular applications, these ROI database

results were used to plan stained images using

spectral parameter images of intercept and mid-

band fit (see Figs. 5 and 6). Paired local values of

these parameters were analyzed together with the

patient’s PSA level. (PSA provides no spatial in-

formation, but it has been found to alter spectralparameter values associated with prostate cancer.)

In order to expedite image synthesis, the NN, de-Fig. 13. ROC curves for prostate-cancer classification.

652 F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658

veloped from the ROI studies, was used to estab-

lish a 3-D array containing a score indicative of the

likelihood of cancer (LOC) as a function of in-

tercept, midband fit, and PSA. This array is now

employed as a lookup table to evaluate LOC at

each image site. Sites whose LOC exceeds a se-lected threshold appear as a red overlay on a B-

mode or midband-fit image.

3-D stained images have been generated by

applying the above procedures to RF data ac-

quired in sets of parallel planes. First, the color

overlay is applied to highlight high LOC regions in

each scan plane. Second, the prostate capsule is

demarcated manually and the extraprostaticregions are masked. Finally, the masked, color-

encoded images are depicted as surfaces (the cap-

sular and tumor-foci surfaces) by assembling the

set of 2-D images into a 3-D rendering. 3-D ren-

derings are generated using available software

such as VTK, AVS, or Noesys. Fig. 14 shows a

black-and-white reproduction of an interactive 3-

D rendering in which the smooth prostate capsulebounds several foci of suspected cancer. A subse-

quent biopsy verified that cancer was present in the

right apex of the gland, consistent with Fig. 14.

Such images have substantial potential for treat-

ment planning; for example, they could be used to

select optimal sites for the radioactive seeds im-

planted for cancer therapy. Based on ocular-tumor

results, these images may also delineate regions

responding or not responding to therapy, permit-

ting treatment to be progressively adapted in each

patient.

4.3. Breast examinations

Spectral procedures have been employed to

examine breast lesions in order to more reliably

identify those tumors that are benign and, thus, do

not require biopsies. The goal of these studies is to

avoid the risks, expenses, and patient anxiety as-

sociated with unnecessary negative biopsies, which

currently account for 70–90% of the one millionannual biopsies in the US (Stavros et al., 1995).

Progress towards this goal has already been

made using subjective interpretation of lesion

features in conventional ultrasonic images (Stav-

ros et al., 1995; Advanced Technology Laborato-

ries (ATL), 1994). Both boundary and internal

features are evaluated. Images of malignant (can-

cerous) lesions typically exhibit an irregular shape(often with protruding speculations), low echoge-

nicity with a heterogeneous texture, and a poste-

rior ‘‘shadow’’ arising from a relatively high

attenuation coefficient within the lesion. In con-

trast, benign lesions typically exhibit smooth, well-

defined boundaries and higher echogenicity with a

homogeneous texture. While these diagnostic cri-

teria can help in selecting cases for biopsies, theyare inherently subjective and dependent upon

physician skill as well as instrument characteris-

tics.

We conducted an initial study to explore whe-

ther spectral procedures can be used to quantify

several features corresponding to the subjective

features now being employed (Alam et al., 2000),

our ultimate goal is to replace current assessmentswith objective, user-independent determinations.

In order to investigate this concept, we modified

our approach to utilizing spectrum analysis and

included a set of lesion-boundary features, as

described below.

In our studies, digital RF data were acquired

from patients with mammographically visible

breast lesions, scheduled for subsequent biopsy.The data were acquired using a Spectrasonics

Imaging Inc. (Wayne, PA) acquisition moduleFig. 14. 3-D image showing capsule of prostate and foci of

suspected cancer.

F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658 653

interfaced with an ATL (Bothell, WA) Ultramark

9 scanner. An L10-5 linear array (7.5-MHz center

frequency) was employed at a single transmit focal

length. Data were sampled (14 bits) at a 20 MHz

rate, and time gain control (TGC) data were ac-

quired so that RF data could be corrected forTGC settings prior to analysis. Calibration data

were acquired from planar and diffuse targets and

calibrated spectra were computed over the 5–9

MHz bandwidth with L ¼ 2:5 mm.The initial step in data analysis was the gener-

ation of B-mode images from captured RF data.

As shown in Fig. 15, the boundary of the lesion

was manually traced on these images, and addi-tional rectangular analysis regions were placed

about the lesion. Parameter images of spectral in-

tercept and midband fit were generated and stored

for analysis using these demarcated regions.

To evaluate the interior lesion properties, we

defined quantitative measures corresponding to

the subjective features used by clinicians. ‘‘Echo-

genicity’’ was defined as the average interceptvalue within the traced lesion boundary: intercept

was selected since it does not require attenua-

tion compensation. ‘‘Heterogeneity’’ was defined

as the standard deviation of midband fit within

the lesion, after attenuation compensation (1 dB/

MHz cm): this parameter was selected because the

estimator for midband fit has high precision, and

the standard deviation for homogeneous scatterers

is simply 5:6=ðBLÞ1=2 (dB). ‘‘Shadowing’’ mea-surements estimated the lesion’s attenuation coef-

ficient by computing average midband-fit values in

comparable shadowed and unshadowed analysis

regions posterior to the lesion; these measurementswere normalized by lesion thickness and provide

an attenuation coefficient relative to that of sur-

rounding normal tissue if the analyzed posterior

segments contain similar structures.

We also determined several morphometric fea-

tures, which were computed from the traced lesion

boundary. These included the aspect ratio (verti-

cal-to-horizontal ratio), a fractal dimension char-acterizing boundary roughness, and convexity.

Convexity is defined as the ratio of the perimeter

of the convex polygon bounding the lesion contour

to the perimeter of the lesion; this parameter de-

creases with increasing spiculation and has a

maximum value of unity.

These features were computed for 119 patients

with biopsy-proven lesions. Nine spectral andmorphometric features were employed to differ-

entiate malignant from benign lesions using jack-

knife procedures with nearest-neighbor classifiers.

While the optimal feature set remains to be iden-

tified, results were very encouraging producing

an ROC area of 0:87� 0:04.This breast study indicates how spectral proce-

dures may be used to quantify subjective criterianow used by clinicians. It also shows how spectra,

which measure ultrasonic scattering properties,

may be complemented by quantitative boundary

features, which are affected by tumor growth pat-

terns. These studies are being expanded to improve

upon the definition of each feature and to identify

optimally efficient sets of parameters for objective

classification. More recent analysis using refinedprocedures yielded an ROC area of 0:9164�0:0346 (Alam et al., 2002a,b).

4.4. Cardiac examinations

An extensive series of cardiac investigations

(O’Donnell et al., 1979, 1981; Vered et al., 1987;

Perez et al., 1994) has been conducted by Miller

and associates. While these investigations have

examined various spectral parameters (e.g., fre-Fig. 15. Analysis regions for breast lesion L.

654 F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658

quency dependence of backscatter), they have

concentrated on the use of IB. As noted above, IB

measures the area under measured spectra (in dB)

and is directly related to spectral midband fit. IB

values have been shown to be affected by cardiac

ischemia, angulation of cardiac muscle fibers, anddegree of muscle contraction during the cardiac

cycle.

IB values, like midband-fit values, are affected

by intervening attenuation, so that absolute IB

values are difficult to employ in standard (closed

chest) examinations of the heart. However, the

above investigations have shown that temporal

variations in IB may be used to evaluate the statusof the myocardium. In particular, the amplitude

and temporal pattern of IB variations during the

cardiac cycle is affected by ischemia. Overall,

clinical examinations measuring IB may be of

significant use in echocardiographic examinations

of infarction and reperfusion of the myocardium.

Real-time cross-sectional images of IB values

could be especially useful in these examinations(Perez et al., 1994).

4.5. Additional frequency-domain investigations

Significant frequency-domain results have been

obtained in other investigations. Insana, Hall and

coworkers have employed a form-factor model to

analyze scattering, and they have generated imagesof IB and scatterer size in the kidney (Insana et al.,

1991; Garra et al., 1994). Their animal studies have

shown how spectra can be analyzed to separately

study kidney microstructure in terms of spherical

glomeruli and cylindrical tubules. This approach

may be extremely useful in diagnosing kidney

disease and elucidating its development in vivo.

Several investigators (Oosterveld et al., 1991;King et al., 1985) have shown that sets of spectral

parameters can provide diagnosis of diffuse and

focal diseases of the liver. Vascular plaque has also

been characterized by Sigel and coworkers (Lee

et al., 1999) and by Spencer et al. (1997).

The frequency dependency of backscatter from

blood has been extensively examined by Kuo and

Shung (1994). Recent in vitro studies (Kolios et al.,1999) have also shown that cellular level phe-

nomena (e.g., apoptosis in drug-induced cell

death) cause measurable changes in spectral pa-

rameters, supporting the use of spectral assays for

treatment monitoring.

Spectral studies of ultrasonic contrast agents

have been conducted in our laboratories (Deng

et al., 1998, 2000). These small (e.g., 3 lm) parti-cles often consist of encapsulated gas bubbles

which are injected in the bloodstream to enhance

the ultrasonic detection of blood in the body. We

have adapted our theoretical framework to include

scattering from these agents and shown that, at

sufficiently high frequencies, spectral intercept can

provide quantitative estimates of their in vivo

concentrations and radii. Procedures incorporat-ing this finding are being investigated for quanti-

tative evaluations of flow and perfusion in the

body.

5. Summary and conclusion

Frequency-domain analysis of ultrasonic echoeshas been examined by a substantial number of

investigators. Spectral techniques offer the poten-

tial for new improvements in medical imaging, but

their full potential for conveying relevant infor-

mation and for use in tissue segmentation have

yet to be fully realized.

There now exists a coherent framework for

understanding how spectral features are related totissue microstructure and for evaluating the sta-

tistics of spectral estimators in terms of system

characteristics and processing parameters. Several

topics warrant further investigation. Most theo-

retical models assume a specific isotropic function

to characterize tissue microstructure. Investiga-

tions using acoustic microscopy may help improve

these models and could support initial studies of2-D and 3-D spectra, which incorporate coher-

ent scanning of tissue structures. Calibration pro-

cedures for complex multifocus arrays require

further investigation as do the spectral effects of

non-linear propagation and beam aberrations

caused by fluctuations in propagation velocity.

Additional clinical studies are required to vali-

date the utility of spectral procedures in specificapplications, and long-term studies are needed to

identify the incremental benefits of treatment

F.L. Lizzi et al. / Pattern Recognition Letters 24 (2003) 637–658 655

monitoring afforded by these techniques. The ap-

plication of independent sets of spectral parameter

images in segmentation and boundary detection

clearly warrants further investigation. These topics

are assuming increasing importance for automated

volume computations, morphology descriptors,and 3-D imaging.

Spectral imaging techniques are likely to as-

sume more significance in view of demands for

precise tissue data imposed by the variety of

emerging non-invasive and minimally invasive

procedures for therapy. 3-D spectral images could

be of extreme importance in planning the use of

techniques including high-intensity focused ultra-sound (ter Haar, 1995; Lizzi et al., 2001), and they

could become a key tool for monitoring the acute

and chronic effects of such procedures.

Acknowledgements

Portions of this research were supported byNIH Grants EY01212, CA53561, and HL59302

and by US Army Medical Research and Materiel

Command grant DAMD17-98-1-8331. We wish to

gratefully acknowledge the dedicated collabora-

tion of Drs. D.J. Coleman and R.H. Silverman at

the Weill Medical College of Cornell University,

Dr. W.R. Fair, formerly at the Memorial Sloan-

Kettering Cancer Center, Dr. C.R. Porter at theWashington, DC Veterans 30. Affairs Medical

Center and their staffs, as well as our colleagues

at Riverside Research Institute.

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