OReview ArticleO

Elastography: Imaging the Elastic Properties of Soft Tissues withUltrasoundJonathan OPHIR1.2, S. Kaisar ALAM1.3, Brian S. GARRA4, Faouzi KALLEL1, Elisa E. KONOFAGOU1.Thomas KROUSKOp6, Christopher R. B. MERRITT?, Raffaella RIGHETTr.2, Remi SOUCHON8,Seshadri SRINIVASAN1,2. and Tomv VARGHESE1.9

AbstractElastography is a method that can ultimately generate several new kinds of images, called elastograms. As

such, all the properties of elastograms are different from the familiar properties of sonograms. While sonogramsconvey information related to the local acoustic backscatter energy from tissue components, elastograms relateto its local strains, Young's moduli or Poisson's ratios. In general, these elasticity parameters are not directlycorrelated with sonographic parameters, i.e. elastography conveys new information about internal tissue structureand behavior under load that is not otherwise obtainable. In this paper we summarize our work in the field ofelastography over the past decade. We present some relevant background material from the field ofbiomechanics. We then discuss the basic principles and limitations that are involved in the production ofelastograms of biological tissues. Results from biological tissues in vitro and in vivo are shown to demonstratethis point. We conclude with some observations regarding the potential of elastography for medical diagnosis.

1,,-1'71J Med Ultrasonics 2002; 29 (Winter)

Keywordselastography, ultrasound

1. IntroductionThe elastic properties of soft tissues depend on their

molecular building blocks, and on the microscopicand macroscopic structural organization of theseblocks (Fung 1981). The standard medical practice ofsoft tissue palpation is based on qualitative assessmentof the low-frequency stiffness of tissue. Pathologicalchanges are generally correlated with changes intissue stiffness as well. Many cancers, such as cancersof the breast, appear as extremely stiff nodules(Anderson 1953). However, benign tumors of thebreast may appear stiff as well, but possibly not quiteas stiff as the cancers. In many cases, despite thedifference in stiffness between the lesion and thesurrounding normal tissue, the small size of apathological lesion and/or its location deep in thebody make its detection and evaluation by palpation

difficult or impossible. In general, the lesion mayormay not possess sonographic contrast that wouldmake it ultrasonically detectable. For example,tumors of the prostate or the breast might be invisibleor barely visible in standard ultrasound examinations,yet be much stiffer than the embedding tissue (Garraet al. 1997). Diffuse diseases such as cirrhosis of theliver are known to significantly increase the stiffnessof the liver tissue as a whole (Anderson 1953), yetthey may appear normal in conventional ultrasoundexamination.

Since the echogenicity and stiffness of tissues arecaused by unrelated mechanisms and are thusuncorrelated, it is expected that imaging tissuestiffness, or a related parameter such as local tissuestrain, will provide new information that is related totissue morphology and architecture. This expectationhas now been confirmed in the breast (Garra et al.

IThe University of Texas Medical School at Houston, Houston, TX, USA, 2The University of Houston,Department of ECE, Houston, TX, USA, 3Riverside Research Institute, New York, NY, USA, 4University ofVermont, Fletcher Allen Medical Center, Burlington, VT, USA, 5Brigham and Women's Hospital, Boston, MA,USA, 6Baylor College of Medicine, Houston, TX, USA, 7Thomas Jefferson University, Philadelphia, PA, USA,81'Institut National de la Sante et de la Recherche Medicale (INSERM) Unite 556, Lyon, France, 9University ofWisconsin, Madison, WI, USAReceived on May 23,2002; Accepted on September 13,2002

155T Mprl Tntr...nn;,.. Vnl ?Q W;ntpr (?011?1

motions must be provided. Such means may includeultrasound, MRI or other diagnostic imagingmodalities that can track minute tissue motion withhigh precision. In the last fifteen years, interest hasbeen mounting in the ultrasonic imaging of tissueelasticity or stiffness parameters. A comprehensiveliterature review of this field can be found in Ophir etal. (1996) and in Gao et al. (1996). Tissue elasticityimaging methods based on ultrasonics fall currentlyinto two main groups: 1) methods where a quasi-static compression is applied to the tissue and theresulting components of the strain tensor areestimated (Ophir et al 1991, O'Donnell et al. 1994) ;and 2) methods where a low frequency vibration( < 1 kHz) is applied to the tissue, and the resultingtissue behavior is inspected by ultrasonic or audibleacoustic means (Krouskop et al. 1987, Lerner andParker 1987, Lerner et al. 1990, Yamakoshi et al.1990, Alam et al. 1994, Fatemi et al. 1999, Walker etal., 2000).

In this review, we concentrate on describing therecent progress using the first approach that we callelastography, which has been under development inour laboratory since 1989. We first present a shortsummary of the theory of elasticity as it pertains tothe quasi-static application of loads to biologicaltissues. We then give some basic tissue stiffness resultsthat demonstrate the existence of stiffness contrastamong normal tissues, and between normal andpathological tissues in the breast and prostate. Weproceed to describe the elastographic imaging process,starting from the tissue elastic modulus distribution,progressing through various algorithms for precisiontime-delay estimation of echoes from strained tissues,and culminating in the production of the elastogram,or strain image. The use of ultrasound to acquiretissue motion information results in certain basiclimitations on the attainable elastographic imagequality, which may be described by the theoreticalframework known as the Strain Filter (Varghese andOphir 1997b). The Strain Filter may be used topredict and design important improvements to variouselastographic image attributes, such as dynamic rangeexpansion (Konofagou et al. 1997) and improvementin in the elastographic signal-to-noise ratio (SNRe)through multiresolution processing (Varghese et al.1998) or compensation for undesired axial distortions(Cespedes et al. 1993) and undesired lateral tissuemotion (Konofagou and Ophir 1998). In combinationwith certain Contrast Transfer Efficiencies (CTE)inherent in the conversion of modulus to straincontrast (Ponnekanti et al. 1995, Kallel et al. 1996),the Strain Filter formalism may be used to predict theupper-bound as well as the practically attainableContrast-to-Noise-Ratio (CNRe) performance ofelastography and its tradeoffs with elastographicresolution (Varghese and Ophir 1998, Righetti et al.

1997, Rosenthal et al. 2002) and in animal studies(Merritt et al. 2002). In addition to pathology, wenow have new evidence that various normal tissuecomponents possess consistent differences in theirstiffness parameters as well. For example, in the ovinekidney, the stiffness contrast between the cortex andthe medullary pyramids has recently been measured tobe only about 6 dB at low strains, and correspondingstrain images showing easily discernible straincontrast have been made (Kallel et al. 1998). Similarobservations have been made in the normal canineprostate, where consistent stiffness and strain contrasthas been demonstrated between the outer and innergland, and between the urethra, the verumontanumand the normal prostatic tissue (Kallel et al. 1999).These observations provide the basis for elastographicimaging the normal anatomy as well. Anotherobservation that has been made recently in vitro isthat some normal and pathological tissues maypossess nonlinear stress/strain behavior (Krouskop etal. 1998). This means that their stiffnesses are afunction of strain. This property may be useful indifferentiating normal from abnormal tissues in thefuture.

Over the past 20 years there have been numerousinvestigations conducted to characterize themechanical properties of biological tissue systems(Bakke 1973, Chen et al. 1996, D'Angelo 1975,Fukaya et al. 1969, Galey 1969, Gao et al. 1996,Harley et al. 1977, Malinauskas et al. 1989, Sarvazyan1993, Yamada 1970), which have been often idealizedas homogeneous, isotropic elastic materials. Much ofthe work has focused on bone, dental materials andvascular tissue. There are articles that discussmethods used to characterize these tissues, and thereis a large volume of experimental data on themechanical response of these tissues to various typesof loading (Gao et al. 1996, Demiray 1972, Krouskopet al. 1987, Ophir et al. 1991, Ophir et al. 1996, Ophiret al. 1997, Cespedes et al. 1993). However, there is anear void in the literature regarding the mechanicalproperties of tissue systems tested in vivo. There iseven less information available on the elasticproperties of pathological tissues. Yamada's book(1970) presents a relatively broad range of data, butmuch of the data are derived from experiments usinganimal tissues and all of the information relates toresults from uniaxial tensile tests of the tissue, and notfrom compressional tests. A recent article byKrouskop et al. (1998) provides compressionalstiffness values for normal and pathological breastand prostate tissues in vitro.

The stiffness parameter is a function of the elasticmodulus of the tissue and its geometry. It cannot bemeasured directly. A mechanical stimulus of somekind must be propagated into the tissue, and precisionmeans for detecting the resulting internal tissue

J Med Ultrasonics Vol.29 Winter (2002)156

2002 a, Righetti et al. 2002 b). We conclude withsome recent results that demonstrate that qualityelastograms may be produced both in-vitro and in-vivo, with high contrast-to-noise ratios and at highresolutions.

2. Basic Elasticity Theory for Static Compressions

For a large number of solids, the measured strain isproportional to the load over a wide range of loads.This linear relationship is known as Hooke's law,which states that each of the components of the stateof stress at a point is a linear function of thecomponents Qf the state of strain at the point (Saada1983). Mathematically, this is expressed as aconstitutive equation, which may be written in tensornotation as:

Okl= Cklmnemn'

where the components of the matrix Cklmn are elasticconstants that are intrinsic properties of the material.There are generally 81 (=34) such constants,corresponding to the indices, k, 1, m, and n takingvalues equal to 1,2, and 3. Since both the stress tensorakl and the elasticity tensor Cklmn are symmetric, thenumber of elastic constants reduces to 21. Theseconstants characterize a general anisotropic, linearlyelastic material. Since the elastic properties of anisotropic material are independent of the orientationof the axes, the number of elastic constant is furtherreduced to 3 constants which may be expressed interms of only two independent parameters known asthe Lame's constants A and J1. These 3 elasticconstants are given by

C1122=A, C1111~A+2.u, C'2!' ..!--(Cml2

OIl Lt

(2)The constant 11, also known as G, is referred to as theshear modulus.The volume change per unit volume due to sphericalstress is dependent on the bulk compressionalmodulus, K, which is related to the Lame's constantsbv

., r ,

3l'+2.u~~

K= (3)

There are also two other engineering parameterscommonly used to characterize the mechanicalproperties of solid materials: Young's modulus, E,and Poisson's ratio, ]). These are related to K and G bythe following expressions:

14'K= . and (4 a)

3(-21.1

In general, soft tissues are anisotropic, viscoelasticand non-linear. However, it is usually assumed thatthey behave as linear, elastic, isotropic materials inorder to simplify the analysis. These assumptions arelikely to be reasonable for small strains, rapid loadapplication and a spatial scale that is large comparedto the relative correlation length of the elasticvariability in the tissue sample (Krouskop et al.1998).

Soft tissues contain both solid and fluidcomponents and therefore may have mechanicalproperties that fall somewhere between those of bothmaterials (Sarvazyan et al. 1995). The ratio G/K isclose to a few tenths for solid materials, while itequals zero for liquids (i.e. liquids are incompressibleand their Poisson's ratio equals 0.5, and from equation1, K -+ 00). Many soft tissues are nearlyincompressible with Poisson's ratios ranging from0.49000 to 0.4999, which make them mechanicallysimilar to liquids. For most solids, Poisson's ratios arebetween 0.2 and 0.4. Note that from equation 4 b forincompressible tissues (v=0.5), the relationship E=3 G holds. This means that for incompressiblematerials there exists a simple proportionalitybetween the shear and the Young's moduli.

The bulk modulus K may be estimated from thepropagation speed of bulk compressional waves c andthe material density (p,i.e. K == pc2. Since it is wellknown from the literature that the dynamic ranges ofthe speed of sound as well as the density in soft tissuesare small, the dynamic range of the bulk modulus oftissues is small as well. Hence in traditional medicalultrasound imaging, the speed of sound in tissue isassumed to be a constant 1540 m/s. Thus, the abilityto create properly scaled sonograms of soft tissues isin part due to this small variability in the speed ofsound. Recently, it has been shown that the shearmodulus of normal and abnormal soft tissues mayspan much more than an order of magnitude(Sarvazyan 1993, Krouskop et al. 1998). The graphsof Fig. 1 summarize tissue shear modulus dataobtained by Krouskop et al. (1998) from differentbreast and prostate tissues. As can be seen, a relativelylarge dynamic range of the shear modulus exists innormal and abnormal breast and prostate tissues. Thisrelatively large dynamic range of the shear modulus isresponsible for the increased interest in developingnew techniques for imaging information related tothis modulus. By contrast, attempts to image the bulkmoduli of tissues via their speeds of sound havelargely been unsuccessful in the past due to the smalldynamic range of this modulus and the concomitantlow contrast-to-noise ratios.

It is known that the force generated by the verticalindentation of a piston into soft tissue is determinedby the shear modulus (Sarvazyan et al. 1995). Toillustrate this. consider the classical solution of the

E(4 b)G

?(1

1~7T U~.1 TTltT~on..;"o Vnl ?Q W;..t~T (?M?

Fig. 1 Tissue elastic moduli obtained from normal and abnormal breast and prostate tissues (Krouskop et al. 1998).

force generated by the vertical displacement W of acircular piston of radius R into a semi-infinite elasticmedium with shear and bulk elastic moduli G and K.This force is given by,

p= 8GR W1+ G/K (5)

I+G/3K,

where the terms containing the ratio G/K nearlyvanish in soft tissues, and where G«K. Thus, therelationship between the force P and the displacementW is determined by the shear modulus and thegeometry. In other words, information from manualpalpation is independent of the bulk compressionalmodulus K. Since the force P is also related to thegeometry, the stress/strain behavior measured in suchan indentation experiment is generally indicative ofthe stiffness of the particular tissue/geometry setup,and not necessarily of the pure shear modulus of thetissue sample.The equations describing the equilibrium-state of alinear, isotropic elastic material is given in (Sarvazyan1993) as

orthogonal stress tensor components. In principle, fora given Poisson's ratio, any equation relating a givenstrain distribution to a corresponding set of stressdistributions may be used to estimate thecorresponding Young's modulus distribution. Forexample in the case of a plane-strain state problem,the modulus distribution may be obtained using thefollowing relation

(1+1J) (l-1J)o=-1JOuu)R= (7)

~ err "/

In general, however, only the strain distributionmay be directly estimated in practice, This straindistribution is not an intrinsic tissue property, It isdependent on both internal and external boundaryconditions, as well as on the distribution of shearmoduli in the tissue. The external boundaryconditions depend on the three-dimensional shape andrelative size of the compressor compared to the tissue,as well as on the degree of friction between theinternal and external contact surfaces. The shape aridtype of the tissue components determine the internalboundary conditions. Therefore, a map of the straindistribution in tissue reveals not only informationabout tissue shear modulus distributions, but alsoabout tissue connectivity (interfaces between tissuecomponents) and other geometrical considerations.Alternatively, the map may be designated as astiffness distribution, which includes the effects of themodulus and the geometry. An incorrectinterpretation of the stiffness distribution as being theshear modulus distribution may in some cases resultin some known image artifacts due to stressconcentrations that may be misinterpreted as areas oflow modulus. However, we have previously

1 1+11el/l/=E[ul/I/-lI(UX1/+uzz)], e~=~u~

(6)

1 1+1.1eZZ=E[O'ZZ-1.I(O'zx+ 0'",,)] , ezz=-yO'zz

where err, eYYI ezz etc. are the orthogonal strain tensorcomponents and err, eyy, ezz etc. are the corresponding

J Med Ultrasonics Vol.29 Winter (2002)

demonstrated (Kallel et al. 1998) that for lowmodulus contrast and simplified geometricalboundary conditions, the stiffness distribution may bea relatively good representation of the underlyingmodulus distribution.

Pre-compression RF line

3. Elastography-Imaging Tissue Strain

When a constant uniaxial load deforms an elasticmedium, all points in the medium experience aresulting level of longitudinal strain whose principalcomponent is along the axis of compression. If one ormore of the tissue elements has a different stiffnessparameter than the others, the level of strain in thatelement will generally be higher or lower; a stiffertissue element will generally experience less strainthan a softer one. The longitudinal axial strain isestimated in one dimension from the analysis ofultrasonic backscattered signals obtained fromstandard diagnostic ultrasound equipment. Thismeans that ultrasonic speckle may be used for thispurpose, and no discrete resolvable targets must bepresent. This estimation is accomplished by acquiringa set of digitized radio-frequency echo lines fromscatterers contained in the tissue region of interest;compressing the tissue with the ultrasonic transducer(or with a transducer/compressor combination)along the ultrasonic radiation axis by a small amount(generally about 1 % or less of the total tissue depth),and; acquiring a second, post-compression set of echolines from the same region of interest. Congruentecho lines are then subdivided into small temporalwindows that are compared pair-wise by using one ofa variety of possible known time-delay estimationtechniques such as cross-correlation, from which thechange in arrival time of the echoes before and aftercompression can be estimated. Due to the smallmagnitude of the applied compression, there are onlysmall distortions of the echo lines, and the changes inarrival times are also small. The local longitudinalstrain under the assumption of constant speed ofsound is estimated as the gradient of the displacement,viz.

Post-compression RF line

Fig. 2 A schematic showing the process of computing thestrain in a tissue segment. Congruent windowedsegments of the pre-compression and post-compressionsignals are compared by crosscorrelation. While theearly windowed segments exhibit virtually no delay, afinite delay (designated del (t)) is detected between thelater segments. The strain is computed as the gradientof the time delay (or displacement), i.e. strain=del (t)IT, where T is the initial (pre-compression) separationbetween the windowed segments.

(t1b-t1) - (t2b-'-'t2a)"II,local t - t ' (8)

Ib la

where tla is the arrival time of the pre-compressionecho from the proximal window; tlb is the arrivaltime of the pre-compression echo from the distalwindow; t2a is the arrival time of the post-compression echo from the proximal window; andt2b is the arrival time of the post-compression echofrom the distal window. Fig. 2 shows a schematicrepresentation of the time delay and straincomputation process. The windows are usuallytranslated in small overlapping steps along thetemporal axis of the echo line, and the calculation isrepeated for all depths. The fundamental assumption

0 - -= -! ,

made is that speckle motion adequately represents theunderlying tissue motion for small uniaxialcompressions. This assumption appears to bereasonable as long as the distributions of the scatterersbefore and after compression remain highlycorrelated. We have shown recently (Konofagou andOphir 1998) that the lateral motion of the scatterersdue to tissue compression may also be estimated withhigh precision using novel interpolation techniquesoperating on signals obtained from two partiallyoverlapped beams. This allows the generation ofelastograms that depict the lateral tensor componentsof the strain and at least partial re-correlation of thesignals prior to the computation of the axial strains,resulting in better elastographic image quality, and/orthe generation of elastograms depicting the localratios of the lateral-to-axial strains (effectively, thePoisson's ratio)

The general process of creating elastograms isshown in Fig. 3, showing a block diagram of theprocess. The first block of the process corresponds toan example of a uniform target containing a simplecircular pattern of higher tissue modulus. Theintermediate block corresponds to the ideal straindistribution in the target due to the behavior of thistarget under a compressive load. The transformationfrom modulus contrast (first block) to strain contrast

T Mpti TTltr".nni,.. Vnl ?Q Wintpr (?M?) 159

Fig. 3 The general block diagram process of creating an elastogram. The modulus contrast distribution isconverted to a strain contrast distribution using the Contrast-Transfer Efficiency (CTE). The idealstrain contrast distribution is estimated from ultrasonic strain estimates by the ultrasound system,whose performance is controlled by the derated Strain Filter (SF) for particular acoustic,instrumentation and algorithmic parameters. The result is an estimated strain contrast distribution(elastogram), which is a somewhat corrupted version of the ideal strain image.

(second block) involves a certain loss of efficiency.This may be computed for such simple targets by theContrast Transfer Efficiency (CTE) function. Theoutput image corresponds to the strain (axial and/orlateral) image (elastogram) , which is a corrupted(noisy) version of the ideal strain image. The noiseand contrast properties of the elastogram arecomputed from the Strain Filter (SF), which takesinto account the engineering, signal processing andacoustical parameters that corrupt the ideal strainimage and limit the ultimate quality of the attainableelastogram. The block describing the instrumentincorporates the Strain Filter (Varghese and Ophir1997 b), which embodies the selective filtering of thetissue strains by the ultrasound system and signalprocessing parameters. The SF predicts a finitedynamic range and respective elastographic signal-to-noise ratio (SNRe) at a given resolution in theelastogram, limited by noise and/or decorrelation.The contributions of the signal processing andultrasound system parameters and other algorithmsare indicated as inputs into the SF. Combining theCTE and the SF formulations leads to the descriptionof the elastographic contrast-to-noise ratio (CNRe)in the elastogram. All these blocks are described laterin this article. A complete description may be foundin Ophir et al (1999).

indeed what is desired. The CTE is defined as theratio of the observed (axial) strain contrast ratio Comeasured from the strain elastogram, and theunderlying true modulus contrast ratio Ct, using aplane-strain state model. Expressed in decibels, theratio becomes a difference that is given by:

CTE(dB) = I Co (dB) I-I Ct(dB) I, (9)

where the magnitude is used iff order to have CTEnormalized to the zero dB level; i.e. the maximumefficiency is reached at 0 dB for both hard and softinclusions. This behavior has been verified by finite-element simulations and was also corroboratedtheoretically, using models of simple geometry(Ponnekanti et al. 1995, Kallel et al 1996). Fig. 4shows the behavior of the CTE parameter over an 80dB dynamic range of modulus contrast as measuredfrom simulated data (data points), and as predictedusing an analytical model (smooth curve). It is clearfrom the Figure that for low modulus contrast levels(a high level of target modulus homogeneity), theelastographic strain contrast is relatively close to themodulus contrast (the contrast transfer efficiencyCTE;:::; 1, or 0 dB). This is a very importantobservation, since it suggests that for tissues that havestructures that possess low modulus contrast, thesimply computed axial strain elastogram itself is verysimilar to the inverse of the true shear modulusdistribution in the tissue. This expected result hasbeen verified experimentally using actual indentationmeasurements and elastograms, using ex-vivo ovinekidneys and phantoms (Kallel et al. 1998). Hardinclusions embedded in softer background have arelatively high level of contrast-transfer efficiency(CTE;:::; 0 dB). However, soft inclusions that are

4, Contrast-Transfer Efficiency (CTE)

Using ultrasonic techniques, it is only possible tomeasure some of the local longitudinal components ofthe strain tensor in the tissue. The local componentsof the stress tensor remain largely unknown. Thestrain elastogram is all that is available to representthe distribution of tissue elastic moduli, if this is

160 J Med Ultrasonics Vol.29 Winter (2002)

True Modulus Contrast (dB)

Fig. 4 The behavior of the Contrast Transfer Efficiency function for a plane-strain-state circular inclusion. Notethat the strain contrast is close to the modulus contrast (and hence the efficiency is high, i.e., CTE= 1, or 0dB) for low «<0 dB) modulus contrast lesions. Note also that the function is asymmetric, demonstratinghigh efficiency for stiff inclusions, and low efficiency for soft inclusions.

completely surrounded by harder backgroundmaterial have low contrast-transfer efficiency (CTE«0 dB), and thus may not be well visualized byelastography. The reason for this limitation lies in thefact that due to the incompressible nature of manysoft tissues (Poisson's ratio-O.S), the soft inclusionwill be constrained so that it will be unable to deformunder load, as it might otherwise do withoutconstraints. It will thus assume instead effectiveelastic properties that are closer to those of theembedding, stiffer material.

First, random noise introduces errors in the TDE,which are especially disruptive at small time delays.Second, since the tissue needs to be compressed toproduce elastograms, this very same compression ofthe tissue also distorts the post-compression signalsuch that it no longer is an exact delayed version ofthe pre-compression signal. This decorrelationincreases with increasing strain and is independent ofthe signal-to-noise ratio of the echo signals. Anyphenomenon (such as lateral and elevational motion)that degrades the precision of the time-delay estimateswill also degrade the strain estimates, thusintroducing additional noise into the elastogram.

Echo signal decorrelation is one of the majorlimiting factors in strain estimation and imaging. Forsmall strains, it has been shown that temporalstretching of the post-compression signal (or temporalcompression of the pre-compression signal) by theappropriate factor can almost entirely compensate forsignal decorrelation. When the post-compression echosignal is stretched, it in effect realigns all thescatterers within the correlation window. Globaluniform stretching was found to significantly improvethe elastographic signal-to-noise ratio (SNRe) andexpand the strain dynamic range in elastograms(Alam and Ophir 1997). Moreover, this step iscomputationally simple. Thus, a global uniformstretching of the post-compression A-line prior to thedisplacement estimation is highly advisable, unless theapplied compression is very small «< 1 %) and thus

5. Time Delay Estimation (TDE) in Strained Tissues

Time delay estimation is a very important aspect ofelastography. The literature on TDE is extensive.Tissue strain is typically estimated from the axialgradient of tissue displacements. The local tissuedisplacements are estimated from the time delays ofgated pre-compression and post-compression echosignals. Time delays are classically estimated from thelag of the peak of the crosscorrelation functionbetween the pre- and post-compression gated echosignals. It is also possible to use other estimators oftime delay, such as the frequency shift of the cross-spectrum (Konofagou et al. 1999), or the point ofzero phase of the crosscorrelation function (Pesaventoet a11999, Lorenz et al. 2001).

The quality of elastograms is highly dependent onthe optimality of the TDE estimation procedure. TDEin elastography is mainly corrupted by two factors.

T Mpti TTltr".nni". Vnl ?Q Wintpr (?M?, 11;1

results from the unintended stretching of thetransducer point-spread function (PSF) when thepost-compression signal is stretched (Alam et al.1998 a).

stretching may not be necessary. In low contrasttargets and/or low strains, this is a very effectiveprocedure. In these situations, it produces qualityelastograms without significantly adding to thecomputational load. However, in high contrasttargets, there will be significant over-stretching in theareas of low strains, which by itself can significantlydegrade elastograms in these areas. For thesesituations, an adaptive axial stretching algorithm(Alam et al. 1998 b, Brusseau et al. 2000) may benecessary. If high strains are applied, significantdecorrelation occurs, which cannot effectively becompensated by stretching. Axial stretching ismandatory in the presence of intermediate strains;otherwise the elastograms become so noisy that theyare practically useless. It must be remembered thataxial stretching can only recover most of thedecorrelation suffered due to scatterer motion in theaxial direction; decorrelation due to lateral andelevational motions, as well as other sources ofdecorrelation, cannot be compensated this way.Konofagou and Ophir (1998) have demonstrated thatdecorrelation due to lateral motion may becompensated with high accuracy by using a signalinterpolation technique. This technique, whenapplied alternately with axial stretching, was shown toresult in large improvements in elastographic imagequality. A deconvolution filtering approach may beuseful in reducing the remaining decorrelation that

6. The Strain Filter (SF)The SF (Varghese and Ophir 1997 b) describes the

important relationship among the resolution, dynamicrange (DRe), sensitivity (Smin) and e1astographicSNRe (defined as the ratio of the mean strain to thestandard deviation of the strain in the elastogram),and may be plotted as a graph of the upper bound ofthe SNRe vs. the strain experienced by the tissue, fora given elastographic axial resolution (as defined bythe data window length (Righetti et al. 2002 a). TheSF is a statistical upper bound of the transfercharacteristic that describes the relationship betweenactual tissue strains and the corresponding strainestimates depicted on the elastogram. It describes thefiltering process in the strain domain, which allowsquality elastographic depiction of only a limited rangeof strains from tissue. This limited range of strains isdue to the limitations of the ultrasound system and ofthe signal processing parameters and algorithms. TheSF is obtainable as the ratio between the mean strainestimate and the appropriate lower bound on itsstandard deviation. On a logarithmic scale, this ratiois seen as a difference (Fig. 5). The SF is based onwell-known theoretical lower bounds on the TDE

100 meanstrainestimate

5

tra

1.0

1

s.d. ofstrainestimate

1

.01

.001n.0001

10 100.001 ,01 1 1,0001

Tissue strainFig. 5 Mean strain estimate and standard deviation of the strain as a function of the applied strain. Observe that while

the mean estimate is proportional to the tissue strain, the behavior of the standard deviation (s.d.) is highlynonlinear. At low strains, the s.d. is constant and low, and is determined by the Cramer-Rao Lower Bound(CRLB). At higher strains, phase ambiguities in the signal cause a sharp increase of the s.d. The ratio of themean to the lower bound of the s.d. of the strain estimate, as a function of tissue strain, is defined as the StrainFilter. In logarithmic units, the ratio is simply the difference between the two curves. Hence it is expected thatthe Strain Filter will have a bandpass characteristic, where the SNRe is low at low and high strains, and highat intermediate strains between the crossover points.

J Med Ultrasonics Vol.29 Winter (2002)162

25

,,! ~15m

'"

~ 10

5~i

... 0i_'fOO

OJD:Z(/)

Tissue Strain (dB)

Fig. 6 Typical appearance of the strain filter. Observe that theSNRe has a bandpass characteristic in the straindomain, and the magnitude of this bandpasscharacteristic is diminished at higher (smaller valued)axial resolutions. Hence, for a given strain, there is atradeoff between SNRe and axial resolution.

u~-80

-..70

~

-60

. .-50 -40

lissue Strain (dB)

~

-30~

-20

Fig. 7 A typical appearance of a family of Strain Filters at afixed axial resolution. The member Strain Filters havebeen derated to account for attenuation in tissue at 3cm and 6 cm depths. Note the axial nonstationarity ofthe strain filters due to attenuation, and the systematicerosion of the sensitivity (lowest measurable strain)and dynamic range (width of the Strain Filter) of thestrain in the elastogram.

variation in the SNRe . Both the SNRe and thedynamic range are reduced with an increase in lateraldecorrelation. As long as any stationary ornonstationary additive noise source can be described,its effect may be incorporated into the Strain Filterformalism, resulting in a more realistic, derated (suboptimal) Strain Filter. An example of a successivelyderated Strain Filter due to increasing tissueattenuation at larger depths (in two dimensions only(at a fixed resolution)) is shown in Fig. 7.

6.2 Contrast-to-noise Ratio in ElastographyThe contrast-to-noise ratio (CNRe) in elastography

is an important quantity that is related to thedetectability of a lesion. The properties of theultrasound imaging system and signal processingalgorithms described by the SF can be combined withthe elastic contrast properties (CTE) of tissues withsimple geometry, enabling prediction of theelastographic contrast-to-noise ratio (CNRe)parameter. This combined theoretical model enablesprediction of the elastographic CNRe for simplegeometry such as layered (l-D model) or circularlesions (2-D model) embedded in a uniformly elasticbackground. An upper bound on the CNRe may beobtained using the Fisher discriminant statistic, viz.:

2(s -s )2I'"'1\TD-l02 {In\...,lVl\'e- 2 i \~V)

Usl + Us2

The CNRe for specific geometry that possess ananalytic or experimental CTE description can beobtained (Varghese and Ophir 1998) by substitutingthe strains obtained using the elasticity model andtheir respective variances from the SF into Eq. (10).

variance, available in the literature. The low-strainbehavior of the SF is determined by the variance ascomputed from the Cramer-Rao Lower Bound(CRLB) (modified for partially correlated signals).The high-strain behavior of the SF is determined bythe rate of decorrelation of a pair of congruent signalsdue to tissue distortion as shown in Fig. 5, 6 illustratesthe general appearance of the SF in three dimensions,demonstrating the tradeoffs between SNRe and strainat all resolutions. An important extension to the SF isits combination with the CTE formalism to produceelastographic Contrast-to- Noise (CNRe) vs. straincurves. This allows the description of the CNRe ofsimple elastic inclusions or layers in terms of both themechanical strain contrast limitations in the target,and the noise properties of the apparatus.

6.1 Nonstationarity of the Strain FilterEstimation of tissue strains is inherently a

nonstationary process, since the pre- and post-compression RFecho signals are jointly nonstationary(due to signal deformation caused by strainingtissue). However, the pre- and post-compressionsignals can be approximated to be jointly stationary, ifthe tissue strain is estimated using small windoweddata segments in conjunction with temporal re-stretching of the post-compression signal. Frequencydependent attenuation causes additional (axial)nonstationarity into the strain estimation process vs.depth (Varghese and Ophir 1997 a), while lateral andelevational signal decorrelation introducenonstationarities in the strain estimation processalong the lateral and elevational directionsrespectively (Kallel et al. 1997). The SF can bederated by these corrupting processes to predict theeffect of these nonstationarities on the elastogram.For example, The effect of lateral decorrelationcontributes predominantly to the nonstationary

J Med Ultra"onic" Vo!.29 Wint"r (7007) II;.

generally a number between I and 2. This limit is notalways achieved (Alam et al. 2000) due to noiseconsiderations.. The practically attainable resolutionfor a given system, however, is generally limited bythe choice of window size and overlap, as long as thewindow size is larger than the PSF of the system.This bodes well for the feasibility of micro-elastographic imaging at high frequencies (Righetti etal. 2002 a). The lateral resolution of elastography hasalso been investigated in detail, and it was shown to beproportional to the beamwidth of the transducer(Righetti et al. 2002 b). Hence the best achievablespatial resolutions of elastography and sonography aresimilar, which means that comparisons betweensonograms and elastograms may be made on a similarscale and with good registration.

Fig. 8 A typical upper bound on the elastographic Contrast-toNoise ratio (CNRe) as a function of modulus contrastand strain. This function (nicknamed the "OperaHouse") is obtainable by combining the CTE and SFformalisms.

7. Applications of ElastographyIn principle, elastography may be applied to any

tissue system that is accessible ultrasonically andwhich can be subjected to a small static (or dynamic)compression. The compression may be appliedexternally or internally. Any physiologicalphenomena, such as pulsating arteries or respiration,may be used as a source of tissue compression. In thissection a summary of results from some of theseapplications is presented.

A typical example of the elastographic visualizationof a canine prostate in vitro is shown in Fig. 9. In theelastograms, the white (stiff) rim, depicted in boththe transverse and sagittal views and in each slice,corresponds to the outer gland that surrounds a softer(gray) inner gland. In the center of the prostate, theverumontanum is elastographically demonstrated as asmall stiff (white) ridge along the urethra. The lumenof the urethra is depicted as a soft (black) inverted"V" or "U" shaped area. By comparison, thecompanion sonograms do not provide a clearvisualization of the aforementioned anatomicalstructures in the prostate. It should be noted that theeach elastogram was derived from two of very similarsonograms, one of which is shown.

The first in vivo application of elastography was tothe imaging of the breast and skeletal muscle(Cespedes et al. 1993). An example of thevisualization of breast carcinoma is given in Fig. 10.Both the B-scan and the corresponding elastogramshow a large lesion at 3 o'clock. The size of this lesionon the elastogram is larger compared to its size on thecorresponding sonogram. The elastogram also depictsa second, much smaller lesion at 11 o'clock, which isnot demonstrated in the sonogram. Both lesions werepathologically confirmed. Further work hasdemonstrated that unlike benign breast tumors,cancers were consistently larger on the elastogramcompared to their corresponding size on thesonogram. This size discrepancy was hypothesized to

Fig. 8 illustrates the general appearance of theupper bound on the CNRe, demonstrating thetradeoffs among CNRe and modulus contrast for allapplied strains. Note from Fig. 8 and Eq. (10) thatthe highest values of the CNRe are obtained wheretwo conditions are satisfied; firstly, the differences inmean strain values must be large, and secondly thesum of the variances of the strain estimates should besmall. The improvement of the CNRe at low moduluscontrasts is primarily due to the small strainvariances, while at high modulus contrasts theimprovement in the CNRe is due to the largedifference in the mean strains. Note from the 3-Dvisualization of the CNRe curves in Fig. 7, that whenthe differences in the mean strain values are small (inthe region around the middle of the graph at lowcontrasts), the CNRe value obtained is close to zero.In addition, the regions with large strains(corresponding to large variances in the strainestimate due to signal decorrelation) also contributeto low CNRe values. Knowledge of the theoreticalupper bound on the CNRe in elastography is crucialfor determining the ability to discriminate betweendifferent regions in the elastograms. The CTE for theelasticity models and the elastographic noisecharacterized by the SF determine the CNRe inelastography. The 3-D visualization of the CNRecurves illustrate the strain dependence of theelastographic CNRe . The 3-D plot provides a meansof maximizing the CNRe in the elastogram for thegiven ultrasound system and signal processing

parameters.6.3 Resolution in ElastographyIt has recently been demonstrated (Righetti et al.

2001) that the upper bound on the elastographic axialresolution is proportional to the length of the point-spread-function (PSF) of the transducer. Theconstant of proportionality depends on the exactdefinition that is used for the axial resolution, but is

J Med Ultrasonics V 01.29 Winter (2002164

elastograms

transverse

sonograms

elastograms

sagittal

sonograms

Fig. 9 Matching elastograms and sonograms obtained from I mm equally spaced parallel transverseand sagittal cross-sections of a typical canine prostate at 5 MHz. The prostate size isapproximately 3 X 3 X 3 cm'. The elastograms are displayed using a reversed gray-scale mapwhere white means stiff and black means (Kallel et al. 1999). Note the clear depiction of theurethra, consistently stiffer outer gland and softer inner gland, the soft acini and the stiffverumontanum in the corresponding elastograms.

Fig. 10 From left to right, matching sonogram and elastogram of breast carcinomas obtainedin vivo in the erect position at'S MHz (Ophir et aI1996). Note the demonstration oftwo hard nodules and the torturous soft subcutaneous fat layer on the elastogram.Note also that the sonogram demonstrates only one hypoechoic nodule and that a sizediscrepancy exists between the sonographic and elastographic appearance of the largenodule (presumably due to desmoplasia). (Courtesy of Dr. Nabil Makled).

be associated with desmoplasia surrounding thecancerous lesion.

The earliest breast images were obtained in a sittingposition, which limited the number of accessiblecancers for elastographic imaging. More recently,breast elastograms were obtained in the supineposition, which allowed the imaging of cancers that

were close to the chest wall. An example ofelastograms and corresponding sonograms of afibroadenoma and a carcinoma (Garra et al. 1997)obtained in the supine position is shown in Fig. 11.Observe the size discrepancy between the sonographicand elastographic appearance of the carcinoma.

Another example of the visualization of normal

J Med Ultrasonics Vol.29 Winter (2002) 11;~

Fibroadenoma

Sonograms Elastograms

Infiltrating DuctalCarcinoma

Fig. 11 Sonogram and elastogram pairs from fibroadenoma and infiltrating ductal carcinoma (Garra et at. 1997) of the breast(Courtesy of Dr. B. Garra) in vivo at 5 MHz. Observe the clear depiction of the carcinoma on the elastogram (includingthe distal margins), as well as the size discrepancy between the sonographic and elastographic appearance of the carcinoma,as shown also in Fig. 10.

-

Sonogram Elastogram Photograph

J Med Ultrasonics Vol.29 Winter (2002)166

Fig. 12 From left to right, longitudinal sonogram, elastogram and gross pathological specimen from an ovinekidney in vitro. The elastogram demonstrates structures that are consistent with a stiff (black) renalcortex and medullary pyramids (of which at least seven are seen), softer (white) columns of Bertin andvery soft fatty areas at the base of the columns in the renal sinus. Areas of sonographic echo dropoutsoutside the kidney and in the acoustically shadowed areas distal to the renal sinus are intentionallyblanked in the elastogram. Note that the renal sinus is hypoechoic and is not well visualized on thesonogram (Katlel et al. 1998).

tissue stiffening due to thermal ablative procedures.An example of the visualization of HIFU lesioninduced in a canine liver in vitro is shown in Fig. 13,where the lesion appears as a hard nodule. It is notedthat the sonogram does not demonstrate the lesion.An example of prostate trans-rectal elastography invivo incorporating HIFU effects (Souchon et al.2001) is shown in Fig. 14, where an ablated area is

tissue architecture is shown in Fig. 12. The panelsshow an ovine kidney in-vitro as seen in a sonogram(left), elastogram (center), and gross pathologicalslice. It is evident that elastography may be able todemonstrate normal tissue structures, such as thepyramids and columns of Bertin, that are not wellvisualized on the sonogram.

Elastography has shown promise for monitoring

elastogram T2 MRI Sonogram Pathology

Sonogram Elastogram

MRIFig. 14 Matching sonogram, elastogram and MRI image of the transverse prostate in vivo. The prostate has undergone HIFU

ablation in the lower half of the gland. The rectangular ablated region is visible as a stiff region in the elastogram, and is alsowell shown in the MRI image. The red regions in the elastograms have been automatically added to mask out extra-prostaticregions of high decorrelation noise due to undesired tissue motions. No echo contrast between the ablated and normal partsof the prostate is shown on the sonogram (Souchon et al. 2001, unpublished).

J Med Ultrasonics Vol.29 Winter (2002) 11;7

Fig. 13 From left to right: elastogram, sonogram, coronal T2-weighted-MR image and gross (stained) pathological specimen of aHIFU lesion induced in a canine liver in vitro. Note that the sonogram does not demonstrate the HlFU lesion (Righetti etal. 1999).

Fig. 16 shows the appearance of a 6 mm VX2carcinoma in a rabbit liver. Note again the clearappearance of the tumor as a stiff region, and the lackof tumor contrast in the corresponding sonogram.

shown as a stiff (darker) area in the peripheralproximal area of the gland, and is confirmed by MRIimaging.

Some work in animals in vivo is shown in Fig. 15,16 (Merritt et al. 2002). Fig. 15 shows the appearanceof a 3 mm thermal lesion created in the liver of arabbit. Note the clear visualization of the lesion as astiff (dark) region in the elastogram, and thecorresponding isoechoic appearance on the sonogram.

8. Discussion and Conclusion

The assumption driving the development ofelastography has been that significant soft tissuemodulus (and hence strain) contrast exists, especially

0 1 2 3

I I I I I I Icm

elastogramsonogram

Fig. 15 Rabbit liver in vivo, bearing a 3 mm thermal lesion. Note the good contrast between the stifflesion and the embedding normal liver in the elastogram, and the lack of echo contrast in thesonogram. The sonograms were taken with a Philips/ A TL HDI -1 ()()() scanner at 7.5 MHz(Merritt et al., 2002).

0 1 2 3

I I I I I I Icm

sonogram elastogram

168 J Med Ultrasonics Vol.29 Winter (2002)

Fig. 16 Rabbit liver in vivo, bearing a 6 mm VX2 carcinoma.Note the good contrast between the stiff carcinoma andthe embedding normal liver in the elastogram, and thelack of echo contrast in the sonogram. The sonogramswere taken with a Philips/ ATL HDI-lOOO scanner at7.5 MHz (Merritt et al.. 2002).

correcting for lateral displacements and linear axialdistortions. Given further that axial or lateralelastograms display the distributions of the respectivestrains and not of the moduli, a contrast-transfer-efficiency (CTE) metric has been defined andcalculated. This metric adds a description based onelasticity theory of the efficiency with which actualmodulus contrast is converted to elastographic axialstrain contrast under known conditions. We haveshown that for low contrast situations such as in thenormal ovine kidney, the strain image is a reasonablerepresentation of the actual inverse modulus image.We have also shown that elastography holds promisein the evaluation of breast and prostate masses in vivo.

Many interesting challenges remain in thedevelopment of this new field. In principle, it shouldbe possible to generate elastograms in real-time,perhaps by reducing the cross-correlationcomputations to I-bit hardware operations, whichhave been shown to be effective, or by using fastDigital Signal Processing (DSP) chips. The ultimatelimitation on speed is the speed of sound and thespeed of propagation of the elastic wave in tissue(which is on the order of 1-10 m/s). The current needfor a transducer holding apparatus is another majorlimitation. This could be overcome by increasing theframe rate of elastographic image acquisition tomaintain better inter-frame coherence, by estimatingthe (Doyley et al. 2001), and correcting the axial-elastogram appropriately so that quality images can begenerated. Another solution may involve the use ofincoherent strain estimators that are less sensitive tojitter and other undesired motions. A "stress meter" inthe form of an elastic layer attached to the transduceror the target may be used in conjunction with a hand-held device to allow automatic nonstationary imagecalibration for uneven compressions. The optimalelastographic protocols that are to be followed whenimaging certain tissues are as yet unknown. Theseinclude the amount of pre-compression, the appliedimaging compression, the number of sonographicframes and the (adaptive) algorithm(s) to be used forimage optimization, and the relationship of theseprotocols to the specific elastic properties (such ascontrast and nonlinear stress/strain behavior) of mosttissues. While elastographic artifacts are fairly wellunderstood, their possibly ambiguous role asdetractors or facilitators of lesion detection and/ordiagnosis remains unknown. Related techniques, suchas high frequency, high-resolution methods appliedintravascularly may also develop as useful adjuncts tothe current sonographic methods. Another importantarea that could greatly benefit from the incorporationof elastographic techniques is the area of thermal orcryogenic tissue ablation monitoring. It is known thatstandard sonographic techniques are not well suitedfor monitoring such procedures due to their poor

between normal and abnormal tissues. Perhaps notsurprisingly, it has been recently demonstrated thatmodulus contrast exists not only between normal andpathological tissues, but also generally to a lesserdegree also between and within normal tissues. Theexistence of this lower contrast could be ascertainedonly after recent vast improvements in theelastographic image quality due to a betterunderstanding of the theory of elastographic imageformation that led to the development of betteralgorithms. These observations, together with someinitial clinical data showing the ability ofelastography to detect and characterizesonographically occult breast cancers (Garra et al.1997), are providing the catalyst for continuing thevigorous development and application ofelastographic methods to medical imaging problems.

The estimation and imaging of tissue strains is bydefinition a three-dimensional problem. When thetissue is compressed, the near incompressibility ofmost soft tissues means that finite strain tensorcomponents are generated in all directionssimultaneously. Until recently, workers in the fieldhad assumed that single-view ultrasonic methodscould not be used for precision lateral displacementand strain estimates. As a result, they were essentiallylimited to displacement and strain estimations in theaxial direction only. It has recently been demonstrated(Konofagou and Ophir 1998) that it is in fact possibleto make precision estimations of lateral displacementsand produce images of lateral strain and Poisson'sratio distributions in tissues, if proper overlap betweenadjacent ultrasonic beams is maintained. With 1.5-0arrays, or by using a 1-0 array and measuring theresidual elevational decorrelation after correcting forthe other two components, it should be possible toprecisely estimate all three longitudinal componentsof the strain tensor in tissues using clinical arrayscanners. Poisson-elastograms may be important inthe imaging of poroelastic, edematous and viscoelastictissues (Konofagou and Ophir 1998).

Given the fortunate existence of significantmodulus contrast in many normal and abnormaltissues, and the ability to estimate some of thecomponents of the strain tensor, the noiseperformance of these estimations becomes theimportant parameter that dictates the achievablecontrast-to noise ratio in elastograms. The StrainFilter framework has been developed to describe thetradeoffs among all the technical parameters of theultrasound instrumentation in terms of their influenceon the elastographic image parameters. Using thisformalism, it has been demonstrated that axial-elastograms with high CNRe, wide strain dynamicrange and good strain sensitivity can be achieved atresolutions that are on the order of the ultrasonicpulse width. These can be further improved by

J Med Ultrasonics Vol.29 Winter (2002) 169

contrast. We have recently shown that elastographyoffers high contrast and precision in monitoring laserand High Intensity Focused Ultrasound (HIFU)applications (Righetti et al. 1999). This has now beendemonstrated in vivo as well from the work ofSouchon et al (Fig. 14).

In conclusion, we believe that while elastographyhas progressed rapidly in the past several years, muchprogress has yet to be made in order for elastographyto become a viable clinical and investigational tool.Even at this early stage, however, it is evident thatthere exists a fortunate set of favorable biological,mechanical, statistical and acoustical circumstancesthat, when combined, will inevitably allow theattainment of this goal.

AcknowledgementThis work was supported in-part by the National

Cancer Institute (USA) Program Project Grant P 01-CA 64597 to the Ultrasonics Laboratory at theUniversity of Texas Medical School in Houston.Subcontractors of this Program Project are BaylorCollege of Medicine, the University of Vermont,Thomas Jefferson University and INSERM.

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