Vas cu lar elas tic ity from re gional dis place ment es ti mates

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1 ULTRASONIC IMAGING 5, 7-9 (3) Vas cu lar elas tic ity from re gional dis place ment es ti mates JEROME J. MAI, FERMIN A. LUPOTTI AND MICHAEL F. INSANA Department of Biomedical Engineering Uni ver sity of Cal i for nia Da vis, CA 9566 mfinsana@ucdavis.edu A recently-developed ultrasonic technique for measuring elastic properties of vascular tissue is evalu - ated using computer simulations, phantom and in vivo hu man mea sure ments. A time se quence of dis - place ment im ages is mea sured over the car diac cy cle to de scribe the spa tial and tem po ral pat terns of deformation surrounding arteries. This information is combined with a mathematical model to estimate an elas tic modulus. Com puter sim u la tions of ul tra sonic echo data from de formed tis sues are an a lyzed to de fine a sig nal pro cess ing ap proach. Mea sure ments in flow phan toms, with and with out ves sel-sim u lat - ing chan nel walls, pro vide an as sess ment of the ac cu racy and pre ci sion of this tech nique for vas cu lar elas tic ity mea sure ments. Fi nally, pre lim i nary re sults for the stiff ness in dex () in a study group of healthy hu man vol un teers are com pared with pre vi ously re ported data. We find that care ful mea sure - ment tech nique is re quired to con trol mea sure ment vari abil ity. KEY WORDS: Brachial ar tery; dis place ment es ti mates; phan tom elas tic ity; stiff ness in dex; ul tra sound; vas cu lar com pli ance.. IN TRO DUC TION One es sen tial func tion of healthy vasculature is the stor age of me chan i cal en ergy be tween cardiac pulses., Elastic arteries minimize the mean arterial pressure necessary to maintain con stant per fu sion. Ad vanc ing age and dis ease stiffen ves sel walls and in crease wall thick - ness, of ten pro duc ing sys temic hy per ten sion that dam ages or gan tis sues. 3 In vivo mea sure - ments of vas cu lar elas tic ity can help ex plain the causes of ath ero scle ro sis and hy per ten sion, and guide treat ment strat e gies. The mechanical properties of arteries are determined by the material properties and microstructure of the ves sel wall and sur round ing me dium. Large ar ter ies have three lay ers con tain ing col la gen, elastin, and smooth mus cle cells. 4, 5 Mus cle cells in flu ence dy namic vas cu lar prop er ties but af fect static me chan i cal prop er ties very lit tle. Most data in the lit er a - ture de scribe the ves sel s re sponse to static loads. The highly flex i ble elastin fi bers (.3 MPa stiff ness) dis trib ute forces uni formly over the lu men sur face. As the pulse pres sure peaks and the lu men reaches max i mum di am e ter, stress is pro gres sively trans ferred to the in flex i - ble col la gen fi bers ( MPa stiff ness). 7, 8 The mix ture of fi bers gives ar ter ies non lin ear me - chan i cal prop er ties over the phys i o log i cal range of pres sure. The dis tri bu tion of fi brous ma te ri als in ar ter ies var ies with po si tion of the ves sel in the body; ves sels lo cated fur ther from the heart tend to be less elas tic, stiffer and more mus cu lar. For ex am ple, in normotensive in di vid u als, the aorta and ca rot ids have highly elas tic me dia lay ers and there fore lumens that ex pand nearly lin early with pres sure. The more dis tal brachial and fem o ral ar ter ies have less elas tic, more mus cu lar me dia that re spond non - linearly by ex pand ing more at low pres sure than at high pres sure. Mea sure ments of car diac pulse wave ve loc i ties, lu men sizes and pres sures yield com mon in di ces de scrip tive of vas cu lar elas tic ity, and ul tra sonic im ag ing is widely used for these stud ies. 5, 9-3 Many meth ods use ul tra sound to track ves sel di am e ter changes dur ing the car /3 $8. Copy right 3 by Dynamedia, Inc. All rights of re pro duc tion in any form re served.

2 7 MAI ET AL diac cy cle, then mea sure sys tolic and di a stolic pres sures by in de pend ent means and com pute an in dex that is based on a math e mat i cal model of elas tic ity. Lon gi tu di nal de for ma tion of the ves sel is usu ally ig nored. How ever, it is dif fi cult to track the low-ul tra sonic-con trast lu - men-in tima sur face of the ar te rial wall, par tic u larly in older pa tients where the wall can be loosely teth ered to sur round ing tis sues. The high-con trast me dia-adventitia sur face is eas ier to track but the lu men can not be de fined with out a wall thick ness mea sure ment. We have pre vi ously de scribed a tech nique for mea sur ing the in stan ta neous de for ma tion of tis sues sur round ing pulsatile ves sels. 4 This pa per ex pands the tech nique by add ing elas tic mod els that pro vide es ti mates of stiff ness moduli and as so ci ated mea sure ment er rors. Three lev els of anal y sis of in ter nal de for ma tion are stud ied here. D echo sim u la tions of fer echo data with known de for ma tion but un der ide al is tic mea sure ment con di tions. Tis sue mea sure - ments were added to pro vide re al is tic con di tions but they are dif fi cult to ver ify by in de pend - ent means. Phan toms of fer a mid dle ground. The com bi na tion of these three ex per i men tal re sults is an a lyzed to as sess our abil ity to mea sure vas cu lar elas tic ity in vivo.. METH ODS Two ap proaches to math e mat i cal mod el ing of the me chan i cal be hav ior of blood ves sels un der static loads are used; one is a rig or ous model of a sim pli fied lin ear-elas tic tube and the other is an em pir i cal model based on lab o ra tory mea sure ments of blood ves sels.. Linear-elastic media Volterra and Gaines 5 de rived con sti tu tive equa tions for a hol low chan nel of uni form lin - ear-elas tic ma te rial that is sub jected to a static transmural pres sure. Al though blood ves sels are com plex mul ti lay ered struc tures, this sin gle-layer model serves to pre dict prop er ties of sim ple flow phan toms with well de fined flow ge om e try and tis sue-like ma te rial prop er ties, en abling the as sess ment of ul tra sonic mea sure ment re li abil ity un der ex per i men tal con di - tions. The com pli ance of a purely elas tic flow-chan nel ma te rial that is ho mo ge neous and iso tro pic is a sim ple func tion of Young s modulus, E. The chan nel is as sumed to be a thick walled, straight, cy lin dri cal tube of length ori ented per pen dic u lar to the z-axis (Fig. ). Ini - tially at equi lib rium, the cy lin dri cal chan nel has in ner and outer ra dii r and r, with wall thick ness h = r r. 6, 7 Uni form pres sures p and p are then ap plied to the in side and out side of the chan nel. The equi lib rium chan nel di am e ter changes in re sponse to the transmural pres sure P = p p by an amount pro por tional to E. The ex tra mu ral pres sure p can rep re sent a re ac tive stress from the ma te ri als sur round ing the fi nite-thick ness chan nel as the chan nel ex pands. Thus, p may de pend on me chan i cal prop er ties of ma te ri als out side the chan nel wall. The ini tial state for an elas tic ar tery places r and p at a min i mum, cor re spond ing to end di - as tole in the car diac cy cle; at peak sys tole, r and p are max i mum. In prac tice, how ever, there will be a time lag be tween the extrema of r and p de ter mined by the pulse-wave ve loc - ity and viscoelastic prop er ties of the ar ter ies. 6 Gel a tin phan toms are known to be lin ear elas - tic for low-am pli tude har monic stress stim uli at fre quen cies in the range of Hz. 7 There fore, the fol low ing anal y sis, which as sumes elas tic me dia, is ex pected to be more pre - dic tive of phan tom mea sure ments than of ar ter ies in vivo. Nevertheless, measurement errors produced in either situation will be similar. Stress com po nents in cy lin dri cal co or di nates are la beled r,, and z. In fig ure, the l-axis is along the length of the ves sel, whereas z-axis is the ax ial depth of the cross-sec tional im ag ing plane and is in te grated in our equa tions later. Geo met ric sym me try and ma te rial

3 VASCULAR ELASTICITY 73 l z r u(r) r p p FIG. The chan nel is as sumed as be ing a thick-walled cyl in der, with ini tial in ner and outer ra dii r and r and wall thick ness h = r - r. Uni form pres sures p and p are then ap plied to the in side and out side of the chan nel. u(r) is the ra dial dis place ment of the wall at r dis tance away from the cen ter. Depth z is the dis tance away from the trans - ducer. is the an gle be tween the di rec tion of u(r) and the ax ial line. l-axis is along the length of the ves sel, where the ends of the chan nel are re strained. h uni for mity per mit the rea son able as sump tion that r and are in de pend ent of, and the shear stress r = (Fig. ). The dis place ments in po lar co or di nates cor re spond ing to r,, and z are u, v, and w. An gle-in de pend ent stresses im ply a zero an gu lar dis place ment, v =. The ends of the ves sel are as sumed to be teth ered to the sur round ing me dium, pre vent ing move ment along the l-axis; con se quently, w = and, thus, a two-di men sional plane-strain prob lem is con sid ered. For these con di tions and at ra dial po si tion r r r, the relationships among strains, stresses, dis place ments, and po si tion are: 3 du r r dr E u r E l z E ( ( ( ), r r z z ) ) () where is Pois son s ra tio of the wall ma te rial. Be cause of the cy lin dri cal ge om e try, the an - gular strain is non zero even though the an gu lar dis place ment is zero. Volterra and Gaines 3 found the cy lin dri cal com po nents of stress from the Airy stress func tion in a lengthy der i va - tion. As sum ing the bound ary con di tions r (r ) = p and r (r ) = p, and re ar rang ing the last line of Eq. () to elim i nate z from the first two equa tions, the fol low ing re la tion ships be - tween pres sure and stress were found: As sum ing incompressibility ( =.5) in the ap plied pres sure range and let ting p p, the elas tic (Young s) modulus of the wall is found in terms of ex per i men tally mea sur able quan - ti ties by com bin ing Eqs. () and (),

4 74 MAI ET AL r z r r ( p p ) r p r r r r r r ( p p) r p r r r r ( r p r p ) r r. r p r r p r () Eq. (3) is used in the Re sults sec tion be low to es ti mate the elas tic modulus of the rub ber tub ing wall in the flow phan tom (E rt ). 3P r r E ru( r) r r r r r (3) The ex pres sion for a wall-less flow chan nel, e.g., a cy lin dri cal hole in the gel a tin phan tom where r > r, is found from Eq. (3), E g 3P( t) r lim E r ru( r, t ) r r (4) E g is the Young s modulus of the gel a tin. Ex plicit time de pend ence is in di cated to sug gest Eq. (4), which is de rived for static loads, nev er the less re mains valid even if the pres sure and dis place ment vary slowly with time be cause gel a tin is a Hookean solid un der these con di - tions. How ever, Eq. (4) is un likely to pre dict dy namic be hav ior in viscoelastic me dia such as ar ter ies pulsed at car diac rates. Eq. (3) can be re lated to the widely used pres sure-strain modulus, E p = p / (u/r ), found through out the lit er a ture 8, 9 by as sum ing a thin walled ves sel, h/r < and r = (r + r ) / to find E 3r E / 4h p (5) Eq. (5) links our phan tom mea sure ments to ar te rial elas tic ity in di ces found in the lit er a - ture, whereas Eqs. (3) and (4) en able com par i son of Young s modulus es ti mates of the phan - tom from in de pend ent ul tra sonic and me chan i cal mea sure ments, as shown be low. E p ig nores the de pend ence of elas tic modulus on ves sel di am e ter and wall thick ness, yet is use - ful in measurement situations where accurate measurements of h and r are un avail able. A re sult iden ti cal to Eq. (5) us ing a pulse-wave ve loc ity mea sure ment is il lus trated in Lehmann 9 and Bergel. These sum ma rize the ba sic equa tions for lin ear-elas tic vas cu lar me - dia.. Nonlinear elastic media Lin ear elas tic ma te ri als yield Young s modulus mea sure ments that are con stant at all ap - plied stresses. In the pres sure range of our ex per i ments, gel a tin phan tom ma te ri als are iso - tro pic, lin ear and elas tic. How ever, ar ter ies ex hibit non lin ear prop er ties un der nor mal phys i o log i cal con di tions as a re sult of their lay ered struc ture. 5, 6 Tanaka and Fung have

5 VASCULAR ELASTICITY 75 shown that there is a non lin ear re la tion ship be tween modulus and stress dur ing ten sile tests of the ar tery seg ments and that the cir cumfer ential and lon gi tu di nal prop er ties are dif fer ent. Within the phys i o log i cal range where the elas tic modulus in creases pro por tion ally with ten - sion, how ever, a sim ple equa tion re lates ten sile stress T along a cir cumfer ential seg ment to the stretch ra tio = + : dt d ( T ) (6) where and are con stants. is usu ally larger (less elas tic) in pe riph eral ar ter ies than in cen tral ar ter ies. Solv ing Eq. (6) for T shows an ex po nen tial re la tion ship be tween ten sile stress and the stretch ra tio, T ( ) T e (7) where (T, ) is a point on the stress-strain curve where Eq.( 6) is valid for the ex per i ment be ing con sid ered. Tak ing the nat u ral log a rithm of Eq. (7) and re ar rang ing fac tors gives ( ln T ) /( T ) (8) If from in Eq. () is used to rep re sent the ten sile stress T in the ves sel wall at r = r and p > p, then T = p (r + r ) / (r - r ) is pro por tional to the intraluminal pres sure. Sub sti tut ing this ex pres sion into Eq. (8) and set ting =, =, (p - p ) max = P s (sys tole) and (p - p ) min = P d (diastole), then ln( P / P ) u( ln( P / P ) D s d s d r ) / r ( D D ) / s d d (9) This ex pres sion shows that the ad di tional as sump tions re duces to the stiff ness in dex pro - posed by Kawasaki et al, 3 where D s and D d rep re sent the ar tery di am e ter at sys tole and di as - tole re spec tively. Lehmann et al 9 found the stiff ness in dex to be in de pend ent of pres sure in normotensive sub jects but not for pa tients at risk for vas cu lar dis ease. Val ues of the stiff ness in dex, for healthy vol un teers, are re ported here and com pared with pub lished data. is unitless and not di rectly com pa ra ble to an elas tic modulus. How ever, it is de rived from ob - ser va tions (Eq. (6)) and thus ac counts for non lin ear prop er ties of the ves sel tis sue within the limitations of the assumptions..3 Displacement estimation method We estimate displacement using a strain imaging algorithm 3 mod i fied for im ag ing vas cu - lar de for ma tion. Lo cal dis place ments are de ter mined by com par ing pairs of rf data frames ac quired at dif fer ent stages of de for ma tion. Lo cal strains can thus be cal cu lated from dis - place ments mea sured along the ul tra sonic beam axis. The al go rithm is de signed to first es ti - mate lo cal dis place ments on a coarse scale to im prove pre ci sion of mea sure ments made at a sec ond finer scale. A -D sum-ab so lute-dif fer ence companding pro cess, which also ac - counts for trans ducer and pa tient mo tion, first de tects and re cords the coarse scale dis place -

6 76 MAI ET AL ments and warp the echo fields ac cord ingly. With the avail able higher sen si tiv ity and sam pling along the beam axis, finer scale ax ial dis place ments are then es ti mated from the warped echo fields us ing -D cross cor re la tion. The re sults from both stages are then summed to gether to yield ax ial dis place ment es ti mates. The ax ial dis place ment is given by u z = u cos and the ax ial strain is = du / dz given the ge om e try shown in fig ure. Dis place - z z ment to ward the trans ducer is ar bi trarily de fined as pos i tive while dis place ment away from trans ducer is neg a tive. Pulse prop er ties and the sizes of the companding and cor re la tion data win dows de ter mine the spa tial res o lu tion and noise in the fi nal dis place ment and strain im - ages.. mm x. mm data win dows search ing in. mm x 3. mm re gions of the echo fields are used for companding. The length of the -D cor re la tion win dows ap plied is. mm, ex cept when spec i fied..4 Echo sim u la tion To eval u ate dis place ment er rors, the al go rithms were first tested on sets of sim u lated rf echo sig nals re corded through the cross sec tional di am e ter of a wall-less flow chan nel. The -D scat ter ing func tion for the phan tom is mod eled as a col lec tion of ran domly-po si - tioned, spa tially-uncorrelated point tar gets. Out side the flow chan nel (graph ite-gel a tin), the scat ter ing func tion is a(r, t i ), and in side the flow chan nel (blood-mim ick ing fluid) the scat - ter ing func tion is b(r, t i ). Both scat ter ing func tions are zero-mean, wide-sense sta tion ary (WSS), white Gaussi an pro cesses that rep re sent ob ject scat ter ers at dis crete mea sure ment times. To re flect the weaker scat ter ing from fluid, we set the ra tio of vari ances var(a)/var(b) to 3 or 3 db. The ob ject func tion at time t i is a( r u( r, ti )) ; f ( r) i b( r, t ) ; i r r u( r, t ) r r u( r, t ) i i i,,.. () Ob ject scat ter ers are dis placed de pend ing on their lo ca tion and mea sure ment time ac cord - ing to Eq. (4), which shows the ra dial dis place ment pro file is in versely pro por tional to the distance (r) from the cen ter of the chan nel, where max i mum dis place ment u max = 3r P max /E at r = r and =,. We se lected t as the ref er ence time such that u(r, t ) = and a(r, t i ) for i > is the dis placed ver sion of a(r, t ). In this sig nal model, wave forms are in di vid u ally piecewise WSS but jointly nonstationary with the fol low ing ob ject cor re la tion func tion, Fi nally, the sim u lated echo sig nal g(r) is ob tained by convolving the ob ject f(r) with a lin - ear shift-in vari ant im ag ing sys tem hav ing im pulse re sponse h(r): E g ( r) dr' h( r r') f ( r') n ( r) i f i i var( b) ä i ä( r r') ; r r * ( r) f ( r') Ea ( r, t ) a ( r', t ) ; r r and r' r u( r, t ) i i ; otherwise i () () where n is an ad di tive, sig nal in de pend ent, white Gaussi an noise pro cess iden ti cal to b. Sig nals in the intraluminal re gion sim u late ech oes from high ve loc ity blood flow ing nor - mal to the im age plane. The length of the intraluminal re gion is u max larger at P max than the ini tial.7 mm at P min. The im pulse re sponse sim u lates a broad band Gaussi an-apodized, 7. MHz lin ear ar ray with a Gaussi an pulse. Sim u lated data are sam pled at 57.6 Msamples/s,

7 VASCULAR ELASTICITY 77 (a) (b) FIG. (a) Set-up of the wall-less chan nel phan tom. ( b) Sam ple B-mode im age of the cross-sec tion of the phan - tom. and a set of 3 in de pend ent wave forms is sim u lated. Two cor re la tion win dow lengths,. mm and.7 mm, are used to il lus trate the ef fect of vary ing win dow size. Sim u la tion data en - abled com par i sons of true and es ti mated dis place ments to as sess mea sure ment er rors un der ideal con di tions..5 Ultrasound data ac qui si tion Dig i tized in-phase and quad ra ture (I/Q) echo data are re corded at 5 fps from a Siemens Elegra sys tem us ing a 7.5 MHz lin ear ar ray trans mit ting 7. MHz broad band pulses. Ech oes are dig i tized at 36 Msamples/s, de mod u lated and down sam pled by a fac tor of.5 be fore be - ing trans ferred to a PC. I/Q sig nals are later remod u lated and upsampled to 57.6 Msamples/s to re pro duce rf data for off-line pro cess ing. Un like the sim u la tion data, ad ja cent wave forms in the re corded echo data frames are par tially cor re lated. Any par tial vol ume ef fects caused by the out-of-plane beam width are min i mal with re spect to dis place ment es ti mates since the ves sel is as sumed to de form only in the ra dial di rec tion and only cross-sec tional views are ob tained..6 Flow phan toms Two ul tra sonic flow phan toms were con structed: one with a wall-less flow chan nel and the other with a la tex wall. The bulk ma te rial of both phan toms is a con gealed ma trix of an i - mal-hide gel a tin in which a fine graph ite pow der is ran domly sus pended (83.93% dis tilled wa ter, 7.7% n-propanol, 5.4% an i mal-hide gel a tin pow der (75 bloom),.5% form al de - hyde, and 3.6% graph ite pow der). Con struc tion de tails of this stan dard phan tom ma te rial are de scribed else where. 4, 7, 8 The attenuation coefficient of the phantom material was.9 db/cm and the speed of sound was 567 m/s at 7.5 MHz when mea sured in dis tilled wa ter at o C. Young s modulus E g of the gel a tin was mea sured via the in den ta tion test de scribed by Kargel et al 9 and found to be 7.4 kpa. Each phan tom con tained a straight cy lin dri cal flow chan nel, 3.75 mm in di am e ter, lo - cated near the cen ter of the gel a tin block. Phan tom I (Fig. a) has a wall-less chan nel that is formed by cast ing a brass rod into the gel a tin block that is later re moved and filled with a weak sus pen sion of corn starch as blood mim ick ing fluid. The chan nel in phan tom II (Fig. 3a) is lined with la tex tub ing (7 mm long, r = 3.75 mm in ner di am e ter, h =.794 mm wall-thick ness, Hygenic Hytone, Kent Elas to mer Prod ucts, Kent, OH, USA). Gel a tin phan - toms are cast into acrylic cyl in ders, 75 mm in di am e ter and 5 mm in height, to pro vide rigid sup port and to act as an chors for the rigid plas tic in lets and out lets to the chan nels. The top

8 78 MAI ET AL (a) (b) FIG. 3 (a) Set-up of the walled chan nel phan tom. (b) Sam ple B-mode im age of the cross-sec tion of the phan tom, with shadow trail ing the rub ber tub ing. and bot tom sur faces of the phan tom are cov ered by a thin flex i ble plas tic film that min i mizes des ic ca tion while pro vid ing acous tic cou pling to the trans ducer with min i mal trans mis sion loss. Hy dro static pres sure in wall-less flow phan tom Hy dro static pres sure was ap plied to the chan nel in a con trolled en vi ron ment to mea sure chan nel-wall ex pan sion u as a func tion of pres sure P. The zero pres sure wa ter height was es tab lished by let ting wa ter move freely through the un sealed ends of the chan nel when the phan tom was com pletely sub merged in wa ter. The echo frame ac quired at this zero pres - sure was used as the ref er ence frame for gen er at ing dis place ment es ti mates. The hy dro - static pres sure was gen er ated by con nect ing one end of the chan nel to a vari able-height wa ter col umn while seal ing off the other end (Fig. a). Af ter seal ing off the out let of the chan nel, wa ter was added to the col umn at cm in cre ments to a max i mum height of 5 cm (.7 mmhg). Pro longed sub mer sion in wa ter was avoided dur ing ex per i ments to pre vent change in phan tom elas tic ity caused by wa ter dif fu sion. E cho data were ac quired at a fixed im ag ing plane and in creas ing pres sure. Fig ure b pres ents a sam ple B-mode im age of the cross sec - tion of the phan tom chan nel. Hy dro static pres sure in walled flow phan tom Prior to data ac qui si tion, the flow chan nel was filled with wa ter for two days to al low air trapped in the la tex wall to dis solve. Since la tex rub ber is much stiffer than gel a tin, the ex - pan sion of the walled chan nel is cre ated by con tin u ously pump ing wa ter into one end of the tub ing with a peri stal tic pump while seal ing the other end (Fig. 3a). The chan nel grad u ally in creased in di am e ter while echo data were con tin u ously re corded. The pres sure in side the chan nel (p ) was also re corded (Medex Log i Cal pres sure trans ducer, Pu ri tan-bennett Co. PB4 pa tient mon i tor). The echo data frame ac quired at at mo spheric pres sure was the ref - er ence frame used to cal cu late dis place ments. A B-mode im age of the cross-sec tional view (Fig. 3b) shows the acous tic shad ow ing cased by the la tex tube. Eqs. ()-(4) ap ply since the pres sure changes were slowly in tro duced to ap prox i mate static equi lib rium. To cal cu late the elas tic modulus of the la tex tub ing via Eq. (3), p must be known. We es ti - mate p by as sum ing it is a re ac tive stress from the gel a tin act ing on the la tex tub ing as the chan nel ex pands. 5 As sum ing con ti nu ity of the outer la tex-gel a tin sur face, p is the pres sure re quired to ex pand a wall-less gel a tin chan nel with in ner ra dius r by the same amount as the outer la tex sur face at r. Thus, p = E g u(r )/3r, where E g is the elas tic modulus of the gel a tin

9 material and u(r ) is the dis place ment of the outer wall of the la tex tub ing. Al though u(r ) is com pa ra ble to the dis place ment from the in ner wall of the la tex tub ing, we found p << p since E g is ~ times smaller than the elas tic modulus given by man u fac turer; there fore, p is as sumed to be neg li gi ble. Ten sile test of rub ber tub ing VASCULAR ELASTICITY 79 A ten sile test was used to mea sure the elas tic modulus of the la tex tub ing. The mea sure - ment set-up was based on a 3D mo tion sys tem, con trolled by a com puter pro gram im ple - mented in LabView (Na tional In stru ments, Aus tin, TX, USA), and a dig i tal scale (6 bits, 3 sam ples/s, mg force res o lu tion, Den ver In stru ment, Den ver, CO, USA) that dis places neg li gi bly when ten sile force is ap plied. To study the ef fects of sam ple ge om e try and vis - cous re sponse, three sam ples of the same la tex tub ing with dif fer ent ge om e tries were used to mea sure Young s modulus: a closed piece of tub ing, a piece of tub ing cut open into a small sheet and a thin strip of la tex. Sam ples were preloaded by stretch ing them %. The sam ple length at this point, L, is man u ally mea sured. The sub se quent elon ga tion ap plied to the tub - ing sam ple was re corded by the LabView com puter pro gram to cal cu late the elas tic modulus via the en gi neer ing stress-strain curve. Then a cy clic elon ga tion (L) of the sam ple (3 cy - cles of a si nu soi dal mo tion at.3 Hz with a peak-to-peak elon ga tion of 5 mm) was si mul ta - neously re corded along with the ap plied force (F). The Young s modulus of the rub ber tub ing (E rt ) is cal cu lated as: E rt = (F /A )/(L /L ) (3) where A is the ini tial cross-sec tional area of the sam ple. The mean value for the three la tex sam ples is ± 6 kpa for strains greater than 6% dur ing the stretch ing phase. Our mea - sured value is about twice the mean value of 655 ± 7 kpa quoted by man u fac turer..7 In vivo brachial ar tery Hu man sub jects were ex am ined us ing an In sti tu tional Re view Board ap proved pro to col. Brachial ar tery cross-sec tional im ages are ac quired from the un der side of the up per right arm of seated sub jects as shown in fig ure 4a. The weight of the arm is sup ported by a fix ture that ori ents the trans ducer scan plane so that the ves sel and the sur round ing tis sue can be clearly vi su al ized on the B-mode dis play (Fig. 4b). Sub jects were asked to hold their breath and min i mize vol un tary move ment dur ing ac qui si tion. Echo frames were re corded at 5 fps for a pe riod cov er ing about 5 car diac cy cles. The frame with the small est ar te rial di am e ter in each cy cle was se lected as the ref er ence frame for dis place ment es ti ma tion. Sys tolic and di - astolic arterial pressures were later obtained with a sphygmomanometer near the ultrasonic measurement site..8 Average angle-compensated displacement method Ul tra sonic mea sure ments are most sen si tive to dis place ments oc cur ring along the beam axis z. Con se quently, only the ax ial com po nent u z of ra dial dis place ments is es ti mated with our al go rithm. For uni form chan nel ex pan sion, the ra dial dis place ment is found from its ax - ial com po nent us ing the equa tion u(r) = u z (r, )/cos, where is an an gle with re spect to the z axis as shown in fig ure. z is the depth of the field point from the trans ducer sur face and r is the dis tance from the cen ter of the chan nel; they are par al lel at =,. Al though u z (r, ) = u(r), the echo noise lim its es ti ma tion pre ci sion. Er rors are re duced by averaging estimates over seg ments,

10 8 MAI ET AL (a) 33 mm FIG. 4 (a) Set-up of the in vivo brachial ar tery im ag ing. (b) Sam ple B-mode im age of the cross-sec tion of the brachial ar tery where the ul tra sound trans ducer is lo cated at the top of the B-mode im age. u ( r) N u ( r, ) z cos( ) u ( r, ) z cos( ) (4) where we found that =/6 yields ro bust es ti mates. N is the num ber of dis place ment es ti - mates in the sum at the dis tance r; this value de pends of echo sam pling. Since N is small for small r, es ti mates near the chan nel wall con tain fewer sam ples. Dis place ments in re gions above the chan nel [-, ] and be low the chan nel [, +] may be treated sep a rately to main tain directionality and de tect asym met ric ex pan sion..9 Statistical anal y sis The pre ci sion of our tech nique was com pared to a widely used method for es ti mat ing lu - men di am e ter in volv ing im age seg men ta tion of B-mode im ages. 9, 3 Ten man u ally-seg - mented frames at both sys tolic and di a stolic pres sures were used to es ti mate lu men diameters and arterial wall displacements; these parameters were also used to calculate the stiff ness in dex. Co ef fi cients of vari a tion (in %) are pre sented for intra- and inter-ob server com par i sons. 3. Echo sim u la tion 3. RE SULTS Two sets of sim u lated chan nel dis place ments were pro duced, with u max =.7 mm in fig ure 5 and u max =.4 mm in fig ure 6, both within the range of ar te rial wall dis place ments., 3 Dis - place ments were mod eled to de crease with dis tance from the cen ter of the chan nel ac cord ing to Eq.( 3). Dis place ments are mea sured us ing the -D lo cal companding and the -D cross-cor re la tion es ti ma tor with a cor re la tion win dow of ei ther. mm (Figs. 5a, 6a) or.7 mm (Figs. 5c, 6c). The ver ti cal dot ted lines in the fig ures in di cate the lo ca tion of the predis - place ment chan nel walls. Fig ure 5a and 5c show the mean de tected dis place ments and stan - dard de vi a tions over 3 noise less ech oes along the -D chan nel di am e ter when the edge of the sim u lated chan nel wall is dis placed out wardly by u max =.7 mm, re spec tively pro cessed with. mm and.7 mm cor re la tion win dows. Fig ures 5b and 5d show the dif fer ence be -

11 VASCULAR ELASTICITY 8 a) b) c) displacement (mm) d) depth (mm) FIG. 5 Av er aged dis place ments com puted from 3 sets of sim u lated echo data plot ted as a func tion of im age depth, where u max =.7 mm and cor re la tion win dow lengths (a). mm and (c).7 mm. Two stan dard de vi a tions (± std) are plot ted as the gray ver ti cal bars. Dif fer ences be tween known and es ti mated dis place ments are also plot ted for cor re la tion win dows of lengths (b). mm and (d).7 mm. In this and sub se quent fig ures, the trans ducer is lo - cated at the left. tween the ex pected (i.e., mod eled, u max =.7 mm) dis place ment and the de tected dis place - ments us ing cor re la tion win dows of. mm and.7 mm, re spec tively. Sim i lar re sults are pre sented in fig ure 6, but for a larger mod eled dis place ment u max =.4 mm at the ves sel wall. There is an un deres ti ma tion of dis place ment near the chan nel in ter face that ex tends into the outer scat ter ing me dia a dis tance that de pends on the pulse length, the cor re la tion win dow length and the am pli tude of the mod eled dis place ment. The large de vi a tions in side the chan - nel lu men show the ech oes are com pletely uncorrelated frame-to-frame. Fig ures 5 and 6 provide a measure of displacement measurement accuracy and precision. 3. Phantom stud ies Wall-less flow phan tom Fig ure 7a shows the mea sured dis place ment pro file u z along the cross sec tional di am e ter of the phan tom chan nel un der 3 cmh O pres sure and pro cessed with a. mm cor re la tion

12 8 MAI ET AL a).4 b) c) displacement (mm) d) depth (mm) FIG. 6 Av er aged dis place ments com puted from 3 sets of sim u lated echo data plot ted as a func tion of im age depth, where u max =.4 mm and cor re la tion win dow lengths (a). mm and (c).7 mm. Two stan dard de vi a tions (± std) are plot ted as the gray ver ti cal bars. Dif fer ences be tween known and es ti mated dis place ments are also plot ted for cor re la tion win dows of lengths (b). mm and (d).7 mm. win dow. The ver ti cal dot ted lines near the cen ter of these plots rep re sent the lo ca tion of the chan nel wall at min i mum pres sure. Fig ure 7b pres ents the mean with two stan dard de vi a - tions of the an gle-com pen sated dis place ment u( r) (Eq. 4). The sim i lar ity of fig ures 7a and 7b sug gest that u z (r, ) u(r). Also, the mea sured dis place ment com pares well with the con - stant/r curves (black dot ted lines in figure 7b); dis place ment is in deed in versely pro por tional to dis tance from the wall. Phan tom re sults are very sim i lar to sim u la tion re sults, sug gest ing that simulations are predictive of the simple soft-tissue displacements. Fig ure 8 shows the mean and stan dard de vi a tion of the change in chan nel size as a func tion of ap plied hy dro static pres sure mea sured us ing a cor re la tion win dow of. mm and.7 mm, compared to an averaged manual segmentation (ten trials of manual segmentation at each frame of B-mode im age to es ti mate chan nel di am e ters). Mean mea sured dis place ment us ing a small cor re la tion win dow cor re sponds to the man ual seg men ta tion better than a larger cor - re la tion win dow that blurs the dis place ment more and gives an un der es ti ma tion for high strain re gions. A lin ear re la tion ship be tween the change in lu men di am e ter and the ap plied in ter nal pres sure is ob served here, as pre dicted by Eq. (4). How ever, our echo-sig nal dis - place ment es ti ma tor is bi ased to ward low val ues as the win dow length in creases.

13 VASCULAR ELASTICITY 83 a) b) displacement (mm) displacement (mm) depth (mm) FIG. 7 (a) Axial displacement u z along the cen ter of the wall-less flow chan nel un der p = 3-cm H O pres sure. (b) Mean and two stan dard de vi a tion (± std) er ror bars for the av er aged an gle-com pen sated dis place ment com pared to the the o ret i cal func tion constant/r (black dot ted lines). Fig ure 9 pres ents the mean and two stan dard de vi a tions of the elas tic modulus for the gel a - tin ma te rial as a func tion of dis tance from the chan nel wall (r-r ) at p = 3 cmh O. Mean dis - place ment es ti mates (Eq. (4)) are ap plied in the cal cu la tion of the elas tic modulus (Eq. (4)). The av er age elas tic modulus within the first 5 mm of the ves sel wall is E g = 7.67 ±.4 kpa, in close agree ment with 7.4 kpa, the value mea sured from the in den ta tion test (dot ted line in figure 9). Walled flow phan tom In fig ure a, the change in tub ing in ner di am e ter (u(r )) was es ti mated from the echo sig - nals us ing a. mm cor re la tion win dow as a func tion of p. A lin ear re la tion ship can be ob - served between diameter and pressure. As above de scribed in the Meth ods sec tion, p is con sid ered neg li gi ble; there fore, us ing these data at and Eq. (3), the elas tic modulus of the tub ing can be ob tained as a func tion of pres sure in side the chan nel (Fig. b). The av er age elas tic modulus of the tub ing over the whole time se ries is 3 kpa, which is about twice the modulus listed by the man u fac turer of 655 kpa, but within % of the value we ob tained from in de pend ent ten sile mea sure ments, kpa. 3.3 In vivo brachial ar tery Fig ure a shows an ex am ple echo wave form re corded near the cen ter of the brachial ar - tery at di as tole. The lu men of the ar tery, marked be tween the dot ted gray lines, is eas ily rec - og nized as the low am pli tude re gion at the cen ter of the plot. Sig nals in side the lu men are re flec tions of the ar te rial walls and ech oes from red blood cells. Fig ure b shows the mea - sured dis place ment pro file along the cen ter of the brachial ar tery, pro cessed with di a stolic and sys tolic frames us ing a. mm cor re la tion win dow. Fig ure c pres ents the mean and two stan dard de vi a tions of the an gle-com pen sated dis place ment pro file. The max i mal down ward dis place ment cor re sponds to the lo ca tion of the pos te rior wall (right of the ves - sel), al though the dis place ment deep in the tis sue is not zero as ex pected. Con versely, the dis place ment near the trans ducer is zero, but the an te rior wall does not match with an eas ily iden ti fied max i mal up ward dis place ment. Fig ure b and c show asym met ric dis place - ments on the two sides of the ar tery. This com mon ap pear ance of asym me try is an over all

14 84 MAI ET AL change in diameter (mm) Manual segmentation Corr. win. mm Corr. win.7 mm pressure (cm H O) FIG. 8 The change in wall-less chan nel di am e ter is plot ted as a func tion of ap plied hy dro static pres sure. Gen er - ated from the same data set, the three plots rep re sent the re sult of us ing. mm cor re la tion win dow dis place ments estimate,.7 mm correlation window displacements estimate, and averaged B-mode manual segmentation. Two stan dard de vi a tions (± std) are in cluded for each plot. While man ual seg men ta tion s stan dard de vi a tion is cal cu - lated from a sin gle ob server s tri als, the other two plots stan dard de vi a tions are from an gle-com pen sated dis - placements at r. 5 elastic modulus, Eg (kpa) distance from channel wall (mm) FIG. 9 The es ti mated mean ± std for the elas tic modulus of the phan tom gel a tin E g is plot ted as a func tion of dis - tance from the chan nel wall (r-r ). The in ter nal pres sure p = 3 cmh O. The dot ted hor i zon tal line is an in de pend ent modulus measurement. shift in po si tion caused by large com pres sion of the skin sur face by the ul tra sound trans - ducer. Al though the mean an gle-com pen sated dis place ment es ti mate is bi ased away from the ar tery, a sim i lar con stant/r be hav ior pre dicted by Eq. (3) can still be ob served. As ex - pected, re gions far ther away from the trans ducer have nois ier dis place ment es ti mates due to re duced echo SNR. Noisy but nonzero up ward dis place ments, due to re verbs from the ar te - rial wall, are ob served in the lu men, which can be eas ily mis taken as dis place ment of the ar - terial wall.

15 VASCULAR ELASTICITY. change in diameter (mm) a) b) modulus (kpa) pressure (kpa) FIG. (a) The estimated change in latex tube inner diameter is plotted as a function of the intra-luminal. (b) The elastic modulus of the tube is calculated using the measured pressure and estimated displacement at the channel wall plotted as a function of p. The gray dotted line ( kpa) shows the elastic modulus value obtained independently. a) - b) disp (mm). -. c) disp (mm) depth (mm) 5 3 FIG. (a) Rf data at the brachial artery for subject, with the gray dotted lines showing the lumen. (b) Axial displacement at the brachial artery between diastole and systole. (c) The estimated mean and two standard deviations averaged angle-compensated displacement. Table summarized the parameters measured from the right brachial artery of four healthy male volunteers between the ages of 4 and 7. The change in arterial diameter is calculated as the difference between the upward displacement at the proximal wall and the

16 86 MAI ET AL Change in diameter (mm) D avg displacement D displacement manual segmentation -. down ward dis place ment at dis tal wall, since down ward dis place ments are treated as neg a - tive val ues. The change in di am e ter of the brachial ar tery mea sured dur ing one car diac cy cle for sub ject is plot ted in fig ure, and com pared with the av er aged an gle-com pen sated dis - place ment and that found by man ual seg men ta tion of the cor re spond ing B-mode im ages. Re sults pre sented in fig ure are qual i ta tively com pa ra ble to nor mal brachial ar tery pres - sure pro files. 3 The mea sured pres sure and di am e ter val ues from ta ble are mostly within one stan dard de vi a tion of the mean listed val ues in lit er a tures for that age group. 5, 33 How - ever, our calculated stiffness indices ( apw ) are much higher and more vari able than those pre - vi ously re ported ( = 8.68 ± 3.79 in Kawasaki et al 5 ). The stiff ness in dex based on man ual lu men seg men ta tion data ( man ual ) is also pre sented in ta ble as well as ves sel wall dis place - ment. 3.4 Sta tis ti cal anal y sis frame (at 5 fps) FIG. The change in brachial ar tery di am e ter dur ing one car diac cy cle for sub ject is plot ted, us ing dis place - ment along cen ter ax ial line (dashed line), av er aged an gle-com pen sated dis place ment (solid line), and B-mode man - ual segmentation (dotted line). Val ues ob tained for the intra- and inter-ob server com par i son based on man ual lu men seg - men ta tion are pre sented in ta ble and 3, re spec tively. Intra-ob server vari abil ity is pre sented for the di a stolic ar te rial di am e ter for four ob serv ers and for all sub jects (ta ble ); sim i lar vari - abil ity was found for sys tolic di am e ter mea sure ments but is not pre sented here. For inter-ob - server com par i son, di a stolic (D d ) and sys tolic (D s ) lu men di am e ters as well as ar te rial wall displacement (D s -D d ) are pre sented (ta ble 3). Intra- and inter-ob server variabilities (in %) are ob tained as the stan dard de vi a tion over the mean of each pa ram e ter. As ex pected, intra-ob server vari abil ity is smaller than inter-ob server vari abil ity. 4. DISCUSSION Ar te rial lu men size is dif fi cult to track pre cisely us ing seg mented B-mode im ages be cause the amount of dis place ment is smaller than the im age res o lu tion. The intimal sur face of the ves sel is de tected for this pur pose with lim ited suc cess, as edge de tec tion in ul tra sound B-mode im ages is hin dered by speckle, poor qual ity edge def i ni tion, low echo SNR from acous tic shad ow ing and large op er a tor vari abil ity.

17 VASCULAR ELASTICITY 87 TA BLE Mea sured brachial ar tery pa ram e ters and mean ± one stan dard de vi a tion for four sub jects: age, sys tolic P s and di a stolic P d blood pressures, diastolic arterial diameter and diameter change D s - D d, and stiff ness in dex as based on the an te rior and pos te rior wall dis place ments ( apw ), on manual lumen segmentation ( manual ) and on twice the dis place ment of the pos te rior wall ( ppw ). Sub ject Sub ject Sub ject 3 Sub ject 4 Mean ± Std Age (years) ±.5 P s (mmhg) ± 8 P d (mmhg) ± 8 D d (mm) ±.3 (D s -D d ) apw (mm) ±.4 apw ±.7 (D s -D d ) manual (mm) ±.3 manual ± (D pws -D pwd ) ppw (mm) ±. ppw ±.7 TA BLE Val ues ob tained for the intra-ob server com par i son (in %) based on man ual lu men seg men ta tion of di a - stolic B-mode im age (D d ) for four ob serv ers and for all sub jects. Intra-observer variability for D d (%) Sub ject Sub ject Sub ject 3 Sub ject 4 Observer Observer Observer Observer The echo sim u la tion re sults pre sented in this study pro vide in sights on the de sign lim i ta - tions of our method. Dis place ment is un der es ti mated in highly strained re gions near the lu - men when large cor re la tion win dow lengths are se lected for noise sup pres sion (Figs. 6, 8). The need for noise sup pres sion is great est near the lu men where tis sue mo tion is great est. To main tain high echo SNR near the ves sel and re duce decorrelation noise so that small cor re la - tion win dows may be ap plied, we rec om mend use of 5-7 MHz trans duc ers. Lower fre quen - cies have a re duced sen si tiv ity to mo tion and higher fre quen cies in crease decorrelation er rors be cause of at ten u a tion and am bi gu ity er rors for dis place ment es ti mates. De pend ing on the mag ni tude of ves sel wall move ment and depth in the body, the trans ducer should be se lected to al low the use of the short est pos si ble cor re la tion win dow length. The max i mum change in brachial ar tery di am e ter ob served in our lim ited study was in the range of. mm to.3 mm (Ta ble ). 5, 33 Cen ter fre quen cies with wave lengths in this range (5-7.5 MHz) are well suited for this es ti ma tion. From the wall-less flow phan tom dis place ment pro file (Fig. 7), an off set in dis place ment was ob served near the edges of the phan tom. The un con fined sur faces of the phan tom may

18 88 MAI ET AL TA BLE 3 Val ues ob tained for the inter-ob server com par i son (in %) based on man ual lu men seg men ta tion of di a - stolic (D d ) and sys tolic (D s ) B-mode im ages, and ves sel wall dis place ment (D s -D d ) for all sub jects. Inter-ob server vari - abil ity (%) Sub ject Sub ject Sub ject 3 Sub ject 4 D d D s (D s -D d ) bulge out as the phan tom ex pands with the in creas ing chan nel pres sure. The to tal dis place - ment at the lu men wall ob tained as the sum ma tion of the mea sured dis place ment at the lu men wall (.8 mm) and the off set in dis place ment ob served at the edges of the phan tom (.35 mm) approaches the expected theoretical maximum displacement u max at the lu men wall of.94 mm by us ing Eq. () with E = 7.4 kpa and P = 3 cmh O. A lin ear re la tion ship was ob - served be tween the change in di am e ter and the ap plied intraluminal pres sure for the walled phan tom, which sug gests that the la tex tub ing has a lin ear elas tic be hav ior for the pres sure range ap plied (Fig. a). If a sim i lar sit u a tion ex ists in the more elas tic ar ter ies of the body, even for a lim ited pres sure range, then this tech nique could be used to mea sure lo cal intraluminal blood pres sure. The elas tic modulus mea sured ul tra son i cally for the la tex tub - ing cor re sponded closely to the value found from our ten sile mea sure ments, fur ther suggesting that ul tra sonic mea sure ments can pro vide ac cu rate es ti mates of ves sel Young s modu lus. The modulus for the rub ber tub ing de creased with in creas ing pres sure (Fig. b), con trary to con ven tional strain hard en ing. 34 This de crease could be at trib uted to the un der es ti ma tion in ves sel wall dis place ment at low-ex pan sion (low in ter nal pres sure) that is more likely to af - fect the modulus than the same er ror at larger ex pan sions. Highly scat ter ing con nec tive tis sues (fasciae) sur round ing the brachial ar tery, as seen in the B-mode im age (Fig. 4b), are likely to cre ate re ver ber a tions. Since some re ver ber ated ech oes may travel a far ther span than sin gle-scat ter ech oes, high am pli tude re ver ber a tions lead to es ti ma tion er rors. Re ver ber a tions were not an is sue in phan toms but did lead to un - usual re sults in vivo. The o ret i cally, in an im age where only the chan nel or ves sel is ex pand - ing, the ax ial (ver ti cal) cen ter of the chan nel can be found at the mid point be tween the lo ca tions with max i mum up ward and down ward dis place ments. How ever, lo cal max ima and min ima in the dis place ment pro file of ten ex ist within the lu men as a re sult of decorrelation due to blood flow and noise (Figs. b, c). A tis sue thresh old could be used to re ject sig nal from blood and thus cal cu late dis place ments based only on tis sue sig nal since the sig nal am pli tude from ves sel wall and sur round ing tis sue is of ten higher than that from blood and tis sue re verbs. An ap par ent over es ti mate bias on the stiff ness in dex with re spect to pub lished data may be ex plained by the de gree of trans ducer com pres sion ap plied to the arm. This com pres sion dis torts the ar te rial ex pan sion pat tern. Un for tu nately, we were un able to es ti mate this com - pres sive stress. How ever, for the pres ent study, the pos te rior ar te rial wall is likely to be less af fected by ex ter nal stresses than the an te rior wall. When we con sid ered only the pos te rior wall move ment, we ob tained a mean stiff ness in dex (.5 ±.7 in ta ble ) much closer to val - ues 8.68 ± 3.79 re ported by Kawasaki et al. 5 It is crit i cal to min i mize, or at least stan dard ize, the force of the trans ducer on the skin sur face. An other prob lem with in vivo im ag ing is the abun dant sources of sig nal decorrelation. Any mo tion caused by breath ing and un in ten - tional mus cle con trac tions in tro duces out-of-scan-plane mo tion, es pe cially in re gions far away from the trans ducer. Re frac tion, re ver ber a tion, and spa tially vary ing echo am pli tudes

19 VASCULAR ELASTICITY 89 all con trib ute to er rors in dis place ment es ti ma tion. Le sion for ma tion of the ar te rial wall or the pres ence of bone in the sur round ing tis sues may also cause the ar tery to ex pand asym - met ri cally. Ar ter ies are likely to ex hibit an over all shift in lo ca tion dur ing the car diac cy cle due to the vary ing bound ary con di tion and inhomogeneous tis sues in the sur round ing. Con - se quently, it could be very dif fi cult to se lect the cen ter of the ar tery to cal cu late an gle-com - pen sated ra dial dis place ments and thus in crease the vari a tion of the an gle-com pen sated dis place ment mea sure ment. The an gle av er ag ing method of Eq. (4) is most use ful in sit u a - tions where the echo SNR near a ves sel is low or the echo am pli tude is highly het er o ge neous. Ad di tion ally, al though care was taken to en sure that the trans ducer is per pen dic u lar to the arm, the trans ducer may still be placed at an an gle to the ar tery, caus ing the echo pro file of the blood ves sel to be el lip ti cal. None the less, in de pend ent ax ial dis place ment pro files of the cross sec tion of an ar tery can still be as sumed cor rect, sim i lar to stud ies done on the lon gi tu - di nal view of the ar tery. The D dis place ment field can pro vide in for ma tion about ex is tence of nonsym met ric ex pan sion of the ar tery by study ing the lo cal dis place ments in sur round ing re gions. Fur ther more, only D in for ma tion is avail able in the data frames to cor rect a prob - lem that is es sen tially 3D in na ture. Elec tronic and quantization noises are also well known sources that can de crease the sig nal cor re la tion. 35 Noise out side the sig nal band can be re - duced by band-pass fil ter ing the rf sig nals with a cor re spond ing in crease of echo SNR. Of course, it is the noise in the fre quency chan nels of the sig nal that is most crit i cal since it can - not be re duced by fre quency fil ter ing. 36 Since the band-lim ited echo SNR is high for most com mer cial sys tems (> db), the dis place ment es ti mates from echo sig nals for the in vi tro and in vivo stud ies would be slightly in flu enced by noise in the sig nals. 37 The ef fect of these sources of decorrelation noise is re vealed by the in crease of the stan dard de vi a tions of the dis place ment pro file from the wall-less flow phan tom (ideal con di tion, Fig. 7b) to the in vivo brachial ar tery (Fig. c). The mean dis place ment and two stan dard de vi a tions at the ves sel wall of the wall-less flow phan tom (.8 ±.6 mm) and the brachial ar tery (. ±. mm) give er rors of 7.5% and 6.6%, re spec tively. From man ual lu men seg men ta tion, low intra-ob server variabilities were found (~.5% in ta ble ), which may be ex plained by the ten dency of the ob server to mark al ways the same spot as the ves sel wall and by the low num ber of data frames at each stage of the car diac cy - cle. The inter-ob server vari abil ity for di a stolic and sys tolic di am e ter was also low (~ 5%), which com pares with pre vi ously re ported data by Sonka et al; 38 how ever, the vari abil ity of ar te rial wall dis place ment was found very high and rang ing from 3% to 8% (ta ble 3). Such high variabilities from man ual seg men ta tion will in tro duce large vari a tions in any pa - ram e ter used for the as sess ment of vas cu lar elas tic ity based on ar te rial wall dis place ment. Al though apw and man ual are highly bi ased from the nor mal value for our group of vol un teers, the in di vid ual stiff ness in dex and the mean and stan dard de vi a tion val ues ob tained by both meth ods cor re spond to each other. As man ual lu men seg men ta tion is the gold stan dard method for such pur poses, the agree ment found here dem on strates that our method is able to track ves sel wall dis place ment well. Pre vi ous re ports have noted a cor re la tion be tween ab nor mal i ties in the in tima-me dia thick ness (IMT), 39 and flow-me di ated di la tion (FMD) of the brachial ar tery and the pres ence of cor o nary ar tery dis ease (CAD). 4-4 FMD (ex pressed as vasodilation in re sponse to an in - crease of blood flow) is a noninvasive tech nique that uses an in ter nal or ex ter nal hy per emia stim u lus to study vasculature health. Blood ves sels have the ca pac ity to re spond to phys i cal stim u lus such as the in crease in shear stress at the ves sel wall by the in crease in blood flow fol low ing a hypoxia via ar te rial oc clu sion and to chem i cal stim u lus such as cir cu lat ing hor - mones (e.g. vasopressin) or me di a tors re leased by plate lets (e.g. se ro to nin), such stim uli pro mote the re lease of vasodilating ni tric ox ide. En do the lium de rived ni tric ox ide is the prin ci pal me di a tor for FMD 4 and arterial elasticity. 43 Such stud ies of ten use lon gi tu di nal in -