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Intenational Jounal of Compute Science Issues, Vol. 4, No., 9 ISSN (Online): ISSN (Pint): D/D Registation of Mapping Cathete Images fo Ahythmia Inteventional Assistance Pascal Fallavollita

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Intenational Jounal of Compute Science Issues, Vol. 4, No., 9 ISSN (Online): ISSN (Pint): D/D Registation of Mapping Cathete Images fo Ahythmia Inteventional Assistance Pascal Fallavollita School of Computing, Queen s Univesity, Kingston, Ontaio, Canada Abstact Radiofequency (RF) cathete ablation has tansfomed teatment fo tachyahythmias and has become fist-line theapy fo some tachycadias. The pecise localization of the ahythmogenic site and the positioning of the RF cathete ove that site ae poblematic: they can impai the efficiency of the pocedue and ae time consuming (seveal hous). Electoanatomic mapping technologies ae available that enable the display of the cadiac chambes and the elative position of ablation lesions. Howeve, these ae expensive and use custom-made cathetes. The poposed methodology makes use of standad cathetes and inexpensive technology in ode to ceate a 3D volume of the heat chambe affected by the ahythmia. Futhe, we popose a novel method that uses a pioi 3D infomation of the mapping cathete in ode to estimate the 3D locations of multiple electodes acoss single view C-am images. The monoplane algoithm is tested fo feasibility on compute simulations and initial canine data. Key wods: 3D econstuction, monoplane imaging, navigation system, cathete ablation, cadiac ahythmias. 1. Intoduction Sevee disodes of the heat hythm that can cause sudden cadiac death o mobidity, can be teated by adiofequency (RF) cathete ablation, which consists of inseting a cathete inside the heat, nea the aea fom which oiginates the abnomal cadiac electical activity, and deliveing RF cuents though the cathete tip so as to ablate this ahythmogenic aea. The pecise localization of the ahythmogenic site and positioning of the RF cathete at that site ae poblematic: they can impai the efficacy of the pocedue and the pocedue can last many hous, especially fo complex ahythmias. To shoten the duation of RF cathete ablation and incease its efficiency, commecial systems that povide a 3D colo display of the cadiac electical activation sequence duing the ahythmia have been poposed. These systems incopoate basket electode aays (Constellation, EPT Inc.), cathetes with a balloon electode aay (Ensite 3, Endocadial Solutions Inc.) and cathetes with magnetic position detectos (CARTO TM, Biosense Webste Inc.). A complete navigation and egistation famewok is also available (CatoMege, Biosense Webste Inc.). All these systems including puchase of system-specific cathetes ae costly fo hospitals. The fist two technologies can map the cadiac activation sequence using data ecoded duing a single beat wheeas the CARTO TM system elies on data ecoded point-by-point duing numeous beats, which implies that the ahythmia must emain stable duing the pocedue. Othe appoaches have also been poposed to guide RF ablation theapy, such as the visualization of an optically tacked cathete by making use of magnetic esonance imaging (MRI) [1-], the combination of MRI and fluooscopy [3], ultasound imaging of the ablation cathete [4], the combination of ultasound and peopeative compute tomogaphy (CT) [5], o peopeative imaging (CT/MRI) fo ablation planning [6-7]. These appoaches omit incopoating the all impotant electophysiological data which allows the inteventionist to detemine the oigin of the ahythmia. Invese electocadiogaphy, an established fomulation is the imaging of the activation time map on the entie suface of the heat fom ECG mapping data. A few examples computed fom body suface potential measuements have been incopoated to segmented MRI images by Tilg et al. [8-9] and to biplane econstuctions of the cadiac geomety by Ghanem et al. [1-11]. DeBuck et al. [] have constucted a patient-specific 3D anatomical model fom MRI and meged it with fluooscopic images in an augmented eality envionment that enables the tansfe of cadiac activation times onto the model. Cistofoetti et al. [13] have developed a stategy fo the spatial egistation of the coase electoanatomic map obtained by the CARTO TM system, and the detailed geometical econstuction of the left atia and pulmonay veins etieved fom CT images. Methods based on eal-time integation of electoanatomic and tomogaphic modalities ae being developed and offe an intemodal fusion based on semi-automatic egistation pocedues initialized by fiducial point paiing [14-15]. The above methods make use of peopeative data which do not eflect the eal-time movement of the heat at the time of intevention, and intoduce a logistical poblem as these technologies ae not pesent in the electophysiological intevention oom. Intenational Jounal of Compute Science Issues, Vol. 4, No., 9 11 Recently, we have poposed a moe affodable fluooscopic navigation, emulating CARTO TM, by obtaining local activation times fom a oving cathete whose positions ae computed point-by-point fom biplane fluooscopic pojections. We also poposed a novel concept by supeimposing the isochonal map depicting the cadiac electical activation sequence diectly ove the D fluooscopic image of the heat [16], a method that the CARTO TM technology lacks. Howeve, biplane fluooscopy systems ae ae in the clinical setting which in tun emphasizes the impotance of developing singleview 3D econstuction algoithms. The focus of this pape is a continuation of ou pevious wok, but with two significant modifications. To begin with, we conside implementing a full pespective camea model instead of the paallel pojection concept so as to ceate a moe pecise 3D geomety of the heat chambe affected by the ahythmia. Second, ou aim is to answe the following question: is it possible to estimate pecisely the 3D locations of the mapping cathete acoss all C-am image fames in a cadiac cycle using only a single view? We popose to use a pioi 3D infomation of the mapping ablation cathete positions in ode to achieve this. If this is possible, then the inteventionist could possibly educe pocedue time accodingly as a monoplane C-am fluooscope is the pimay imaging modality used in clinic and can povide eal-time data images as well. To ou knowledge this is the fist wok epoted on estimating 3D locations using single view sequences in ode to assist cathete ablation pocedues. Theefoe, we tag this wok as a feasibility study by pesenting a pactical implementation and expeimental analysis using compute simulations and initial esults on canine data.. Methodology.1 Cental Intuition Clinical accuacy is detemined by 3D econstuction pecision in the ode of mm o less and we don t expect to achieve this using a monoplane sequence. As showed in [16], using only a single D C-am image the ecoveed cathete depth had an eo of about 1 mm. We believe that by incopoating tempoal knowledge of the cathete coodinates may help impove depth estimation esults. Initial a pioi 3D infomation of the mapping cathete can be obtained using pe-opeative data fom CT/MRI o via two-view econstuction by otating the monoplane C- am fluooscope at two pependicula angulations and acquiing monoplane sequences. In this pape, we focus on the latte since the pincipal imaging modality used to guide cadiac ablation pocedues is the C-am fluooscope. Like most wok in the cadiac field, the 3D a pioi coodinates ae econstucted in the diastolic cadiac phase as heat motion is consideed to be minimal at this instant. We then poceed to select one of the monoplane sequences acquied and estimate the depth of the mapping cathete at each image fame. The idea is to detemine if o when the 3D econstuction becomes inaccuate. In the end, what will be equied is poviding a 3D visual aid to the inteventionist of the heat chambe and fusing the isochonal times on it in ode to help them position coectly the mapping ablation cathete on the ahythmogenic site.. C-am Fluooscopy Calibation Full Pespective Camea Model: Figue 1 shows the full pespective camea model that will be used fo the 3D econstuction poblem. If we define a thee dimensional point P wold [X Y Z 1] T in the wold coodinate system, then its D pojection in an image, m [u v 1] T, is achieved by constucting a pojection matix: P mat kf kf uo v o 1 m P mat P wold t x t y t z The intinsic matix of size [3x3], contains the pixel coodinates of the image cente, also known as the pincipal point (u o, v o ), the scaling facto k, which defines the numbe of pixels pe unit distance in image coodinates, and the focal length f of the camea (in metes). The extinsic matix of size [3x4] is identified by the tansfomation needed to align the wold coodinate system to the camea coodinate system. This means that a tanslation vecto, t, and a otation matix, R, need to be found in ode to align the coesponding axis of the two efeence fames. Lastly, image esolution (usually mm/pixel) is calculated fom the imaging intensifie size divided by the actual size of the image in pixels. Y C (,) v o Z C XC m u o f Image P WORLD Fig 1. The pespective camea model. Any 3D wold point can be pojected onto a D plane and its coodinates would be (u, v) R,T Z W Y W X W (1) Intenational Jounal of Compute Science Issues, Vol. 4, No., 9 pixels. The camea model is taken fom the Epipola Geomety Toolbox [17]. Image esolution would be equal to C-am intensifie size divided by image size in pixels. Paallel & Weak Pespective Camea Models: An othogaphic camea is one that uses paallel pojection to geneate a two dimensional image of a thee dimensional object. The image plane is pependicula to the viewing diection. Paallel pojections ae less ealistic than full pespective pojections, howeve they have the advantage that paallel lines emain paallel in the pojection, and distances ae not distoted by pespective foeshotening. The paallel pojection matix is given by: P affine k * k * 11 1 k * k * k * k * 13 3 ( k * t x ) + uo ( k * t ) + y vo 1 The weak pespective camea is an appoximation of the full pespective camea, with individual depth points Z i eplaced by an aveage depth Z avg. We define the aveage depth, Z avg as being located at the centoid of the cloud of 3D points in the wold coodinate system. The weak pespective pojection matix is given by: P weak whee f * k * f * k * Z avg 11 1 f * k * f * k * ([ T ] f * k * f * k * 13 3 centoid) + t.3 Mapping Cathete Segmentation ( f * k * t ) + ( u * Z z x y Z avg o o avg ( f * k * t ) + ( v * Z We have ecently developed a fou-step filte in ode to enhance coonay ateies visible in C-am fluooscopy images [18]. Optimal filte paametes ae pesented thee and omitted in this pape fo bevity. We applied the same filte to enhance the cathetes and extact electode coodinates. Following is a bief desciption of these filtes. Homomophic Filteing: A homomophic filte is fist used to denoise the fluooscopic image. The illumination component of an image is geneally chaacteized by slow spatial vaiation. The eflectance component of an image tends to vay abuptly. The homomophic filte tends to decease the contibution made by the low fequencies and amplify the contibution of high fequencies. The esult is simultaneous dynamic ange compession and contast enhancement. The homomophic filte is given by: H L c ( D ( u, v ) / D o H ( u, v) ( γ γ ) (1 e ) + γ with γ L 1 and γ H 1. The coefficient c contols the shapness of the slope at the tansition between high and L avg ) ) () (3) (4) low fequencies, wheeas D o is a constant that contols the shape of the filte and D(u,v) is the distance in pixels fom the oigin of the filte. Peona-Malik Filteing: The Peona-Malik filte is implemented hee in ode to educe and emove both noise and textue fom the image, as well as, to peseve and enhance stuctues. The diffusion equation is given by I t div( c( x, y, t) I) Whee I is the input image and c(x, y, t), the diffusion coefficient, will contol the degee of smoothing at each pixel point in the image. The diffusion coefficient is a monotonically deceasing function of the image gadient magnitude. It allows fo locally adaptive diffusion stengths; edges ae selectively smoothed o enhanced based on the evaluation of the diffusion function. Although any monotonically deceasing continuous function of the gadient would suffice as a diffusion function, two functions have been suggested: I c ( x, y; t) exp( ( ) ) Κ Κ is efeed to as the diffusion constant o the flow constant. The geatest flow is poduced when the image gadient magnitude is close to the value of Κ. Theefoe, by choosing Κ to coespond to gadient magnitudes poduced by noise, the diffusion pocess can be used to educe noise in images. Complex Shock Filteing: The complex shock filte couples shock and linea diffusion in the discete domain, showing that the pocess conveges to a tivial constant steady state. To egulaize the shock filte, the authos suggest adding a complex diffusion tem and using the imaginay value as the contolle fo the diection of the flow instead of the second deivative. The complex shock filte is given by I ~ I t π θ (5) (6) actan ( a Im( )) I + λiηη + λ Iξξ (7) whee a is a paamete that contols the shapness of the slope, λ eiθ is a complex scala, λ is a eal scala, ξ is the diection pependicula to the gadient and η is the diection of the gadient. As fluooscopy images have a low signal to noise atio they tend to be noisy with atifacts pesent in them. Hence, we believe that applying a complex filte will esult in a obust and stable debluing pocess fo the images as the filte is effective in vey noisy envionments. Intenational Jounal of Compute Science Issues, Vol. 4, No., 9 13 Mophological Opeation: Mophological filteing was applied as a final image pocessing step in ode to eliminate backgound elements aound the object of inteest. The stuctuing element consists of a patten specified as the coodinates of a numbe of discete points elative to a defined oigin. We chose a disk stuctuing element that has a adius of a few pixels, since the contous of the cathetes and electodes can be modeled as a disk. Electode Segmentation & Convex Hull: Using MatLab, the 4-step filte was implemented and applied on both monoplane C-am datasets, beginning with the diastolic image. The smoothed images wee then automatically thesholded using Otsu s method. We then labeled connected components in this image using the bwlabel function in MatLab. The centoid of the electodes in each labeled egion was then calculated using the egionpops function so as to obtain the coodinates equied in the two C-am views. The algoithm outputs the centoid automatically and in case of failue, due to electodes o cathetes ovelapping, we manually segment the image to obtain the desied coodinates. The convex hull algoithm is a classical and popula method used to econstuct a 3D object fom an unoganized set of points. The D vesion of this algoithm (which is easie to undestand) is descibed as follows. Let S be a finite set of twodimensional points in the plane. The convex hull of S is the smallest convex set that contains S. This means that the bounday of the convex hull is a convex polygon, whose vetices ae points of S, and whose edges ae line segments joining pais of points of S..4 A Pioi 3D Monoplane Algoithm We suppose that we have at ou disposal a set of n 3D ablation cathete electode coodinates (X n, Y n, Z n ) at time t obtained fom two-view fluooscopic data. These a pioi coodinates ae expessed in the camea efeence fame in ode to have a Z-diection coesponding to cathete electode depth. Secondly, we have at ou disposal the C-am fluooscope ganty paametes which can be extacted fom the image heade DICOM files. These paametes enable us to constuct a pojection matix fo a specific viewing angle. By selecting one of the two acquied monoplane datasets, we can solve fo the 3D displacements (dx i,i+1, dy i,i+1, dz i,i+1 ) between consecutive C-am image fames beginning with the fist image i1. Expanding equation (1) and using an additional C-am image i, we obtain ou fist two equations as follows u v m ( X + dx m ( X + dx 5 m ( X + dx m ( X + dx ( Y + dy ( Y + dy ( Y + dy ( Y + dy ( Z + dz 3 11 ( Z + dz 7 11 ( Z + dz ( Z + dz 4 8 Both equations descibe the pixel coodinates in the second image (u, v ) and the twelve coefficients m i 1: ae the values of the pojection matix. By adding an additional C-am image fame i 3 we obtain two new equations with thee additional unknowns in 3D u3 v3 m1 ( X + dx + dx3 ( Y + dy + dy 3 3 ( Z + dz + dz 3 4 m9 ( X + dx + dx3 1 ( Y + dy + dy 3 11( Z + dz + dz 3 m5 ( X + dx + dx3 6 ( Y + dy + dy 3 7 ( Z + dz + dz 3 8 m9 ( X + dx + dx3 1 ( Y + dy + dy 3 11( Z + dz + dz 3 These fou equations take into account the spatial positions of a pojected 3D wold point on the acquied C-am images. As we have fou equations with six unknowns we can extact two additional equations based on the fact that the Euclidean distances in pixels, d, between cathete electode points in two consecutive images ae known. It is to note that the distance between 3D points is not the same as the distance between thei pojected image points. Thus, we conside othogonal pojection estimations in this case and we deem that this appoximation is suitable enough fo the poposed analysis. We aive at the following two equations d d 3 ( u u1) + ( v v1) ( u3 u ) + ( v3 v ) (8) (9) (1) We can now solve fo the thee dimensional displacements. A Levenbeg-Maquadt optimization scheme [19] can be used hee in ode to solve fo the unknown displacements. Fo the optimization scheme, initial appoximations ae a equiement to initialize the pocess. Hence, a suitable appoximation fo the displacements dx and dy can be obtained if we conside a paallel back pojection of the D image points into the wold coodinate system. As fo the displacements dz, if we assume that the aveage depth of the cathete electodes emains elatively constant in consecutive time fames (i.e. weak pespective camea model), then we can calculate the aveage depth of the 3D points (X, Y, Z). This aveage depth should be elatively the same at futue time instants t, 3, etc., signifying that depths dz will be equal to zeo fo the optimization scheme. Howeve, fo the sake of a moe exhaustive analysis, we also conside depth displacements dz [1-5] millimetes as well. To justify the ange of appoximations, we note that the acquisition fame ate of the fluooscopy images was such that the movement between cathete electodes in two adjacent images Intenational Jounal of Compute Science Issues, Vol. 4, No., 9 14 esulted in displacements less than ten pixels. Finally, we note that the poposed equations do not incopoate nonigid constaints implying that the monoplane 3D econstuction of igid moving objects (i.e. cathete electodes) might be feasible..5 Clinical Data Acquisition A mongel dog was anesthetized and laid on its ight side on a fluooscopy table (Integis Allua, Philips Inc.). A efeence cathete and a pacing cathete wee inseted into the ight venticle, close to the septal wall. The ole of the efeence cathete was to define an oigin fo ou 3D coodinate system. This was impotant as motion atifacts ae eve pesent duing the expeiments (heat beat, espiation, etc.), hence we deemed it appopiate to position it nea a igid landmak so that it expeiences less movement due to atifacts. The ole of the pacing cathete was to poduce a simple electical activation sequence so as to validate the isochonal maps. Finally, a standad RF ablation cathete was inseted fom the femoal vein into the left venticle (LV) of the dog. Duing the couse of the expeiment, this mapping cathete was moved to diffeent sites (i.e. point-by-point as the CARTO TM system) within the venticle in ode to obtain electical and geometical data fom sufficient sites to map the activation sequence. The landmaks wee selected to eflect as closely as possible the entie volume of the venticle. Electogams wee ecoded using the CadioMap softwae system (Reseach Cente at Sacé Coeu Hospital, Monteal, Canada). Specifications fo the acquisition softwae wee: 1 samples/second,.5 Hz high-pass and 45 Hz low-pass fequencies. Local activation time was measued (ms) as the diffeence in the times of the fastest negative deflections (dv/dt) see

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