Ul tra sound At ten u a tion Im ag ing Us ing Com pound Ac qui si tionand Processing

HAIFENG TU,1 TOMY VARGHESE,1, 2 ER NEST L. MADSEN,1 QUAN CHEN1

AND JAMES A. ZAGZEBSKI1

1De part ment of Med i cal Phys ics2De part ment of Bio med i cal En gi neer ingThe Uni ver sity of Wis con sin-Mad i son

Mad i son, WI 53706htu@wisc.edu

A method that com bines both spa tial and fre quency com pound ing is de scribed for mea sur ing at ten u a -tion in tis sue. The tech nique ap plies a ref er ence phan tom to ac count for im ag ing sys tem de pend en cies of echo sig nals. Em pha sis is given to lo cal at ten u a tion es ti mates, to re duce the vari ance of the at ten u a tionmea sure ments over small re gions of in ter est (ROI) and to en able coarse at ten u a tion im ag ing. Ex per i -ments us ing a uni form phan tom show that the stan dard de vi a tion of lo cal at ten u a tion es ti mates within aROI drops when greater de grees of com pound ing are ap plied. At ten u a tion im ages of a spe cially de -signed phan tom con tain ing in clu sions with at ten u a tion con trast il lus trate the ac cu racy and pre ci sion ofthe tech nique.

KEY WORDS: At ten u a tion; com pound ing; fre quency com pound ing; im ag ing; spa tial com pound ing; ul -tra sound.

IN TRO DUC TION

Quan ti ta tive meth ods that en hance di ag nos tic ca pa bil i ties of med i cal ul tra sound in stru -ments have re ceived sig nif i cant at ten tion over the past three de cades. Re search ers have pro -posed ap proaches to mea sure first and sec ond or der sta tis ti cal prop er ties of echo sig nals,1 the scat ter num ber den sity,2 the mean scat ter spac ing,3, 4 the autocorrelation func tion5, 6 and thescat ter size.7, 8 In re cent years, ul tra sound based elas tic ity im ag ing has also been in ves ti gatedas a method that ex pands the role of this mo dal ity.

This pa per de scribes a method for mea sure ment and dis play of acous tic at ten u a tion frompulse-echo data. Ob jec tively-de ter mined at ten u a tion val ues could pro vide valu able in for -ma tion in as sess ing var i ous forms of dif fuse and fo cal liver dis ease,9, 10 dis tin guish ingischemic from nor mal zones of the myocardium,11 differenting be tween uter ine fib roids andadeno myosis,12 and di ag nos ing breast masses. ‘Shadow’ signs on B-mode im ages are al -ready used ex ten sively to as sess the like li hood of a ma lig nant breast tu mor.13, 14 How ever, es -ti mates of the ac tual ul tra sound at ten u a tion within such masses and cor re la tion of re sultswith pa thol ogy has not been done. Our mo ti va tion is to pro vide a means of mea sur ing at ten -u a tion within small, lo cal ized re gions viewed on ul tra sound B-mode im ages and to pro duceat ten u a tion im ages.

Many meth ods based on pulse echo tech niques have been pro posed for es ti mat ing the ul -tra sound at ten u a tion co ef fi cient. In gen eral, they can be clas si fied as ei ther time do main orfre quency do main meth ods. In the fre quency do main, Kuc and Schwartz15 es ti mated at ten u -a tion us ing the slope of the dif fer ence be tween the log a rithms of the echo sig nal power spec -tra from two dif fer ent tis sue depths. They de vel oped a max i mum like li hood es ti ma tor basedon this method and mea sured at ten u a tion of liver in vi tro. Cloostermans et al16 pro posed a

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multi-narrowband method in which the slope of at ten u a tion vs. fre quency was de rivedthrough changes of the echo sig nal power spec tra vs. depth, us ing short time Fou rier anal y -sis. Yao et al17 fur ther de vel oped the idea by pro pos ing a ref er ence phan tom method to ac -count for ma chine and trans ducer beam de pend en cies.

Fink et al18 es ti mated fre quency-de pend ent at ten u a tion us ing down-shifts of the cen troidof the echo sig nal power spec trum ac quired from in creased depths. Kasai et al19 pro posed acen troid es ti ma tor us ing the first autocorrelation lag of the phase of the com plex echo sig nal.An other cen troid es ti ma tor was pro posed by Kuc and Li20 us ing a sec ond-or der auto -regressive model, and this tech nique was fur ther de vel oped by Baldeweck et al.21 Yet another fre quency do main method is the matched fil ter, pulse com pres sion ap proach de vel oped byMeyer,22 said to be ca pa ble of pro vid ing re sults that are in de pend ent of over lap ping echowavetrains from ad ja cent tis sue re gions sep a rated by 2/Df, where Df is the sys tem band -width.

In the time do main, Flax et al23 pro posed a zero cross ing method, which is a coun ter part ofthe cen troid shift method. Later, an ‘en ve lope peak’ method was pro posed by He and Green -leaf,24 which uses the lo cal max i mum of the echo sig nal en ve lope in the at ten u a tion es ti ma -tion. Jang et al25 es ti mated at ten u a tion by mea sur ing the en tropy dif fer ence be tween twoad ja cent seg ments of en ve lope-de tected, narrowband echo sig nals. Walach et al26 pro ducedone of the first ul tra sound at ten u a tion im ages, yield ing a res o lu tion of about 1.6 cm, uti liz ing the ex tended prony method. Knipp et al27 de vel oped the video sig nal anal y sis method to es ti -mate the at ten u a tion di rectly from B-mode im ages.

Ex cept for work by Walach et al,26 ‘lo cal at ten u a tion es ti mates,’ that is, at ten u a tion withinsmall, se lected re gions of the scanned field, have re ceived lit tle at ten tion by re search ers, par -tially be cause of the re quire ment for large data seg ments to achieve sta tis ti cally-ac cu rate re -sults. Here we pres ent a method that de creases er rors of at ten u a tion es ti ma tions made oversmall vol umes of tis sue. The method uses spa tial and fre quency com pound ing in the data ac -qui si tion and anal y sis, es ti mat ing at ten u a tion for the same vol ume but from sta tis ti cally-in -de pend ent sig nal sam ples. Ex per i ments us ing a uni form phan tom show that the stan dardde vi a tion of lo cal at ten u a tion es ti mates drops when greater de grees of com pound ing are ap -plied. Coarse at ten u a tion im ages of a spe cially-de signed at ten u a tion phan tom il lus trate ac -cu racy and pre ci sion of the tech nique.

METH ODS

A. Ref er ence phan tom method (RPM)

It is nat u ral to con sider ex am in ing the loss of echo sig nal in ten sity or am pli tude with depthto cal cu late the at ten u a tion. How ever, beam dif frac tion and ma chine-de pend ent fac tors,such as trans mit fo cus, gain, etc., need to be ac counted for to make ac cu rate and com pa ra bleat ten u a tion es ti ma tions. The ref er ence phan tom method de vel oped by Yao et al17 is ef fec tive for ac cu rate at ten u a tion and back scat ter es ti ma tions. In this method, the echo sig nal in ten -sity from a sam ple is com pared to the sig nal in ten sity at the same depth from a ref er encephan tom, whose at ten u a tion and back scat ter prop er ties are known. The ref er ence phan tomdata are ac quired us ing the same trans ducer and sys tem set tings used for ac quir ing echo datafrom the sam ple. Af ter bandpass fil ter ing, ri(f,z), the ra tio of the echo sig nal in ten sity fromthe sam ple to that from the ref er ence at fre quency f and depth z, can be ex pressed as17

246 TU ET AL

z))f(r)f(s(

r

s

r

s e)f(

)f(

)z,f(i

)z,f(i)z,f(ri aa

h

h --== 4 (1)

where i is the echo sig nal in ten sity; sub scripts s and r re fer to the sam ple and ref er ence, re -spec tively; the h’s are back scat ter co ef fi cients; and a’s are sam ple and ref er ence phan tomat ten u a tion co ef fi cients at f.

Af ter a least squares line-fit of the curve ln(ri(f,z)) vs. depth, z, the slope is pro por tional tothe dif fer ence be tween the sam ple and ref er ence at ten u a tion co ef fi cients. Since the lat ter isknown, this pro vides the at ten u a tion co ef fi cient of the sam ple. For a uni form sam ple, thezero depth in ter cept yields the ra tio of the sam ple and ref er ence back scat ter co ef fi cients.

B. Spa tial and fre quency com pound ing

There are two types of un cer tainty as so ci ated with these at ten u a tion es ti ma tions. One ismeth od olog i cal, con trib uted by, for ex am ple, in stru men tal in ac cu racy, nonuniformities inthe me dium and elec tronic noise. An other is due to the pres ence of sta tis ti cal fluc tu a tions inthe back scat tered sig nals from tis sue. It is this lat ter sta tis ti cal un cer tainty that we ad dress inthis pa per.

An anal y sis of the sta tis ti cal un cer tainty of at ten u a tion val ues de rived us ing the ref er encephan tom method has been pre sented by Yao et al.28 Re sults show that s

a, the stan dard de vi a -

tion of the sam ple at ten u a tion co ef fi cient as at a given fre quency f, is:

Terms used in Eq. (2) are il lus trated in fig ure 1. Here N and N¢ are the num ber of in de pend -ent acous ti cal lines over which echo data are ac quired and an a lyzed from the ref er ence andthe sam ple re spec tively; Z is the length of the line seg ment over which the least squares anal -y sis is ap plied; n is the num ber of in de pend ent es ti mates of ri(f,z) over the in ter val Z; and the

ATTENUATION IMAGING USING COMPOUNDING 247

'

'

NNZn

NNk.)f(

+=

527a

s(2)

(dB/cm)

FIG. 1 Data ac qui si tion and pro cess ing us ing a ref er ence phan tom to de ter mine at ten u a tion over a re gion whoseax ial length is Z. In de pend ent echo sig nals from N¢ beam lines in the sam ple and N beam lines in the ref er ence are in -volved.

fac tor k is the in verse of the ‘sig nal to noise ra tio’ that is, the mean of the sig nal in ten sity to itsstan dard de vi a tion. This ra tio is 1 if Ray leigh sta tis tics ap ply.29 Since n is pro por tional to Z,the un cer tainty is in versely pro por tional to the 3/2 power of the length of the data seg ments.

As sume the at ten u a tion in the sam ple is lin early pro por tional to the fre quency, which isap prox i mately true in tis sue for fre quen cies in the range of 1 to 10 MHz. Thus,

We will seek the at ten u a tion co ef fi cient slope, bs (dB/cm/MHz) as an at ten u a tion pa ram e -ter through out this pa per. From Eq. (3), s

bi , the stan dard de vi a tion of the at ten u a tion co ef fi -cient slope at a cer tain fre quency fi is:

One means to de crease the un cer tainty in at ten u a tion co ef fi cient es ti ma tions with out ex -ces sively ex pand ing the re gion over which the es ti ma tion is done is to ap ply spa tial an gu larcom pound ing. Spa tial an gu lar com pound ing dur ing echo data ac qui si tion has proven to bean ef fec tive tech nique for re duc ing speckle noise to im prove B-mode im age qual ity.30 How -ever, an gu lar com pound ing has not yet been used for quan ti ta tive ul tra sound im ag ing in thepulse echo mode. An an gu lar com pound ing scheme de scribed be low will be ap plied for re -duc ing sta tis ti cal fluc tu a tions.

An other means to de crease er rors in at ten u a tion co ef fi cient es ti ma tions is to av er age at ten -u a tion co ef fi cients de rived from dif fer ent fre quency com po nents of the echo sig nal spec -trum. This tech nique called ‘fre quency com pound ing’ has been pre vi ously ap plied tore duce speckle in ul tra sound im ages.31, 32

The sta tis ti cal un cer tainty of an at ten u a tion co ef fi cient slope es ti ma tion when both spa tialand fre quency com pound ing are ap plied can be de scribed us ing the fol low ing ex pres sion(see Ap pen dix):

where sb¢ is the stan dard de vi a tion of the at ten u a tion co ef fi cient vs. fre quency slope af terspa tial and fre quency com pound ing, sa(fi) is the stan dard de vi a tion of the at ten u a tion co ef -fi cient at a fre quency fi be fore com pound ing, Nc is the ef fec tive num ber33 of in de pend ent sig -nals used for spa tial an gu lar com pound ing, Nf is the ef fec tive num ber of in de pend entfre quency com po nents used and nf is the num ber of par tially-cor re lated fre quency com po -nents used. It is readily seen from Eq. (5) that as Nc and fi in crease, sb¢ de creases. Also, it isgen er ally true that as Nf in creases, sb¢ drops. The fre quency de pend ence of sa(fi) re flects thefact that when at ten u a tion is com puted for a small re gion (see next sec tion), N and N¢ in Eq.(2), the num ber of in de pend ent beam lines avail able var ies with fre quency be cause ech oesfrom closely spaced beam lines are less cor re lated at higher fre quen cies.

EX PER I MEN TAL PRO CE DURES

Ini tial work was di rected to wards view ing trade offs be tween res o lu tion and noise dur ingat ten u a tion es ti ma tions with com pound ing. A uni form phan tom hav ing an at ten u a tion co ef -

248 TU ET AL

å=

··=fn

i

i

ifc

' )f(fNN 1

2

2

111ab

ss(5)

)f(f

i

i

i abss

1=

(4)

f)f(ss

ba = (3)

fi cient slope of 0.5 dB/cm/MHz was scanned. The phan tom con sists of a wa ter based gel(agarose) with graph ite pow der uni formly dis persed to pro vide the needed at ten u a tion. Thegraph ite also serves as a source of back scat tered ech oes. Be cause we were in ter ested only inthe sta tis ti cal prop er ties of our es ti mates, the same phan tom was used both as a sam ple and aref er ence by scan ning dif fer ent re gions to as sure in de pend ent data.

In ad di tion, a spe cial-pur pose phan tom was con structed (Fig. 2) to as sess the ac cu racy ofthe method for de ter mi na tion of lo cal at ten u a tion val ues, where the above uni form phan tomserved as the ref er ence and this spe cial-pur pose phan tom was des ig nated as the sam ple. Thetis sue-mim ick ing ma te ri als are sol ids made rigid through the pres ence of agarose.34 In theab sence of added scat ter ers, the back scat ter level of these ma te ri als is neg li gi ble, while theat ten u a tion and prop a ga tion speeds are in the range of soft tis sue val ues. At ten u a tion in -creases with con cen tra tion of bo vine milk sol ids in the ma te rial. Milk was con cen trated viare verse os mo sis at Diehl, Inc., De fi ance, Ohio, USA. Back scat ter is pro vided through thepres ence of var i ous con cen tra tions of glass beads with a mean di am e ter of about 20 µm(Type 3000E, Pot ters In dus tries, Parsippany, NY, USA). The pres ence of the beads con trib -utes lit tle to the at ten u a tion.

As shown in the di a gram in fig ure 2, there are four par al lel cy lin dri cal in clu sions in thephan tom in which the at ten u a tion co ef fi cient is greater than the sur round ing. Cyl in ders Aand D are 1 cm in di am e ter and are in tended for at ten u a tion stud ies us ing high fre quencytrans duc ers. Cyl in ders B and C are 3 cm in di am e ter and are for eval u a tions with low fre -quency probes. The back scat ter co ef fi cient of the ma te rial form ing cyl in ders A and B is thesame as that in the back ground ma te rial (at any fre quency). In cyl in der C, the back scat terco ef fi cient is higher than the back ground value, and in cyl in der D it is lower.

Dur ing the man u fac tur ing pro cess of each com po nent of the phan tom, a 2.5 cm thick, 7.6cm di am e ter test cyl in der was also made for mea sure ments of prop a ga tion speed and at ten u -a tion co ef fi cients. Mea sure ments were made us ing a com monly-used through-trans mis sionmethod.35 Val ues of prop a ga tion speed and at ten u a tion co ef fi cients for the var i ous ma te ri als

ATTENUATION IMAGING USING COMPOUNDING 249

FIG. 2 Sche matic of the at ten u a tion con trast phan tom. The tar gets are cyl in ders whose di am e ters are 1 cm (Aand D) or 3 cm (B and C). Two scan ning win dows en able the ob jects to be im aged at dif fer ent depths.

at 22°C are shown in ta ble 1. Also shown in this ta ble are the back scat ter co ef fi cients rel a tive to that in the back ground, mea sured us ing ap pa ra tus that in cor po rates a ref er ence phan tom.35

Echo data were ac quired from each phan tom us ing an Aloka SSD-2000 scan ner (Aloka,Wallingford, CT) equipped with a 3.5 MHz phased ar ray trans ducer. Be cause only a lowfre quency trans ducer was avail able for these stud ies, we ad dressed only the larger cyl in dersB and C in the in clu sion phan tom ac qui si tions. The scan for mat of this sys tem con sists of120 acous ti cal lines spread uni formly over a 90° sec tor. Sig nals were ac quired by tap pingthem from a test point in the re ceiver of the scan ner af ter TGC, but prior to non lin ear pro cess -ing. Rf echo data were re corded to 12-bit pre ci sion at a sam pling rate of 50 MHz us ing a dataac qui si tion board (CompuScope 12100, Gage Ap plied Sci ences, Inc., Lachines, QUE, Can -ada) housed in a PC work sta tion.

To achieve the ef fects of spa tial com pound ing as would be ob tained us ing a lin ear ar raytrans ducer, the trans ducer was trans lated in 0.5 mm in cre ments (Fig. 3) in a di rec tion par al lel

250 TU ET AL

TA BLE 1 Acous ti cal prop er ties of the back ground and the cy lin dri cal tar get ma te ri als in the at ten u a tion phan tom.

Ma te rial Speed(m/s)

(±1 m/s)

At ten u a tion co ef fi cient(dB/cm)

( ±0.1 dB/cm)

Slope of at ten u a tionco ef fi cient

(dB/cm/MHz)

Rel a tiveBSC(dB)

2.5 MHz 4.5 MHz 6.2 MHz 8.0 MHz

Back ground 1536 1.14 2.08 3.06 3.97 0.48

Cyl in der A 1547 1.86 3.55 5.04 6.47 0.79 0

Cyl in der B 1547 1.89 3.57 5.12 6.63 0.80 0

Cyl in der C 1546 1.91 3.54 5.07 6.61 0.80 +3

Cyl in der D 1547 1.89 3.57 5.12 6.45 0.80 -3

FIG. 3 Setup to ac quire echo data for spa tial com pound ing. The phased ar ray trans ducer is trans lated par al lel tothe im age plane and rf data are ac quired ev ery ½ mm.

to the ul tra sound im age plane, stop ping af ter each trans la tion step to dig i tize echo sig nals.For the uni form phan tom ex per i ment, a to tal of 80 such ac qui si tions were used for both theref er ence and the sam ple ac cord ingly, cov er ing a 3.95 cm lin ear range. For the in clu sionphan tom ex per i ment, 100 ac qui si tions cov er ing a 4.95 cm lin ear range were taken for boththe sam ple and the ref er ence.

Offline anal y sis con sisted first of re group ing the rf echo data to form ‘an gled rf data sets,’as di a grammed in fig ure 4, each set con sist ing of data from a spe cific beam di rec tion but with suc ces sive beam lines sep a rated lat er ally by 0.5 mm. 120 such an gled rf data sets were gen -er ated, each cov er ing an area of 12.6 cm ́ 3.95cm ́ cos(q) for the uni form phan tom ex per i -ment and 12.6 cm ́ 4.95cm ́ cos(q) cm in the in clu sion phan tom ex per i ment. The an gle q isthat be tween the beam line di rec tion of an an gled rf data set and the per pen dic u lar.

In the uni form phan tom ex per i ment, the ref er ence phan tom method was then ap plied tothe echo data within lo cal ized data blocks of each an gled rf data set. First, echo sig nal powerspec tra were com puted by ap ply ing a slid ing 200 point (3 mm) Hanning win dow and tak inga FFT. The win dows were al lowed to over lap by 50%, pro vid ing an op ti mal com pro mise be -tween vari ance re duc tion in spec trum cal cu la tions us ing the fast Fou rier trans form and com -pu ta tion time.36 This cal cu la tion was done both for the sam ple and ref er ence data of eachan gled rf data set. For the uni form phan tom, the ma tri ces of Fou rier spec trum val ues werethen each di vided into equal sized, nonoverlapping ax ial seg ments along the beam di rec tion. Dif fer ent seg ment sizes were stud ied, rang ing from 0.5 cm to 2.5 cm. In the cross-beam (lat -eral) di rec tion, spec tral data for neigh bor ing beam lines were grouped, where the lat eral ex -tent of a group ranged from 0.25 cm to 1 cm. Thus, nonoverlapping cal cu la tion blocks,whose ax ial ex tent var ied from 0.5 to 2.5 cm and lat eral ex tent from 0.25 to 1 cm wereformed (Fig. 5).

Fou rier spec trum val ues at the same depth were av er aged within these groups of lines forthe sam ple. Be cause each an gled rf data set was ob tained us ing the same beam line, ref er -ence spec tra were formed by av er ag ing the Fou rier spec tra at each depth to de crease the vari -abil ity of the ref er ence data (Fig. 5). Then the dif fer ence be tween the sam ple and ref er encespec tra from the same depth was cal cu lated and plot ted ver sus depth over the ax ial seg mentof each block. The slope (dB/cm) of the line-fit of these spec tral dif fer ence val ues at a spe -cific fre quency was de rived. Each slope di vided by fre quency gives the at ten u a tion co ef fi -cient slope (dB/cm/MHz) for the block.

The cal cu la tion was re peated for se lect fre quen cies over the band width of the echo sig nal. Then fre quency com pound ing was ap plied by com put ing the av er age at ten u a tion co ef fi cient vs. fre quency slope among the dif fer ent fre quen cies. This fi nal step yielded ‘an gled at ten u a -tion im ages.’

An gled im ages were scan con verted to a com mon ref er ence frame us ing a reg is tra tion al -go rithm that uti lized the geo met ri cal re la tion ship be tween an gled rf data sets and the ref er -ence frame. Spa tial com pound ing was then used to av er age at ten u a tion co ef fi cient slopes

ATTENUATION IMAGING USING COMPOUNDING 251

FIG. 4 An gled rf data sets af ter rebinning the orig i nal data. Beam lines in an gled sets are sep a rated by 0.5 mm. Lo cal at ten u a tion is es ti mated for each an gled data set.

com puted for dif fer ent an gles but at the same spa tial lo ca tion. For the in clu sion phan tom ex -per i ment, sim i lar pro cess ing was done ex cept that an 80% ax ial over lap and a 75% lat eralover lap were ap plied to the cal cu la tion blocks, which en hances the smooth ness of the at ten u -a tion im age.

RE SULTS

A. Uni form phan tom re sults

Af ter at ten u a tion es ti mates were de rived for all an gled data sets in the uni form phan tomand scan con ver sion was done to con vert to a rect an gu lar ma trix, the mean and stan dard de -vi a tion of lo cal at ten u a tion val ues were cal cu lated for dif fer ent block sizes. The stan dard de -vi a tion of the at ten u a tion es ti mates can be re garded as one cri te rion that de ter mines thesta tis ti cal ac cu racy of the es ti ma tion. Stan dard de vi a tions vs. ax ial ex tent of the cal cu la tionblock are pre sented in fig ure 6 for dif fer ent de grees of spa tial com pound ing and dif fer entblock widths. Fig ure 6a pres ents re sults for a 1 cm wide cal cu la tion block, with the ax ial sizerang ing from 0.5 cm to 2.5 cm. Sep a rate data points are used for no spa tial com pound ing (nc

= 1), 7 an gled data sets com pounded (nc = 7) and 15 an gled data sets com pounded (nc = 15). Fig ure 6b pres ent sim i lar re sults, but for a 1 cm long cal cu la tion block, with the lat eral sizerang ing from 0.25 cm to 1 cm. In our no men cla ture, nc is dif fer en ti ated from Nc (Eq. 5) inthat Nc is the ef fec tive num ber of in de pend ent an gles used in spa tial com pound ing while nc

may con tain par tially-cor re lated data. Data from neigh bor ing beam an gles may not be in de -pend ent, es pe cially be cause the V-3.5 trans ducer has an an gu lar sep a ra tion be tween ac qui si -tion lines of only 0.75°. There fore, we in cluded an ex am ple where ev ery sixth an gled data set sep a rated by 0.75 ´ 5 = 3.75° was used in com pound ing, while the num ber of an gles usedwas still 15 (nc¢ = 15). Only the cen ter fre quency 3.5 MHz (no fre quency com pound ing) wasused in these ini tial spa tial com pound ing cases.

252 TU ET AL

FIG. 5 Cal cu la tion blocks used to mea sure lo cal at ten u a tion.

Each ex am ple in fig ure 6 shows that for a given block size, as the num ber of an gles used inspa tial com pound ing in creases, the stan dard de vi a tion drops. More im prove ment is seen us -ing 15 an gled data sets com posed of ev ery sixth an gled set (nc¢ = 15) than 15 sets sep a rated

ATTENUATION IMAGING USING COMPOUNDING 253

FIG. 6 Stan dard de vi a tion of at ten u a tion de ter mi na tions in the uni form phan tom vs. ax ial and lat eral ex tent of the cal cu la tion block for dif fer ent de grees of spa tial com pound ing. nc is the num ber of an gles from which at ten u a tionval ues were com pounded. (a) Results for a 1 cm wide cal cu la tion block, with ax ial size rang ing from 0.5 cm to 2.5cm; (b) sim i lar re sults, but for a 1 cm long cal cu la tion block, with lat eral size rang ing from 0.25 cm to 1 cm

(b)

(a)

by only 0.75° (nc = 15). Thus, a spa tial com pound ing scheme with more in de pend ent datawill re sult in sta tis ti cally more ac cu rate lo cal at ten u a tion es ti ma tions.

The ef fect that dif fer ent fre quency com pound ing schemes has on the lo cal at ten u a tion es -ti ma tions was eval u ated in a sim i lar way. Only one an gled data set was used (no spa tialcom pound ing) while the num ber of fre quen cies com pounded was var ied from nf = 1 (3.5MHz) – no fre quency com pound ing to nf = 3 (3, 3.5 and 4 MHz) to nf = 5 (3, 3.25, 3.5, 3.75,and 4 MHz) and fi nally to nf¢ =5 (2.5, 3, 3.5, 4, and 4.5 MHz). The re sults are shown in fig ure 7. Fig ure 7a pres ents re sults for a 1 cm wide cal cu la tion block of ax ial sizes rang ing from 0.5 cm to 2.5 cm; fig ure 7b pres ents sim i lar re sults, but for a 1 cm long cal cu la tion block of dif -fer ent lat eral sizes, rang ing from 0.25 cm to 1 cm. As the num ber of fre quen cies used in fre -quency com pound ing in creases, the stan dard de vi a tion drops for the same block size.Sim i lar to the spa tial com pound ing case, nf is dif fer en ti ated from Nf (Eq. (5)) in that Nf is theef fec tive num ber of in de pend ent fre quency com po nents, while nf is the num ber of par tiallycor re lated fre quency com po nents used. Com par i son of re sults for nf¢ = 5 with those for nf = 5il lus trates that a fre quency com pound ing scheme with more in de pend ent data will re sult in asmaller stan dard de vi a tion of lo cal at ten u a tion es ti ma tions. The mean at ten u a tion dif fer ence for the sam ple and the ref er ence mea sured in all the above cases is close to zero, which is ex -pected since the sam ple and the ref er ence are from the same uni form phan tom.

B. At ten u a tion phan tom re sults

For the at ten u a tion im ages of the in clu sion phan tom, a com bined com pound ing scheme inwhich fif teen an gles with 0.75 ́ 5 = 3.75° an gu lar sep a ra tion (nc¢ = 15) and 5 fre quency com -po nents – 2.5, 3, 3.5, 4, and 4.5 MHz (nf¢ = 5) was uti lized. The cal cu la tion block used was 1cm ax i ally by 1 cm lat er ally, with an over lap of 80% in the ax ial di rec tion and 75% in the lat -eral di rec tion. This scheme should re sult in a stan dard de vi a tion of the at ten u a tion co ef fi -cient slope of ap prox i mately 0.07~0.1dB/cm/MHz, which can be pre dicted as fol lows.

For a sin gle ac qui si tion an gle, the stan dard de vi a tion with fre quency com pound ing (Eq.(5)) for this scheme can be es ti mated to be 0.2 dB/cm/MHz. This value is ob tained by look -ing at the 1 cm data point on the nf¢ = 5 curve in fig ure 7a. For spa tial com pound ing, each cyl -in der was cen tered at a depth of 5.5 cm dur ing the scan and has a di am e ter of 3 cm. Fig ure 8il lus trates the num ber of an gled data sets avail able through out the im aged field for this setup; in the area of the in clu sions, there are be tween nc¢ = 8 and nc¢ = 15. Thus, the min i mumvalue of Nc

-1/2 (in Eq. (5)) can be es ti mated by tak ing the ra tio of sb¢ for the case of nc¢ = 15 to

sb¢ for nc = 1 (no com pound ing) for the 1 cm ax ial block size in fig ure 6a. This yields Nc

-1/2 »0.357, which means NcMAX » 7.8. If we as sume the num ber of in de pend ent es ti ma tions is pro -por tional to the num ber of par tially-cor re lated es ti ma tions, then, NcMIN = 7.8´15/8 » 4.2 , andthe max i mum value of Nc

-1/2 is roughly 0.488. Sub sti tut ing these ex tremes into Eq. (5) along with the stan dard de vi a tion for fre quency

com pound ing, we get 0.07 dB/cm/MHz £ sb¢ £ 0.1 dB/cm/MHz. Since the con trast be tween

cyl in ders and back ground is roughly 0.3 dB/cm/MHz, the contrast- to-noise ra tio is ex pected to be be tween 3 and 4.5 in the in clu sion area.

At ten u a tion im ages that in clude cyl in ders B and C in the at ten u a tion phan tom are pre -sented in fig ure 9. From the at ten u a tion im age data, we mea sured mean at ten u a tion val uesto be 0.73 dB/cm/MHz for cyl in der B and 0.70 dB/cm/MHz for cyl in der C. The back groundre gion im age data are at 0.42 dB/cm/MHz. These data should be com pared with the di rectmea sure ments of val ues us ing test cyl in ders in a wa ter tank (Ta ble 1). Also, we can see theim prove ment gained with com pound ing by com par ing fig ures 9b and 9d with their noncom -pounded coun ter parts fig ures 9a and 9c. The con trast- to-noise ra tio in the in clu sion ar eas of

254 TU ET AL

fig ure 9 are 4.2 for in clu sion B and 3.4 for in clu sion C. Both val ues are in the ex pectedrange, as de tailed in the pre vi ous para graph.

ATTENUATION IMAGING USING COMPOUNDING 255

FIG. 7 Stan dard de vi a tion of at ten u a tion de ter mi na tions in the uni form phan tom vs. ax ial and lat eral ex tent of the cal cu la tion block for dif fer ent de grees of fre quency com pound ing. As in fig ure 6, nf is the num ber of fre quen ciesfrom which at ten u a tion val ues were com pounded. Fig ure 7a pres ents sim i lar re sults for a 1 cm wide cal cu la tionblock of ax ial sizes rang ing from 0.5 cm to 2.5 cm; fig ure 7b pres ents sim i lar re sults, but for a 1 cm long cal cu la tionblock of dif fer ent lat eral sizes, rang ing from 0.25 cm to 1cm.

(a)

(b)

DIS CUS SION

This pa per shows that by us ing com pound data ac qui si tion and anal y sis with a ref er encephan tom, it is pos si ble to mea sure at ten u a tion co ef fi cients in small, lo cal ized blocks and de -rive coarse at ten u a tion im ages. Us ing a manually-trans lated 3.5 MHz phased ar ray trans -ducer to sim u late com pound ac qui si tion, 1 cm ́ 1 cm cal cu la tion blocks (20 acous tic lines)yielded ac cu rate at ten u a tion im ages of a phan tom con tain ing 3 cm di am e ter in clu sions. Thestan dard de vi a tion of the at ten u a tion co ef fi cient vs. fre quency slope was less than 0.1dB/cm/MHz for 1 cm ´ 1 cm cal cu la tion blocks.

In a sim i lar study, He37 re ported a stan dard de vi a tion of at ten u a tion co ef fi cient vs. fre -quency to be about 0.2 dB/cm/MHz for a cal cu la tion block size of 2 cm by 350 A lines, cov -er ing all avail able cross sec tion of a phan tom with a di am e ter of 7.5 cm. Walach26 es ti matedthe stan dard de vi a tion to be about 0.14 dB/cm/MHz for a 1.6 cm ́ 0.4 cm cal cu la tion block. Nei ther of these stud ies ap plied spa tial com pound ing. The cal cu la tion block used in this pa -per is still rel a tively large, which puts a limit on the res o lu tion of pres ent at ten u a tion im ages. As a re sult, smaller, 1 cm di am e ter cyl in ders in the at ten u a tion phan tom were not im agedwith this im ple men ta tion, al though they likely will be im aged when this method is ap pliedus ing higher fre quency trans duc ers.

256 TU ET AL

FIG. 8 Im age whose gray scale value at each lo ca tion in di cates the num ber of an gled data sets avail able for com -pound ing for the data ac qui si tion ap plied to the at ten u a tion con trast phan tom.

ATTENUATION IMAGING USING COMPOUNDING 257

FIG. 9 At ten u a tion im ages of re gions in the at ten u a tion phan tom which in clude the 3 cm di am e ter cy lin dri caltar gets whose at ten u a tion is 0.3 dB/cm/MHz greater than that of the back ground. Pan els (a) and (b) are noncom -pound at ten u a tion im age and at ten u a tion im age with both spa tial and fre quency com pound ing of cyl in der B, whoseback scat ter is the same as that of the back ground. Pan els (c) and (d) are noncom pound at ten u a tion im age and at ten u -a tion im age with both spa tial and fre quency com pound ing of cyl in der C, whose back scat ter is 3 dB greater than theback ground. The units of the color-bar are dB/cm/MHz.

(c) (d)

(a) (b)

In this work, we as sumed a lin ear re la tion ship be tween the at ten u a tion co ef fi cient and fre -quency. In fact, a non lin ear de pend ence of at ten u a tion on fre quency, such as as = Bs f

q canalso be ac com mo dated by a least-squares fit of at ten u a tion co ef fi cients at dif fer ent fre quen -cies, where both Bs and the power term q can be de rived from ex per i men tal data. The er rorprop a ga tion for Bs would be anal o gous to that used for Eq. (5) and the er ror prop a ga tion forthe power term q could be de rived as well.

Eqs. (2) and (5) pro vide use ful guid ance on the de gree of sta tis ti cal ac cu racy that can beob tained us ing com pound ing. Ob vi ously, in creas ing the num ber of in de pend ent data setsthat can be ap plied to any given area im proves the re sults. This pa per has em pha sized bothspa tial and fre quency com pound ing to in crease Nc and Nf . Other meth ods that will be ap plied in fu ture re search in clude in creas ing the slice thick ness and spa tial com pound ing frompoints out side the im age plane.

The cur rent al go rithm is sen si tive to changes in back scat ter. An in crease in echogenicitywill be viewed as a neg a tive change in the at ten u a tion and vice versa, which can be seen inthe at ten u a tion im age of cyl in der C (Fig. 9d). Here, an in crease in back scat ter at the topbound ary of the cyl in der is in ter preted by the al go rithm as a sharp de crease in at ten u a tion. We are study ing whether this lim i ta tion can be over come us ing an adap tive at ten u a tion fil terthat would omit abrupt sig nal am pli tude changes. Ad mit tedly, the work was done for rel a -tively uni form sam ples and any in crease in the ho mo ge ne ity of the im aged re gion will add toim age fluc tu a tions.

Clin i cally, the ap pear ance of ‘pos te rior ech oes,’ ei ther ‘en hance ment’ or ‘shad ow ing,’ isthe fun da men tal cri te ria for as sess ing at ten u a tion within fo cal le sions such as the breast, kid -ney or thy roid. The at ten u a tion co ef fi cient slope has been iden ti fied by d’Astous and Fos -ter38 and Landini et al39 as a dis crim i nat ing pa ram e ter for breast tis sue. Us ing a 3.5 MHztrans ducer, the er ror of lo cal at ten u a tion es ti mates within a 3 cm mass in a phan tom was pre -dicted to be less than 10 %. Al though the masses stud ied here are ho mo ge neous, the tech -nique shows prom ise for pro vid ing meth ods to quan tify at ten u a tion within breast masses,par tic u larly for scans de rived at ul tra sound fre quen cies above 7 MHz. Our vi sion is that aclin i cal user will draw a re gion of in ter est within the sus pected mass on an ul tra sound breastim age. The al go rithm then will re trieve all rf data as so ci ated with that re gion and com putethe at ten u a tion. Sim i larly, the rel a tive dif fi culty of beam pen e tra tion is the cur rent cri te rionfor es ti mat ing ul tra sound at ten u a tion in large or gans such as the liver. The at ten u a tion es ti -ma tion method de scribed in this pa per could readily be in cor po rated into mod ern dig i talscan ners and its role as sessed for aid ing these sub jec tive as sess ments. Maklad et al40 in an invivo study, re ported at ten u a tion val ues in nor mal liv ers of 0.52 ± 0.03 dB/cm/MHz, while inal co holic cir rho sis, they were es ti mated as 0.83 ± 0.09 dB/cm/MHz. Sim i larly, Lu10 re -ported val ues for nor mal liver to be 0.55 ± 0.07 dB/cm/MHz and val ues of 0.85 ± 0.08dB/cm/MHz for fatty in fil trated liver. Thus, in large or gans, if the at ten u a tion co ef fi cient de -pends on the de gree of in fil tra tion, the com pound schemes de scribed here should en able es ti -ma tion of de gree of steatosis eas ily. Fur ther more, in cases where the liver ex hib itsinhomogeneous at ten u a tion caused by fo cal fatty in fil tra tion, the abil ity to quan tify at ten u a -tion over lo cal re gions on the or der of 2-3 cm should add value to clin i cal use of this data andas sist in dif fer en ti a tion of this con di tion.

CON CLU SION

A method for mea sur ing ul tra sound at ten u a tion, which uses both spa tial and fre quencycom pound ing in data ac qui si tion and anal y sis, has been de scribed. The tech nique ap plies aref er ence phan tom to ac count for im ag ing sys tem de pend en cies of echo sig nals and com -putes at ten u a tion over seg ments of 0.5 cm to 2.5 cm in length. Re sults dem on strate an ef fec -

258 TU ET AL

tive re duc tion of the vari ance in at ten u a tion mea sure ments when com pound ing is ap plied vs. when no com pound ing is used. The tech nique is use ful for mea sur ing at ten u a tion over small re gions on ul tra sound im ages and for con struct ing coarse at ten u a tion im ages.

AC KNOWL EDGE MENTS

The au thors thank Gary Frank, An thony Gerig and Udomchai Techavipoo for their tech ni -cal as sis tance. This work was sup ported in part by NIH grants R21EB00722, R01CA39224and R42GM54377.

AP PEN DIX

Let Nc be the ef fec tive num ber of in de pend ent sig nals used for spa tial an gu lar com pound -ing, Nf the ef fec tive num ber of in de pend ent fre quency com po nents used in fre quency com -pound ing, and nf the num ber of par tially-cor re lated fre quency com po nents used.

Us ing fre quency com pound ing, the av er age slope of at ten u a tion co ef fi cient vs. fre -quency, b¢ (dB/cm/MHz) is ob tained from bi , the at ten u a tion co ef fi cient slope at each mea -sure ment fre quency fi . That is,

So the stan dard de vi a tion of b¢, sb¢ is:41

Let

where sbi2 is the vari ance of the es ti mate at fre quency fi; r(bi, bj) is the cor re la tion of at ten u a -

tion co ef fi cient slope, es ti mated at fre quency fi and fj.

ATTENUATION IMAGING USING COMPOUNDING 259

f

fn

i

fn

ji

jii

f

fn

i

fn

j

ji

'

n

),cov(

n

),cov( å ååå= ¹= =

+

==1

2

1 1

bbsbb

s

b

b

(A.2)

f

fn

i

i

'

n

å== 1

b

b

(A.1)

å

å

=

¹+nf

ii

fn

ji

jiji

f

),(

n

1

2

1

bs

bbrss

=

+

=

å

å

=

¹

fn

ii

fn

ji

ji

f

f

),cov(

nN

1

2

1

bs

bb

(A.3)

å=

=fn

ii

f

'

N 1

21bb

ss(A.4)

Combining with Eq. (4),

Af ter spa tial com pound ing,

REF ER ENCES

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260 TU ET AL

å=

··=fn

i

i

ifc

' )f(fNN 1

2

2

111ab

ss(A.6)

)f(fN

fn

i

i

if

' å=

=1

2

2

11ab

ss(A.5)

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ATTENUATION IMAGING USING COMPOUNDING 261