Data for MBI Workshop Statistics of Time Warpings and Phase Variations. Three-dimensional vascular geometry dataset

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1 Data for MBI Workhop Statitic of Time Warping and Phae Variation Mathematical Biocience Intitute, November 13-16, 2012 Three-dimenional vacular geometry dataet May 30, Data background Thee data have been collected within the AneuRik project 1 i a cientific endeavour that aimed at invetigating the role of veel morphology, blood fluid dynamic and biomechanical propertie of the vacular wall, on the pathogenei of cerebral aneurym. The project ha gathered together reearcher of different cientific field, ranging from neurourgery and neuroradiology to tatitic, numerical analyi and bio-engineering. 1 The project involved MOX Laboratory for Modeling and Scientific Computing (Dip. di Matematica, Politecnico di Milano), Laboratory of Biological Structure Mechanic (Dip. di Ingegneria Strutturale, Politecnico di Milano), Itituto Mario Negri (Ranica), Opedale Niguarda Ca Granda (Milano) and Opedale Maggiore Policlinico (Milano), and ha been upported by Fondazione Politecnico di Milano and Siemen Medical Solution Italia. 1

2 More information about the project can be found at the AneuRik webpage AneuRik data can be acceed from the AneuRik Web Repoitory managed by Emory Univerity and Orobix. Detailed decription of the project aim can be found e.g. in [6]. The iue of phae variation i decribed in [6]; how thi iue interplay with data claification i decribed in [8] and [9]. In thi report we give a hort decription of the problem and data. Reference. When uing thee data, pleae reference the AneuRik webpage and any among [6], [7] or [8]. 1.1 Problem and data Cerebral aneurym are deformation of cerebral veel characterized by a bulge of the veel wall. Thi i a common pathology in the adult population, i uually aymptomatic and not dirupting. Epidemiological tatitic (ee, e.g., [5]) ugget that between 1% and 6% of adult develop a cerebral aneurym during their live. The rupture of a cerebral aneurym, even if quite uncommon (about one event in every 10,000 adult per year), i uually a tragic event. Unfortunately, rupture-preventing therapie, both endovacular and urgical treatment, are not without rik; thi add to the fact that in clinical practice general indication about rupture rik are till miing. Even the origin of the aneurymal pathology i till unclear. Poible explanation that have been dicued in the medical literature focu on interaction between the biomechanical propertie of artery wall and hemodynamic factor, uch a wall hear tre and preure; the hemodynamic i in turn trictly dependent on vacular geometry. In particular, it ha been conjectured that the pathogenei of thee deformation i influenced by the morphological hape of cerebral arterie, through the effect that the morphology ha on the hemodynamic. For thi reaon, main goal of the AneuRik project ha been the tudy of relationhip between veel morphology and aneurym preence and location. Thee leion may originate along the left or right Internal Carotid Artery (ICA, in hort), two large arterie bringing blood to the brain, or at or after terminal bifurcation of the ICA, in the o-called Willi Circle. Each of the two ICA it for mot of it length outide the kull, along the neck, urrounded by mucle tiue; jut before it terminal bifurcation it enter inide the kull, paing through a dural ring (i.e., a hole in the kull bone). See Figure 1 and 2. Arterie downtream of ICA terminal bifurcation float 2

3 Figure 1: Left: draw of an Internal Carotid Artery (ICA); the ICA it for mot of it length outide the kull, urrounded by the neck mucle tiue; jut before it terminal bifurcation it enter inide the kull, paing through a dural ring (i.e., a hole in the kull bone). Right: the Willi circle, located ad the bae of the brain, inide the kull, i a net of mall arterie and capillarie connecting the main arterie bringing blood to the brain; the terminal part of the left and right ICA, clearly viible in the image, are indicated by arrow. Figure 2: Left: X-ray image of an aneurym along an ICA; the artery, with it iphon, i clearly viible in the image. Right: image recontruction of an ICA with aneurym (different ubject with repect to left panel). 3

4 Figure 3: Three-dimenional image of an Internal Carotid Artery with an aneurym [ubject 1]; the black line inide the veel i it centerline. in the brain humor, inide the kull. For thi reaon, aneurym located at or after ICA terminal bifurcation are more life-threatening; the poible rupture of one uch aneurym i fatal in mot cae. The AneuRik data et i baed on a et of three-dimenional angiographic image taken from 65 ubject, hopitalized at Niguarda Ca Granda Hopital (Milan), who were upected of being affected by cerebral aneurym. Out of thee 65 ubject, 33 ubject have an aneurym at or after the terminal bifurcation of the ICA ( Upper group), 25 ubject have an aneurym along the ICA ( Lower group), and 7 ubject were not found any viible aneurym during the angiography ( No-aneurym group). A commented above, Upper group ubject are thoe with the mot dangerou aneurym; for thi and other clinical reaon, for ome tatitical analye it might make ene to join the Lower and No-aneurym group in a unique group, to be contrated to the Upper group. Percentage of female and male and of right and left ICA do not differ ignificantly from 50% (the p-value of the tet for equal proportion are 0.14 and 0.78, repectively). Age, apart from a uperior outlier, appear normally ditributed (the p-value of the Shapiro- Wilk tet i 0.29), with a ample mean equal to year and a ample tandard deviation equal to year. Gender, ICA ide, and age are not included in the tatitical analyi becaue they are uppoed to be related to the aneurymal pathology only through their effect on geometry. Notice that due to the high radiation quantity implied by the can, thi exam i only performed in cae of acute ymptom and if the doctor trongly upect an aneurym may be the caue; alo, no follow-up i performed. The analye conducted within the AneuRik project have focued on the ICA, which i clearly recognizable in each of the 65 angiographie. Starting from the three-dimenional array of grey-caled voxel that i gener- 4

5 x y z Figure 4: Recontructed pace coordinate of ICA centerline for ubject 1, (x 1j, y 1j, z 1j ), veru the abcia parameter 1j, for j = 1,..., n 1 (n 1 = 1350). ated by the angiography (with lighter voxel howing the preence of flowing blood), the artery lumen (i.e., the volume that i occupied by flowing blood) i identified by a recontruction algorithm that i coded in the Vacular Modeling ToolKit (VMTK). See [3] and [4]. Figure 3 how the draw of the recontruction of the ICA of the firt ubject in the dataet, and alo diplay the recontructed centerline of the veel. The centerline i computed a the et of center of maximal phere incribed in the artery lumen. In particular, for every ubject i in our dataet (i = 1,..., 65), VMTK recontruction of ICA centerline i a et of point in R 3, {(x ij, y ij, z ij ) : j = 1, 2,..., n i }, where x, y, and z denote repectively the left/right, up/down and front/back coordinate of each point. It hould though be noticed that the x, y, and z coordinate are not abolute, but are relative to the cubic volume analyzed during angiography, that in turn depend on where the angiographic image ha been centered; thi mean that thee coordinate are not directly comparable acro ubject, ince they vary with the location of the canned volume. Point along the centerline are ordered moving downward along the ICA, from the point cloet to it terminal bifurcation (detected by VMTK) toward the proximal ditrict, i.e., aorta and heart. The reaon for thi choice i that the terminal bifurcation of the ICA i preent in each angiography, even if the portion of ICA captured by the angiography varie from ubject to ubject (depending on where the angiographic image ha been centered). For each ubject i, we can aociate the et of pace coordinate with an index et { ij : j = 1, 2,..., n i }, which meaure an approximate ditance along the ICA centerline, thu providing an approximate curvilinear abcia. More preciely, i1 i the ditance of the point (x i1, y i1, z i1 ) from the terminal bifurcation of the ICA (a determined by VMTK), and, for j = 2,..., n i, ij ij 1 = (x ij x ij 1 ) 2 + (y ij y ij 1 ) 2 + (z ij z ij 1 ) 2. The conventional negative ign highlight that we are moving uptream, i.e., in oppoite direction with repect to blood flow. Figure 4, for intance, 5

6 x Etimated centerline firt derivative, 65 patient y z Figure 5: Firt derivative {x0 (), y 0 (), z 0 ()} of etimated ICA centerline for the 65 ubject. diplay the recontructed pace coordinate of ICA centerline for ubject 1, (x1j, y1j, z1j ), veru the approximate curvilinear abcia parameter 1j, for j = 1,..., n1 (n1 = 1350). The number ni of data point available for each ubject range from 350 to 1380, and i almot perfectly correlated to the approximate length i ni i 1 of the recontructed centerline (correlation coefficient=0.999), which in turn varie from mm to mm. In other word, the grid denity of the 65 recontruction i the ame, even if the 65 grid are different. The grid are not equipaced; their average tep i 0.079mm. The recontruction algorithm alo provide, for each of the grid point, the radiu Rij of the veel lumen ection, computed a the radiu of the local maximal incribed phere. 1.2 Data preproceing Recontructed ICA centerline are of coure affected by meaurement and recontruction error. The multidimenional free-knot pline technique detailed in [7] might for intance be ued to obtain accurate etimate of thee three-dimenional curve and their derivative. Thi technique i ued to obtain the pre-proceed data provided for the workhop, including, for each ubject i = 1,..., 65, the etimated ICA centerline {xi (), yi (), zi ()}, their 6

7 firt two derivative {x i (), y i (), z i ()} and {x i (), y i (), z i ()}, and the correponding curvature of the centerline Curv i (). The firt derivative of the etimated ICA centerline of the 65 ubject are diplayed in Figure 5; in the picture, left carotid have been left-right reflected (o that the orientation in the three-dimenional pace of all recontructed ICA i the ame). The pre-proceed data include alo left-right reflected coordinate of the etimate of centerline and their derivative. 1.3 Phae variation Figure 5 how that the three-dimenional centerline diplay a coniderable mialignment. Thi mialignment i the expreion of a trong phae variability preent among the data, largely due to the different dimenion of the ICA of the variou ubject; if not taken properly into account, thi mialignment act a a confounding factor in the data analye. To enable meaningful comparion acro ubject, it i thu neceary to efficiently decouple the phae and the amplitude variability, the former being mainly due to the difference in the dimenion of ubject carotid and the latter intead to the difference in their morphological hape. [6], [8] and [9] decribe the anwer to thi problem given within the AneuRik project, conidering alo the iue of claification of thee three-dimenional curve. It hould be treed again that the portion of ICA captured by the angiography varie from ubject to ubject, depending on where the angiographic image ha been centered (moreover, even if the terminal bifurcation of the ICA i preent in each angiography, the bifurcation point identified by VMTK depend on bifurcation angle and other geometrical quantitie). For thi reaon, it eem unappropriate to ue directly on thee data a regitration method that force the tarting and ending abcia of the variou curve to be the ame. 1.4 Some goal of the analye Overall goal of the analyi hould be the tudy of relationhip between ICA morphology and aneurym preence and location. Two geometrical quantitie that trongly influence the hemodynamic, and hence may in turn play a role on the aneurym pathogenei, are the artery radiu and the artery curvature (the latter might be identified by the curvature of the artery centerline). Hence thee are good quantitie to have a look at. In general, one would of coure like to conider the three-dimenional hape of the carotid; in particular, the hape of the iphon characterizing the dital part of the ICA i certainly fundamental in determining the hemodynamic. Becaue of the complexity of the data, variou level of analyi are poible. For intance, analytic group intereted only in one-dimenional regi- 7

8 tration might focu their attention on one-dimenional curve uch a the ICA curvature function (we never carried out direct regitration of AneuRik data baed directly on the curvature profile). It would be then of interet to ee how the regitered curvature (or radiu) function relate to the preence and location of the aneurym, and to the grouping of ubject in the Upper, Lower and No-aneurym group. Certainly of big interet i the claification (unupervied clutering) of ICA depending on their morphological hape ([8] and Section 5 of [9] report ome of the reult in thi direction, given within the AneuRik project). Again, depending on the interet of the analytic group, thi might perhap be done by looking only at one-dimenional curve, or intead by working on the full three-dimenional geometrie. Studying how the obtained ICA claification relate to the ubject group, Upper, Lower and No-aneurym, can hed ome light on the pathology. When dealing with the problem of claification of ICA morphologie, it might alo be of interet to know that one of the claification motly ued in the medical literature, propoed by [1], dicriminate between Γ-haped, Ω-haped, and S-haped ICA, according to the form of iphon in their dital part, which may reemble the letter Γ, Ω or S (in preence of zero, one, or two large bend in the iphon, repectively). It hould be mentioned that, beide the data provided for the workhop analyi, the AneuRik data-warehoue alo include the full 3D recontruction of the ICA wall, and of the connecting arterie, a well a data concerning hemodynamical quantitie, uch a wall hear tre and preure, imulated via computational fluid dynamic in the real ubject-pecific ICA geometrie (ee [2]). 2 Data file The file Patient.txt contain: patient patient number, from 1 to 65 code type AN_Abcia patient code patient type: "U" (Upper group) if at leat one aneurym at or after ICA bifurcation "L" (Lower group) if aneurym before ICA bifurcation (and no viible aneurim at or after ICA bifurcation) "N" (No-aneurym group) if no viible aneurym location of the aneurym along the ICA centerline or at 8

9 ICA centerline bifurcation (not available if type = N or if aneurym i after ICA bifurcation) left_right left or right carotid: "LC" Left Carotid "RC" Right Caotid For each ubject, from 1 to 65, the file Rawdata-FKS-patientnumber.txt contain both raw and preproceed data: Curv_Abcia MISR X0_ob, Y0_ob, Z0_ob X0_FKS, Y0_FKS, Z0_FKS X0_FKS_ref X1_FKS, Y1_FKS, Z1_FKS X1_FKS_ref curvilinear abcia of ICA centerline Maximum Incribed Sphere Radiu of the ICA, i.e., radiu of the veel lumen ection (raw data) oberved value of the three pace coordinate of ICA centerline (raw data) three pace coordinate of free-knot-pline etimate of centerline (preproceed data) left-right reflected firt coordinate of centerline etimate; for right carotid equal X0_FKS for left carotid equal -X0_FKS (preproceed data) firt derivative of centerline etimate (preproceed data) left-right reflected firt coordinate of firt derivative of centerline etimate; for right carotid equal X1_FKS for left carotid equal -X1_FKS (preproceed data) X2_FKS, Y2_FKS, Z2_FKS X2_FKS_ref econd derivative of centerline etimate (preproceed data) left-right reflected firt coordinate of econd derivative of centerline etimate; 9

10 for right carotid equal X2_FKS for left carotid equal -X2_FKS (preproceed data) Curvature_FKS curvature of centerline etimate (preproceed data). Aitance when analyzing the data Pleae, write to Reference [1] Krayenbuehl, H., Huber, P., and Yaargil, M. G. (1982), Krayenbuhl/Yaargil Cerebral Angiography, Thieme Medical Publiher, 2nd ed. [2] T. Paerini, L.M. Sangalli, S. Vantini, Marina Piccinelli, S. Bacigaluppi, L. Antiga, E. Boccardi, P. Secchi, A. Veneziani (2012), An Integrated CFD- Statitical Invetigation of Parent Vaculature of Cerebral Aneurym, Cardiovacular Engineering and Technology, DOI: / x. [3] M. Piccinelli, S. Bacigaluppi, E. Boccardi, B. Ene-Iordache, A. Remuzzi, A. Veneziani, and L. Antiga (2011), Geometry of the ICA and recurrent pattern in location, orientation and rupture tatu of lateral aneurym: an imagebaed computational tudy, Neurourgery, 68, 5, [4] M. Piccinelli, A. Veneziani, D.A. Steinman, A. Remuzzi, and L. Antiga (2009), A framework for geometric analyi of 852 vacular tructure: application to cerebral aneurym, IEEE Tran. Med. Imaging, 28, 8, [5] Rinkel, G. J., Djibuti, M., Algra, A., and Van Gijn, J. (1998), Prevalence and Rik of Rupture of Intracranial Aneurym: A Sytematic Review, Stroke, 29, [6] Sangalli, L. M., Secchi, P., Vantini, S., and Veneziani, A. (2009a), A Cae Study in Exploratory Functional Data Analyi: Geometrical Feature of the Internal Carotid Artery, J. Amer. Statit. Aoc., 104, [7] (2009b), Efficient etimation of three-dimenional curve and their derivative by free-knot regreion pline, applied to the analyi of inner carotid artery centreline, Journal of the Royal Statitical Society Ser. C, Applied Statitic, 58, 3, [8] L.M. Sangalli, P. Secchi, S. Vantini and V. Vitelli (2010a), K-mean alignment for curve clutering, Computational Statitic and Data Analyi, 54, [9] (2010b), Claification of Functional Data: Unupervied Curve Clutering When Curve are Mialigned, 2010 JSM Proceeding, pp