3-d vascular skeleton extraction and decomposition

IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 1, JANUARY 2014 139

3-D Vascular Skeleton Extraction and DecompositionAshirwad Chowriappa, Yong Seo, Sarthak Salunke, Maxim Mokin, Peter Kan, and Peter Scott

Abstract—We introduce a novel vascular skeleton extraction anddecomposition technique for computer-assisted diagnosis and anal-ysis. We start by addressing the problem of vascular decomposi-tion as a cluster optimization problem and present a methodologyfor weighted convex approximations. Decomposed vessel struc-tures are then grouped using the vessel skeleton, extracted usinga Laplace-based operator. The method is validated using preseg-mented sections of vasculature archived for 98 aneurysms in 112patients. We test first for vascular decomposition and next for ves-sel skeleton extraction. The proposed method produced promisingresults with an estimated 80.5% of the vessel sections correctly de-composed and 92.9% of the vessel sections having the correct num-ber of skeletal branches, identified by a clinical radiological expert.Next, the method was validated on longitudinal study data fromn = 4 subjects, where vascular skeleton extraction and decompo-sition was performed. Volumetric and surface area comparisonswere made between expert segmented sections and the proposedapproach on sections containing aneurysms. Results suggest thatthe method is able to detect changes in aneurysm volumes andsurface areas close to that segmented by an expert.

Index Terms—Analysis, decomposition, skeleton, vascular.

I. INTRODUCTION

SUBARACHNOID hemorrhage caused by the rupture of ananeurysm is one of the common causes of stroke. Each year,

approximately 795 000 Americans experience a new or recur-rent stroke [1]. To perform pre- or poststroke assessment, someform of analysis of the vasculature has to be carried out [2], [3].In this paper, we focus on vascular decomposition and vesselskeleton extraction as a fundamental approach to understand thenature of complex vascular structures in computer-assisted di-agnosis (CAD) and analysis. The weighted approximate convexdecomposition (WACD) methodology for vessel decompositionwas first proposed in [4]. We extend this prior work and proposea twofold vessel segmentation approach. We first decomposethe vasculature into substructures. Next, the substructures aregrouped using the extracted vessel skeleton (see Fig. 1).

Manuscript received October 28, 2012; revised February 20, 2013 and April22, 2013; accepted April 27, 2013. Date of publication May 7, 2013; date ofcurrent version December 31, 2013.

A. Chowriappa and P. Scott are with the Department of Computer Scienceand Engineering, The State University of New York, Buffalo, NY 14214 USA(e-mail: [email protected]; [email protected]).

Y. Seo and S. Salunke are with the Department of Mechanical and AerospaceEngineering, The State University of New York, Buffalo, NY 14214 USA(e-mail: [email protected]; [email protected]).

M. Mokin and P. Kan are with the Department of Neuroscience, BuffaloGeneral Hospital, Buffalo, NY 14214 USA (e-mail: [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JBHI.2013.2261998

A. Previous Work on Decomposition and Skeleton Extraction

The literature shows several 2-D/3-D vascular segmentationand skeleton extraction methods [4]–[9]. For extended reviewson vessel segmentation algorithms, we refer the reader to the fol-lowing surveys [10]–[12]. Methods adapted from generic seg-mentation algorithms generally use a model-based approach,whereas others use the notion of vessel skeleton (centerline) forsegmentation.

On skeleton-based approaches, Ertan et al. [13] presented aunified coarse-to-fine approach for extracting the medial axisof the vascular tree. An innovative 3-D multibranch tubularstructure and centerline extraction method is proposed in [14].Although the classical minimal path techniques can only detecta single curve between two predefined initial points, this methodpropagates outward from only one initial seed point to detect 3-Dmultibranch tubular surfaces and centerlines simultaneously. In[15], vessel centerlines are obtained from a homotopic thinningof the vessels segmented using a level set method.

In contrast to skeleton-based methods, model-based tech-niques naturally capture the physics and geometry of vascu-lar structures (more generally, tube-like structures) that varyspatially. A geometric deformable model for segmenting tubu-lar structures is presented in [16]. The main advantage of thistechnique is its ability to segment twisted, convoluted, and oc-cluded structures without the need for user interaction. Christianet al. [17] present an approach for simultaneously separating andsegmenting multiple interwoven tubular tree structures. Alsoin [18], the authors discus a deformable model for detectingbifurcations and providing structural analysis.

B. Our Vascular Decomposition Approach

In this paper, we propose a hybrid approach that 1) first de-composes the vasculature into subcomponents. 2) Next, a group-ing of subcomponents is performed from the extracted vesselskeleton. Our approach uses convex decomposition, a topic thathas been significantly investigated [19], [20]. However, exactconvex decomposition is not well suited for complex shapessuch as vascular structures. An exact decomposition of a com-plex shape such as a vascular tree can lead to unacceptablylarge number of components which may not have meaningfulrelationships. To overcome this problem, we propose a WACDmethodology that is well suited for vessel decomposition illus-trated in Fig. 1. It can be seen that an approximate decomposi-tion [see Fig. 1(c)] produces a parsimonious representation ofthe vessel structure.

Our proposed vascular decomposition approach can be di-rectly performed on the surface mesh without the need for skele-ton extraction. However, when dealing with complex and highlytortuous structures seen in the vasculature, such decomposi-tion would produce subcomponents without correct anatomical

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140 IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 1, JANUARY 2014

Fig. 1. (a) Reconstructed surface mesh of a tortuous vessel tree, followed by (b) decomposition using the WACD strategy produces nine clusters for the vesseltree. Clusters are shown as different colored convex hulls of varying sizes. (c) Vessel skeleton is extracted and (d) decomposed clusters are grouped according toskeleton branches.

associations [since several decomposed components can belongto the same vessel branch, shown in Fig. 1(b)]. Using the vesselskeleton, we group the decomposed components into parsimo-nious descriptions with useful physiological significance [seeFig. 1(d)].

C. Our Vascular Skeleton Extraction Approach

We introduce a new vessel skeleton extraction technique thatis applied directly on the vascular mesh representation. Themethod that we propose is similar to that of Cao et al. [21].However, their approach only works on point cloud models anddoes not consider the mesh topology. In our approach, the vesseltwo-manifold surface is iteratively shrunk into an approximatezero-volume degenerate mesh that abstracts the given vesselskeleton topology [see Fig. 1(c)]. The contraction process issetup as an energy minimization problem involving a discreteLaplace operator [22], [23] that removes the vessel geometry de-tails along the normal directions. Appropriate weight functionsare chosen such that the surface mesh contracts into a minimalvolume skeletal representation. This skeleton representation ofthe vasculature is also important for diagnosing and treatingpathologies, and in follow-up study analysis.

The two main contributions of this paper are as follows: 1)We propose a novel Laplacian-based vessel skeleton extractionmethodology. 2) We extend our WACD approach [4] and use theproposed vessel skeleton methodology to perform vascular seg-mentation (aneurysm and bifurcation decomposition) in CADanalysis.

This paper is organized as follows. In Section II-A, we intro-duce surface mesh generation for clinical data. In Section II-B,we compute the dual graph and define curvature parameters thatdrive the decomposition cost function. Vessel skeleton extrac-tion using the Laplace smoothing is discussed in Section II-C.Finally, we present our results in Section III and conclude inSection IV.

II. MATERIALS AND METHODS

A. Data Preprocessing and Mesh Generation

The clinical dataset consisting of contrast enhanced CTA data(slick thickness: 1.25 mm, stored using DICOM standards) wasused for the mesh generation. Volumes of interest around iden-tified vascular structures are specified using maximum inten-sity projections (MIP). More specifically, the following vessel

sections are reconstructed: basilar artery (BA), anterior commu-nicant artery (ACoA), posterior communicant artery (PCoA),middle cerebral artery (MCA), internal carotid artery (ICA),and superior cerebelar artery (SCA). Prior to segmentation andreconstruction, an anisotropic diffusion filter is applied [24].This filter reduces the noise while preserving small vascularstructures enabling better segmentation, which is important inthe region of the brain. Next, we remove the skull bones, thesinuses and the skin, having similar intensity as the vessels, us-ing double thresholding (dt1 , dt2 , dt3 , dt4). A 3-D model of thevessel is obtained as an isosurface of intensity zero, resultingfrom the level set evolution, implemented utilizing ITK [25].For a detailed description, we refer the reader to [26]. In orderfor small vessels to be included, isosurface Iiso = 118 valueis used. Values for the level set threshold lt = 36, variancelσ2 = 0.3, and number of iteration it = 120 in ITK were chosen.The parameter settings that were used in double thresholdingwere dt1 = 183 (bone), dt2 = 318 (bone boundary), dt3 = 714(mean bone boundary), and dt4 = max(I) (maximum intensityof the dataset).

B. Vascular Decomposition

In this section, we summarize our WACD methodology [4].From the computed vessel surface representation, convex de-composition is employed to partition the mesh into a minimalset of convex subsurfaces,S = {s1 , s2 , ..sn}. The two-manifoldsurface S is defined in R3 as V = {v1 , v2 , v3 , .., vi}, T ={t1 , t2 , t3 , .., tj}, and E = {e1 , e2 , e3 , . . . , ek} (where V is thevertex set, T is the set of triangles, and E is the edge set). Wedefine the dual graph D∗ associated with the surface mesh S.Edge weights for D∗ are computed from shape indices to favorcertain features over others. In mesh decimation, vertices of D∗

are iteratively clustered by applying a decimation operator thatminimizes a weighted cost function.

1) Computing Shape Index and Edge Weights: The curva-ture of a point on the surface can be defined by its maximumand minimum curvatures (k1 , k2). Using these curvature mea-sures, we determine whether the given point lies on a concave,convex, ridge, or saddle region (see Fig. 2). Saddle regions arecharacterized by being concave on one plane and convex fromanother (e.g., horse saddle) and most frequently correspond tosurfaces at vessel bifurcations. Ridges on the other hand can befound on aneurysm heads and ostiums (neck). For each nodein the graph D∗, we define a set of rings around the node as

CHOWRIAPPA et al.: 3-D VASCULAR SKELETON EXTRACTION AND DECOMPOSITION 141

Fig. 2. Primitive shape types for corresponding surface characteristics of ananeurysm sac.

Fig. 3. Decomposition using WACD on sections of vasculature, (a) and (b)shows decomposition of vessel tree with bifurcations, (c)–(f) shows decompo-sition used to separate vessel sections fused with sections of cranium.

follows: the ith ring around node vj is defined as the set ofvertices v∗ ∈ V for which there exists a shortest path from vj

to v∗ containing i edges. The L−ring neighborhood of node vj

is defined as the set of rings i < L about node vj . To capturethe shape of the L−ring neighborhood (in our implementationa three-ring neighborhood), we use the shape index introducedby Cees et al. [27], where the shape index SI derived from theprincipal curvatures is given as

SI =12− 1

πarctan

kmin + kmax

kmin − kmax. (1)

The values of SI varies in the closed interval [0.0, 1.0] andevery distinct surface shape (see Table I) corresponds to a uniquevalue of SI (except for planar surfaces, which will be mappedto the value 0.5, together with saddle shapes).

Edge weights are then computed from the SI ranges as fol-lows. Two neighboring vertices connected by an edge in thedual graph D∗ are assigned an edge weight λ determined by the

TABLE ISHAPE TYPES FOR SI RANGE

following criteria:

λ =

⎧⎪⎨

⎪⎩

θ1 , 0 < SI ≤ 0.5 (umbilicpoints)

θ2 , 0.5 < SI ≤ 0.75 (hyperbolicpoints)

θ3 , 0.75 < SI ≤ 1.0.

(2)

One advantage of using shape indices as edge weights is thattransition from one shape type to another is continuous; hence,they can be used to describe subtle vessel shape variations.

2) Mesh Decimation: Following the assignment of the edgeweights to the dual graph D∗, convex decomposition is initi-ated by iteratively applying a half-edge collapse operation onneighboring vertices. A half-edge collapse operator, defined ashcol(u, v), when applied to two vertices (u, v) connected by anedge in 50 < ε < 250 merges v with u and all incident edgeson v are connected to u. The decimation process using the half-edge collapse operator is governed by a cost function that isweighted on λ and minimizes for concavity. The cost associatedwith hcol(u, v) is given by

C(u, v) = αAR(u, v) + λCon(S(u, v))

N(3)

where Con is the concavity of surface S(u, v) and N is thenormalization factor which is set as the diagonal of the boundingbox of S(u, v). The parameters α and λ control contributions ofthe aspect ratio AR and concavity Con(S(u, v)). We set α = 2to favor the generation of compact disks in which case the costis unity. The aspect ratio AR of the surface S(u, v) is definedby

AR(u, v) =γ(S(u, v))2

2π ∗ σ(S(u, v))(4)

where γ is the perimeter and σ is the area of the surface S(u, v).After each edge collapse operation, λ is locally recomputed forsurface S(u, v) and the new edge weight λnew obtained from(5) is used in the update of D∗:

λnew =(

1 − δ

δ

)

λ. (5)

An influence parameter δ is used in order to minimize theinfluence of newly formed surface features caused by the deci-mation in successive iterations of hcol.

3) Mesh Partitioning: With each iteration of the hcol op-erator, the lowest mesh simplification cost is applied to a newpartition ϕ(n) = {ϕn

1 , ϕn2 , ϕn

3 , ϕn4 , . . . , ϕn

P (n)} minimizing Cthe cost function.

C(u, v) ∀k ∈ {1, . . . , P (n)} , ϕnk = pn

k ∪ H(pnk ) (6)


Fig. 4. Contraction of vassel manifold surface for aneurysm sac and inlets through three iterations of Laplace contraction.

Fig. 5. Decomposition of vessel branch section for ε values.

TABLE IIDECOMPOSITIONS OBTAINED FOR CONCAVITY RESOLUTION RANGES,50 < ε < 250. COMPARISONS MADE BETWEEN NUMBER OF WACD

SEGMENTED PARTS (WP) AND WACD SEGMENTED VOXELS (WV), NUMBER

OF EXPERT SEGMENTED PARTS (EP), AND EXPERT SEGMENTED VOXELS (EV)

where (pnk )k ∈ {1, . . . , P (n)} represents the dual graph D∗ ob-

tained after n edge collapse operations on P clusters. This proce-dure is iteratively performed until all edges of D∗ are in clusterswith concavity lower than a determined concavity resolutionvalue ε. In the next section, these clusters (subcomponents) aregrouped using the vessel skeleton.

4) Parameter Estimation: Estimation of the concavity res-olution ε was determined by volumetric comparisons madeon n = 65 preselected sections that were segmented by anexpert (containing cerebral aneurysms and vessel bifurca-tions). In order to obtain topological consistence, it is essen-tial that the WACD algorithm not separate the volumes intomore parts (Fig. 5). Vessel sections were decomposed usingWACD and voxelized. In our experimental setup, parametersθ1 = −0.78, θ2 = 0.04, θ3 = 0.83, and δ = 0.67 were used. Ta-ble II shows the decomposition obtained (for a single branchsection and aneurysm section) for various concavity resolution

ranges. We determined on optimal range of 150 < ε < 200 thatmatch closest to expert segmented section both in volume andnumber of decomposed parts.

C. Vascular Skeleton Extraction

The vascular skeleton extraction technique that we propose isapplied directly on the vascular mesh representation. Skeletonextraction is addressed as follows: we start with formulatingthe problem of global surface contraction [22]. We contractthe mesh so that it continues to conform to the geometry ofthe initial vessel surface. Anchor points are used that act asattractors, causing the mesh vertices to contract (converge) toan approximate skeleton of the vessel shape (see Fig. 4).

1) Differential Coordinates: The vessel two-manifold sur-face Sis defined in R3 as an undirected weighted graphD∗ = {V,E}. We define the differential coordinates of a vertexvi as

L(vi) =1

∑ωij

∑

j∈N (i)

ωij (vi − vj ) =1

∑ωij

⎡

⎣∑

j∈N (i)

ωij vj

⎤

⎦ − vi

(7)where L(vi) is the Laplace operator on vi,N (i) is the set ofneighbors of the ith vertex, and ωij is the edge weight ofedge E(i, j). Weighting is utilized to approximating the geo-metric properties of the mesh. The literature shows two gener-ally used approaches; cotangent weighting and uniform weight-ing [28]. In uniform weighting, edges are assigned unit weightswij = 1 ∀i, j. In this approach, only the mesh topology is con-sidered and not its geometry. For a complete approximation ofthe surface geometry, it is necessary to include information ofthe angles formed between the edges of the mesh. We use cotan-gent weights that are more effective for mesh contraction. Usingcotangent weights, the differential coordinates approximate thecurvature normal to the surface mesh [28], [29].

2) Laplace Contraction: The vessel surface is contractedby the Laplace operator that removes surface features alongthe vertex curvature normal directions. In our approach, vertexcontractions are obtained by equating

LcV = 0 (8)


Fig. 6. Cotangent weights of vertex vi used to approximate the local shapecharacteristics (normal direction and mean curvature) of the surface.

where Lc is the Laplacian matrix with cotangent weights definedby

Lc =

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

ωij = cot αij + cot βij , if (i, j) ∈ E

l∑

(i,l)εE

−ωil , if i = j

0, otherwise.

(9)

Angles α and β used in (9) are shown in Fig. 6. The verticesof the surface mesh V are contracted by solving (8), where meshvertices are moved along the direction of their curvature normal.

3) Anchor Constraints: Iteratively solving LcV′ = 0 im-

plies that we remove the normal component and contract themesh geometry [30], where V ′ represents the displaced (con-tracted) geometry. However, the contracting mesh is requiredto abstract the original vessel shape as close as possible ratherthan contract to a singular point. For this anchor, constraints areset on the mesh geometry. All vertices are constrained to theircurrent position using weights and solving the linear system

[WcLc

Wa

]

V ′ =[

0

WaV

]

(10)

where Wa and Wc are the anchor and contraction weight ma-trices used to regulate the contraction forces, respectively. Thesolution to (10) is equivalent to minimizing the quadratic en-ergy [31]

‖WcLV ′‖2 +∑

k

W 2a ‖v′

k − vk‖2. (11)

The first term shrinks the mesh by smoothing the mesh sur-face characteristics along the normal direction, while the secondterm preserves the vessel geometry. In this sense, the rows ofthe Laplacian act as contraction constraints that provide forcesto contract the mesh. In Fig. 4, after the first iteration of con-traction, it can be seen that high-frequency mesh characteristicsare filtered out, leaving the resulting vessel shape noticeablycontracted. However, initial mesh connectivity is not changedafter the mesh contraction process.

In order for the vessel shape to converge to a 1-D vesselskeleton, several iterations of (11) are required while updatingWc and Wa . Using the same contraction and anchor weightsdoes not contract the mesh to a singular (≈0) volume skele-ton. Hence, the weights of Wc are updated for each vertex vk

according to the area of its Lk1 -ring neighborhood. Since we

Fig. 7. 1-D vessel skeleton obtained by the Laplace contraction. Vesselconnectivity is performed on the induced skeleton mesh to identify skeletonbranches.

want vertices with smaller L1-ring area to contract less. Eachiteration is evaluated as follows:

1) solve

[Wi

c Lic

W ia

]

V i+1 =[

0Wi

aLic

]

, for V i+1

2) update Wi+1c = ρcW

ic , and Wi+1

a = Wic (σ

0k/σi

k )3) compute new Laplace operator Li+1

c with contracted ver-tices V i+1

where σ0k , σt

k are the initial and current L1- ring areas of vertexvk , and ρc is the convergence rate constant. In general, largerweights in Wa enforce positional constraints and thus preservethe original geometry, which can be useful for tortuous vesselsection and branch sections (see Fig. 7). On the other hand,larger weights in Wc enforce regular triangle faces in surfacecontraction. We iterate until the ratio of the current and the initialvessel volume is smaller than the threshold γ.

Parameters: The key to contraction lies in the initializationof weights Wc and Wa . These forces are defined such that thecontracted regions at the thinner vessel branches act as stronganchors retaining the key structural features of the vessel. Thesethinner vessel branches always collapse first, while the thickerstructures take more iterations to collapse. In our experiment, weuse the following initial setting: W 0

a = 1.2 and W 0c = 10−2√ρc .

By setting ρc = 3.0 and γ = 1e − 4, the vessel surface wasfound to contract efficiently, usually in less than six iterations.

4) One-Dimensional Skeleton Extraction and Vessel Con-nectivity: After mesh contraction, the resultant vascular meshhas close to zero volume and is geometrically a 1-D skeleton ofthe vessel shape. However, this contracted mesh has the connec-tivity of the initial vessel mesh and needs to be converted intoa vessel skeleton graph (see Fig. 8). To distribute the verticesof the vessel skeleton uniformly, vertices within a minimumEuclidean distance are selected, and edges incident on thesevertices are then removed.

The skeleton structure is built from the condensed mesh Sby imposing initial connectivity, and then by applying an edgecollapse operation. Using farthest-point sampling with ball ra-dius sr , the set of points closest to vertex vk are merged by a


Fig. 8. Four iteration of surface contraction is performed to obtain a minimalvolume mesh. Merging of vertices using a half-edge collapse operator results ina 1-D vessel skeleton graph.

Fig. 9. (a) Half-edge collapse of contracted mesh, (b) and (c) merging ofbranches (G1–G9) with intersecting nodes within sphere radius SR resulting invessel branches (G1–G3).

half-edge collapse operator. For each half-edge collapse oper-ation hcol (k → j), the operator mergers vertex vk to vj andremoves all faces that are incident on vertex vj [see Fig. 9(a)].

However, this may result in the skeleton having more complexbranching structures than the anatomical relevant branches ofthe vessel skeleton. We further simplify the skeleton ∀k �= j, weconnect vk and vj if they share a commonL1 -ring neighborhoodand merge branch nodes using hcol (k → j) where |vk | < |vj |that are within the larger sphere radius sR [see Fig. 9(b)]. Askeleton graph of uniformly distributed nodes is obtained shownin Fig. 9(c).

5) Vessel Skeleton-Based Grouping: This skeleton meshconnectivity process removes all the faces in the contractedmesh, leaving a 1-D connected graph as the vessel skeleton. Us-ing the adjacency matrix of the skeleton graph, vessel branchesGi are identified (vertices that have three or more adjacentnodes). Next, the WACD algorithm is used to decompose thesurface mesh into subcomponents, components belonging tothe same vessel branch are grouped together. WACD decom-posed vessel sections are formed by the union of subcomponentsPi ∈ S that belong to the same skeleton branch Gk = ∪iPi ,where Gi ∩ Gi = ∅,∀i �= j. In Fig. 10, we illustrate this group-ing approach; the vessel skeleton is extracted and branches areidentified [see Fig. 10(a) and (c)]. After WACD, vessel subcom-ponents that belong to the same branch are grouped together[shown in Fig. 10(b) and (d)].

Fig. 10. (a) Skeleton extraction and decomposition of vascular tree, (b) de-composed parts belonging to the same branch are grouped together (G1–G8).(c) Skeleton extraction and decomposition of vessel section with aneurysm (G4),and (d) decomposed parts (G1–G6) are grouped.

III. EXPERIMENT AND RESULTS

We demonstrate our vessel decomposition and skeleton ex-traction methodology in Figs. 3, 4, 7, and 10. In addition,the methodology was tested on labeled sections of the neuro-vasculature: BA, ACoA, PCoA, MCA, ICA, and SCA extractedfrom clinical datasets. Presegmented sections (that included sec-tions containing aneurysms and vessel bifurcations) of vascula-ture was archived for 98 aneurysms in 112 patients, and usedfor validation and testing.

A. Section Decomposition and Skeleton Extraction

Sections of vasculature (n = 256) were classified by a clini-cal radiological expert into linear, curved, branch, and aneurysmsections. For each class of vessel sections, the cluster range (de-composed subcomponents) and the number of skeleton brancheswere identified, yielding the ground truth data. Table IV docu-ments our results for vessel decomposition and skeleton extrac-tion; using our WACD approach approximately 80.5% of thestructures were decomposed into the same number of compo-nents and 92.9% of the vascular skeletons extracted had correctnumber of branches identified as the ground truth. In Fig. 3, weillustrate the decomposition using WACD where close confor-mity with ground truth was obtained. For vessel branches [seeFig. 3(b)], WACD clustered bifurcations with minimal numberof cluster while maintaining close structural representation ofthe branched section. In Fig. 3(d) and (f), WACD was used to


TABLE IIIVOLUMETRIC AND SURFACE AREA COMPARISONS BETWEEN WACD VOLUME (VOX), WACD SURFACE AREA (SA) OF EXTRACTED ANEURYSM SAC SECTIONS

AND EXPERT SEGMENTED ANEURYSM SAC VOLUME (EV) AND SURFACE AREA (EA)

TABLE IVEXPERT CLASSIFIED SAMPLES (EC) AND EXPERT SPECIFIED CLUSTER RANGE

(CR) FOR EACH OF THE SHAPE CLASSES; CORRECTLY DECOMPOSED SAMPLES

(CDS) USING WACD; EXPERT SPECIFIED SKELETON BRANCHES (ESB) FOR

THE SHAPE CLASS AND CORRECTLY EXTRACTED SKELETON BRANCHES (CSB)

cluster vessel sections fused with the skull. Although we didnot intend to use it for separation of vessels fused to othercranial structures, preliminary results seemed to favor its use.Figs. 7 and 10 show vascular skeletons extracted using ourmethod. It can be seen that all the extracted skeletons representwell the geometry and topology of the original vessel structure.Fig. 7 demonstrates that our method also works well for vesselaneurysm and bifurcation vessel shapes.

B. Skeleton Extraction and Decompositionof the Circle of Willis

Studies have suggested that identifying geometric character-istics of the cerebral vessels of the circle of Willis may pro-vide meaningful association with vascular disease formationand progression [32], [33]. In particular, cerebral aneurysmsare frequently located at or near arterial bifurcations and afterregions of high vascular curvature, in arteries of the circle ofWillis [33]. We test the effectiveness of the methodology inextracting the vascular skeleton and segmenting the circle ofWillis. In Fig. 12, we illustrate the decomposition of the cir-cle of Willis using our vascular skeleton WACD approach. InFig. 12(b), and (e), the decomposition of the ACoA and the

detection of ACoA aneurysm sac [pathological dilation of thevessel shown in Fig. 12(a) and (d)], one of the most commonaneurysms [33] is shown.

C. Longitudinal Study Analysis

The proposed methodology is to provide a means for CAD.To demonstrate the clinical benefits of this approach, we testfor automated vessel skeleton extraction and decomposition us-ing longitudinal study data on four patients with a prior his-tory of unruptured and untreated cerebral aneurysms. Theseaneurysms were not treated because they were determined to besmall and nonthreatening. We perform analysis on the follow-ing subjects: Case 1: A 31-year-old male with known historyof bilateral ICA dissection and EC-IC bypass due to a moy-amoya type changes, post-ICA dissection having tiny basilarapex aneurysm. CT stroke study showed enlargement of theknown basilar aneurysm. Case 2: A 44-year-old female withknown history of aneurysms and had previously stent coiledposterior communicating artery aneurysm on the right. A 5 ×5 mm incidental R PCoA aneurysm, unchanged in size was fol-lowed over a period of two months. Case 3: A 62-year-old femalewas followed for incidental right-sided middle cerebral artery(MCA) aneurysm, overall appeared stable (shown in Fig. 11).Case 4: A 54-year-old female with post carotid sacrifice andclipping of right MCA aneurysm and clipping of the left PCoAaneurysm. Follow-up studies show a small A1 aneurysm thatappeared stable in size.

1) Aneurysm Data: Data were acquired on the aforemen-tioned cases that had pretty much diffused vascular aneurysms(ten CTA datasets). Segmentation of the vasculature and 3-Dsurface reconstruction was performed. Measurements were per-formed on the sections containing aneurysms; aneurysm maxi-mum diameters ranged from 1 to 5 mm (mean, 2 mm± 1[stan-dard deviation]), and aneurysm neck sizes ranged from 1 to 3mm (mean, 1.4 mm±1.2). Volume of aneurysm in terms of vox-els ranged from 116 to 873 and aneurysm surface area rangedfrom 10.63 to 35.31mm2 (see Table III). None of the aneurysmshad previously been treated with coils.

2) Skeleton Extraction and Decomposition: Using the pro-posed vascular skeleton extraction and WACD, the reconstructedvasculature was decomposed resulting in subcomponents ofvessel sections (see Fig. 11). Follow-up analysis (volumetricand surface area computation) was performed on the extractedaneurysm sacs from longitudinal data (preliminary, follow-up I,


Fig. 11. Case 3: A 62-year old female was followed for incidental right-sided MCA aneurysm. (a) Maximum intensity projection (MIP) of the internal carotidartery and MCA shows a 4-mm aneurysm (arrow) with a 3-mm wide neck in the M1 segment of the right MCA; (b) and (c) 3-D reconstruction and vessel skeletonextraction of the patient vasculature. (d) WACD extraction of MCA aneurysm.

Fig. 12. Vascular skeleton is extracted for the circle of Willis, (a), (c), and(d) with large Anterior Communicating Artery (ACoA) aneurysm, and (b, andc) using WACD aneurysm sacs are identified.

follow-up II). Expert segmented aneurysm sections are usedas ground truth. Table III documents our results; volumet-ric and surface area comparisons were made between expertsegmented aneurysm sections and the proposed approach. Weobtained a mean error rate of 7.78% for volumetric compari-son and 10.38% for surface area comparisons between expert

segmented aneurysm sections. Fig. 11(a) and (b) illustrates Case3, where MCA aneurysm on right-hand side followed overa period of two months; MIP indicated noticeable change inaneurysm size (see Table III). Using skeleton extraction andWACD [see Fig. 11(b), (c), and (d)], the decomposed aneurysmsac was extracted. We were able to detect changes in aneurysmvolumes (4.5% error) and surface areas (8.4% error) that wereclose to that segmented by an expert.

IV. DISCUSSION AND CONCLUSION

The quantitative results above validate the feasibility ofthe proposed vascular skeleton extraction and decompositionmethodology. Results obtained suggest that we attain near op-timal decomposition close to expert segmented sections, withapproximately 80.5% of the vessel sections decomposed into thecorrect number of components and 92.9% of the sections havingthe correct number of skeleton braches. This skeleton represen-tation of the vasculature is important for diagnosing and treatingpathologies, and follow-up studies. The method was also val-idated for CAD on a longitudinal study of four cases havinginternal cerebral aneurysms. The main reason for the follow-upstudy analysis was to demonstrate the effectiveness of this ap-proach in automated segmentation of aneurysms. Results showthat we were able to segment aneurysms and detect changes inaneurysm sac volumes and surface areas that are close to expertsegmented sections.

Our primary objective was the decomposition of the vascu-lature and extraction of the vessel skeleton for CAD analysis.We have demonstrated that the proposed approach is a promis-ing method for vascular analysis capable of producing effectivedecomposition (which include bifurcations and aneurysms), aparsimonious description on which vascular analysis can beperformed. From our initial longitudinal study, findings sug-gest that our methodology can provide a basis for vascularanalysis. However, a much larger follow-up study, and also acomparative study with patients with ruptured and unrupturedaneurysms, would be necessary to determine the clinical efficacyof this methodology on decomposing and identifying vascularaneurysms.


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3-d vascular skeleton extraction and decomposition

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