Im por tance of Ax ial Com pres sion Ver i fi ca tion to Cor rect In ter pre ta tion of Ax ial-shear Strain Elastograms In Breast Le sions

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1 ULTRASONIC IMAGING 32, 1-15 (2010) Im por tance of Ax ial Com pres sion Ver i fi ca tion to Cor rect In ter pre ta tion of Ax ial-shear Strain Elastograms In Breast Le sions ARUN K.THITTAI, BELFOR GALAZ AND JONATHAN OPHIR The Uni ver sity of Texas Med i cal School De part ment of Di ag nos tic and Interventional Im ag ing Ultrasonics Lab o ra tory Hous ton, TX Jon a than.ophir@uth.tmc.edu We have re cently shown that the ap pear ance of Ax ial-shear Strain Elastograms (ASSEs) for the case of loosely-bonded, el lip ti cal in clu sions (like fibroadenomas in the breast) is unique and there fore has the po ten tial to dis tin guish be nign fibroadenomas from ma lig nant tu mors in the breast. The ASSEs were ob - tained us ing quasi-static ax ial com pres sions, in a like man ner as in nor mal ax ial-strain elastography. How ever, strict ax ial com pres sion is achieved most of ten only by com puter-con trolled ac qui si tions and not by more prac ti cal free hand ac qui si tions. In a free hand ac qui si tion, the frame se quence may con tain sev eral frames that do not ex pe ri ence strict ax ial com pres sion but may also ex pe ri ence ro ta tion or shear de for ma tions. In this pa per, we dem on strate the im por tance of ac count ing for the type of de for ma tion ap plied to a tar get tis sue for the cor rect in ter pre ta tion of the re sult ing ASSEs. Us ing free hand ac quired in vivo ex am ples, we show that such a frame ex pe ri enc ing ro ta tion or shear de for ma tions re sults in ASSEs that may po ten tially be mis in ter preted. This may be far more det ri men tal com pared to the cor re - spond ing ax ial elastogram frames that may only suf fer from in fe rior im age qual ity in terms of con - trast-to- noise ra tio (CNR). Fur ther, we show that we may be able to elim i nate these frames from a se quence of free hand ac quired in vivo breast le sion data by im ple ment ing a spe cial fil ter ing scheme, thus sig nif i cantly im prov ing the re li abil ity of the re main ing ASSE frames. This work fur ther sug gests that un der free hand con di tions, frames have to be checked for the pres ence of un de sir able de for ma tions. KEY WORDS: Ax ial-shear strain; ax ial strain; be nign breast dis ease; elastogram; elastography; fibroadenoma; frame fil ter; im ag ing; le sion; ma lig nant; ul tra sound. IN TRO DUC TION Ul tra sound (US) elastography is now a well-es tab lished tech nique that uti lizes frames ob - tained be fore and af ter a quasi-static com pres sion to vi su al ize the stiff ness vari a tions within inhomogeneous tis sues. 1, 2 The im age of the ax ial strain dis tri bu tion due to quasi-static com - 1, 3, 4 pres sion is com monly known as ax ial strain elastogram or ax ial elastogram. We have shown that in ad di tion to im ag ing the ax ial strain, one can im age the ax ial-shear strain dis tri - bution at clinically-useful image levels. 5, 6 The im age of the ax ial-shear strain due to quasi-static ax ial com pres sion is re ferred to as an ax ial-shear strain elastogram (ASSE). 6, 7 Us ing sim u la tions, gel a tin-phan tom ex per i ments and breast le sions in vivo, we have pre - vi ously dem on strated that the ax ial-shear strain dis tri bu tion pat terns around an in clu sion is di rectly in flu enced by tis sue bond ing at the in clu sion-back ground bound ary. 5, 6 In fact, re - sults from the ini tial study to eval u ate the po ten tial of ASSEs to dif fer en ti ate be tween fibroadenomas (thought to be loosely-bonded to sur round ing host tis sue) 8 and ma lig nant tu - mors (thought to be firmly-bonded to the sur round ing tis sue) 8 in the breast have been very prom is ing. 6 How ever, all prior work on ASSEs has as sumed the in clu sion shape to be cir cu - lar. In a series of finite-element simulations, we have recently demonstrated 9-12 experimental val i da tion in phan toms, as well as in ini tial ex am ples from ret ro spec tive in vivo data that the /10 $18.00 Copy right 2010 by Dynamedia, Inc. All rights of re pro duc tion in any form re served.

2 2 THITTAI ET AL ax ial-shear strain zones near firmly-bonded el lip ti cal or elon gated in clu sions oc cur only out - side these in clu sion. More im por tantly and clin i cally rel e vant, ax ial-shear strain zones oc - cupy most of the in te rior por tion of the in clu sion ex clu sively in loosely-bonded el lip ti cal in clu sions that are in clined with re spect to the com pres sion axis, even at small not-nor mal ori en ta tions and that have even a slight ec cen tric ity. The ASSEs ob tained from the ma lig - nant and be nign cases in vivo ap peared to be in gen eral agree ment with our sim u la tion and ex per i men tal re sults, sug gest ing that gen er at ing ASSEs of such le sions may have im por tant implications. Specifically, axial-shear strain fill-in inside an inclusion may be a unique sig - na ture of loosely-bonded con di tions at not-nor mal ori en ta tions of el lip soi dal or elon gated in clu sions. Thus, this fill-in may have po ten tial as a marker of benigness of be nign breast le - sions (e.g., fibroadenomas) that are known to be stiff, elon gated and loosely bonded to the host tis sues. We pos tu late that the use of this spe cific sig na ture may in crease the neg a tive pre dic tive value (NPV) of stan dard prac tice ul tra sound eval u a tions of be nign breast le sions. How ever, pre vi ous dem on stra tions of ASSE in tis sue-mim ick ing phan tom ex per i ments and in vivo breast le sion ex am ples uti lized a com puter-con trolled dig i tal mo tion con trol ler (DMC) to ap ply pre cise ax ial com pres sion. 5-7 In a prac ti cal clin i cal set ting, one may de sire a free hand ac qui si tion in stead. In such cases, there are sev eral fac tors that in flu ence the re sult - ing elastographic qual ity (both ax ial and ax ial-shear strain). Over the last few years, sev eral schemes have been pro posed in the lit er a ture to im prove the im age qual ity of ax ial elastograms from se quence of free hand-ac quired frames for real-time feed back as well as near-real time offline pro cess ing. 17 More re cently, Basarab et al 16 investigated the effect of the di rec tion of ax ial com pres sion on the ax ial elastogram frames that are ac quired free hand from thy roid nod ules. They showed that for frames in which the di rec tion of ax ial com pres - sion was not nearly-ax ial, the re sult ing ax ial strain elastograms were of in fe rior CNR. They cor rectly ar gue that it is not un com mon to find sev eral such frames in a se quence of free handac quired frames and there fore not elim i nat ing these frames could de grade the whole scan se - quence. We be lieve what was de scribed as di rec tion of ax ial com pres sion therein could more broadly be de scribed as type of de for ma tion. Nev er the less, we hy poth e size that such ef fect of the type of de for ma tion on ASSE could have im por tant con se quences in the in ter pre ta tion of ax ial-shear strain dis tri bu tions. There fore, it may be come nec es sary to ac count for the type of de for ma tion dur ing post pro cess ing to re li ably uti lize ASSEs in a rou tine clin i cal set - ting. In this pa per, we will dem on strate the ef fect of the type of de for ma tion on the re sult ing ASSE through ex am ples from free hand-ac quired in vivo breast le sion data. There af ter, we de scribe a method to iden tify the type of de for ma tion in an in di vid ual frame and a method for elim i nat ing such frames from se quences of freehand-acquired frames. In vivo data ac qui si tion and pro cess ing MA TE RI ALS AND METH ODS The data used in this work were cho sen from our ex ist ing rf da ta base of in vivo breast fibroadenomas and can cers ac quired free hand. In to tal, the da ta base con sisted of 33 cases but, at the time of this study, we had ac cess to only about six cases at our lo ca tion. The data were ac quired at the Uni ver sity of Ver mont by Brian Garra us ing a Sonix-500RP (Ultrasonix Med i cal Cor po ra tion, Rich mond BC, Can ada) scan ner op er at ing at 10 MHz. The num ber of cine-loop frames saved for each of the case dif fered but there were at least 200 frames in the cases used for this study. Fur ther, some cases had more than one ac qui si tion cine-loop saved and we ran domly se lected one such se quence. All the cases were histopathologically

3 IM POR TANCE OF AX IAL COM PRES SION TO COR RECT IN TER PRE TA TION OF ASSEs 3 (a) (b) (c) (d) Fig. 1 Simulation show ing ex am ple im age of ax ial dis place ment that dem on strates the ori en ta tion of ax ial-dis - place ment con tour for (a, b) ax ial-com pres sion and (c, d) ax ial-com pres sion along with ax ial-shear de for ma tion for (a, c) ho mo ge neous and (b, d) inhomogeneous tar get. conirmed and de-identified. For the pur poses of this pi lot study, we iden ti fied ex am ple cases of a can cer and fibroadenoma that sat is fied the fol low ing cri te ria: the sonographic le sion shape was ap prox i mately el lip ti cal and the ma jor axis of the le sion was not nor mally ori ented with re spect to the di rec tion of com pres sion. These cri te ria were cho sen be cause of the po - ten tially im por tant and unique ASSEs for these cases, as dem on strated in our pre vi ous pa pers Suc ces sive frames were treated as pre- and postcompression and the dis place ment map was com puted us ing a pro pri etary mul ti level coarse-to-fine 2D block match ing al go rithm implemented in Matlab. 18,9 The ASSEs were gen er ated by ex tend ing the stag gered-straines ti ma tion method as de scribed in the ref er enced pa pers. 5, 19 A 55 me dian fil ter ing scheme was ap plied to the dis place ment maps be fore es ti mat ing the ASSE. Compression type identification The ax ial dis place ment map ob tained through fi nite el e ment mod el ing (FEM) for a ho mo - ge neous and inhomogeneous tar get when sub jected to ei ther ax ial com pres sion de for ma tion or ax ial-shear de for ma tion is shown in fig ure 1 to dem on strate the dif fer ence in the ori en ta - tion of the con tour lines. Note that FEM was done us ing ANSYS as de tailed else where. 5 As - sum ing that the US trans ducer (with/ with out com pres sor plate) is used as a com pres sion device in freehand acquisitions, a typical axial-displacement map within an elastically-ho - mo ge neous tar get sub jected to ax ial com pres sion will have dis place ment con tour lines par - al lel to the sur face (Fig. 1a). How ever, in the case of an inhomogeneous tar get, the par al lels may be lo cally dis torted around the in clu sion (Fig. 1b). The dis place ment con tour lines may not be par al lel if the type of de for ma tion ex pe ri enced by the tar get dif fers from ax ial com - pres sion (Figs. 1c, d). There fore, de fin ing a met ric for the de vi a tion from par al lel ism of the dis place ment con tour may pro vide a way to de ter mine if the ap plied de for ma tion con sti tutes the de sired ax ial com pres sion or an un de sired de for ma tion like shear or ro ta tion. Note that the global shear or ro ta tion due to im proper ex ter nal com pres sion is un de sir able, whereas the lo cal shear or ro ta tion due to the shape, ori en ta tion and bound ary con di tion of the in clu sion is the de sired sig na ture. There fore, the met ric that mea sures the de vi a tion from par al lel ism of the dis place ment con tour should be more sen si tive glob ally than lo cally. The method we em - ployed to estimate the average deviation from parallelism (ADP) is described below.

4 4 THITTAI ET AL Fig. 2 Ex per i men tal ex am ple show ing an im age of ax ial dis place ment that dem on strates seg ment ing of the frame into 33 re gions of be nign breast fibroadenoma. The dis place ment map at a fine-level from each frame is seg mented into nine re gions, as shown in fig ure 2, and sub jected to the fol low ing com pu ta tions. di,1 Di mean max( d - d i,1 i,2, d i,2, ) d i,2 max( d - d i,2 i,3, d i,3, ) d i,3 max( d - d i,3 i,1, d i,1 ) (1) ADP MaxD i for i = 1, 2, 3. (2) where d i,j is the av er age of all the ax ial dis place ment pix els in the re gion (i, j) that have cor re - spond ing cor re la tion co ef fi cient value >0.75. The thresh old on the cor re la tion co ef fi cient was used to avoid low-qual ity dis place ment pix els from en ter ing the com pu ta tion. D1, D2 and D3 cap ture the dif fer ence be tween the av er age dis place ment val ues in re gions lo cated at dif fer ent depths (Eq. 1). The ra tio nale be hind the method is that the av er age dis place ment in each re gion at a par tic u lar depth will be sim i lar for an ax ial com pres sion and there fore will re sult in low val ues for D1, D2 and D3. The max i mum of these three val ues is used as a mea - sure that in di cates the amount of ADP (Eq. (2)). Note that ADP is nor mal ized such that it ranges from 0 to 1. Clearly, val ues close to 0 in di cate more par al lel ax ial-dis place ment con - tour, as would be ex pected from an ideal ax ial com pres sion, and are de sir able. Per cent age fill-in of ax ial-shear strain in side le sion Re call that as de scribed in the ref er ence 9, we would ex pect ax ial-shear strain fill-in only in loosely-bonded fibroadenomas that are el lip ti cally-shaped, ori ented le sions and are not in firmly-bonded ma lig nant tu mors, when sub jected to ax ial com pres sion. There fore, the pres - ence or ab sence of ax ial-shear strain fill-in in side a le sion may be a unique sig na ture of the type of le sion, and its in ter pre ta tion is crit i cal. If there is fill-in of ax ial-shear strain that is not

5 IM POR TANCE OF AX IAL COM PRES SION TO COR RECT IN TER PRE TA TION OF ASSEs 5 (a) (b) Fig. 3 Plot of the met ric ADP ob tained for each frame of the free hand -cquired se quence from (a) fibroadenoma and (b) ma lig nant tu mor. due to bond ing con di tions but rather to un de sired tis sue de for ma tion, ASSEs may po ten - tially be mis in ter preted. There fore, it be comes nec es sary to see the ef fect of de for ma tion on the fill-in of ax ial-shear strains in side the le sion. In or der to study this ef fect, we cal cu lated the per cent age area of the le sion that ex pe ri enced ax ial-shear strain. This was cal cu lated by us ing the for mula shown be low in Eq. (3). (3) where the ax ial-shear strain thresh old was ar bi trarily cho sen as 40% of the frame-av er age ax ial strain value. Here again, only pix els with cor re spond ing cor re la tion co ef fi cient val ues greater or equal to 0.75 were in cluded in the cal cu la tion. The le sion area vis i ble in the sonogram was out lined by one of the au thor (BG) and used in the com pu ta tions. Note that the le sion out line can also be ob tained from the cor re spond ing ax ial elastogram if the sonographic le sion is not com pletely vis i ble. How ever, in this pa per, the case schosen had an un am big u ous sonographic le sion ap pear ance. Cine-loop postpro cess ing The met ric re lat ing to the qual ity of the ax ial com pres sion, ADP, and per cent age fill-in value were com puted for each of the frames from the se quence of a free hand-ac quired cine-loop. We im ple mented de for ma tion fil ter ing by im pos ing an ar bi trary thresh old on ADP. Apart from this fil ter ing, one could im ple ment var i ous other postpro cess ing schemes to im prove the elastographic (ax ial strain and ax ial-shear strain) im age-qual ity of the cine loop How ever, the scope of the cur rent work is lim ited to study the ef fect of the more fun - da men tal de for ma tion ac qui si tion pa ram e ter on ASSEs. There fore, we did not sub ject the frame se quence to any post pro cess ing be yond ap ply ing a per sis tence of six frames in or der to smooth interframe jit ter.

6 6 THITTAI ET AL (a) (b) Fig. 4 (Left) sonograms, (cen ter) ax ial dis place ment im ages and (right) ASSEs from a rep re sen ta tive frame with low value for ADP from (a) fibroadenoma and (b) ma lig nant tu mor in the breast. Fig. 5 (Left) sonogram, (cen ter) ax ial dis place ment im ages and (right) ASSEs from a rep re sen ta tive frame from ma lig nant tu mor case with high value for ADP. Ob serve a mis lead ing fill-in of ax ial-shear strain in side the tu mor due to the na ture of the de for ma tion. RE SULTS AND DIS CUS SION Fig ure 3 shows a plot of the met ric, ADP, for each of the 200 frames from an ex am ple case of a fibroadenoma and ma lig nant tu mor. This plot clearly dem on strates the ex is tence of sev - eral frames that ex pe ri enced ro ta tion/shear de for ma tion dur ing sup pos edly free hand, purely-ax ial com pres sion (in di cated by the peaks). Fig ure 4 shows the set of sonograms, ax ial-dis place ment map and ASSE from a rep re sen - ta tive frame at a low value of ADP (= 0.14 can cer; 0.18 fibroadenoma). Rec ol lect that value of ADP closer to 0 in di cates a purer ax ial-com pres sion. Ob serve that the dis place ment con - tour is par al lel to the sur face of com pres sion, as is typ i cal for ax ial-com pres sion. Fur ther, ob - serve the pres ence of high-con trast mar gins of op po site po lar ity along with fill-in of ax ial-shear strain in side the le sion for the case of fibroadenoma. There is no such fill-in of ax ial-shear strain in side a ma lig nant tu mor (Fig. 4b). The ASSE shown here for a free -

7 IM POR TANCE OF AX IAL COM PRES SION TO COR RECT IN TER PRE TA TION OF ASSEs 7 (a) (b) Fig. 6 Plot show ing the per cent age fill-in value for each of the frames (fibroadenoma ( ) and ma lig nant tu mor (-)) (a) be fore and (b) af ter re mov ing frames based on a thresh old of 0.25 for ADP. Fig. 7 Plot show ing the per cent age of frames that sur vive at a par tic u lar thresh old of ADP and have at least 50% of le sion fill-in with ax ial-shear strain. Ob serve that for a thresh old of ADP around , the fill-in oc curs only in fibroadenoma ( o ) and not can cer ( x ). hand-ac quired frame is con sis tent with the ASSE re ported ear lier by Thittai et al 9 for the frames ac quired through com puter-con trolled com pres sion. Fig ure 5 shows the set of sonograms, ax ial-dis place ment maps and ASSEs from a rep re - sen ta tive frame at a high value of ADP (= 0.65) for a ma lig nant case. Ob serve that the dis - place ment con tour is not as par al lel to the surface as the case shown in fig ure 4. It can be seen from the ASSEs that the fill-in of ax ial-shear strain oc curs even in the case of ma lig nant tu -

8 8 THITTAI ET AL mor. How ever, the ax ial-shear strain fill-in this case is most likely due to the ax ial-shear/ro - ta tion de for ma tion ap plied (look at the ax ial dis place ment con tours) and not due to le sion bound ary bond ing con di tions. This im age clearly dem on strates the need to con sider the type of de for ma tion to avoid misinterpretation of the ASSE. Fig ure 6a shows a plot of the per cent age fill-in value for each frame for the fibroadenoma and ma lig nant tu mor cases shown in fig ure 2. It can be seen that both the fibroadenoma and can cer have frames with high fill-in val ues but more such frames are found in the case of fribroadenoma. Fig ure 6b in cor po rates the ef fect of the type of de for ma tion by elim i nat ing frames that have ADP val ues greater than an ar bi trary thresh old of Ob serve that most of the frames that had fill-in due to un de sired de for ma tion got re moved in the case of ma lig - nant tu mor. The cine-loop movie of these two cases is posted on line (movie 1 & movie 2). Fig ure 7 sum ma rizes the ef fect of ADP by show ing the per cent age of frames that have at least 50% fill-in at dif fer ent thresh olds for ADP. Note that for each value of ADP the num ber of frames that sur vive is dif fer ent, i.e., smaller val ues im poses stricter cri te rion on the ax ial com pres sion, re sult ing in fewer frames, while larger val ues are more le nient and al low cap - ture of more frames. Ob vi ously, the per cent age of frames with fill-in will de pend on op er a tor training and experience as well as the fundamental model parameters of shape, orientation and le sion type. Nev er the less, it is clear that by ap pro pri ately ac count ing for the type of de - for ma tion by con trol ling the thresh old of ADP, we could gain greater cer tainty for the in ter - pre ta tion of the ASSE. CON CLU SIONS We have dem on strated through ex am ple of free hand-ac quired, breast-le sion data in vivo that the type of de for ma tion plays an im por tant role in the in ter pre ta tion of the re sult ing ASSE. It is clear from the re sults that dur ing free hand ac qui si tion, there may be some frames that do not ex pe ri ence the ide ally-in tended quasi-static ax ial com pres sion. We have shown that it is im por tant to iden tify such frames (pref er a bly in real-time) in or der to im prove the re - li abil ity of the cine loop and thus improve the diagnostic accuracy. AC KNOWL EDGE MENT This work was sup ported in part by NIH grants R21-CA and 1R21CA The in vivo sonographic data were ac quired and patho log i cally con - firmed by Brian Garra, MD from the Uni ver sity of Ver mont un der a sub con tract from the Uni ver sity of Texas with sup port from NIH Pro gram Pro jects P01-CA64597 and P01 EB REF ER ENCES 1. Ophir J, Céspedes I, Ponnekanti H, et al. Elastography: a method for im ag ing the elas tic ity of bi o log i cal tis - sues, Ul tra sonic Im ag ing 13, (1991). 2. O Donnell M, Skovoroda AR, Shapo BM. In ter nal dis place ment and strain im ag ing us ing ul tra sonic speckle track ing, IEEE Trans Ultrasonics Ferroelec Freq Cont 41, (1994). 3. Ophir J, Alam SK, Garra BS, et al. Elastography: ul tra sonic es ti ma tion and im ag ing of elas tic prop er ties of tis - sues, Proc Instn Mech Engrs (UK) 213, (1999).

9 IM POR TANCE OF AX IAL COM PRES SION TO COR RECT IN TER PRE TA TION OF ASSEs 9 4. Céspedes I. Elastography: Im ag ing of bi o log i cal tissue elas tic ity, Ph.D. Dis ser ta tion. (Uni ver sity of Hous ton, 1993). 5. ThitaiKumar A, Krouskop TA, Garra BS, Ophir J. Vi su al iza tion of bond ing at an in clu sion bound ary us ing ax ial-shear strain elastography: a fea si bil ity study, Phys Med Biol 52, (2007). 6. Thitaikumar A, Mobbs LM, Kraemer-Chant CM, Garra BS, Ophir j. breast tu mor clas si fi ca tion us ing ax ial shear strain elastography: a fea si bil ity study, Phys Med Biol 53, (2008). 7. ThitaiKumar A, Ophir J, Righetti R, Krouskop TA. Res o lu tion of ax ial-shear strain elastography, Phys Med BiBreol 51, (2006). 8. Fry KE. Be nign Le sions of the breast, CA Can cer J Clin 4, (1954). 9. Galaz B, Thitai Kumar A Ophir J. Ax ial-shear strain dis tri bu tions in an el lip ti cal in clu sion model: a sim u la tion study, Ul tra sonic Im ag ing (sub mit ted, 2010). 10. Thitai Kumar A, Galaz B, Ophir J. Ax ial-shear strain dis tri bu tions in an el lip ti cal in clu sion model: ex per i - men tal val i da tion and in vivo ex am ples with im pli ca tions to breast tu mor clas si fi ca tion Ul tra sound Med Biol 36, (in press, 2010). 11. Galaz B, ThitaiKumar A, Ophir J. Ax ial-shear strain dis tri bu tion in an el lip ti cal in clu sion model (Part I): a sim u la tion study, in Proc Eighth Internatl Con fer ence Ultrason Mea sure ment Im ag ing, p. 99 (Vlissingen, Zeeland, Neth er lands, 2009). 12. ThitaiKumar A, Galaz B, Ophir J. Ax ial-shear strain dis tri bu tion in an el lip ti cal model (Part II): Ex per i men - tal val i da tion and in vivo ex am ples with im pli ca tion to breast tu mor clas si fi ca tion, in Proc Eighth Internatl Con fer - ence Ultrason Mea sure ment Im ag ing, p. 100 (Vlissingen, Zeeland, Neth er lands, 2009). 13. Jiang J, T. Hall TJ, A. Sommer AM. A novel per for mance descriptor for ul tra sonic strain im ag ing: a pre lim i - nary study, IEEE Trans Ultrason Ferroelec Freq Contr 53, (2006). 14. Lindop JE, Treece GM, Gee AH, Prager RW. Frame fil ter ing for im proved free hand 3D US elastography, in Proc Fourth Internatl Con fer ence Ultrason Mea sure ment Im ag ing, p. 74 (Aus tin, TX, 2005). 15. Lindop JE, Treece GM, Gee AH, Prager RW. An In tel li gent in ter face for free hand strain im ag ing. Tech. Rept. CUED/F-INFENG/TR 578, (Cam bridge Univ. Dept. of En gi neer ing, May, 2007). 16. Basarab A, Lyshchik A, Grava C, Buzuloiu V, Delachartre P. Ul tra sound im age se quence reg is tra tion and its ap pli ca tion to thy roid nod u lar dis ease. J Sign Pro cess Syst 55, (2009). 17. Jiang J, Hall TJ, Sommer AM. A novel im age for ma tion method for ul tra sonic strain im ag ing. Ul tra sound Med Biol, 33, (2007). 18. Shi H, Varghese T. Two-di men sional multi-level strain es ti ma tion for dis con tin u ous tis sue. Phys Med Biol 52, (2007). 19. Srinivasan S, Ophir J, Alam SK. Elastographic im ag ing us ing stag gered strain es ti mates, Ul tra sonic Im ag - ing 25, (2002).