Sin gle-el e ment Fo cused Ul tra sound Trans ducer Method for Har monic Mo tion Im ag ing

Transcription

1 ULTRASONIC IMAGING 28, (2006) Sin gle-el e ment Fo cused Ul tra sound Trans ducer Method for Har monic Mo tion Im ag ing CAROLINE MALEKE, MATHIEU PERNOT AND ELISA E. KONOFAGOU Department of Biomedical Engineering Columbia University New York, NY ek2191@columbia.edu The harmonic motion imaging (HMI) technique for simultaneous monitoring and generation of ultrasound therapy using two separate focused ultrasound transducer elements was previously demonstrated. In this study, a new HMI tech nique is de scribed that im ages tis sue dis place ment in duced by a har monic radiation force using a single focused-ultrasound element. A wave propagation simulation model first indicated that, unlike in the two-beam configuration, the amplitude-modulated beam produced a stable fo cal zone for the ap plied har monic ra di a tion force. The AM beam thus of fered the unique ad van tage of sustaining the application of the spatially-invariant radiation force. Experiments were performed on gel - atin phantoms and ex vivo tis sues. The ra di a tion force was gen er ated by a 4.68 MHz fo cused ul tra sound (FUS) trans ducer us ing a 50 Hz am pli tude-mod u lated wave. A 7.5 MHz pulse-echo trans ducer was used to ac quire rf ech oes dur ing the ap pli ca tion of the har monic ra di a tion force. Con sec u tive rf ech oes were ac quired with a pulse rep e ti tion fre quency (PRF) of 6.5 khz and 1D cross-cor re la tion was per formed to es ti mate the re sult ing ax ial tis sue dis place ment. The HMI tech nique was shown ca pa ble of es ti mat ing stiffness-dependent displacement amplitudes. Finally, taking advantage of the real-time capability of the HMI technique, temperature-dependent measurements enabled monitoring of HIFU sonication in ex vivo tis sues. The new HMI method may thus en able a highly-lo cal ized force and stiff ness-de pend ent mea sure ments as well as real-time and low-cost HIFU mon i tor ing. Key words: Ablation; amplitude modulated; displacement; FUS; HIFU; harmonic motion imaging; monitoring; oscillatory; radiation force. IN TRO DUC TION Pal pa tion is rou tinely used by phy si cians to dis tin guish can cer ous tis sues from nor mal tis - sues in or gans such as the breast and the pros tate. This tech nique is ef fec tive be cause can cer - ous tis sues typ i cally have higher stiff ness com pared to that of nor mal soft tis sues such as the breast. 1 Over the past 20 years, re search ers have de vel oped elas tic ity im ag ing tech niques with var i ous forms of tis sue per tur ba tion meth ods for de tec tion of tis sue re sponse or tis sue elasticity. The tis sue per tur ba tion meth ods can be di vided into two groups: ex ter nal and in ter nal stim u lus meth ods. In the ex ter nal meth ods, the tis sues are ex ter nally com pressed (static) 2 or dy nam i cally ex cited us ing a vi bra tory de vice. 3-5 Krouskop et al. 3 ap plied an ex ter nal vi bra - tion at low fre quency (10 Hz) to the sur face of mus cle tis sue and es ti mated the re sult ing tis - sue ve loc ity us ing a Dopp ler-based tech nique. A sim i lar ap proach was later used in MR im ag ing. 4, 5 The dif fi cul ties in the ex ter nal method are the fact that they rely upon knowl edge of the bound ary con di tions for modulus re con struc tions and the in duced mo tion may not ef - fi ciently prop a gate to deeper tis sues, such as the liver /06 $18.00 Copy right 2006 by Dynamedia, Inc. All rights of re pro duc tion in any form re served.

2 SIN GLE-EL E MENT FO CUSED TRANS DUCER METHOD FOR HAR MONIC MO TION IM AG ING145 On the other hand, the in ter nal meth ods can pro duce a con cen trated force in a tar geted re - gion, deep in side the tis sue, and can be used for prob ing and an a lyz ing tis sue prop er ties point-by point di rectly or re motely within the tar geted re gion. 6 In 1990, Sugimoto et al. 7 were the first to use a fo cused trans ducer to pro duce an im pulse ra di a tion force that caused a lo cal ized static com pres sion deep in side tis sue spec i mens, such as the hu man liver, kid ney and heart mus cle. Their ob jec tive was to eval u ate lo cal ized tis sue stiff ness. The tis sue dis - place ment was mea sured as a func tion of time by us ing pulse-echo meth ods and ex hib ited an ex po nen tial de cay over time af ter the ap plied force was re moved. This mea sure ment tech - nique first in tro duced the idea of em ploy ing a fo cused trans ducer to gen er ate a force deep in - side the tis sue. Some years later, sev eral re search groups pro posed the use of an im pulse ra di a tion force to in duce brief me chan i cal ex ci ta tions lo cally and im age the re sult ing tis sue re sponse while rf data were col lected dur ing tis sue re lax ation (ARFI) 8-10 or shear wave prop - a ga tion, i.e., su per sonic shear im ag ing 11, 12 and shear wave elas tic ity im ag ing (SWEI). 13 In 1998, Fatemi and Green leaf 14 in tro duced ul tra sound-stim u lated acous tic emis sion (USAE) that used two con fo cal trans ducer el e ments of a spher i cally-fo cused an nu lar ar ray driven at slightly dif fer ent fre quen cies, f 1 and f The trans ducer they de signed pro duced a si nu soi dal mod u la tion of acous tic en ergy at the fo cus that re sulted in a lo cal os cil la tory ra di - a tion force. The re sult ing tis sue dis place ment pro duced a lo cal ized acous tic source that emit ted an acous ti cal sig nal re corded by a hydrophone. Fol low ing Fatemi and Green leaf s dis cov ery, fur ther stud ies have shown that an os cil la tory acous tic ra di a tion force can be gen - 11, 12, er ated in bi o log i cal soft tis sues at vari able depths within the tis sue. In ad di tion to mea sur ing tis sue dis place ments, the use of a fo cused trans ducer can be ad - van ta geous for an all-ul tra sound-based tech nique that can both gen er ate and mon i tor the treat ment dur ing high in ten sity fo cused ul tra sound (HIFU) ab la tion. In a pre vi ous study, the USAE tech nique was ap plied for mon i tor ing of HIFU ther apy us ing two sep a rate fo cused ul - trasound transducer elements at different frequencies (f 1 and f 2 ). 16, 20 Lizzi et al. 10 also de vel - oped a method to mon i tor the for ma tion of le sions dur ing HIFU ther apy us ing the im pulse ra di a tion force. They es ti mated the tis sue dis place ment dur ing HIFU ab la tion us ing the ARFI tech nique and showed that the dis place ment in duced by the ra di a tion force was much smaller in the co ag u lated tis sue than in the nor mal tis sue. A lim i ta tion of both afore men - tioned tech niques for ul tra sound ther apy mon i tor ing lies in the re quire ment to interrupt the treat ment in or der to es ti mate the tis sue dis place ments. In 2002, we de vel oped a new tech nique called har monic mo tion im ag ing (HMI) 17, 18 that uti lized the same trans ducer con fig u ra tion as that used for USAE but used a pulse-echo trans ducer and rf track ing to ac quire the ech oes dur ing os cil la tion of the tis sue and es ti mate the cor re spond ing dis place ments. The ad van tage of this tech nique is that it does not de pend on the acous tic prop er ties or is not as af fected by the acous tic noise dur ing sig nal ac qui si tion, as the USAE tech nique may be. Michishita et al. 19 used a sim i lar pulse-echo tech nique to es - ti mate small cy cli cal dis place ments of the sil i cone rub ber phan tom in or der to lo cally mea - sure its com plex elas tic modulus. The in tended goal of this tech nique was to mea sure the com plex elas tic modulus of tis sues on or close to the sur face such as the skin and the breast. The ul tra sonic trans ducer pro duced a low acous tic in ten sity (1W/cm 2 ) for force gen er a tion and was paused when dis place ment was mea sured. Thus, the mea sure ment of the sil i cone rub ber mo tion was not ob tained dur ing force ac ti va tion. Re cently, an im prove ment of the orig i nal HMI tech nique 17, 18 was shown us ing a sin gle-el - e ment FUS that was am pli tude-mod u lated (AM) 21 as op posed to two sep a rate el e ments pre - 17, 18 vi ously used. Thus, the new HMI tech nique could re quire a sin gle high power FUS beam for sonication and ra di a tion force gen er a tion and for es ti ma tion of the dis place ments dur ing the ap pli ca tion of the ra di a tion force. To our knowl edge, this is the only tech nique that can mea sure the me chan i cal re sponse dur ing the ap pli ca tion of the force.

3 146 MALEKE ET AL In this pa per, the po ten tial for the use of the HMI method for HIFU treat ment mon i tor ing is ex am ined. First, sim u la tions are per formed show ing that the AM beam of fers the ad van tage of sus tain ing the ap pli ca tion of the ra di a tion force at a con stant, sta ble fo cus within the tis sue re gion, un like with the pre vi ously-used two-trans ducer con fig u ra tion. Sec ond, ex per i ments are per formed in gel a tin phan toms and ex vivo por cine liver. This is to test whether HMI is ca pa ble of map ping the dis place ment am pli tude and phase shift of the ma te rial at high res o - lu tion. The dis place ment am pli tudes are mea sured at the lo ca tion of the ap plied force us ing a pulse-echo trans ducer. Given that the me chan i cal prop er ties of bi o log i cal tis sues change dur ing HIFU ab la tion, this tech nique could po ten tially be used for real-time mon i tor ing of the me chan i cal prop er ties of tis sues dur ing HIFU treat ment. 21 One ma jor ad van tage of this tech nique is that the dis place ment is mea sured dur ing the ap pli ca tion of the acous tic ra - di a tion force and HIFU ab la tion so that no in ter rup tion of the treat ment is re quired. METH ODS In or der to first iden tify the ad van tages of us ing an am pli tude-mod u lated FUS trans ducer ver sus the two-trans ducer con fig u ra tion, sim u la tions of the pres sure field were per formed. The pres sure fields were cal cu lated us ing the Field II sim u la tion pack age. 25 Two dif fer ent types of trans duc ers were de signed. The first was a sin gle-el e ment trans ducer op er at ing at 1 MHz cen tral fre quency with a 70 mm di am e ter and a fo cal length of 100 mm. A 1 MHz con - tin u ous wave with si nu soi dal am pli tude mod u la tion at 50 Hz was sim u lated for this trans - ducer. The sec ond trans ducer was a con fo cal and con cen tric trans ducer. It had two sep a rate el e - ments: the first el e ment had a di am e ter of 50 mm and a fo cal length of 100 mm. It was sur - rounded by the sec ond an nu lar el e ment that had an in ner di am e ter of 50 mm, an outer di am e ter of 70 mm and a fo cal length of 100 mm. A 1 MHz con tin u ous wave was sim u lated for the first el e ment and a MHz con tin u ous wave was sim u lated for the sec ond el e - ment. Both trans ducer types had the same to tal surface. For both sim u la tions, the sam pling fre quency was 100 MHz and the pres sure field p(x,z) was cal cu lated in a re gion around the fo cus of 40 mm (lat eral) x 60 mm (ax ial) with a pitch of 0.1 mm and a band width for both AM and con tin u ous waves of ap prox i mately 100%. The average acoustic intensity (I ave ) was then cal cu lated us ing the equa tion 26 I ave p k dz Z 2 2 / k 0 2 p cos Z f t kz cos 2 f t kz kp 2 dz 2Z 4k 2 p 4Z (1) where p de notes the pres sure and Z de notes the im ped ance. Thus, the in ten sity of the high power FUS beam with AM wave is half of the max i mum al low able in ten sity of the trans - ducer. Fig ure 1 shows the acous tic intensities emit ted by the two types of trans ducer con fig - u ra tions over one pe riod of os cil la tion. Since the acous tic ra di a tion force is lin early re lated to the acous tic in ten sity, these re sults show that, in the two-beam con fig u ra tion (Fig. 1(a)), the over lap ping, fo cused beams pro duced an acous tic ra di a tion force field con tin u ously mov ing across the fo cal re gion at the dif fer ence fre quency (f). On the other hand, the AM beam of fered the ad van tage of sus tain ing the ap pli ca tion of the ra di a tion force at the same sta ble fo cus within the tis sue through the en tire ex ci ta tion time (Fig. 1(b)). Our ex per i ments were performed on tis sue-mim ick ing phan toms and ex vivo tis sues. Gel - a tin ma te rial (Gel a tin 50 bloom, MP Biomedicals, Irvine, CA, USA) was used to con struct

4 SIN GLE-EL E MENT FO CUSED TRANS DUCER METHOD FOR HAR MONIC MO TION IM AG ING147 FIG. 1 (a) Simulated intensity map of acoustic radiation force produced by two overlapping, focused ultrasound beams at two dif fer ent fre quen cies, f 1 = 1 MHz and f 2 = MHz. The force field is shown ev ery 4 ms (top to bot tom). (b) Acous tic ra di a tion force mod u lated at 50 Hz pro duced by one fo cused ul tra sound trans ducer. the tis sue-mim ick ing phan toms. Five ho mo ge neous phan toms with dif fer ent elas tic moduli (20 kpa, 30 kpa, 40 kpa, 50 kpa, and 60 kpa) and a 20 kpa tis sue mim ick ing phan tom with a 40 kpa cy lin dri cal in clu sion were con structed. Phan tom prep a ra tion was com pleted us ing the fol low ing steps: de gassed, de-ion ized wa - ter and gel a tin pow der were mixed in a 500 ml so lu tion. The amount of gel a tin pow der was calculated according to reference 27: E gelatin 0.003C 2.09 (2) where E gel a tin de notes the Young s modulus of the gel a tin in kpa and C de notes the con cen tra - tion of gel a tin pow der in g/l. The con cen tra tion was var ied be tween 63 g/l and 107 g/l in or der to ob tain stiffnesses be tween 20 kpa and 60 kpa (Eq. 2). The mix ture was con stantly stirred and heated un til the tem per a ture reached 50 o C. The gel a tin pow der was as sumed to have been uni formly dis solved at this state. The mix ture was then placed into a waterbath for cool ing un til the tem per a ture de creased to 35 o C. Isopropanol and agar pow der were then added to the mix ture. Isopropanol was added to in crease cross-link ing and thus in crease the

5 148 MALEKE ET AL FIG. 2 Overview of experimental setup for the generation of harmonic acoustic radiation force and measurement of HMI displacement amplitude. melt ing point of the gel a tin while solid agar pow der was added to in duce scattering. Note that agar only bloomed at tem per a tures above 80 o C; thus, it did not con trib ute sig nif i cantly to the in crease of the phan tom stiff ness. The amount of agar pow der (Acros Organics, Geel, Bel gium) was equal to 10% of the to tal gel a tin pow der added. The stir rer was re moved from the mix ture when the tem per a ture reached 30 o C. The so lu tion was cov ered with plas tic wrap to min i mize de hy dra tion and was placed in a re frig er a tor for ap prox i mately 12 hours. Sim i - larly, ex vivo por cine liver was sub merged in a phos phate buf fered sa line (PBS) so lu tion and de gassed for 30 min utes prior to use for the ex per i ments. The ex per i men tal setup is shown in figure 2. The har monic ra di a tion force was gen er ated by a 4.68 MHz FUS trans ducer us ing an am pli tude-mod u lated wave. The di am e ter of the FUS trans ducer (Riv er side Re search In sti tute, New York, NY) and the ra dius of cur va ture were 84 mm and 90 mm re spec tively. A 7.5 MHz pulse-echo trans ducer with di am e ter of 12 mm was placed through the cen ter of the FUS trans ducer. This trans ducer de sign is safe be cause the FUS trans ducer is not di rectly fac ing the pulse-echo trans ducer. The pulse-echo trans ducer has a smaller di am e ter by seven times com pared to that of the FUS trans ducer; this will de crease the prob a bil ity of dam age by a high power FUS beam. In ad di tion, a sil i con rub ber/ab sorber (McMaster-Carr, Dayton, New Jer sey, USA) was placed be neath the spec i men in or der to re duce spec u lar re flec tions at the in terface be tween the spec i men and the bot tom of the con tainer. There fore, no heat ing of the pulse-echo trans ducer by the high power FUS beam was ob served in all the ex per i - ments performed. The goal of the new HMI tech nique is to pro duce a sin gle os cil la tory fre quency at the mod - u la tion fre quency f m. The mod u la tion in dex (m) is de fined as the ra tio of the max i mum to the min i mum volt age of the mod u lated sig nal. The con ven tional am pli tude mod u la tion has mod u la tion in dex m equal to 1 (i.e. 100% mod u la tion), which in di cates that the mag ni tude of the mod u lat ing sig nal is equal to that of the car rier sig nal. If this con ven tional am pli tude mod u la tion is ap plied to gen er ate the ra di a tion force, the re sult ing acous tic pres sure at the fo -

6 SIN GLE-EL E MENT FO CUSED TRANS DUCER METHOD FOR HAR MONIC MO TION IM AG ING149 FIG. 3 Illustration of amplitude-modulated signal process. (a) High-frequency input, (b) low-frequency modula tion (m 50), (c) AM sig nal out put of the func tion gen er a tor and (d) acous tic in ten sity gen er ated at the fo cus. cus would con sist of three os cil la tory fre quen cies, i.e., f c, f c ± f m, where f c and f m represent the car rier and mod u la tion fre quency, re spec tively. The car rier sig nal was thus overmodulated (m 50) to in duce os cil la tion of the re sult ing acous tic pres sure at the only de sired fre quency, i.e., f m (Fig. 3(c)). There fore, the sin gle-el e ment FUS trans ducer was driven by a 50 Hz am pli tude-mod u - lated wave with a high mod u la tion in dex (m 50) in or der to pro duce an acous tic pres sure os cil lat ing at the mod u la tion fre quency f m at the fo cus. The first func tion gen er a tor (Agilent (HP) 33120A, Palo Alto, Ca, USA) gen er ated the car rier sig nal given by X ( t) X sin(2f t) c c c (3) where f c was at 4.68 MHz and X c was the car rier sig nal am pli tude (Fig. 3(a)). The sec ond func tion gen er a tor (Agilent 33220A) gen er ated the low-fre quency mod u la tion sig nal given by X ( t) msin(2f t) m m (4) where f m was equal to 50 Hz and X m was a mod u la tion sig nal am pli tude (Fig. 3(b)). The re - sult ing mod u lated sig nal was then equal to X ( t) X ( t) 1 X ( t) c m (5) or, 1 msin2 f t sin2 f t X ( t) X c m c (6)

7 150 MALEKE ET AL FIG. 4 Over view of the real-time mon i tor ing method used in the ex vivo tissue experiment. (a) Continuous wave at f = 4.68 MHz for two sec onds, (b) am pli tude-mod u lated fre quency at f = 50 Hz for 100 ms (same as fig ure 3(c)). Se quence (a) is the sonication pe riod and se quence (b) is the im ag ing pe riod. Both se quences are al ter nated through - out for the en tire sonication time. There fore, the pres sure field (Fig. 3(c)) and acous tic in ten sity (Fig. 3(d)) os cil lated at the de sired mod u la tion fre quency f m of 50 Hz at the fo cus. Note that the ex ci ta tion pa ram e ters, such as the mod u la tion fre quency and in put power, af - fect the ra di a tion force pro file, which in turn also re lates to the dis place ment dis tri bu tion in the tis sue. There fore, a pre lim i nary ex per i ment was per formed us ing ex vivo por cine liver, where the mod u la tion fre quency f m was var ied from 20 Hz to 300 Hz us ing a fre quency sweep for 10 sec onds. The in ten sity of the high power FUS beam was set to 237 W/cm 2. If the am pli tude mod u la tion fre quen cies were be low 20 Hz, the es ti mated dis place ment im - ages would be at sig nif i cantly low res o lu tion and, thus, higher am pli tude mod u la tion fre - quency was pre ferred. The pre lim i nary ex per i ment showed that the dis place ment am pli tudes at the fo cus de creased rap idly at fre quen cies above 74 Hz, thereby mak ing it very dif fi cult to ac cu rately es ti mate dis place ment am pli tudes at higher fre quen cies, pos si bly due to higher damp ing ef fects. 16 This pre lim i nary study pro vided the re la tion ship be tween the fre quency mod u la tion and the tis sue re sponse. Hence, the op ti mal mod u la tion fre quency f m can be se - lected. A fre quency of 50 Hz was thus cho sen for the am pli tude mod u la tion fre quency in this ex per i ment. The out put of the func tion gen er a tor was var ied from 100 to 600 mvpp and then am pli fied by a 50 db rf am pli fier (ENI 3100L, ENI Prod ucts di vi sion of MKS in stru - ments Inc., Roch es ter, NY, USA). The two func tion gen er a tors were con nected in se ries and con trolled au to mat i cally us ing Matlab 7.0 (MathWorks Inc., Natick, MA, USA) to gen er ate se quences of con tin u ous and AM waves. The real-time mon i tor ing method was ad justed to in duce a two-sec ond con tin u ous wave sonication (Fig. 4(a)), im me di ately fol lowed by a 100 ms am pli tude-mod u lated wave for ra di a tion force gen er a tion (Fig. 4(b)). Both the con tin u - ous and am pli tude-mod u lated waves were man u ally ad justed to have the same in ten sity at the fo cal zone, i.e., the heat ing was not in ter rupted. This se quence was re peated un til the to - tal sonication time was ap prox i mately 80 sec onds at 100% duty cy cle (Fig. 4). The sonication time of 80 s was used to en sure that a ci gar-shaped le sion with a di am e ter of 1 cm was well formed. In the new AM-HMI tech nique, the high power FUS beam is used to gen er ate a ra di a tion force at the tar geted re gion in the tis sue be low the dam age thresh old and the tis sue re sponse is im aged at the same time us ing a di ag nos tic (pulse-echo) trans ducer. A pulse-echo trans - ducer with a cen ter fre quency of 7.5 MHz, a di am e ter of 12.5 mm and a fo cal length of 60 mm (Panametrics, Waltham, MA, USA) was placed through the cen ter of the FUS so that the beams of the two trans duc ers were prop erly aligned. Con sec u tive, fil tered rf sig nals were ac quired at a pulse rep e ti tion fre quency of 6.5 khz (Panametrics 5051PR, Waltham, MA, USA). A bandpass an a log fil ter (Reactel, Inc., Gaithersburg, Mary land, USA) with cut-off

8 SIN GLE-EL E MENT FO CUSED TRANS DUCER METHOD FOR HAR MONIC MO TION IM AG ING151 frequencies of f c1 = 5.84 MHz and f c2 = 8.66 MHz was used to fil ter out the spec trum of the high power FUS beam prior to dis place ment es ti ma tion. In or der to study the in ter fer ence be tween the di ag nos tic and high power FUS beams, the spec tra of the two beams in in vi tro bo vine liver tis sue are shown be fore (Fig. 5(a)) and af ter (Fig. 5(b)) bandpass fil ter ing us ing the an a log fil ter as de scribed in the previous paragraph. Fig ure 5(c) shows the cor re spond ing rf sig nals be fore and af ter bandpass fil ter ing. It can clearly be seen that the fun da men tal fre quency (f c = 4.68 MHz) and the har mon ics of the FUS trans ducer have been suc cess fully fil tered. Fig ure 5 there fore dem on strates that the rf sig nal can be fully re cov ered af ter the high power FUS beam spec trum has been re moved, indicating low interference between the two beams. An ac qui si tion board (CS14200, Gage Ap plied Tech nol o gies, Lachine, Can ada) was used to cap ture fil tered rf data with a sam pling fre quency of 80 MHz. For the ras ter-scanned pro - cess, the trans ducer was moved along a 2D grid us ing a com puter-con trolled positioner (Velmex Inc., Bloomfield, NY, USA) with a step size of 1 mm. The time shift oc cur ring be tween the two con sec u tively ac quired rf ech oes was cal cu lated us ing a speckle-track ing tech nique. One-di men sional cross-cor re la tion was per formed along the ul tra sound beam axis with a small data win dow of 1.3 mm and 85% over lap. 18 This method is sim ple to im ple ment, computationally ef fi cient and pro vides an ac cu rate es ti ma - tion of small dis place ments (on the or der of 1-10 m at 7.5 MHz). The dis place ment am pli tude and phase shift be tween the in put force and re sult ing dis - place ment at the fre quency of am pli tude mod u la tion (or vi bra tion) were ex tracted for each re gion where dis place ments were es ti mated. These two pa ram e ters were ob tained by com - put ing the fre quency re sponse of the es ti mated time-shift at the fre quencyf mod u la tion. The phase shift () between the radiation force and estimated displacement was calculated (Fig. 6). The phase shift has been shown to re late more closely to the vis cos ity of the tis sues than does the dis place ment am pli tude RESULTS 1. Tissue-mimicking phantom experiments In or der to in ves ti gate the stiff ness-de pend ence of the tis sue dis place ment, this ex per i - ment was first performed in five gel a tin phan toms of dif fer ent stiffnesses. The in ten sity of the high power FUS beam used in this ex per i ment was 658 W/cm 2 and the AM fre quency was 50 Hz. Fig ure 7(a) shows that the av er age dis place ment am pli tude de creases from 10.3 m to 4.15 m as the gel a tin stiff ness in creases from 20 kpa to 60 kpa. The HMI dis place ments clearly in di cate the stiff ness vari a tion. The av er age force-dis place ment phase shift de - creases from 66.4 o to 30.4 o, potentially consistent with decreasing gel viscosity (Fig. 7(b)). Inhomogeneous phan tom ex per i ments were then per formed in a 20 kpa gel a tin phan tom with a 40 kpa cy lin dri cal in clu sion (Fig. 8(a)). Two-di men sional maps of the dis place ment am pli tudes and force-dis place ment phase shifts are shown in fig ures 8(b) and (c), re spec - tively. The av er age dis place ment in the in clu sion is 3.3 m (Fig. 8(b)) and the av er age phase shift is 34 o (Fig. 8(c)) while in the sur round ing gel the dis place ment is 6.1 m (Fig. 8(b)) and the phase shift is 65.9 o (Fig. 8(c)). Note that the av er age dis place ment am pli tude in the 20 kpa re gion is twice as high as the av er age dis place ment am pli tude in the 40 kpa cy lin dri - cal in clu sion re gion. These re sults are con sis tent with the in verse re la tion ship be tween the dis place ment and elas tic modulus dur ing har monic ex ci ta tion. 16

9 152 MALEKE ET AL FIG. 5 Spec tra of the high power FUS beam (dot ted line) and di ag nos tic beam (solid line) be fore (a) and af ter (b) bandpass fil ter ing. Dot ted line spec trum in di cates pres ence of high power FUS beam with the high est peak in di cat - ing fun da men tal fre quency fol lowed by its har monic peak. Solid line shows re flec tion of tis sue re sponse with no high power FUS beam pres ent. Spec tra af ter fil ter ing at fre quency 7.5 MHz dem on strate that the tis sue re sponse is imaged at diagnostic frequency (f c = 7.5 MHz). (c) Rf sig nal be fore (dot ted line) and af ter (solid line) re moval of high power FUS beam in in vi tro bo vine liver: (c 1 ) PBS so lu tion, (c 2 ) spec i men and (c 3 ) silicon rubber/absorber.

10 SIN GLE-EL E MENT FO CUSED TRANS DUCER METHOD FOR HAR MONIC MO TION IM AG ING153 FIG. 6 Over view of phase shift cal cu la tion method. (a) Dis place ment in a gel a tin phan tom, (b) ra di a tion force in ten sity (nor mal ized) and (c) phase shif FIG. 7 Result of tissue-mimicking phantom experiment with five different stiffnesses. (a) Estimated displace - ment am pli tude and (b) cal cu lated phase shift. 2. Mon i tor ing HIFU ab la tion A 20 x 20 x 30 mm 3 piece of ex vivo por cine liver was sub merged in phos phate-buf fered sa line (PBS) so lu tion and de gassed for 30 min utes. The 20 x 20 mm 2 area was ras -

11 154 MALEKE ET AL FIG. 8 Result of tissue-mimicking phantom experiment with 40 kpa cylindrical inclusion. (a) Photograph of the gelatin phantom, (b) estimated displacement amplitude and (c) calculated phase shift. FIG. 9 Dis place ment am pli tude im ages from the 2D ras ter-scanned ex vivo tissue be fore (a) and af ter (b) le sion for ma tion. (c) Sub tracted im ages be fore and af ter le sion for ma tion in di cates a cir cu lar le sion with 10 mm di am e ter. ter-scanned be fore and af ter the le sion for ma tion. The in ten sity of the FUS used in the ras - ter-scan pro cess was 237 W/cm 2 with an am fre quency of 50 Hz. The dis place ment am pli tudes at the fo cus of the ex vivo por cine liver, be fore and af ter the le sion for ma tion, were ap prox i mately equal to 25 m (Fig. 9(a)) and 10 m (Fig. 9(b)), re spec tively. The im - age re sult ing from the sub trac tion of the im age af ter, from the im age be fore the le sion for ma - tion is shown in fig ure 9(c). The neg a tive dis place ment am pli tude ( 5 m) de fines a cir cu lar le sion with a di am e ter of 10 mm (Fig. 9(c)). These re sults in di cate that the dis place - ment am pli tude de creases af ter le sion for ma tion due to the as so ci ated higher tis sue stiff ness. They also re veal an inhomogeneous le sion with two sep a rate zones with the cen tral zone hav ing the low est dis place ment. In this case, the dif fer ence im age was nec es sary to high - light the ab lated, or stiffer, re gion un like in the case of the gels where the HMI am pli tude im - age was suf fi cient (Fig. 8(b)). This is most likely due to in creased post-ab la tion ab sorp tion that has the op po site ef fect, i.e., of in creas ing the ap plied force and there fore, es ti mated dis - placement, after coagulation. 16 For the real-time mon i tor ing ap pli ca tion, the ex per i ment was com pleted in an ex vivo por - cine liver with a sonication time of a to tal of 80 sec onds. Fig ure 10(b) shows the tis sue dis - place ment am pli tude at the fo cal depth ver sus sonication time. The fo cus is lo cated at 16.5 mm and has dis place ment am pli tude of 50 m, which then de creases to about 15 m (Fig. 10(c)). The re gions above and be low the fo cus have ap prox i mately con stant dis place ments (Fig. 10(c)). This in di cates that the acous tic ra di a tion force is pro duced and main tained at the fo cus and that af ter 20 sec onds of sonication time, the prop er ties of the liver tis sue ir re - vers ibly changes due to tis sue co ag u la tion (Fig. 10(a)).

12 SIN GLE-EL E MENT FO CUSED TRANS DUCER METHOD FOR HAR MONIC MO TION IM AG ING155 FIG. 10 Re sult of real-time mon i tor ing in the ex vivo tis sue dur ing 80 s sonication. (a) M-mode HMI dis place - ment am pli tudes at fo cal zone (depth = 16.4 mm) dur ing sonication, (b) dis place ment am pli tude, above and be low the fo cus and (c) pho to graph of the le sion. Note that dis place ment am pli tude de creases dur ing le sion for ma tion. Unlike the surrounding area, the displacement amplitudes remain invariable. Fur ther more, it should be noted that the ef fect on the ech oes in duced by the in crease in the speed of sound with tem per a ture also in tro duced a lin ear shift in the HMI dis place ment in time (Fig. 11(a)). The lin ear shift was then sep a rated from the HMI dis place ment by re mov - ing the lin ear slope in curred (Fig. 11(c)). The re sult is shown in Fig. 11(b). This tech nique is there fore able to ac cu rately mon i tor the stiff ness-re lated heat ing pro cess, pos si bly de tect ing the time of co ag u la tion as well as sep a rat ing the speed-of-sound ef fect from stiff ness-re lated changes. DIS CUS SION AND SUM MARY Ex per i men tal re sults of the HMI tech nique in the tis sue-mim ick ing phan toms and ex vivo por cine liver were shown in re la tion to the po ten tial for the use of the HMI tech nique for mon i tor ing HIFU treat ment. Low in terference be tween the high power FUS and di ag nos tic beams is a achieved af ter bandpass fil ter ing and, thus, tis sue dis place ments us ing the fil tered rf sig nals can be ac cu rately es ti mated. Al though the tis sue-mim ick ing phan toms might pres - ent small dis crep an cies in an ab so lutely uni form stiff ness re ported, the new HMI tech nique is still ca pa ble of de tect ing the dis place ment changes caused by changes in the ma te rial stiff - ness. Our tech nique in di cates that the HMI dis place ment am pli tude and force-dis place ment phase shift vary with ma te rial stiff ness and vis cos ity. The max i mum temperature change mea sured dur ing HMI was 1 o C. The phase shift might be ben e fi cial for es ti mat ing the vis -

13 156 MALEKE ET AL FIG. 11 Il lus tra tion of re moval of tem per a ture-de pend ent speed of sound ef fect on the dis place ment as a re sult of tem per a ture change that in duces (a) a lin ear shift, which can then be succesfully sep a rated (b) from the HMI dis - place ment vari a tion. (c) Slope of the HMI dis place ment shift. cos ity of the me dium in the fu ture. The re la tion ship be tween the dis place ment am pli tude and the phase shift is a topic of on go ing in ves ti ga tion. A phan tom with a cy lin dri cal in clu sion was gen er ated to mimic HIFU le sions and a 2D ras ter-scanned pro cess was performed to ob tain an HMI im age. The cy lin dri cal in clu sion was ac cu rately mapped us ing the dis place ment am pli tude and phase shift. The phase shift map shows an ar ti fact be low the in clu sion (Fig. 8(c)). This vari a tion could be the re sult of tem per a ture, at ten u a tion or tis sue ab sorp tion change dur ing the ra di a tion force ap pli ca tion. In ad di tion, we ob tained con sis tent real-time mon i tor ing of tis sue ab la tion in the ex vivo por - cine liver tis sue. The tis sue dis place ment am pli tude ini tially in creased and then de creased at the on set of the le sion for ma tion. A con tin u ous wave was gen er ated dur ing the sonication pe riod in or der to ac cel er ate the le sion for ma tion and re duce the HIFU ther apy du ra tion. De spite the fact that the HMI tech nique shows a high po ten tial for elas tic ity im ag ing, this method was pri mar ily de signed for real-time mon i tor ing of tis sue prop er ties dur ing HIFU treat ment. The acous tic in ten sity of the high power FUS beam (600-1,000 W/cm 2 ) is well adapted for both acous tic ra di a tion force gen er a tion and HIFU ther apy, al low ing dis place - ment am pli tude of 1 to 10 m in the gel a tin and tis sue and 10 to 50 m in the tis sue ab la tion experiments. Thus, the ab la tion of the tis sue and the mon i tor ing can be performed at the same time, which may prove to be a ma jor ad van tage for ef fi cient HIFU ap pli ca tion and real-time mon i - tor ing com pared with other ra di a tion-force-based mon i tor ing tech niques that re quire in ter - rup tion of the treat ment to mea sure the me chan i cal re sponses. This is an im por tant con tri bu tion in the area of noninvasive or min i mally-in va sive ther mal ther apy. In this method, it was also as sumed that the vari a tion of the elas tic ity dur ing HIFU ab la tion is the main ef fect that pro duces the dis place ment am pli tude vari a tion. How ever, for a given trans ducer and in ten sity, the acous tic ra di a tion force gen er ated in bi o log i cal tis sues de pends on sev eral pa ram e ters that can also vary dur ing HIFU ab la tion, such as the den sity and the ul - tra sound ab sorp tion of the tis sue. It has been shown, in par tic u lar, that the at ten u a tion, and tis sue ab sorp tion, of ul tra sound in creases sig nif i cantly dur ing heat ing. 30 If this ef fect were

14 SIN GLE-EL E MENT FO CUSED TRANS DUCER METHOD FOR HAR MONIC MO TION IM AG ING157 pre dom i nant, it would in crease the ra di a tion force and con se quently the am pli tude of the tis - sue dis place ment. How ever, we have shown here that the dis place ment am pli tude de creases con sis tently dur ing ab la tion, which sug gests that this vari a tion is mainly due to the elas tic ity change. The choice of the mod u la tion fre quency plays an im por tant role in this method. It is pos si - ble to in duce me chan i cal os cil la tions in a 1 to 3 mm 3 re gion of the tis sue due to the large at - ten u a tion of low fre quency shear waves. Since the at ten u a tion in creases with fre quency, a higher fre quency mod u la tion (>100 Hz) would al low the os cil la tions to be con tained in a smaller re gion in the vi cin ity of the fo cus. How ever, at high frequencies, the vis cos ity of the tis sue be comes very im por tant and the os cil la tion of the tis sue de creases rap idly. For ex am - ple, be low 10 Hz and above 74 Hz, it be comes very dif fi cult to de tect the tis sue os cil la tions in ex vivo por cine liver us ing an acous tic in ten sity of 237 W/cm 2. At this fre quency, the tis sue os cil la tions are lim ited to a re gion of about 10 mm around the fo cal spot. In con clu sion, the fea si bil ity of us ing an am pli tude-mod u lated ra di a tion force for har monic mo tion im ag ing (HMI) and si mul ta neous mon i tor ing of tis sue stiff ness vari a tion dur ing ul tra sound ther apy was shown in phan toms and ex vivo tis sues. Since it uses os cil la tory tech niques, the HMI tech nique could be used for the es ti ma tion of me chan i cal prop er ties, such as stiff ness and vis cos ity, as well as their sep a ra tion from acous ti cal prop erty changes with tem per a ture, such as those from the speed of sound and ab sorp tion. Fur ther in ves ti ga tions will fo cus on the es ti ma tion of those afore men tioned prop er ties to gether with the pre cise quan ti fi ca tion of the size of the os cil lat ing re gion and the fre quency-de pend ence of the response. AC KNOWL EDGE MENTS This study was sup ported by a Spe cial De vel op ment Award from the Whitaker Foun da - tion and startup funds from Co lum bia Uni ver sity. The au thors also wish to ac knowl edge the Lizzi Cen ter for Biomedical En gi neer ing of the Riv er side Re search In sti tute (New York, NY) for kindly pro vid ing the trans duc ers used for this study. REF ER ENCES 1. Krouskop T, Wheeler TM, Kallel F, Hall T. The elas tic moduli of breast and pros tate tis sues un der com pres - sion, Ultrasonic Imaging 20, (1998). 2. Ophir J, Cespedes I, Ponnekanti H, Yazdi Y, Li X. Elastography: a quan ti ta tive method for im ag ing the elas - tic ity of bi o log i cal tis sues, Ultrasonic Imaging 13, (1991). 3. Krouskop TA, Dougherty DR, Vin son FS. A pulsed Dopp ler ul tra sonic sys tem for mak ing noninvasive mea - sure ments of the me chan i cal prop er ties of soft tis sue, J Rehabil Res Dev 24, 1-8 (1987). 4. Muthupillai R, Lomas DJ, Rossman PJ, et al. Mag netic res o nance elastography by di rect vi su al iza tion of propagating acoustic strain waves, Science 269, (1995). 5. Sinkus R, Lorenzen J, Schrader D, et al. High-res o lu tion ten sor MR elastography for breast tu mour de tec tion, Phys Med Biol 45, , (2000). 6. Green leaf JF, Fatemi M, Insana M. Se lected meth ods for im ag ing elas tic prop er ties of bi o log i cal tis sues, Ann Rev Biomed Eng 5, (2003). 7. Sugimoto TU, Itoh SK. Tis sue hard ness mea sure ment us ing the ra di a tion force of fo cused ul tra sound, in Proc IEEE Ultrasonics Symp, pp , IEEE cat. no. 90CH (1990). 8. Night in gale KR, Kornguth PJ, Trahey GE. The use of acous tic stream ing in breast le sion di ag no sis: A clin i cal study, Ul tra sound Med Biol 25, (1999).

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