Ul tra sonic At ten u a tion Es ti ma tion in Small Plaque Sam ples
Us ing a Power Dif fer ence Method
HAIRONG SHI,1HAIFENG TU,1R.J. DEMP SEY 2 AND TOMY VARGHESE1 1
De part ment of Med i cal Phys ics
2
De part ment of Neu ro log i cal Sur gery The Uni ver sity of Wis con sin-Mad i son
Mad i son, WI 53706 tvarghese@wisc.edu
Many stud ies have shown that ath ero scle ro sis changes the ul tra sonic at ten u a tion prop er ties of the ves -sel wall and plaque. Ac cu rate es ti ma tion of the at ten u a tion co ef fi cient slope could there fore pro vide an early in di ca tion of ath ero scle ro sis and the dif fer en ti a tion be tween low, mild and highly-at ten u at ing plaque within the ves sel. How ever, the tra di tional ref er ence phan tom method that fits the power spec -trum in a re gion of in ter est fails to ac cu rately es ti mate the at ten u a tion co ef fi cient for small ir reg u lar shaped ex-vivo plaque spec i mens. This dis crep ancy was pri mar ily due to par tial vol ume ef fects and the un known back scat ter co ef fi cient of the plaque sam ple. We have de vel oped a method based on the ref er -ence-phan tom method that uti lizes the dif fer ence in the acous tic power above and be low the sam ple to ac cu rately com pute val ues of the at ten u a tion co ef fi cient ex vivo. Our re sults dem on strate that this ap proach over comes the two draw backs men tioned ear lier and pro vides ac cu rate es ti mates of the at ten u a -tion co ef fi cient slope for small ex cised tis sue sam ples.
Key words: Ath ero scle ro sis; at ten u a tion co ef fi cient; power dif fer ence; tis sue char ac ter iza tion; ul tra -sound.
I. IN TRO DUC TION
Ath ero scle ro sis is a ves sel wall dis ease that can oc cur to dif fer ent de grees in all ves sels, such as the aorta, ca rotid and cor o nary. In extracranial ves sels, atherosclerotic plaque is es ti mated to be pres ent in 25% to 50% of all stroke pa tients, mak ing it one of the lead ing risk fac -tors for stroke.1 Eu ro pean and North Amer i can ca rotid sur gery tri als have shown the ben e fits
of ca rotid endarterectomy in pa tients with angiographically-de tected symp tom atic ca rotid ste no sis of 70% or greater.2, 3
Plaque com po si tion has been iden ti fied as an im por tant fac tor in the de vel op ment of stroke symp toms. The main com po nents of atherosclerotic plaque are the con nec tive tis sue extracellular ma trix, in clud ing col la gen, protoglycans and fibronectin elas tic fi bers; crys tal -line cho les terol, cholesteryl es ters and phospholipids; and cells such as monocyte-de rived macrophages, lym pho cytes and smooth mus cle cells.4 Ath ero scle ro sis de vel ops as lipids or
cho les terol de pos its ac cu mu late within the in ner lin ing of the ar ter ies.5 With an in crease in
the lipids or cho les terol de pos its, fi brous con nec tive tis sue and/or cal cium de pos its are also in cor po rated within the plaque. The plaque it self may be fis sured by neovascular chan nels form ing within the le sion. Rup ture of these blood ves sels within the plaque wall or blood en
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ter ing from the lu men af ter plaque fis sur ing, may also re sult in hem or rhage5 and ul cer ation
within the plaque. This pro gres sion in creases the like li hood of embolization.
Many re search ers have shown that ul tra sonic at ten u a tion and back scat ter co ef fi cients are re lated to tis sue struc ture and com po si tion.6-8 These stud ies have shown that these two pa
-ram e ters could be used as in di ces of tis sue type and ma te rial con di tions.9-11 Lizzi et al12-15 and
oth ers16,17 have shown that ul tra sound at ten u a tion and back scat ter-re lated pa ram e ters such as
slope, in ter cept and midband fit of the log a rithm of the power spec trum are re lated to tis sue microstructure. Noritomi et al17 uti lized the slope and in ter cept, in ad di tion to the to tal power
value, to clas sify plaque con stit u ents into fi brous, lipidic and re gions with throm bus. Sev eral meth ods have been uti lized to es ti mate the at ten u a tion co ef fi cient, in clud ing the cen troid fre quency down-shift to es ti mate fre quency-de pend ent at ten u a tion.18 Kuc and
Schwartz19 es ti mated at ten u a tion us ing the slope of the dif fer ence be tween the log a rithm of
the echo sig nal power spec tra from two dif fer ent tis sue depths. Cloostermans et al20 uti lized
a multinarrow-band method to de rive a re la tion ship be tween the at ten u a tion slope ver sus fre quency . He and Green leaf21 pro posed the en ve lope peak method, which uti lizes the lo cal
max i mum of the echo sig nal to es ti mate at ten u a tion. In our lab o ra tory, Yao et al22 pro posed
the ref er ence phan tom method to re move sys tem de pend en cies and this method has been used to es ti mate sev eral prop er ties, such as at ten u a tion and back scat ter co ef fi cient. Tu et al23, 24 uti lized fre quency com pound ing and spa tialan gu lar com pound ing to im prove the ac
-cu racy of at ten u a tion es ti ma tion. Lizzi et al7 have also re lated their spec tral pa ram e ters,
namely the slope and midband fit, to at ten u a tion, scat terer size, scat terer con cen tra tions and rel a tive acous tic im ped ance of tis sue scat ter ers.
Bridal et al25-27 used sin gle el e ment trans duc ers to mea sure the at ten u a tion co ef fi cient of ex-vivo aorta spec i mens in the 25-56 MHz band width range,25 at ten u a tion of atherosclerotic
plaque in the 30-50 MHz fre quency range26 and ca rotid ar tery plaque at ten u a tion in the 5-12
MHz and 12-28 MHz fre quency ranges,27 re spec tively. They uti lized the cen troid fre quency
down-shift method to es ti mate the at ten u a tion co ef fi cient.
Al though many stud ies have been per formed for plaque char ac ter iza tion, very few uti lize clin i cal lin ear ar ray trans duc ers for ex-vivo and in-vivo plaque char ac ter iza tion of the ca rotid ar tery. Most pre vi ous stud ies uti lized sin gle el e ment trans duc ers or intravascular trans duc ers to study plaque tis sue. With prog ress in the tech nol ogy, it is pos si ble to uti lize lin earar -ray trans duc ers and clin i cal sys tems to per form ex-vivo and in-vivo ca rotid-plaque anal y sis. The ad van tage of uti liz ing a clin i cal ul tra sound sys tem with lin ear ar ray trans ducer is that it en ables the iden ti fi ca tion of the tis sue sam ple cross-sec tion from B-mode im ages along with si mul ta neous radio fre quen cy (rf) data ac qui si tion. For ex am ple, the Siemens Antares sys -tem (Siemens Med i cal Sys -tems, Inc. Issaquah, WA) equipped with an ul tra sound re search in ter face can ac quire up to 508 A-lines across a 38 mm width of plaque tis sue. Insana et al28
have also dem on strated that clin i cal lin ear ar ray sys tems can ac cu rately es ti mate the back scat ter co ef fi cient. Sev eral stud ies that uti lize lin ear ar ray trans duc ers for scat terer size es ti -ma tion29 and at ten u a tion es ti ma tion23, 24 have been re ported.
Al though in-vivo scan ning of ca rotid plaque would pre serve all in for ma tion re gard ing plaque struc ture and sur round ing tis sue en vi ron ment, in-vivo scan ning also ex pe ri ences dif -fi cul ties due to the inhomogeneous tis sue back ground, such as lay ers of fat and mus cle that af fect at ten u a tion es ti ma tion.30-32Ex-vivo ex per i ments that en case plaque sam ple within a
uni form tis suemim ick ing (TM) gel a tin phan tom pro vide ex cel lent back ground en vi ron -ments that are suit able for the es ti ma tion of the at ten u a tion in tro duced due to plaque us ing the ref er ence phan tom method.22
How ever, for ex-vivo mea sure ments, the ex cised plaque sam ples ob tained af ter ca rotid endarterectomy are usu ally very small, with di men sions of plaque tis sue be ing around 1-2 cm in length and 0.3-0.5 cm thick (plaque thick ness rep re sent tis sue from the in side ar tery
wall to the plaque sur face). Sev eral meth ods used to es ti mate the at ten u a tion co ef fi cient de -scribed in the lit er a ture23, 24
re quire sam ple thick nesses around 0.5 to 1 cm to pro vide re li able es ti ma tion of the at ten u a tion co ef fi cient. How ever, in our ex-vivo ex per i ments, plaque thick -ness was usu ally around 0.3 to 0.5 cm. Di rect anal y sis of echo sig nal data from the ex-vivo
plaque spec i men em bed ded in a gel a tin phan tom in tro duces er rors due to vari a tions in the back scat tered sig nal from the plaque when com pared to the gel a tin back ground and par tial vol ume ef fects due to the lim ited amount of echosig nal data ob tained from the plaque spec i -men due to the lim ited thick ness of the ex cised plaque sam ple. The ram i fi ca tions of both of these is sues are dis cussed in more de tail later in the pa per af ter we in tro duce the powerdif -fer ence method.
The power dif fer ence method, pro posed in this pa per, avoids par tial vol ume ef fects and the back scat ter dif fer ence prob lem for the es ti ma tion of the at ten u a tion co ef fi cient of small sam ples. In sec tion II, we pro vide a the o ret i cal back ground for the power dif fer ence method. In sec tion III, we pres ent a ver i fi ca tion of the ac cu racy of the power dif fer ence method us ing wellchar ac ter ized TM phan toms with in clu sions with and with out vari a tions in the back -scat ter. Fi nally, we de scribe ex per i men tal re sults from ex-vivo plaque sam ples dem on strat -ing the vari a tion in the at ten u a tion co ef fi cient for dif fer ent plaque spec i mens. The method pro posed in this pa per is spe cif i cally for ac cu rate and un bi ased mea sure ment of the at ten u a -tion co ef fi cient for small ex cised samples.
II. THE O RET I CAL BACK GROUND
Ex-vivo plaque sam ples were em bed ded into a 7×7×7 cm3 cubeshaped TM gel a tin phan
-tom that was also uti lized as the ref er ence phan -tom. Fig ure 1 pres ents a sche matic di a gram of plaque tis sue em bed ded in a ho mog e nous gel a tin phan tom (left di a gram) while the di a gram on the right shows the same ho mog e nous phan tom uti lized as the ref er ence.
Since the thick ness of the plaque sam ple was very small (around 0.3-0.5cm), we were able to ob tain only 156~260 data points along the dig i tized echo sig nal se quence that cor re -sponded to in for ma tion re gard ing the plaque. Radio fre quen cy echo sig nals were sam pled at a 40 MHz sam pling fre quency. This small num ber of data points was barely suf fi cient to ob -tain a sin gle un bi ased Fou rier spec trum mak ing ac cu rate com pu ta tion of the power spec trum of the plaque re gion un fea si ble. The ba sic idea with the new power dif fer ence method is to perform power spec tral anal y sis of the re gion of shad ow ing be neath the plaque sam ple in -stead of the sam ple it self. The ad van tages of this method lie in fact that lon ger seg ments of
n0 L S1 Gel Reference t(n0) Sample Transducer Sample Gel Gel S2 n0 d(n0)
data can be used (e.g., approximately 512 points) to ob tain re li able power spec tral es ti ma -tion. Sec ondly, we over come back scat ter co ef fi cient dif fer ences be tween the plaque and gel a tin back ground used as the sam ple and ref er ence re spec tively. Fi nally, par tial vol ume ef fects are elim i nated and are not en coun tered with the power dif fer ence method.
Many of the power spec tral anal y sis meth ods used for at ten u a tion es ti ma tion are based on the ref er ence phan tom method, where the sam ple and ref er ence phan tom are scanned us ing the same sys tem set tings such as the cen ter fre quency, fo cal depth and timegain com pen sa tion (TGC). There fore, by es ti mat ing the ra tio of the power spec trum ob tained from the sam -ple and ref er ence, sys tem-de pend ent terms can be re duced, leav ing only tis sue-re lated back scat ter and at ten u a tion terms in the power-spec tral ratio, i.e.,
where BSC(w, d) de notes the back scat ter co ef fi cient at depth d, and a(w, d) rep re sents the at -ten u a tion co ef fi cient in the re gion at depth d. The sub scripts la beled “samp” and “ref” de note sam ple and ref er ence, re spec tively. Since the same trans ducer was used for both trans mit -ting and re ceiv ing echo sig nals, for plaque tis sue with thick ness d, the ul tra sound pulse has to prop a gate through a thick ness 2d in tis sue in pulse-echo mode be fore be ing re ceived by trans ducer. Since, the power spec trum is cal cu lated from the ex pected value of the Fou rier trans form of the ac quired rf sig nal mul ti plied by its com plex con ju gate, a fac tor of 4d ap -pears in the ex po nen tial term.
In fig ure 1, the term n cor re sponds to the A-line in dex along the scan plane, where the depth to the top sur face of plaque tis sue is de noted by d(n), and plaque thick ness by t(n);
there fore, the depth of the bot tom plaque sur face is given by d(n)+t(n). Note that for pro cess -ing a seg ment of the rf sig nal with length L in the sam ple at an A-line in dex po si tion of n0 and depth of d(n0)+t(n0)+L/2, we can also se lect a sim i lar seg ment of rf data with length L and at the same depth d(n0)+t(n0)+L/2in the ref er ence phan tom. Com put ing the power spec tral ra -tio for these two seg ments, we ob tain:
where BSC1(w) and BSC2(w) de note the fre quency de pend ent back scat ter co ef fi cient. In this
case, BSC1(w) and BSC2(w) are the same be cause they are ob tained from the same gel a tin
back ground. The term ag(w, n0) de notes the fre quency de pend ent at ten u a tion co ef fi cient for
back ground gel a tin along the x0 th
A-line, and ap(w, n0) is the fre quency de pend ent at ten u a
-tion co ef fi cient for the plaque along the x0 th
A-line. The terms T and T’ de note the trans mis -sion co ef fi cient at the top and bot tom sur face of the plaque:
where r isthe den sity, c de notes the speed of sound and the sub scripts p and g rep re sent plaque and back ground gel a tin, re spec tively. Note that T and T’ are gen er ally in de pend ent of the fre quency. There fore, Eq. (2) can be sim pli fied as
18 SHI ET AL
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BSC d d d BSC d S d S d S ref ref samp samp ref samp norm , 4 exp , , 4 exp , , , , w a w w a w w w w -» = (1)(
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2 2 0 0 2 0 0 2 0 0 2 0 0 1 0 2 0 1 , 4 , 4 exp , 4 , 4 exp , , T T n t n n d n BSC n t n n d n BSC n S n S g L g p L g ¢ ´ ´ -+ ´ -´ -+ ´ -» w a w a w w a w a w w w (2) g g p p g g g g p p p p c c c T c c c T r r r r r r + = ¢ + = ¢ ¢ 2 , 2 (3)Equa tion (4) il lus trates the can cel la tion of the back scat ter co ef fi cient pa ram e ters, both from the plaque and the back ground gel a tin when the back scat ter co ef fi cients are the same. Tak ing the log a rithm on both sides of Eq. (4), we ob tain:
As sum ing that the at ten u a tion co ef fi cient is mod eled in the form:26, 33
Since we al ready know the at ten u a tion co ef fi cient of the ref er ence phan tom ag(f) =bg(f)·f
+ cg and plaque thick ness t(n0) can be mea sured, Eq. (5) can be writ ten as
where C de notes a term that con tains all terms in de pend ent of fre quency. Es ti ma tion of the at ten u a tion co ef fi cient bp(n) from Eq. (7) in volves fit ting the log a rithm of the power spec tral
ra tio to the form y = af+b, where a de notes the slope in units of neper/MHz. Mul ti pli ca tion by a fac tor of 8.686 will con vert the units to dB/MHz. There fore, the at ten u a tion co ef fi cient for the plaque spec i men can be com puted as:
On the other hand if the sam ple is em bed ded within a back ground with dif fer ent val ues of the at ten u a tion and back scat ter co ef fi cient when com pared to the ref er ence phan tom, then the at ten u a tion es ti ma tion pro cess be comes more com pli cated. For this case, we pro pose a mod i fied power dif fer ence method de scribed be low, with a sche matic di a gram shown in figure 2.
In this case, we se lect data seg ments with length of L (Fig. 2) both above and be low the sam ple or re gionofin ter est (ROI). Sim i lar re gions are also se lected in the ref er ence phan -tom. There fore, the re spec tive power spec tra can now be writ ten as:
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10 0 0 0 2 2 10 0 0 0 10 0 2 0 1 10 log 10 , , 372 . 17 log 10 , , 4 log 10 , , log 10 T T n t n n T T n t n n e n S n S g p g p ¢ + ´ -= ¢ + ´ -´ » ú û ù ê ë é w a w a w a w a w w (5)( )
f = b×f +c a (6)(
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n C S n f S g p - ´ ´ + -= ú û ù ê ë é 0 0 0 0 2 0 1 10 17.372 , , log 10 b b (7)( )(
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n cm(
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t dB/MHz a dB/MHz/cm n g p b b + ´ -= 0 0 2 (8)(
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2 2 0 0 0 0 2 0 1 , , 4 exp , , T T n t n n n S n S g p - ´ ´ ¢ -» a w a w w w (4)(
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22 2 0 2 2 0 21 2 2 0 0 2 0 1 1 0 12 2 0 1 1 0 11 4 exp , 4 exp , , 4 exp 4 exp , 4 exp , L bkg bkg L bkg bkg samp L bkg bkg L bkg bkg n t n d BSC n S n d BSC n S T T n t n n d BSC n S n d BSC n S + + ´ -» -´ -» ¢ ´ ´ -´ + ´ -» -´ -» w a w w w a w w w a w a w w w a w w (9)where S11, S12, S21, S22 de note the power spec tra from the four data seg ments shown in fig ure 2. The sub scripts bkg1, bkg2 and samp de note the re spec tive co ef fi cients from the back -ground sam ple ma te rial, ref er ence and the sam ple it self, re spec tively. L de notes the data seg -ment length used to com pute the power spec trum. Tak ing the ra tio of the power spec tra, we ob tain
If abkg1(w) and abkg2(w) are known, the cal cu la tion would be sim i lar to that per formed in Eqs. (5) to (8).
The power dif fer ence method de scribed in this sec tion, ad dresses the at ten u a tion co ef fi -cient es ti ma tion for small ex-vivo plaque sam ples. The two pri mary draw backs as so ci ated with small sam ples in clude:
1. Back scat ter dif fer ence prob lem
Back scat tered sig nals from plaque are sig nif i cantly larger than that from the back ground gel a tin, es pe cially for cal ci fied and fi brous plaques. How ever, the ex act back scat ter de pend -ence with fre quency is un known; there fore, the at ten u a tion co ef fi cient cal cu lated by fit ting an ROI will pro vide in cor rect re sults.
2 Partial vol ume ef fects
The data seg ment used for power spec tral anal y sis con tains sig nals from both the plaque spec i men and the back ground gel a tin, thus bi as ing the at ten u a tion es ti ma tion.
The fol low ing sec tions pres ent ex per i men tal re sults dem on strat ing the abil ity of the power dif fer ence method to ac cu rately es ti mate the at ten u a tion co ef fi cient, ver i fied us ing well-char ac ter ized TM phan toms and, fi nally, on ex cised plaque spec i mens.
III. EX PER I MEN TAL VER I FI CA TION ON TIS SUE-MIM ICK ING PHANTOMS
Method
A TM phan tom with four cy lin dri cal in clu sions with dif fer ent val ues of the at ten u a tion co -ef fi cients was uti lized to ver ify the es ti ma tion ac cu racy of the power dif fer ence method. The
20 SHI ET AL n0 L S12 BKG2 Reference t(n0) Sample Transducer Sample BKG1 BKG2 S11 S21 S22 n0 d(n0) L
FIG. 2 Schematic di a gram of the mod i fied power dif fer ence method.
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2 2 0 2 0 2 1 2 2 0 2 0 0 1 0 22 0 21 0 12 0 11 , 4 exp 4 exp 4 exp , 4 exp 4 exp , , , , T T n t n L T T L n t n t n L n S n S n S n S bkg samp bkg bkg bkg samp bkg ¢ ´ ´ -´ ´ -= ¢ ´ + ´ ´ ´ ´ » w a w a w a w a w a w a w a w w w w (10)sam ple and ref er ence rf data were both ac quired from the same phan tom, with the in clu sion and the back ground hav ing sim i lar back scat ter char ac ter is tics. One of the cyl in ders was scanned along the ax ial di men sion of the in clu sion which was 1 cm in di am e ter. The prop er -ties of the back ground and cy lin dri cal in clu sion are listed in ta ble 1.
The phan tom was scanned us ing a Siemens Antares Ul tra sound Sys tem (Siemens Med i cal Sys tems, Issaquah, WA, USA) equipped with an Ul tra sound Re search In terface (URI). The trans ducer was a VFX 9-4 trans ducer op er ated at a cen ter fre quency of 6.15 MHz. The lat eral res o lu tion was set to the high est value, i.e., 508 Alines for a beam width of 38 mm. The sam pling rate was 40 MHz, with a sin gle trans mit fo cus set at the depth of the cy lin dri cal in clu -sion or plaque with dy namic fo cus ing on re ceive. The phan tom was placed on a lin ear trans la tion stage, with the trans ducer se cured on a me chan i cal arm, the XYZ po si tion of which can be pre cisely ad justed. Af ter scan ning the cyl in der, the trans ducer was moved hor -i zon tally to scan a un-i form back ground re g-ion to ac qu-ire 25 -in de pend ent rf data frames.
Cor re spond ing B-mode im ages were ob tained from the rf data where the top and bot tom bound ary of the in clu sion (since we scanned along the ax ial di men sion of the cyl in der, the in clu sion on B-mode im age was vi su al ized as a band) was marked to cal cu late the thick ness of the band de noted by t(n). For the sam ple or the TM cyl in der in this case, 512 rf data points from each A-line were se lected from just be low the in clu sion re gion to es ti mate the power spec trum. Short-time Fou rier trans form (STFT) anal y sis us ing a Hanning-gated 256 point nonoverlapping data seg ment was used to com pute the power spec trum. Three STFT’s were com puted over each A-line data seg ment. In ad di tion, STFT‘s were com puted over 20 A-lines in the lat eral di rec tion. All of these STFT’s (20´3) were av er aged to com pute the power spec trum as shown in fig ure 4. Since the sam pling rate was 40 MHz and the A-line den sity was 38mm/360 A-lines, the fi nal power-spec trum was ob tained from a 2-D block with di men sions of (512´1.54)/(2´40) = 9.86 mm in the ax ial di rec tion and 20´(38/360) = 2.1 in the lat eral di rec tion.
In a sim i lar man ner, the power spec trum was cal cu lated for the ref er ence phan tom, at the same depth as the sam ple. Since each A-line in the sam ple rf ma trix could be from dif fer ent depths (for ir reg u larly-shaped sam ples), we choose the mean depth for the sam ple. Be cause the in clu sion or em bed ded plaques in later cal cu la tions were usu ally close to the hor i zon tal and the power spec tra from the uni form ref er ence uni form phan tom only var ies min i mally with depth, the av er age depth val ues pro vide an op ti mal com pro mise for ef fi ciency and ac -cu racy. We av er aged 25 in de pend ent STFT re al iza tions to ob tain the ex pected value or the power spec trum for the ref er ence phan tom.
We also mea sured the at ten u a tion co ef fi cient for a sec ond TM phan tom re ferred to as the ef fec tive-fre quency phan tom.34
In this phan tom, the back scat ter co ef fi cient be tween the in -clu sion and the back ground are dif fer ent. This phan tom was pre vi ously stud ied by Wil son et al34
and con sisted of a back ground TM ma te rial with scat ter ing tar gets po si tioned at var i ous
TA BLE 1 At ten u a tion and back scat ter ing prop er ties of back ground ma te rial and cyl in ders of the phan tom uti lized for method ver i fi ca tion. Data on the acous tic prop er ties of the TM phan tom were taken from ref er ence 37.
Ma te rial Speed (m/s)
(± 1 m/s)
At ten u a tion co ef fi cient (dB/cm) (±0.1dB/cm) Slope of at ten u a tion co ef fi cient (dB/cm/MHz) Rel a tive BSC (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 0 Cyl in der 1547 1.89 3.57 5.12 6.45 0.80 -3
depths. The back ground re gion was com prised of 45-53 mm glass beads uni formly dis trib uted in a gel a tin back ground, along with three dif fer ent tar gets with vary ing lev els of back -scat ter in tro duced with poly sty rene beads po si tioned at dif fer ent depths. The di rect fit based method22
and the power dif fer ence method, both de rived from the ref er ence phan tom method,22
was uti lized to cal cu late the at ten u a tion co ef fi cient.
Re sults
The at ten u a tion co ef fi cient of the in clu sion in the first phan tom was cal cu lated us ing Eq. (7) with the re sults ob tained us ing the power dif fer ence method plot ted as solid line in fig ure 3(b). Here, no back scat ter vari a tions are ob served be tween the in clu sion and the back -ground. The mean at ten u a tion co ef fi cient for the cyl in der was 0.79 ± 0.11 (dB/cm/MHz), ob tained us ing the power dif fer ence method. Ob serve from ta ble 1 that the de signed (man u -fac tured) value of the at ten u a tion for the cyl in der was 0.80± 0.1 (dB/cm/MHz), dem on strat -ing the ac cu racy and pre ci sion of the power dif fer ence method for at ten u a tion es ti ma tion. We also uti lized the di rect fit based method to cal cu late the at ten u a tion co ef fi cient map, with the at ten u a tion pro file at the cen ter plot ted as the dashed dot ted line in fig ure 3(b). The at ten -u a tion value for the di rect fit ref er ence phan tom method is es ti mated to be 0.74 ± 0.03dB/cm/MHz. Ob serve also that the rel a tive back scat ter level of the cyl in der with re spect to the back ground does not af fect the at ten u a tion es ti ma tion.
For the ef fec tive fre quency phan tom, we clearly vi su al ize the vari a tions in the back scat ter be tween the in clu sion and back ground, where fig ure 5(a) pres ents the B-mode im age and the ROI used to cal cu late the at ten u a tion co ef fi cient. The power dif fer ence method is used to es -ti mate the at ten u a -tion co ef fi cient in the pres ence of back scat ter vari a -tions in this case. The at ten u a tion co ef fi cient ob tained us ing the power dif fer ence method is shown as the solid line in fig ure 5(b)in the band width range from 2.5~5.5 MHz. The mean value of the at ten u a tion co ef fi cient was es ti mated to be 0.45 ± 0.08dB/cm/MHz. This value is very close to the at ten -u a tion val-ue of 0.5 dB/cm/MHz re ported by Wil son et al34 ob tained us ing a broad band
substitution tech nique. Us ing the di rect fit ref er ence phan tom method to cal cu late the attenuation map of the phan tom, with the at ten u a tion pro file at the cen ter as shown by the dashed dot ted line in fig ure 5(b), the value is es ti mated as 0.51 ± 0.05dB/cm/MHz These phan tom re sults il lus trate the ac cu racy of the power dif fer ence method for es ti ma tion of the at ten u a tion co ef fi cient in the pres ence of back scat ter vari a tions.
22 SHI ET AL
FIG. 3 (a) B-mode im age and the se lected in clu sion re gion uti lized to cal cu late at ten u a tion; (b) Plot of cal cu lated at ten u a tion co ef fi cient ver sus lat eral po si tion.
10 15 20 25 30 35 0.4 0.6 0.8 1 Lateral Position (mm) A tt e n u a tio n C o e ff ic ie n t (d B /M H z/ cm )
Power Difference Method Direct Fit Method
(a)
Lat eral Po si tion (mm)
) m c/ z H M/ B d( t n ei ci f f e o C n oi t a u n e tt A (b)
Note that in both these ex am ples, rel a tively larger ROIs or in clu sions were scanned. Fig -ure 3(a) in di cates that the in clu sion had a thick ness of 1 cm while fig -ure 5(a) shows that the in clu sion thick ness was 2 cm. There fore both the di rect fit and the power dif fer ence method are ex pected to ac cu rately es ti mate at ten u a tion co ef fi cient val ues. The at ten u a tion co ef fi cient re sults pre sented in this sec tion ver ify that the power dif fer ence method pro vides ac cu -rate and un bi ased val ues of the at ten u a tion co ef fi cient.
IV. AT TEN U A TION CO EF FI CIENT ES TI MA TION FOR EX-VIVO
ATHEROSCLEROTIC CA ROTID PLAQUES
Method
Plaque sam ples were ob tained from pa tients who un dergo ca rotid endarterectomy at the UW-Hos pi tals and Clin ics. Tis sue sam ples were col lected and ul tra sound radio fre quen cy data ac quired on the sam ples un der a Uni ver sity of Wis con sin Hos pi tals and Clin ics IRB ap -proved pro to col. Sur gi cally-ex cised plaques were cut lon gi tu di nally into three seg ments and one of the seg ments placed in 0.9% sa line so lu tion, used for ul tra sonic tis sue char ac ter iza tion anal y sis. The sec ond seg ment un der goes patho log i cal anal y sis while the third seg -ment was used for gene chip or lipid anal y sis.
To per form ul tra sonic mea sure ments on each plaque seg ment, we em bed the plaque seg -ment into a TM gel a tin phan tom. To em bed the plaque seg -ment into a TM gel a tin phan tom, a trans par ent plexi glass cu bical mold with in ner di men sions of 7´7´7cm was con structed. A sa ran layer was glued to the bot tom of the mold while the mol ten gel a tin poured from the top open sur face of the cube. Gel a tin phan toms were pre pared us ing 200-bloom calf skin gel at a con cen tra tion of 15.4 grams per li ter of dis tilled wa ter. The gel a tin pow der was mixed with dis tilled wa ter and cooked in a dou ble heated wa ter bath un til the gel a tin clar i fies at tem per a -tures around 800C. Af ter the gel a tin so lu tion clar i fied, glass beads with a mean di am e ter of
18mm were added at a con cen tra tion of 1 gm of beads/li ter of gel a tin to pro vide Ra leigh scat -ter ing. The glass beads were mixed with warm dis tilled wa -ter and stirred care fully into the mol ten gel a tin. Mol ten gel a tin was then poured into the plexi glass mold. First, a layer of mol ten gel a tin about 3.5 cm thick was poured at a tem per a ture of 290C. This layer was al
-lowed to con geal for a few min utes be fore the plaque sam ple was placed on this gel a tin layer. The sur face was then strong enough to hold the plaque seg ment and not al low the plaque spec i men to sink down to the bot tom of the cube. The mold was then filled with mol ten gel at 290C and the en tire phan tom al lowed to con geal for an hour. The molds along with the gel a
-tin phan tom were then re frig er ated for two hours.
256 points 256 points 256 points
20 A-lines
The gel a tin cube with the em bed ded plaque was re moved from the plexi glass mold by peel ing the sa ran layer on the bot tom sur face of the mold, and gently slid ing the gel a tin block out of the mold. The gel a tin block was re moved from the mold and used for ul tra sonic im ag -ing. Prior to ul tra sound im ag ing, the phan tom was brought to room tem per a ture (~20°C) be -fore ex-vivo scan ning was per formed. Sev eral re search ers have dem on strated that plaque prop er ties,35, 36 such as speed of sound, at ten u a tion and level of back scat ter do not change
even for frozen sam ples.
We an a lyzed 44 dif fer ent ex-vivo hu man plaque spec i mens us ing the power dif fer ence method. From these plaque spec i mens, we se lected 114 typ i cal seg ments over which at ten u a tion es ti mates were com puted. Se lec tion of the seg ments was based on the fol low ing cri te -ria: First the at ten u a tion be tween the start point (Pstart) and end point (Pend) should be sim i lar, i.e., bmax-bmin < 0.5 dB/cm/MHz , where bmax and bmin are the max i mum and min i mum at ten u
a tion co ef fi cients in this seg ment. Sec ondly, each seg ment se lected con tains at ten u a tion val -ues over at least con sec u tive 20 A-lines. If more than 40 A-lines had sim i lar at ten u a tion co ef fi cient val ues (bmax-bmin < 0.5 dB/cm/MHz), they were di vided into two seg ments, i.e.,
20 £ Pend- Pstart < 40, in units of A-line num ber. Seg ments that do not sat isfy the above two cri te ria were not in cluded. Fi nally, to com pare the at ten u a tion co ef fi cient val ues cal cu lated from the di rect fit method with the power dif fer ence method, we choose cor re spond ing seg -ments with the same Pstart and Pend points on the at ten u a tion para met ric im age cal cu lated us ing the di rect fit method. Note that our power dif fer ence method pro vides a 1D at ten u a tion pro file while the di rect fit method pro vides 2D at ten u a tion im ages and the midline pro file be -tween the same Pstart and Pend points along the plaque depth cho sen for the anal y sis.
This cri te ria de scribed above was uti lized since the power dif fer ence method av er ages Fou rier spec tra ob tained from 20 con sec u tive Alines to cal cu late the at ten u a tion co ef fi cient. This av er ag ing pro ce dure was mean ing ful only when these 20 con sec u tive Alines ex -hibit sim i lar power-fre quency be hav ior. How ever, this re quire ment was not al ways sat is fied. There fore, al though the at ten u a tion pro file ob tained us ing the power dif fer ence method in -di cated smooth tran si tions be tween sta ble at ten u a tion co ef fi cient val ues (Figs. 6, 7), we only se lect seg ments whose at ten u a tion pro files sat isfy the cri te ria de scribed above in the pre vi -ous para graph. A com par i son of the at ten u a tion co ef fi cient es ti mated us ing the di rect fit and power dif fer ence meth ods for all the ex cised plaque spec i mens used in this study are shown in fig ure 8.
24 SHI ET AL
FIG. 5 At ten u a tion es ti ma tion from cyl in der #3 in the ef fec tive fre quency phan tom. (a) The re gion se lected to cal cu late at ten u a tion co ef fi cient is shown. (b) At ten u a tion co ef fi cient for the re gion se lected.
5 10 15 20 25 30 35 0.2 0.3 0.4 0.5 0.6 Lateral Position (mm) A tt e n u a ti o n C o e ff ic ie n t (d B /M H z /c m )
Power Difference Method Direct Fit Method
(a)
Lat eral Po si tion (mm)
) m c/ z H M/ B d( t n ei ci f f e o C n oi t a u n e tt A (b)
Re sults
Both Bmode and para met ric im ages of the at ten u a tion co ef fi cient ob tained from two rep -re sen ta tive ex-vivo ca rotid ar tery plaque spec i mens are shown in fig ures 6 and 7. Fig ure 6(a) shows the B-mode im age of a plaque sam ple em bed ded within the gel a tin phan tom, where the bound ary of the plaque is marked with a dashed-dot line. The mean ax ial di men sion (plaque thick ness) was 3.0 mm. Fig ure 6(b) shows the lo cal para met ric at ten u a tion im age cal cu lated us ing the di rect fitbased ref er ence phan tom method. Sev eral is sues with the at ten u a tion im age or map can be clearly ob served in fig ure 6(b). Note the pres ence of a neg a -tive at ten u a tion re gion in fig ure 6(b), which is due to the back scat ter co ef fi cient dif fer ence be tween the back ground gel a tin and plaque. Sec ondly, the at ten u a tion map ap pears to be blurred due to fac tors such as the par tial vol ume ef fect and the av er ag ing of the Fou rier spec -tra (over 20 A-lines and 3 con sec u tive 2.5mm gated ax ial win dow seg ments with a 1.25 mm step size) used to com pute the power spec trum. Fi nally, the at ten u a tion value es ti mated is ex tremely high, which is due to the in creased back scat ter co ef fi cient in the plaque sam ple when com pared to the back ground gel a tin region.
FIG. 6 An ex am ple to dem on strate at ten u a tion es ti ma tion us ing the power dif fer ence method and di rect fit-based ref er ence phan tom method. (a) B-mode im age of the plaque in the gel a tin phan tom. (b) At ten u a tion map cal cu lated us ing the fit ting method. (c) Com par i son of the at ten u a tion pro file along the cen ter of the plaque ob tained us ing the power dif fer ence and di rect fit-based ref er ence phan tom method, re spec tively.
0 5 10 15 20 25 30 35 0 1 2 3 4 5 6 7 Lateral Position (mm) A tt e n u a tio n C o e ff ic ie n t (d B /c m /M H z)
Power Difference Method Direct Fit method
(a) (b)
Lat eral Po si tion (mm)
) mc /z H M/ B d( t n ei ci f f e o C n oi t a u n e tt A (c)
Fig ure 6(c) pres ents the com par i son of the at ten u a tion pro file ob tained us ing the di rect fit-based ref er ence phan tom method and that ob tained us ing the power dif fer ence method. Ob serve that af ter ac count ing for the con tri bu tion due to back scat ter dif fer ences, the at ten u -a tion v-alue es ti m-ated us ing the power dif fer ence method is sig nif i c-antly lower th-an the v-alue ob tained us ing the di rect fit-based ref er ence phan tom method.
Fig ure 7 pres ents an other case us ing plaque ex cised from a dif fer ent pa tient, which dem on strates sim i lar re sults as those de scribed in fig ure 6. Note that the ul tra sound Bmode im -age in fig ure 7(a) clearly shows that the plaque has an area of shad ow ing be low the plaque sam ple, in di cat ing in creased at ten u a tion within the plaque. Fig ure 7(b) pres ents the at ten u a tion map cal cu lated us ing the di rect fitbased ref er ence phan tom method. The neg a tive at -ten u a tion ar ti facts still ex ist and the im pact of the back scat ter co ef fi cient dif fer ence be tween the plaque and the back ground is also not com pen sated for us ing the di rect ref er ence phan -tom method. Fig ure 7(c) com pares the at ten u a tion pro file ob tained along the cen ter of the plaque us ing the power dif fer ence method and di rect fit-based ref er ence phan tom method. Note that in a sim i lar man ner to the re sults shown in figure 6 (c), the at ten u a tion pro file ob -tained us ing the power dif fer ence method is sig nif i cantly lower than that ob -tained with the di rect fit-based ref er ence phan tom method.
26 SHI ET AL
FIG. 7 An other ex am ple that dem on strates at ten u a tion es ti ma tion us ing the power dif fer ence method and di rect fitbased ref er ence phan tom method. (a) Bmode im age of the plaque in gel a tin. (b) At ten u a tion map cal cu lated di rect fitbased ref er ence phan tom method. (c) Com par i son of the at ten u a tion pro file along the cen ter of the plaque ob -tained us ing the power dif fer ence method and di rect fit-based ref er ence phan tom method.
10 15 20 0 1 2 3 4 5 6 7 Lateral Position (mm) A tt e n u a tio n C o e ff ic ie n t (d B /c m /M H z)
Power Difference Method Direct Fit method
(a) (b)
(c)
Lat eral Po si tion (mm)
) m c/ z H M/ B d( t n ei ci f f e o C n oi t a u n e tt A (b)
Fig ure 8 shows the at ten u a tion co ef fi cient value b es ti mated for the same ROI, ob tained us ing both the power dif fer ence and di rect fit method plot ted against each other. The dot ted line de notes the plot that would have been ob tained if both meth ods pro vided the same at ten -u a tion co ef fi cient es ti mate. Note that in gen eral, the at ten -u a tion co ef fi cient val-ue ob tained us ing the power dif fer ence method in creases with the in creased at ten u a tion co ef fi cient value ob tained us ing the di rect fit method. Sec ondly, a large num ber of the at ten u a tion co ef fi cient es ti mates ob tained us ing the power dif fer ence method are sig nif i cantly smaller than that ob tained us ing the di rect fit method. Plot ting the his to gram of the at ten u a tion co ef fi cient ob -tained us ing both these meth ods us ing 0.5dB/cm/MHz as the in cre ment, we ob tain fig ure 9. Note that the mean at ten u a tion co ef fi cient slope es ti mated us ing the power dif fer ence method is ~1 dB/cm/MHz, while that ob tained us ing the di rect fit method is ~3.5 dB/cm/MHz.
V. DIS CUS SION
In this pa per, we pres ent a method for ex-vivo mea sure ment of the ul tra sonic at ten u a tion co ef fi cient for small spec i mens or sam ples. The anal y sis in this pa per was performed on ex -cised ca rotid atherosclerotic plaque sam ples. This method is based on the ref er ence phan tom method and uti lizes a clin i cal ul tra sound sys tem to ac quire radio fre quen cy data.
The method pro posed in this pa per has sev eral ad van tages when com pared to the stan dard ref er ence phan tom method that di rectly es ti mates the at ten u a tion co ef fi cient in an ROI in tis -sue. First, we re duce con tri bu tions due to vari a tions in the back scat ter co ef fi cient be tween the ROI and back ground. This is done by the com pu ta tion of the power spec tra in a back ground re gion with sim i lar val ues of the back scat ter co ef fi cient above and be low the in clu -sion or ROI. Sec ondly, this method is par tic u larly suited for sam ples with small ax ial di men sions, where di rect es ti ma tion of the at ten u a tion co ef fi cient would suf fer from par tial vol ume ef fects, i.e., the data seg ment se lected for the com pu ta tion of the power spec trum would also in clude echo sig nal in for ma tion from the sur round ing tis sue or gel a tin back ground. The par tial vol ume ef fect in tro duces sig nif i cant in ac cu ra cies in the at ten u a tion es ti -ma tion with the use of the di rect-fit method. In con trast to the power dif fer ence method, data seg ments uti lized for pro cess ing and ob tain ing the power spec trum are se lected from sur -round ing tis sue or back g-round re gions, thereby avoid ing par tial vol ume effects.
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
Direct Fit Method (dB/cm/MHz)
P o w e r D iff e re n ce M e th o d (d B /c m /M H z)
FIG. 8 Com par i son of at ten u a tion co ef fi cient b us ing the power dif fer ence method and di rect fit method. The dot ted line de notes the equal value line.
How ever, this method also suf fers from some dis ad van tages when com pared to the ref er -ence phan tom-based di rect at ten u a tion co ef fi cient es ti ma tion method. For ex am ple, the power dif fer ence method re quires mea sure ment of the ax ial di men sion of the sam ple, which is not re quired with the di rect es ti ma tion method. This could be prob lem atic in cases where the ROI pos sess sim i lar back scat ter char ac ter is tics as the back ground. As de scribed in Eq. (9), when the at ten u a tion co ef fi cient for the back ground re gion in the sam ple phan tom is dif -fer ent from the at ten u a tion co ef fi cient in the ref er ence phan tom, we have to ac count for the power loss due to the at ten u a tion co ef fi cient dif fer ence.
For tu nately, in our ex-vivo plaque study, back scat ter co ef fi cients of the plaque sam ples are sig nif i cantly stron ger when com pared to the back ground gel a tin. In ad di tion, the sur -round ing gel a tin ma te rial was uti lized as the ref er ence phan tom, thereby avoid ing the above two dis ad van tages.
Due to the ro bust and ac cu rate com pu ta tion of the power spec trum from the gel a tin re -gions be low (and above) the ex-vivo plaque sam ple us ing the power dif fer ence method, at -ten u a tion co ef fi cient es ti mates ob tained are more ac cu rate when com pared to that ob tained us ing the di rect-fit based method. The di rect-fit method re lies on the com pu ta tion of the power spec tra from small over lap ping ROI’s, where par tial vol ume ef fects due to the smaller di men sion of the plaque sam ple pre vail, lead ing to the bias in the at ten u a tion co ef fi cient es ti -mated, which are ob served in fig ures 8 and 9. In ad di tion, the power dif fer ence method does not suf fer from vari a tions in the back scat ter ob served with the plaque sam ples, which also in tro duce er rors into the di rect-fit based method. How ever, it has to be noted that the power dif fer ence method pro vides only one-di men sional es ti mates of the at ten u a tion co ef fi cient while the di rect-fit method pro vides para met ric im ages or maps of the at ten u a tion co ef fi cient.
V. CON CLU SION
We pres ent at ten u a tion co ef fi cient es ti mates com puted over ex-vivo ex cised plaque sam ples ob tained from 44 pa tients. A power dif fer ence method is uti lized for ac cu rate and un bi -ased es ti ma tion of the at ten u a tion co ef fi cient slope for small ex-vivo plaque sam ples en cased in a gel a tin phan tom. This method ef fec tively elim i nates par tial vol ume ef fects and er rors in -tro duced from the lack of in for ma tion re gard ing the back scat ter co ef fi cient. The at ten u a tion co ef fi cient slope ob tained us ing the power dif fer ence method is sig nif i cantly lower than es -ti mates ob tained us ing the di rect fit based ref er ence phan tom method.
28 SHI ET AL
FIG. 9 His to gram of the at ten u a tion co ef fi cient b val ues ob tained us ing the (a) power dif fer ence method and (b) di rect fit method.
0 1 2 3 4 5 0 5 10 15 20 25 30 N u m b e r
b from Power Difference Method (dB/cm/MHz) 0 1 2 3 4 5 6
0 5 10 15 20 25 N u m b e r
b from Direct Fitting Method (dB/cm/MHz)
VI. AC KNOWL EDGE MENTS
The au thors would like to thank Dr. Tim o thy Hall for pro vid ing the Siemens Antares Sys -tem used for this study and Dr. James Zagzebski for pro vid ing the TM phan toms. We would also like to thank Ms. Pam Winne for co or di nat ing the dis tri bu tion of the ex cised plaque sam ples.
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