Freehand 3D Ultrasound Calibration Using an Electromagnetically Tracked Needle

Transcription

1 Freehand 3D Ulraound Calibraion Uing an Elecromagneicall Tracked Needle Hui Zhang a, Filip Banovac a,b, Am Whie b, Kevin Clear a* a Imaging Science and Informaion Sem (ISIS) Cener, Deparmen of Radiolog, Georgeown Univeri Medical Cener 2115 Wiconin Ave. NW, Suie 63, Wahingon, DC, 27, USA b Deparmen of Radiolog, Georgeown Univeri Hopial 38 Reervoir Road, Wahingon, DC, 27, USA ABSTRACT Freehand 3D ulraound allow inra-operaive imaging of volume of inere in a fa and fleible wa. However, he ulraound device m be calibraed before i can be regiered wih oher imaging modaliie. We preen a needlefiducial baed elecromagneic localiaion approach for calibraing freehand 3D ulraound a a prerequiie for creaing an inra-operaive navigaion em. Alhough mo eiing calibraion mehod require a comple and edio eperimen ing a comied calibraion phanom, our mehod doe no. The calibraion e-up require onl a conainer of waer and onl everal frame (hree o nine) o deec an elecromagneicall racked needle ip in a 2D ulraound image. The racked needle i dipped ino he waer and moved freehand o locae he ip in he ulraound imaging plane. The image ha how he needle ip are recorded and he coordinae are manuall or auomaicall idenified. For each frame, he piel indice, a well a he dicree coordinae of he racker and he needle, are ed a he inp, and he calibraion mari i reconruced. Three group poiion, each wih nine frame, are recorded for calibraion and validaion. Depie he lower accurac of he elecromagneic racking device compared o opical racking device, he maimum RMS error for calibraion i 1.22mm wih i or more frame, which how ha our propoed approach i accurae and feaible. Keword: freehand 3D ulraound, ulraound calibraion, elecromagneic racking 1. INTRODUCTION Three-dimenional freehand ulraound ha grea promie for man urgical applicaion, epeciall in minimall invaive procedure. Poenial applicaion include 3D anaomic viualiaion of pahologic iue and vario ulraound-guided procedure. Freehand racked ulraound can been ed o creae image for organ volume meauremen. We are currenl developing a urgical navigaion em for abdominal procedure baed on he elecromagneic racking device. We have uccefull compleed everal phanom and pig udie, bu he em ha e o incorporae real-ime validaion of anaomical locaion and repiraion deformaion. For hi reaon, we inroduced a 3D freehand ulraound device ino our navigaion em. The advanage of he ulraound-baed em are ha i provide real-ime image and can be eail inegraed ino he operaing room. A requiremen for 3D freehand ulraound imaging i a moion racking em ha monior he poiion and orienaion of a racked randucer. Oher inveigaor have creaed 3D freehand ulraound wih racking em ha uilie elecromagneic enor, opical enor, acoic peak gap, or a combinaion of hee pe [1-8]. The advanage of a 3D freehand racked ulraound em over a andard, commercial ulraound machine wih 3D image reconrucion capabiliie i he abili o acquire ulraound image in a univeral coordinae frame, o which oher racked urgical inrumen can be aached. In addiion, he movemen of he racked probe i no rericed b a mall range or limied direcion. B racking he device in a common coordinae em wih he paien, he urgeon can be provided wih 3D informaion regiered o he paien anaom. The fir ep required o inegrae ulraound ino hee em i a calibraion ep a preened in hi paper. * clear@georgeown.edu; Telephone ; Fa

2 In ulraound image calibraion, he 3D phical dimenion of he beam plane are compued wih repec o he racked device. Afer he calibraion proce i compleed, andard 2D B-mode ulraound image can be reconruced ino a 3D volume ing he poiional informaion obained from he racking em. There are four general mehod o conruc an ulraound volume: 1. conrained weeping echnique; 2. 3D probe; 3. enorle echnique; and 4. 2D racked probe (freehand) echnique [9]. Calibraion m be performed o deermine he poiion of he ulraound coordinae em in relaion o he reference coordinae of he racking em. Thi calibraion i mo ofen performed b regiraion beween he ulraound image and a geomerical model of he phanom reconruced from a CT image, or b ouching a pre-calibraed poiner. Thee mehod are referred o a poin-baed calibraion mehod, and are implemened b maching correponding poin from wo differen coordinae frame. The high accurac of poin-baed calibraion mehod ha been demonraed b everal reearch group [1,1]. Thee echnique carr he advanage of having a imple eperimen e-up, bu can be more ime conuming han oher auomaed echnique, uch a urface- and ineni-baed mapping, becae he idenificaion of he poin in he image i a manual proce. The reul of everal ulraound beam calibraion echnique indicae ha he poin-baed cro-wire phanom produced he mo precie and accurae reconrucion. Overall, an opical racking em will provide a beer calibraion reul han elecromagneic em ince opical em are more accurae and no ubjec o diurbance from meal objec. In he cro-wire phanom ud, a RMS of 1.65mm wa obained ing an opical racking em, while an RMS error of 2.41mm wa obained ing an elecromagneic racking em [11]. Inead of ing pecific calibraion phanom, we e a racked needle a he indicaor o avoid he regiraion and ouching ep ha can inroduce unnecear calibraion error. Several reearcher have eperimened wih differen approache ing poin objec (uch a a pinhead or a mall pended head) inead of he cro-wire phanom. For eample, Muraore and Gallowa ed he ip of an opicall racked poiner o find he paial ranformaion [12]. We e an elecromagneicall racked needle, and ake a differen mahemaical approach o calculae he calibraion mari. 2. MATERIALS AND METHODS 2.1. Tracked ulraound image acquiiion The ulraound device ed in he eperimen i a porable em from Teraon Inc. (Burlingon, MA). I ha 128 channel and connec wih he compuer hrough a andard IEEE 1394 firewire por. The elecromagneic racking device i he AURORA from Norhern Digial Inc. (Onario, Canada). The digial ulraound image i acquired from he firewire connecion direcl. We have found he racking accurac of hi em o be minimall affeced b mall meal inrumen in cloe proimi. The racker aached o he ulraound probe m be a i degree of freedom (DOF) racker, which include ranlaion and roaion. The general e-up i hown in Figure 1. The racked ulraound probe i fied b a plaic holder, and he bean urface conac he waer. The racked needle i placed in a plaic cube in he waer, which abilie he needle and can reduce he error generaed b mall uninenional hand movemen. The acquired ulraound image i hown in Figure 2. The brigh line a he boom of he image i he waer conainer. Becae he enire eperimen i e-up in a conainer of waer, he conra allow adequae viualiaion of he needle, and he needle ip can herefore be eail idenified manuall. On ulraound he needle ip i no harpl demarcaed, bu i locaed a he cener of he brigh ignal oberved on imaging a hown in Figure Pivo calibraion of elecromagneic racker Before performing he calibraion, we pivoed he needle o ge he correc offe from he racked enor poiion o he ip [13]. B appling he calibraion ranform ino he racking informaion, he regiraion ep of phical and racking pace, diced previol in he poin-baed calibraion mehod, will be avoided. The poiion and orienaion informaion repored b he AURORA racking em i he cener poiion of he enor coil. When he enor coil i embedded in a urgical ool, he ranformaion beween he coil and he ip of he ool i required. Thi informaion i picall deermined b a pivo calibraion, in which he ip of he inrumen i placed in a mall hole (divo) and he inrumen i roaed back and forh a enor daa i colleced.

3 Figure 1: Eperimenal e-up (elecromagneic field generaor, racked ulraound probe, needle in plaic block, waer conainer) Figure 2: Ulraound image (wih needle ip a brigh po indicaed b arrow) The AURORA em reurn he ranlaional poiion of he enor coil relaive o a coordinae em fied a he cener of he field generaor. The orienaion of he enor i alo reurned and pecified ing quaernion. Tpical AURORA enor are five degree of freedom enor in ha he canno reolve heir orienaion abou heir long ai (he roll ai). The racked needle ed in hi eperimen i 5DOF. From he ranlaional and orienaion informaion, a four b four homogeno ranformaion mari can be conruced. When he enor coil i embedded ino he needle, he long ai of he coil i parallel o he needle uch ha he onl offe from he coil o he needle ip i along he -ai of he needle. The ranformaion from he field generaor coordinae em o he needle ip coordinae em can hen be calculaed from: r r1 r2 r1 r11 r 2 offe (1) In hi equaion, R i he roaion mari, T i he ranlaion vecor and (,, ) i he pivo poiion (in hi cae he ip of he needle). Tpicall, we record everal hundred ample while pivoing he needle. Equaion (1) can be re-wrien a follow where he unknown variable of offe and (,, ) can be een:

4 r r r offe 1 offe offe 1 1 Thee equaion can hen be wrien a: A* offe B * C * D E (3) * In equaion (3), A, B, C, D and E are he column coefficien vecor, which can hen be re-wrien a: offe M N (4) Since M i no a quare mari, he unknown can be found ing he ingular value decompoiion (SVD) or Moore- Penroe invere: offe Addiionall, he RMS error can be compued a: rm where num i he number of ample. M T 1 T M M M N T 2 offe N num 2.3. Calibraion of he ulraound probe To e up he eperimen, we placed he ulraound probe ino a conainer of waer. Afer he probe and he field generaor were fied a everal differen poiion, he racked needle wa dipped ino he waer and moved o deermine he eac poiion where he ip inereced wih he imaging plane. The ranformaion relaionhip of he calibraion em i hown in Figure 3. (2) (5) (6) Figure 3: Calibraion coordinae em, adaped from [5] The poiion of he needle ip, P ip, can be deermined b i piel locaion in he ulraound image, P, he calibraion mari, T c, and he reference racker ranformaion mari, T ref, ing he following equaion:

5 P u, v,, 1 where T P ip T T P (7) ref c, and u and v are he column and row indice of he piel in he acquired image. The inde along he -ai i e o becae we ed a 2D beam. The cale facor are inegraed wih he calibraion mari, T c, uch ha he era cale facor in he compuaion i no required. Afer lef mulipling he invere of he reference ranformaion mari T ref, equaion (7) can be wrien a: 1 P T P T P T u, v,, 1 (8) ip / ref ref ip c c where P ip/ref i a vecor. Afer aking n frame, equaion (8) i accumulaed a: u1 un v1 vn Pip / ref,1, Pip / ref, n Tc Tc T (9) 1 1 u1 un v1 vn where T. The calibraion mari i calculaed b SVD oluion ing 1 1 T T P P T T T 1 T (1) c ip / ref,1, ip / ref, n Thi compuaion reul in a mari wih a ero vecor in he hird column, for he T conain a ero vecor and a 1 vecor in he hird and forh row. The non-ero full mari i compued wih Horn mehod [14] Algorihm validaion The validaion of he calibraion i ignifican ince i confirm ha he calibraion mari compued will accurael reconruc he 3D plane in he racking pace. There are four general mehod o validae he calibraion mari: he fir i o calculae he RMS of he oluion; he econd i o e ome oher poin which are no included in calibraion compuaion o verif he ranformaion accurac; he hird i o meaure he orhgonali and normali condiion of he roaion mari of he calibraion erm; and he fourh i o compare he reliced image wih he acquired ulraound image plane direcl. The general ranformaion mari b he roaion and ranlaion i r11 r13 r23 T (11) r 31 r32 r33 1 Among hem, r11-r33 are he elemen of roaion mari, and hould obe he orhogonali and normali condiion., and are he ranlaion elemen. The indice vecor P wih he calar i u v V (12) 1 and are he cale facor and are changed according o he deph and ome oher parameer from ulraound device. Afer he mari and he vecor are muliplied ogeher, we ge T

6 r11 r13 u r11 r13 u r23 v r23 v T V (13) r 31 r32 r33 r31 r32 r The SVD mehod we ed in he calibraion i o calculae he final mari: r11 r13 r23 T c (14) r 31 r32 r33 1 A hi ime, onl he fir wo column calar and are compared for he hird column i no meaningful for he 2D ulraound probe. The orhogonali hould be. in he idea condiion. 3. RESULTS In he eperimen, we recorded all he daa for hree differen group poiion. For each group, nine differen indice of he needle ip and he racking informaion were recorded a he inpu. In each group, hree o nine frame were ed o compue he calibraion mari ing he previol diced equaion. Two group erved a arge poin e for validaing he generaed mari. The reul are hown in Table 1. Alhough he minimum requiremen o calculae he calibraion mari i hree frame, i or more frame provide increaed accurac. In hee daa, he maimum RMS calibraion error i 1.22mm and he maimum arge validaion error i 3.45mm. Conidering ha we ed he elecromagneic racking em, which i no a accurae a an opical racking em, our propoed mehod eem reaonabl accurae. For each group, he fir row i he RMS calibraion error wih differen frame number, and he following wo row are he repecive RMS arge validaion error. The bold value i he maimum error ing i or more poin for calibraion. Calibraion Validaion Number of poin Group Group Table 1 Calibraion and validaion reul (mm) The validaion mehod we propoed i alo verified b hree differen group. For each group, he orhogonali and he and are calculaed repecivel. The orhogonali hould be cloe o. and he and hould remain conan under ideal condiion. Through he validaion reul, a hown in Table 2, our calibraion mehod give a reaonable oupu and i conidered o fi hoe orhogonali and cale condiion. When he frame number i increaed o more han i, he orhogonali i cloe o. and he cale of he X and Y ai are conien.

7 (a) Group 1 Frame Orhogonali Scale X Scale Y (b) Group 2 Frame Orhogonali Scale X Scale Y (c) Group 3 Frame Orhogonali Scale X Scale Y Table 2 Validaion of orhogonali and cale of calibraion mari Afer he calibraion, he oupu mari i ed in our image-guided urgical em, Navigaor, o dipla he freehand ulraound image plan. The reconruced 2D beam plane i diplaed in 3D o how he correc relaionhip wih he volume-rendered image. The reconruced CT image can alo be diplaed imulaneol o compare he difference beween he wo imaging modaliie, providing more informaion for he planned inervenion. The reul from he phanom ud are hown in Figure 4. Several kin fiducial and one racked needle are ed for regiraion. Afer calibraion and regiraion, he relaed ulraound image and reformaed CT image are diplaed ogeher, in which he imulaed aora i idenified. The co-regiered image from a wine ud are alo hown in Figure 5. The wine ud wa par of an approved proocol. A a par of he open ource projec iled Image Guided Surgical Toolki (IGSTK), he ource code of he pivo calibraion and poin-baed calibraion par can be downloaded from 4. CONCLUSIONS AND DISCUSSIONS We have performed ulraound calibraion ing he ip of an elecromagneicall racked needle a he calibraion device, raher han a phanom. A new mahemaical linear algebra mari operaion wa derived o olve he calibraion mari. The validaion mehod of our algorihm i alo included. The reul of our eperimen prove ha hi i a feaible calibraion mehod for racking-baed urgical navigaion em. There are a number of requiremen for proper implemenaion of our poin-baed calibraion mehod. Fir, a racked enor m be aached o he ulraound probe, which i necear for image-guided procedure. Second, a good image, in which he ip of he racked needle i eail idenified, i alo required. Thi can be een from he acquired image hown in Figure 2. If we fi he ulraound probe in a able poiion and move he racked needle, he eac poiion of where he needle ip i paing b he beam plane can be eail idenified b image ubracion. The

8 racker informaion wih he ame ime amp will be recorded and e a he inpu a well a he poiner coordinae. Thi will greal accelerae he calibraion peed and require onl minue for accurae calibraion. Figure 4: Phanom eup and he US-CT image dipla in Navigaor em Figure 5: Correponding US and CT image from wine ud howing he wine gallbladder ACKNOWLEDGEMENTS Thi work wa funded b US Arm gran DAMD and W81XWH We would like o hank Norhern Digial Inc. for heir echnical aiance and produc uppor wih he AURORA em. REFERENCES 1. R. W. Prager, R. N. Rouhling, A. H. Gee, and L. Berman, Rapid calibraion for 3-D freehand ulraound, Ulraound in Med. & Biol., Vol. 24, No. 6, pp (1998) 2. Pagoulao N, Hanor DR, Kim Y., A fa calibraion mehod for 3-D racking of ulraound image ing a paial localier, Ulraound Med Biol. Vol. 27, No. 9, pp (21) 3. Nicola Andreff, Radu Horand, Bernard Epiau, Robo Hand-Ee Calibraion Uing Srucure-from-Moion, The Inernaional Journal of Roboic Reearch, Vol. 2, No. 3, pp (21) 4. A. Viwanahan, E.M. Bocor, R.H.Talor, G.D. Hager and G. Fichinger, Immediae ulraound calibraion wih hree poe and minimal image proceing, MICCAI 24, Sain-Malo, France. Vol. 3217, pp (24) 5. Bocor, Emad M.; Jain, Amee; Choi, Michael A.; Talor, Rell H.; Fichinger, Gabor, Rapid calibraion mehod for regiraion and 3D racking of ulraound image ing paial localier, Medical Imaging 23: Ulraonic Imaging and Signal Proceing. Edied b Walker, William F.; Inana, Michael F. Proceeding of he SPIE, Vol. 535, pp (23)

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