Myocardial Motion Analysis of Echocardiography Images using Optical Flow Radial Direction Distribution

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1 Journal of Computer Scence 7 (7): , 011 ISSN Scence Publcatons Myocardal Moton Analyss of Echocardography Images usng Optcal Flow Radal Drecton Dstrbuton Slamet Ryad, Mohd Marzuk Mustafa and An Hussan Department of Electrcal, Electronc and Systems Engneerng, Faculty of Engneerng and Bult Envronment, Unverst Kebangsaan Malaysa, Bang Selangor Malaysa Abstract: Problem statement: Myocardal moton s mportant nformaton for physcans n dagnosng cardac abnormaltes. The moton vector of myocardal can be computed usng optcal flow technque, whch then can be further analyzed based on ts magntude and angle. In practce, physcans are not concern about the angle of vector tself, but are more nterested on whether a segment s movng to the center or not. Approach: Therefore, n ths study we propose a relatve moton drecton wth respect to the center of the cardac cavty, called radal drecton, whch s more useful for dagnoss. The radal drecton s computed as the dfference between the angle of optcal flow at a pont of nterest and the angle between the pont and the cavty center. Because of the dffculty n performng analyss based solely on ndvdual vectors, t s helpful to vsualze and extract the overall trend by representng moton vectors by ther angular dstrbuton. Results: Ths method has been tested on clncal echocardography sequences and has been shown to be successful n provdng a radal drecton profle of every segment for each echocardographc frame. A comparson between the normal angular dstrbuton and the proposed radal drecton profle was also presented. Concluson: The proposed profle was shown to be successful n provdng the pattern of segmental moton whch s easer for physcan to analyze the myocardal moton compared wth the normal angular dstrbuton as well as more nvarant to segment locatons. Key words: Echocardography mages, myocardal moton, radal drecton, segmental profle, segmental moton, Parasternal Short Axs vew (PSAX), Sngle Photon Emsson Computed Tomography (SPECT), cardovascular dsease, Left Ventrcular (LV) INTRODUCTION In 004, cardovascular dsease caused 17.1 mllon deaths, whch corresponded to 9% of the global deaths for that year as reported by the World Health Organzaton (010). From these data, 7. mllon ded because of coronary heart dsease, whle the rest were affected by stroke. Coronary heart dsease, whch s also known as heart attack, occurs when there s an nterrupton of blood supply to the heart muscle. It can be detected early by observng abnormalty n the moton of the left ventrcular. Realzng the mportance of ths moton, many researchers have focused on the estmaton, quantfcaton and nterpretaton of cardac moton. In medcal practce, a physcan observes the left ventrcular moton by means of three man magng modaltes: Sngle Photon Emsson Computed Tomography (SPECT), Magnetc Resonance Imagng (MRI) and ultrasound magng. The use of computed tomography and magnetc resonance magng on the Left Ventrcular (LV) moton analyss has been successful because both modaltes generate relatvely nose-free mages (Ln et al., 006; Sundar et al., 009). However, they have a number of drawbacks such as nvasve, radaton and problems wth devce portablty. In order to overcome these problems, an ultrasound scannng method was ntroduced; t s a promsng tool that has proven to be useful n many clncal applcatons. Furthermore, many researchers have been attracted on the use of echo mages to analyze myocardal moton usng block matchng method, 3 dmensonal model and non-rgd regstraton (Boukerrou et al., 003; Papademetrs et al., 001; Ledesma-Carbayo et al., 005). Other popular methods Correspondng Author: Mohd Marzuk Mustafa, Department of Electrcal, Electronc and System Engneerng, Faculty of Engneerng and Bult Envronment, Unverst Kebangsaan, Malaysa Bang 43600, Selangor Tel: Fax:

2 for myocardal moton estmaton have been based on the computaton of optcal flow (Verones et al., 006; Duan et al., 006; Ryad et al., 011). Current research on the cardac moton of echo mages s manly focused on the mprovement of the accuracy of the moton estmaton as there have been dffcultes n the detecton of moton usng echocardography mages. On the other hand, quantfcaton of the computed moton wll be very useful for physcans to nterpret the cardac moton for makng a clncal decson. Few publcatons report on quantfcaton and nterpretaton of computed moton on echo mages. Ledesma-Carbayo et al. (005) computed the mean dsplacement vector and the mean stran tensor of each segment from computed myocardal moton. Both features showed sgnfcant dfferences between normal and abnormal cardac moton. However, the presented features dd not provde a complete segmental profle of cardac moton n a temporal observaton. In another proposed method, Duan et al. (006) developed a four-dmensonal optcal flow frame-work to track the endocardal surface usng real-tme 3 dmensonal ultrasound. Some features, such as flow magntude, radal dsplacement, crcumferental dsplacement, thckenng, crcumferental and longtudnal stretch and twst, were computed to provde dynamc measurement of cardac moton. The extracted nformaton was mostly used to vsualze realtme 3 dmensonal cardac moton rather than to detect cardac abnormalty. J. Computer Sc., 7 (7): , 011 In clncal practce, a cardologst does not only need to observe the magntude of myocardal moton, but also the drecton of ts moton to ensure an effectve LV ejecton fracton. Instead of the vector angle tself, n ths artcle we propose a relatve moton drecton wth respect to the center of cavty, called radal drecton, whch s more useful for dagnoss because ths wll enable the physcan to nfer whether a segment s movng to the center or not more clearly. The rest of ths study descrbes the method of optcal flow used, the computaton of optcal flow angle and radal drecton and fnally we present the comparson of drecton profle of optcal flow usng ts angle and proposed radal drecton method. Understandng LV moton: For magng purpose, the Amercan Heart Assocaton has released four standard vews for my ocardal segmentaton and nomenclature. One of them s Parasternal Short Axs vew (PSAX) as shown n Fg. 1. In ths vew, there are sx segments of the myocardum whch are assocated wth the dstrbuton of three man coronary arteres. For normal cardac functon, the myocardal segments move nward to the cavty center wth unform dsplacement from end dastole to end-systole (Anderson, 007). MATERIALS AND METHODS The extracton of myocardal moton property based on optcal flow nvolves several steps. They are preprocessng stage, estmaton of myocardal moton usng optcal flow, computaton of angle and radal drecton and generatng the angular dstrbuton profle. We start wth takng two consecutve mages of echocardography sequences. Snce t s well-known that echocardography mages contan speckle nose, a quas Gaussan-Dscrete Cosne Transform flter adopted from (Ryad et al., 009) s then appled to mprove the mage qualty. Subsequently, we manually select the cavty center and ntal ponts on endocardum and then apply B-splne to generate other ponts along the endocardum. After the creaton of myocardum boundary, optcal flows for every pxel along the endocardal boundary were computed. A statstcal averagng approach s mplemented to remove outler data along the boundary and to generate a smoother boundary optcal flow vectors. To assst wth the nterpretaton of mycardal moton, we propose a radal drecton dstrbuton for each myocardal segment, nstead of a sngle angular Fg. 1: A standardzed PSAX vew for an dstrbuton of flow vector for all the segments. The echocardography mage radal drecton dstrbuton represents a drecton pattern 1047

3 of segmental myocardal wth respect to the cavty center n such a way that cardologst can drectly know the drecton n whch a segment moves wth respect to the centre of the cavty. The rest of ths secton descrbes the method used to generate smoothendocardal optcal flow and determne radal drecton profle. Generatng smooth endocardal optcal flow: We computed the optcal flow between two consecutve frames usng Horn-Schunck s method. Ths method was selected because of ts smplcty, low computng tme and sutablty for estmaton of small dsplacement. To compute optcal flow, the ntensty of the object s assumed constant. Ths can be represented as: I(x, y, t) = I(x+δx, y+δy, t+δt) (1) The ntensty constrant can be approxmated usng the 1st order Taylor seres expanson snce the δx, δy and δt are wthn small value, as shown below: I(x + δ, y + δ,t + δ t) = c y I I I I(x, y, t) + δ x + δ y + δt x y t () Smplfyng Eq. 1 and, the basc constrant of the optcal flow equaton can be artculated as: Ixdx + Iydy + Itdt = 0or Ixu + Iyv + It = 0 (3) Horn-Schunck s method ntroduces global smoothness error (E S ) and brghtness constancy error (E C ) defned as (Horn and Schuck, 1981): u u v v Es = dxdy (4) x y x y c ( ) (5) E = u x + v y + t + dxdy an example of computed optcal flow before and after the smoothng process, respectvely. Determnng radal drecton: The two parameters of a moton vector are ts magntude and angle. The vector magntude represents the dsplacement of a pxel for two consecutve frames, whle the vector angle s ts drecton n terms of the axal (u) and the ordnal (v) component. The vector angle θ 1 s computed usng: θ 1 = a tan (v,u ) (6) In mathematcs, the two-arguments functon atan(y, x) s a varant of the arctangen functon, whch calculates an angle (n radans) between the postve x- axs and a pont gven by coordnate (x, y). Followng the standard mathematcal conventon, atan functon results angles that ncrease counter-clockwse. However, snce the optcal flow computaton uses clockwse conventon, the vector angle of optcal flow θ 1 also follows the clockwse conventon as shown n Fg. 3. The atan functon produces results n the range (-π, π] that can be convert to [0, π) by addng π to negatve value of θ 1. In clncal dagnoses, the physcan usually does not use the vector drecton to analyze the myocardal moton. The drecton of the vector wth respect to the center of the cavty s more useful nformaton because the physcan observes whether a segment moves to the center of the cavty or not. Therefore, n ths study, we ntroduce a new moton property, whch s called radal drecton defned as the drecton of a moton vector wth respect to the center of the cavty as llustrated n Fg. 3. The radal drecton α of a pont of nterest (x, y ) s the dfference between the angle of optcal flow at the pont of nterest (θ 1 ) and the angle between the pont and the cavty center (θ ), or defned as: α = θ1 θ (7) where, the angle θ can be calculated by the followng equaton: In terms of moton estmaton, pxels should not have abrupt changes n magntude and drecton of ther vector flow compared wth the adjacent pxels. Certan ponts n the neghborhood that have obvously dfferent magntudes or drectons can be consdered as errors due to mscomputaton of optcal flow. To smooth the varaton of the vectors n a neghborhood, we apply statstcal averagng to remove the outler data along the boundary. The outler data on the neghborng ponts are successvely removed and replaced by the average of neghborng vectors. Fgure a and b show 1048 θ = a tan (yc y,xc x ) (8) The Eq. 7 produces radal drecton values n the range (-π, π). To make the value smpler and more nformatve, we normalze ths value usng the followng rules: θ f π θ π θ = θ + π f π θ < π θ π f π>θ π (9)

4 physcan wll be able to quckly recognze the drecton to whch a segment moves. RESULTS (a) (b) Fg. : Example of boundary vectors on a segment (a) before and (b) after the smoothng process Smoothed endocardal optcal flow: Our proposed method was tested wth a set of clncal echocardography data, whch were prevously recorded by a physcan. The data were acqured on a parasternal short axs standard vew usng a Semens Acuson Sequoa scanner wth a 5 frame rate. Manual nterpretatons on the recorded data have been also performed by two cardologsts to provde manual dagnoss on the myocardal moton. At the end, ths manual dagnoss wll be used to valdate the result obtaned by the proposed method. Fgure 4 shows an example of four frames of ten consecutve sequences of PSAX vew echocardography mages. We then computed the optcal flow vectors of two consecutve mages (frames and 3) and appled the proposed method to these optcal flow vectors. In the Materals and Methods, we have seen that smooth and correct drectons were obtaned for the pxels located on the endocardum, whereas many ncorrect optcal flow vectors occurred nsde the myocardum. For ths reason, we should extract only the optcal flow vectors on the endocardum to provde the myocardal moton profle precsely. Pror to extractng the endocardal features, we have to manually select a few ponts dstrbuted along the boundary of the cavty and then generate other ponts along the boundary usng the B-splne algorthm as shown n Fg. 5a and b, respectvely. In the next stage, the vector flows on the boundary were obtaned by averagng 5 5 neghborng vector flows along the boundary and then smoothed as shown n Fg. 5c. Dstrbuton of radal drecton: To llustrate the mdanteror-septum (upper center segment) of Fg. 5c, the zoomed mage of the moton vectors and ther angle dstrbuton are shown n Fg. 6a and c, respectvely. Ths angle dstrbuton shows that these vectors have domnant drectons n the nterval The standard Fg. 3: Radal drecton of an optcal flow vector angle conventon follows a clockwse drecton orentaton where 0, 90, 180 and 70 ndcate the rght, therefore the radal drecton angle α wll be n the down, left and up drecton, respectvely. Accordng to range (0, π). The 0 means that the optcal flow vector ths conventon, a segment wth the domnant drectons drecton s towards the cavty center whereas the π n the nterval moves downward to the center. ndcates the opposte drecton. Smlarly, Fg. 6d shows an angle dstrbuton of the To facltate the nterpretaton of myocardal md-posteror (lower center segment) n Fg. 6b. The moton, we generated the dstrbuton of radal drecton domnant drecton s n the nterval and t for every segment for each frame. Ths dstrbuton ndcates that part of the segment moves upward to the shows the pattern of drecton n such a way that a center. 1049

5 (a) (b) Fg. 4: Four frames of cardac moton from end-dastole to end-systole: (a) 1st, (b) 4th, (c) 7th and (d) 10th frame (c) (d) (e) (f) (a) Fg. 6: Example of the usefulness of provdng the dstrbuton of radal drecton compared wth the vector angle dstrbuton for the mdanteror-septum (frst column) and md-posteror (second column) segment: (a) and (b) the zoomed mage of the moton vectors, (c) and (d) the vector angle dstrbuton and (e) and (f) the radal drecton dstrbuton DISCUSSION These two examples n Fg. 6a-c and b-d show that although the value of domnant drectons s largely (b) dfferent, both segments move towards the center. In other words, because the locaton of md-anterorsegment s on the upper center of myocardal, physcan should remember that t wll move towards the center only f the angle drecton s nearby 90. For the mdposteror whch s on the lower center segment, t moves towards the center f the domnant drecton s about 70. To enable such an nference to be made, t s necessary for the physcan to remember the angle conventon and also the parts of the cardac segment that are beng referred to. Hence, t s not easy to (c) correlate the angle dstrbuton and the center-drected moton for a partcular cardac segment. Fg. 5: (a) Selected cavty center and ntal ponts on If we evaluate the dstrbutons of moton vector The nd frame; (b) contnuous ponts along the based on radal drecton Fg. 6e and f, they are easer boundary and (c) a smoothed vector flow usng a for a physcan to analyze myocardal moton nstead of statstcal approach the angle of the vector flow tself. These fgures show 1050

6 that both segments whch move towards the center have a same domnant angle,.e., n the nterval 0 and 30. Physcans do not need to remember the angle conventon and also the locaton of the segment of nterest. They just to know a smple conventon that a 0 radal drecton means the vector moves to the center of the cavty whereas a 180 radal drecton means that the vector s movng to the opposte drecton of the cavty center. We conclude that the radal drecton s more nvarant to the segment locaton because we have consdered the vector locaton wth respect to the center n the computaton of the radal drecton. Addtonally, usng ths orentaton, the pattern of segmental moton drecton can be smply obtaned by consderng the domnant value of the radal drecton dstrbuton. CONCLUSION A new myocardal segmental moton property based on radal drecton has been descrbed.. The radal drecton s computed by consderng the angle of optcal flow at a pont of nterest and the normal angle between the pont and the cavty center. The ndvdual radal drecton along the boundary s then used to generate a radal drecton profle for every myocardal segment of each frame. The result shows that the radal drecton profle s easer for physcan to analyze the myocardal moton nstead of normal angular dstrbuton as well as more nvarant to segment locatons. ACKNOWLEDGEMENT Researchers would lke to acknowledge the Unversty Kebangsaan Malaysa (UKM-GUP-TKP ) for the fnancal support for ths research. We also thanks to Oteh Maskon and Ika Fazura Mohd Nor, who are wth the Cardac Care Unt, Medcal Center, Unverst Kebangsaan Malaysa, for provdng the cardac mage data and ther contnuous dscussons on the vsual analyss and nterpretaton of the cardac moton. REFERENCES Anderson, B., 007. The Normal Examnaton and Echocardographc Measurements. 1st Edn., Blackwell Publshng, ISBN-10: , pp: 51. Boukerrou, D., J.A. Noble and M. Brady, 003. Velocty estmaton n ultrasound mages: A Block Matchng Approach, LNCS, 73: , DOI: / _49 Duan, Q., E.D. Angeln, O. Gerard, K.D. Costa and J.W. Holmes et al., 006. Cardac moton analyss based on optcal flow on real-tme threedmensonal ultrasound data. Recent Advances n Dagnostc and Therapeutc Ultrasound Imagng for Medcal Applcatons, pp: tons/413-pdf.pdf Horn, B.K.P and B.G. Schuck, Determnng optcal flow. Artfcal Intell.. 9: DOI: / (81)9004- Ledesma-Carbayo, M.J., J. Kybc, M. Desco, A. Santos and M. Suhlng et al., 005. Spato-temporal nonrgd regstraton for ultrasound cardac moton estmaton. IEEE Trans. Med. Imag., 4: DOI: /TMI Ln, G.S., H.H. Hnes, G. Grant, K.Taylor and C. Ryals, 006. Automated quantfcaton of myocardal schema and wall moton defects by use of cardac SPECT polar mappng and 4-D surface renderng. J. Nuclear Med. Technol., 34: Papademetrs, X., A.J. Snusas, D.P. Done and J.S. Duncan, 001. Estmaton of 3D left ventrcular deformaton from echocardography. Med. Image Anal., 5: DOI: /S (00)000-0 Ryad, S., M.M. Musatafa, A. Hussan, O. Maskon and I.F.M. Noh, 011. Enhanced Optcal Flow Feld of Left Ventrcular Moton usng Quas Gaussan DCT Flter. In: Software Tools and Algorthms for Bologcal Systems, Arabna, H.R. (Ed.). Seres: Advances n Expermental Medcne and Bology, pp: DOI: / _46 Ryad, S., M.M. Musatafa, A. Hussan, O. Maskon and I.F.M. Noh, 009. Quas Gaussan DCT Flter for speckle reducton of ultrasound mages. LNCS, 5857: DOI: / _14 Sundar, H., H. Ltt and D. Shen, 009. Estmatng myocardal moton by 4D mage warpng. Patt. Recog., 4: DOI : /j.patcog Verones, F., C. Cors, E.G. Cana and C. Lambert, 006. Trackng of left ventrcular long axs from real-tme three-dmensonal echocardography usng optcal flow technques. IEEE Trans. Inform. Technol. Bomed., 10: DOI: /TITB World Health Organzaton, 010. Cardovascular Dseases