Available online at www.sciencedirect.com

Computerized Medical Imaging and Graphics 32 (2008) 488–501

Estimation of regional myocardial mass at risk based on distal arteriallumen volume and length using 3D micro-CT images�

Huy Le, Jerry T. Wong, Sabee Molloi ∗Department of Radiological Sciences, University of California, Irvine, CA 92697, United States

Received 18 September 2007; received in revised form 1 April 2008; accepted 16 May 2008

Abstract

The determination of regional myocardial mass at risk distal to a coronary occlusion provides valuable prognostic information for a patientwith coronary artery disease. The coronary arterial system follows a design rule which allows for the use of arterial branch length and lumenvolume to estimate regional myocardial mass at risk. Image processing techniques, such as segmentation, skeletonization and arterial networktracking, are presented for extracting anatomical details of the coronary arterial system using micro-computed tomography (micro-CT). Moreover, amethod of assigning tissue voxels to their corresponding arterial branches is presented to determine the dependent myocardial region. The proposedmicro-CT technique was utilized to investigate the relationship between the sum of the distal coronary arterial branch lengths and volumes to thedependent regional myocardial mass using a polymer cast of a porcine heart. The correlations of the logarithm of the total distal arterial lengths(L) to the logarithm of the regional myocardial mass (M) for the left anterior descending (LAD), left circumflex (LCX) and right coronary (RCA)arteries were log(L) = 0.73 log(M) + 0.09 (R = 0.78), log(L) = 0.82 log(M) + 0.05 (R = 0.77) and log(L) = 0.85 log(M) + 0.05 (R = 0.87), respectively.The correlation of the logarithm of the total distal arterial lumen volumes (V) to the logarithm of the regional myocardial mass for the LAD, LCX andRCA were log(V) = 0.93 log(M) − 1.65 (R = 0.81), log(V) = 1.02 log(M) − 1.79 (R = 0.78) and log(V) = 1.17 log(M) − 2.10 (R = 0.82), respectively.These morphological relations did not change appreciably for diameter truncations of 600–1400 �m. The results indicate that the image processingprocedures successfully extracted information from a large 3D dataset of the coronary arterial tree to provide prognostic indications in the form of

arterial tree parameters and anatomical area at risk.© 2008 Elsevier Ltd. All rights reserved.

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eywords: Vessel segmentation; Arterial length; Lumen volume; Coronary arte

. Introduction

Occlusion or partial occlusion of coronary arteries frequentlyccurs in man while imparting high morbidity and mortality.revious studies have shown that the most important determi-ant of infarct size for a given coronary artery occlusion is theize of myocardium that the artery perfuses [1–5]. Therefore,nformation about the perfusion territory, or myocardial mass

t risk, can be used to determine the potential infarct severityf an occluded artery. Current clinical applications of radionu-lide perfusion imaging and contrast echocardiography utilize

� This research is supported in part by Grant R01 HL67159 awarded by theHLBI, DHHS.∗ Corresponding author at: Department of Radiological Sciences, Medicalciences I, B-140, University of California, Irvine, CA 92697, United States.el.: +1 949 824 5904; fax: +1 949 824 8115.

E-mail address: SYMOLLOI@UCI.EDU (S. Molloi).

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895-6111/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.oi:10.1016/j.compmedimag.2008.05.002

Simulation

his concept by identifying inadequately perfused regions with aadiopharmaceutical tracer or contrast material, respectively, tostimate the potential infarct size. Alternatively, previous stud-es have indicated that morphological surrogates for myocardial

ass measurements may exist [6–9]. For example, the sum ofrterial branch lengths distal to the point of occlusion has beenroposed for estimating the corresponding regional myocardialass at risk [6]. Moreover, the total volume of blood in mam-als have been found to scale proportionately with their bodyass [7–9]. More recently, a study using a computer grown

oronary arterial tree has suggested that the blood volume inoronary arteries scales proportionately with the tissue volumehey supply through a power law relation with an exponent of 1.210]. However, the calculation of arterial branch lengths in the

ormer study were made from three-dimensionally (3D) recon-tructed arterial trees using biplane coronary angiograms. 3Deconstruction from biplane projections is known to be limitedy vessel overlap [11]. In addition, existing experimental data

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hat gives rise to blood volume–body mass relation is global inature. Other studies have reported on the relationships betweenhe length [12], volume [13], and the cross-sectional area [14] ofhe main feeder arterial branch versus the perfused myocardialolume. The current investigation provides experimental datahat compares the total distal regional coronary arterial lumenolumes, lengths and myocardial mass. These relations paral-el Zhou et al.’s relationship between the sum of distal branchengths and the sum of distal branch volumes [15].

In the current study, a method for quantifying morphologicalarameters of coronary arterial trees and analyzing the rela-ionships between them was developed using micro-computedomography (micro-CT) and several image processing tech-iques. Micro-CT can obtain 3D anatomical data of biologicalpecimens with a spatial resolution as high as 50 �m [16].ombined with a contrast enhancing agent, micro-CT has been

uccessfully used for imaging the vasculatures of a rat kidney17,18], heart [19], liver [20] and swine heart [21,22]. However,ascular imaging with micro-CT produces 3D images of therterial tree that contains hundreds of branches spanning manyenerations. Methods for analyzing micro-CT images of the rat’soronary system have been developed [23]. While these methodsrovide valuable insight into the extraction and representationf an arterial tree, further improvements in the methodology areeeded in order to reconstruct a more complete coronary arterialree. In the current study, methods for vascular analysis from

icro-CTs involve four principle steps: (1) segmenting arter-es from the background anatomy; (2) labeling the segmentedranches and storing their diameters and lengths; (3) mappinghe connectivity between branches; (4) partitioning myocardialoxels into separate perfusion beds supplied by different arterialranches. The methodology for casting the heart, imaging, seg-entation and quantification of morphological parameters are

lso presented.In addition to the quantification of parameters, the current

tudy also evaluates the relationships between total distal branchength and total lumen volume with respect to regional myocar-ial mass using a volumetric image dataset from a pig’s coronaryrterial tree. Morphological data obtained from micro-CT hasot been previously used to investigate these relationships. These

elationships can potentially provide valuable insight into therognostic significance of an acute myocardial infarction due ton arterial occlusion and aid in the decision-making of treatmentptions. a

Fig. 1. Flow diagram of the ima

g and Graphics 32 (2008) 488–501 489

. Materials and methods

In order to study the relationships between arterial branchength, lumen volume and myocardial mass at risk, methodsor obtaining accurate measurements of these parameters wereeveloped and tested on a porcine heart. 60 cc of saturated KClolution was injected into the right jugular vein of a 35 kg swineo arrest its heart and keep it in a relaxed state. The heartas then excised with the ascending aorta clamped to keep

ir bubbles from entering the coronary vessels. The coronaryessels were immediately perfused with an iso-osmotic, cardio-legic solution to keep the vasculature vasodilated. The excisedeart was then casted with a radio-opaque polymer and imagedith a micro-CT. After image acquisition and reconstruction,umerous post-acquisition image processing techniques weresed to determine arterial branch lengths, lumen volumes andyocardial masses of different arterial perfusion beds. Briefly,

he process began with differentiating voxels belonging to theyocardium versus those belonging to the arterial branches. The

xtracted arterial branches were then thinned until only theirkeletal centerlines remained. These centerlines were used foralculating arterial branch lengths. Moreover, with the densityf the myocardium known, the myocardial masses of perfusioneds could be determined from the total volume of the extractedyocardial voxels. The procedure includes the following steps

Fig. 1):

1) median filtering to suppress noise and improve the extrac-tion of tissue voxels,

2) thresholding to extract tissue voxels,3) morphological filtering of the original image to enhance

coronary vessels,4) region growing to extract continuous vessels,5) 3D thinning to determine vessel centerlines while preserv-

ing shape and topology,6) tree tracking to database individual branches for further

processing,7) B-spline fitting to determine arterial branch lengths more

accurately,8) tissue voxel assignment to divide the myocardium according

to different perfusion beds.

The details of casting, image acquisition, image processingnd analysis are given in the following sections.

ge processing procedure.

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.1. Polymer cast of coronary arterial tree

The arterial trees of the left anterior descending (LAD), leftircumflex (LCX) and right coronary (RCA) arteries were castedith Microfil (Flow Tech Inc., Caver, MA, USA), which isliquid polymer that provides complete filling with minimal

hrinkage in volume after curing. A previous study has reportedn the casting method, which is summarized here with someodifications for this particular application [24]. The LAD,CX and RCA of the excised porcine heart were cannulatednder saline to avoid air bubbles. Three 60 cc syringes connectedo the main pressure source were used for injecting cardioplegicnd casting solutions into the cannulated arteries. Cardioplegicolution was initially used to perfuse the LAD, LCX and RCAn order to wash out remnant blood and to maintain the arteriesn a dilated state. Microfil was then used to make a cast of theoronary vasculature. The Microfil solution solidifies in a spe-ific period of time after it has been catalyzed with 6% stannous-ethylhexoate and 3.0% ethyl silicate. The catalyzed Micro-l solution was stirred and degassed under vacuum to removeir bubbles. After degassing, perfusion with the cardioplegicolution was stopped. The LAD, LCX and RCA were then simul-aneously perfused with the Microfil solution. Each of the three

ain coronary arteries was perfused with Microfil of differentolor. The coloring enabled the three perfusion beds to be dis-ected and weighed. The perfusion pressure was maintained at00 mmHg until the elastomer hardened. Saline and residualasting material that leaked into the ventricles were purged tollow better contrast of the chambers during imaging.

.2. Image acquisition and processing

Images of the casted porcine heart were acquired using aicro-CT scanner (XSPECT, Gamma-Medica, Northridge, CA,SA). The X-ray parameters for volume imaging were 80 kVp,50 mA and 10 ms. The source-to-origin and source-to-detectoristances were 225 and 311 mm, respectively. The casted heartas placed inside a cylindrical container for easy placement in

he center of the detector’s field of view. The heart was care-ully positioned to insure that all vessels were inside the field ofiew. A total of 256 projections spanning 360◦ were acquired.mages were reconstructed with a commercially available soft-are designed for cone-bean reconstruction using a modifiedeldkamp algorithm (Exxim COBRA). The reconstructed vol-me was 512 × 512 × 512 voxel, where the dimension of eachoxel was 0.145 mm × 0.145 mm × 0.145 mm.

.3. Tissue and vessel segmentation

The reconstructed CT volumes have dimensions of15 × 512 × 512 voxel, and each voxel was encoded by 8 bits.median filter with a radius of 2-pixel was used to reduce the

mage noise [25]. The volume was then thresholded to separate

he myocardium from vessels and background. A new, binaryataset was generated where only the myocardium was in theoreground. A cross-platform java image processing applicationas used for the procedure (ImageJ, NIH).

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ng and Graphics 32 (2008) 488–501

A 3D gray-scale morphological filter was used for vesselegmentation. Morphological filters are often used to eliminater enhance information that conforms to certain shapes calledtructuring elements [26]. Since the coronary vasculature in vol-metric images can be approximated as cylinders, a sphericaltructuring element with a diameter slightly larger than the diam-ter of the largest vessel was used to remove all the vessels. Theessels were removed by using the open operator of the mor-hological filter, which eliminated structures smaller than or theame size as the structuring element. The resultant vessel-freeolume was then subtracted from the original volume, leavingn enhanced reconstruction of only the vessels.

Vessel segmentation was performed by using a locally adap-ive region growing algorithm [27]. The procedure combinedhe concept of local cubes [48] and symmetric region grow-ng [49]. The algorithm started with a user determined seedoint. Beginning with the seed point the surrounding voxelsere analyzed to determine the mean and standard deviationf the gray level intensity inside the object. An 80 × 80 × 80ube was created with the seed point as the center. The symmet-ic region growing algorithm, described below, was performedocally in this cube with the given mean and standard devia-ion of the voxel intensities. After the data inside the cube wasegmented, the six faces of the cube were examined to locatehe position of the next cube(s). A connected-component algo-ithm was used to locate the end point of the branches on theaces of the cube. For each of the component found, a newube was created for the next segmentation. If more than oneomponent was present then the new cubes were stored in aueue and waited for their turn to be analyzed. The process wasepeated until the local cube had zero connected components.

hen no connected components were found, the end of theranch was reached. Ideally, the cube must be of the right sizeo completely contain the segmented vessels. If the cube was toomall then the segmentation might not contain useful informa-ion since the cube might be completely circumscribed by theessels. To check if the size of the cube was adequate, a conditionas imposed on the connected components where each compo-ent must not span opposite faces of the cube. If this test failedhen the size of the cube was doubled and the segmentation wasepeated.

A symmetric region growing [49] algorithm was imple-ented to segment the vessels within a local cube. This

lgorithm is a one-pass procedure that does not rely on recur-ions to grow one voxel into the next. The fundamental concepts to segment in one dimension and subsequently builds up towo and three dimensions. The algorithm began by segmentingne line of voxels according to the parameters (mean and stan-ard deviation of gray level intensities inside the vessels) of theegion growing procedure. Then the next line was segmentednd the two regions were merged. The process continued untilwhole slice was analyzed. After one slice was segmented, theext slice was analyzed and merged to the previous one until

he whole 3D dataset was segmented. Since this process wasne-pass, the segmentation information could be stored directlynto the image being analyzed, therefore saving memory. Also,omputational efficiency was achieved because each voxel was

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isited only once as opposed to recursive methods where voxelsight be visited more than once.

.4. Centerline extraction

The next step was vessel skeletonization for branch track-ng and length computation. Skeletonization, otherwise knowns medial axis transform, can usually be achieved in two pri-ary ways. One method calculates the distance transform of the

mage where the value of each voxel belonging to the object iseplaced by its distance to the nearest edge of the object [28].he medial axis transform follows the ridges of the distance

ransform, where the values are higher than their surroundings.he other method morphologically thins the object by repeat-dly eroding boundary voxels until the object cannot be thinnedny further, at which point only the skeleton is left [29]. Forhis study, the latter method was chosen for its robustness inreserving topology and shape [30]. Vessel centerlines werextracted from the binary vessel dataset using a 3D parallelhinning approach as reported by Palagyi et al. [30]. Briefly,his skeletonization technique builds on the concept of simpleoints. Simple points are defined as voxels that can be deletedithout changing the topology of the objects. The skeletoniza-

ion algorithm examines each voxel and determines if it is aimple point that can be deleted. A simple point is deleted if itseighborhood matches a set of 3 × 3 × 3 templates. On the otherand, a simple point is not deleted if it is an endpoint so that thehape of the object is preserved. The algorithm is divided into 12ub-iterations, with each sub-iteration corresponding to a direc-ion relative to a particular point. The 12 directions are up-north,p-east, up-south, up-west, north-east, north-west, north-down,ast-south, east-down, south-west, south-down and west-down.ach direction consists of 14 matching templates. Each of the 12ub-iterations can be operated in parallel, which means the orderf directions analyzed does not affect the results. The algorithmperates on the image repeatedly until no additional point can beeleted.

.5. Tree tracking

The resulting skeleton of the coronary arterial tree was usedo track each of the coronary arteries from its root branch to the

ost distal branches. The tree was broken down into individualranches for the computation of lengths and diameters. First, aeed voxel at the beginning of the root branch was visually cho-en. Then the voxel’s 3 × 3 × 3 neighborhood was examinedo search for other skeleton points. The search for additionalkeleton points continued until no other skeleton points existedn the neighborhood, then the current voxel was considered anndpoint. If exactly one other point was present in the neighbor-ood, then this point was added to the branch. If more than oneoint were found, then the algorithm tentatively assumed thexistence of a multiple branch point (e.g. bifurcation or trifur-

ation). A chain of voxels was defined as a branch if its lengthas greater than 5 voxels. A threshold of 5 voxels was deter-ined by comparing the images of the tracked branches and

he segmented vessels. A series of voxels shorter than 5 voxels

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g and Graphics 32 (2008) 488–501 491

as treated as a false branch and deleted. Each new point washecked to determine if it was part of a new branch. Once a newranch was found, it was tracked to its endpoint and assigned ashe left or right child of its parent branch. If a trifurcation wasncountered, the three children branches were divided into twoandem bifurcations that were connected by an artificial branchf length 0. This artificial branch along with one real branchade up the first bifurcation. The second bifurcation was com-

osed of the remaining two children branches with the artificialranch acting as their parent branch. After the branches wereracked, a B-spline was fitted to each branch before their lengthsere computed. A cubic smoothing B-spline was utilized to

mooth the centerline by taking every third point as a node forhe algorithm.

.6. Tissue voxel assignment

An important characteristic of an arterial tree is the spatialistribution of its terminal arteriole branches that connect to theapillaries. These terminal arterial branches define the area ofhe myocardium that the larger proximal arterial branches per-use. If the locations of the terminating arterial branches are notnown, then an estimate of their location and the correspondingyocardium they perfuse have to be obtained from the existing

ocation of the proximal branches. The two main approaches foretermining the spatial distribution of terminal arterioles are theearest neighbor method [31] and the fractal method [32]. Foretermining the region of myocardium that a terminal arterioleupplies, Karch et al. [10] used voronoi polyhedrals to asso-iate tissue regions to their supplying arterioles. However, theirrteriole-tissue assignment was based on a simulated arterial treehat was fully grown to the pre-capillary level using a methodf constrained constructive optimization. In the current study,re-capillary arterioles were not available because only arteriesith diameters larger than 400 �m were segmented. Segmenta-

ion of smaller arteries was hampered by low contrast to noiseatio. Using the concept of minimized transport cost, regionsccupied by pre-capillary arteriole branches can be assumed torise from the nearest terminal arterial branch, which in turnrises from the nearest conducting arterial branch. Thus theource of blood for different regions of the myocardium can bessumed to arise from the nearest reconstructed terminal arte-ial branches. Based on these assumptions, every reconstructedissue voxel was assigned to a specific branch from one of theoronary arterial trees. This assignment of tissue–branch pairsegan with calculating each voxel’s distance to every terminalranch. Then a search for a minimum distance was performedo find the appropriate blood source for a particular voxel.

.7. Diameter measurement validation

The region growing algorithm requires a range of voxel inten-ities in which it operates. The low-threshold value is more

mportant than the high-threshold value because it defines theutoff intensity below which voxels are considered to be outsidehe vessel. To obtain segmented vessels with the most accurateiameter, an optimal low-threshold value must be chosen. Values

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hat are too high or too low will cause the segmentation processo underestimate or overestimate vessel diameters, respectively.hoosing the thresholds for the region growing algorithm is,

herefore, critical for subsequent calculations of vessel volumes.ppropriate threshold values can be chosen from an analysis ofoxel intensity profiles along vessel edges. Edges were definedrom an analysis of the first and second derivatives of intensityrofiles. A validation procedure was used to compare the accu-acy of measuring diameters from using the first derivative onlyersus using a combination of the first and second derivatives foretermining vessel edges. The validation procedure is describedelow.

Five plastic tubes (Silastic, Laboratory Tubing, Midland,ichigan) of 10 cm in length and varying diameters were used

or the validation process. The inner diameters of the tubes were

.64, 1.98, 1.57, 1.02 and 0.76 mm. They were filled with theicrofil polymer. The plastic tubes were anchored onto the innerall of a styrofoam cup, conforming to its curvature, to simu-

ate the curvature of the coronary vessels as they curve along

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Fig. 2. Maximum intensity images of the raw data (a), the segmented ti

ng and Graphics 32 (2008) 488–501

he epicardium. The cup was then filled with water before it wasmaged. Water was used to simulate cardiac tissue because theensities of the two are similar. After the volume dataset of theiameter was acquired, the segmentation procedure was appliednd the diameters of the plastic tubes were calculated. Diam-ters were computed by utilizing the centerline binary imagend the segmented-vessel image. Starting from the root branch,or each of the skeleton points in each branch, a plane per-endicular to the direction of the branch was calculated. Theross-sectional area of the vessel at this point was determinedy computing the area of intersection between the plane andessel dataset. The diameter was calculated by assuming thathe cross-sectional area of the arteries is circular. Since each ofhe skeleton points was associated with a diameter value, theranch diameter was the average of the individual centerline-

oint diameters. The methods were compared for their accuracyn diameter calculation. The method that produced the mostccurate diameters was used for the quantification of arterial treeroperties.

ssue (b), the segmented vessels (c) and the resulting skeleton (d).

H. Le et al. / Computerized Medical Imaging and Graphics 32 (2008) 488–501 493

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Fig. 3. Visualization of the coronary vessels with their corresp

.8. Length measurement validation

Fig. 2(d) shows the extracted centerlines from the parallelhinning algorithm. Using the centerline data, the location ofifurcation points and the boundaries of branches were deter-ined by tracking the tree voxel by voxel. The length of each

ranch was determined by summing the Euclidean distancesetween consecutive points along the branch. As can be seenn the Fig. 3, the noise in the original segmented vessel datasetaused the centerline to have a zigzag pattern. The zigzag pat-ern will produce an overestimation in the length of the vessel.hus the extracted centerlines were fitted with a cubic smoothing-spline in order to minimize the effect of noise and to obtainmore accurate representation of true vessel centerlines. The-spline fit was determined by choosing appropriately spacedoints along the segments to serve as control points.

To compare the B-spline lengths and non-B-spline lengths,set of plastic tubes with diameter of 1.57 mm and lengths of, 4, 6, 8 and 10 cm were used. The tubes were filled with theicrofil casting material. The elastic polymer, mixed with the

uring catalyst, was injected through a long tube with a syringe.nce the liquid began to exit the other end, a stopcock wassed to close off the opening. A pressure of 100 mmHg heldhe polymer in place until the casting material solidified. Afterhat, the tubes were cut into segments with the aforementionedengths. Random curvatures were applied to the tubes beforemaging.

.9. Morphological relationships

The morphological relationships in a coronary artery treeave previously been reported [15,33,34]. A coronary arteryree can be recursively broken down into a stem and crownystem. A stem is a vessel segment between any two bifurca-ions. A crown is defined as the collection of all distal branches

o a stem with the same terminal diameter. With L, V and Mepresenting the cumulative arterial branch length of a crown,he cumulative arterial lumen volume of a crown and the total

ass perfused by the crown, respectively, some of the previously

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eported morphological relationships are as follows:

= kVVβV , (1)

= kMMβM , (2)

here kV and kM are the proportionality constants that relate theotal crown length to the total crown volume and total perfused

yocardial mass, respectively. βV and βM are the exponentsharacterizing the power relations. Since previous studies haveound βV and βM to be 0.75, V and M can be related linearly asollows:

= kVMMβVM , (3)

here kVM is the proportionality constants and βVM is the powerxponent that should ideally be equal to 1. These relationshipsere tested in one swine heart for the three principle arterial treesf the coronary system—the left anterior descending (LAD), andeft circumflex (LCX) and the right (RCA) coronary artery trees.

The morphological relationships were also examined for thehree trees at different levels of diameter truncations to deter-

ine the impact of imaging system spatial resolution on thebserved morphological relationships. Truncation levels of 600,00, 1000, 1200 and 1400 �m were studied in order to approxi-ately include spatial resolutions of coronary angiography andT angiography. The cumulative lengths and volumes were

ecalculated for each truncation. Moreover, tissue voxel assign-ent was performed on remaining arterial branches for each

runcation level. The CT regional mass of the LAD, LCX andCA were compared to values obtained from the dissected per-

usion beds for each arterial tree.

. Results

.1. Tissue and vessel segmentation

Starting from the micro-CT images of the casted heart, theyocardium and coronary vessels were segmented. Fig. 2 shows

he maximum intensity projections of the original raw data (a),he segmented tissue (b), and the segmented vessels (c) and the

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esulting skeleton (d). The smallest coronary branches that coulde segmented were approximately 400 �m.

.2. Centerline extraction

The parallel thinning algorithm produced the image shownn Fig. 2(d). As seen in the image, the topology of the skele-on was rough, in contrast to the smooth coronary vesselsn Fig. 2(a). This centerline was then pruned and fitted with

B-spline smoothing fit so that the topology of the skele-on more faithfully represents the smoothness of the originalessels.

.3. Tissue voxel assignment

Fig. 3 shows the 3D visualization of the coronary arteries withheir corresponding perfusion beds. In Fig. 3(a), the myocardiumelonging to the LAD is transparent, that belonging to the RCA

s transparent blue, and that belonging to the LCX is green.he demarcation between the LCX myocardium and the RCAyocardium can be seen. In Fig. 3(b), a cross-section of theyocardium shows the demarcation between the three myocar-

ial beds in an axial plane.

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ig. 4. Relationships between the measured diameters and the known diameters for thsing the inner maximum (b) and outer maximum (c) of the second derivative. The d

M = 0.60DK + 0.13 (R = 0.99) and DM = 0.83DK + 0.09 (R = 0.99) for (a), (b) and (c)

ng and Graphics 32 (2008) 488–501

.4. Diameter measurement validation

Fig. 4 shows the linear regression of the computed diame-ers and the true diameters of the tubing phantoms. Diametersomputed from only the first derivative (Fig. 4(a)), a combi-ation of the first and second derivative with inner maximumsFig. 4(b)), and combined first and second derivative with outeraximums (Fig. 4(c)) are shown. The fits for Fig. 4(a)–(c) areM = 0.50DK + 0.37 (R = 0.95), DM = 0.60DK + 0.13 (R = 0.99)

nd DM = 0.83DK + 0.09 (R = 0.99), respectively—where DM ishe computed diameter and DK is the known diameter. The aver-ge errors in diameter measurements for methods in Fig. 4(a)–(c)re 22.8%, 29.4% and 11.2%, respectively. The dotted line rep-esents the line of identity.

.5. Length measurement validation

Fig. 5 shows the linear regressions of the measured lengthsLM) and the known lengths (LK) of the tubing phantoms. In

ig. 5(a), the length was computed before applying the B-splinemoothing algorithm. On the other hand, the length in Fig. 5(b)as computed after B-spline smoothing. The fits for Fig. 5(a) and

b) are LM = 1.19LK − 10.52 (R = 1.00) and LM = 1.07LK − 7.47

e methods utilizing the first derivative (a), the combined first-second derivativeotted lines are the lines of identity. The fits are DM = 0.50DK + 0.37 (R = 0.95),, respectively. DK = known diameter; DM = measured diameter.

H. Le et al. / Computerized Medical Imaging and Graphics 32 (2008) 488–501 495

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ig. 5. Relationships between the measured lengths and the known lengths of thehe lines of identity. The fits are LM = 1.19LK − 10.52 (R = 1.00) and LM = 1.07Length.

R = 1.00), respectively. The errors in length measurements forethods without and with cubic B-spline smoothing are 12.9%

nd 10.9%, respectively. For longer segments (>50 mm), moreccurate length measurements were made with the B-splinemoothing. However, lengths obtained with and without B-pline were similar for shorter segments (<50 mm). Also, lengthsomputed with B-spline smoothing were usually underesti-ated, whereas lengths computed without B-spline smoothingere often overestimated.

.6. Relation of distal branch lengths and lumen volumes toegional myocardial mass

Fig. 6 shows the log–log plots of the total distal coro-ary branch lengths (L) and total distal lumen volumeV) for the LAD (log(L) = 0.76 log(V) + 1.46, R = 0.99),CX (log(L) = 0.78 log(V) + 1.53, R = 0.99) and RCA

log(L) = 0.74 log(V) + 1.45, R = 0.98). Fig. 7 shows theog–log plots of total distal coronary branch length (L) and

yocardial mass (M) for the LAD (log(L) = 0.73 log(M) + 0.09,= 0.78), LCX (log(L) = 0.82 log(M) + 0.06, R = 0.77) andCA (log(L) = 0.85 log(M) + 0.05, R = 0.87). Fig. 8 shows the

og–log plots of total distal arterial lumen volume (V) andyocardial mass (M) for the LAD (log(V) = 0.93 log(M) − 1.66,= 0.81), LCX (log(V) = 1.02 log(M) − 1.79, R = 0.78) andCA (log(V) = 1.17 log(M) − 2.10, R = 0.82). The correlation

etween total distal branch length and regional myocardialass as well as between total distal lumen volume and regionalyocardial mass were good. Table 1 tabulates the exponents

f the morphological relationships for the 600 �m truncation.

able 1ummary of the exponents of the morphological relationships

βV βM βVM

AD 0.76 0.73 0.93CX 0.78 0.81 1.02CA 0.74 0.85 1.17

verage 0.76 0.80 1.04

Tm

TS

TTRRE

R

g phantoms without (a) and with (b) B-spline smoothing fit. The dotted lines are.47 (R = 1.00) for (a) and (b), respectively. LK = known length; LM = measured

he average values of the exponents of the relationships were.76, 0.80 and 1.04 for βV, βM and βVM, respectively. Table 2rovides a summary of length, volume and mass measurementsrom the CT image. The measured regional myocardial masseserfused by the LAD, LCX and RCA were 67.90, 58.67 and4.48 g, respectively. Similarly, the CT computed massesssigned to the LAD, LCX and RCA at 600 �m truncation were0.19, 55.71 and 63.54 g, respectively. The relative error in CTomputed masses are tabulated in Table 2. In addition, the totalomputed mass of 189.44 g compared well with the measuredass of 191.05 g (relative error of 0.84%).Figs. 9–11 compare the different levels of diameter trun-

ations for βV, βM and βVM, respectively. The errors in βMnd βVM increased with increasing truncation level. However,he errors in βV were small and remained relatively constantor different truncations. Errors in βV, βM and βVM intro-uced by truncation ranged from 1.13–1.98%, 4.76–12.74% and.38–10.59%, respectively. Figs. 12–14 compare the differentevels of diameter truncations for log(kV), log(kM) and log(kVM),espectively. These figures show that errors for log(kM) andog(kVM) increased with increasing truncation level while errorsor log(kV) slightly decreased. Fig. 15 shows the error betweenhe CT computed mass and the measured mass for differentevels of truncations. The range of errors were 1.46–5.05%,.01–5.06%, 2.71–5.92%, 5.10–18.35% and 11.18–29.03% for

he errors were calculated relative to the measured regionalass for each coronary arterial bed.

able 2ummary of micro-CT measurements

LAD LCX RCA

otal branch length (cm) 102.60 74.84 61.25otal lumen volume (cm3) 4.01 2.47 2.68egional CT mass (g) 70.19 55.71 63.54egional measured mass (g) 67.90 58.67 64.48rror of CT mass (%) 3.37 5.05 1.46

egional myocardial masses at 600 �m are compared to the measured masses.

496 H. Le et al. / Computerized Medical Imaging and Graphics 32 (2008) 488–501

F volum( (R = 0

4

toosacpFnrtfmrptrgsmr

tpcmriiimrlrotatasfi

ig. 6. Relationships between the total distal branch lengths and total distal lumenR = 0.99), log(L) = 0.78 log(V) + 1.53 (R = 0.99) and log(L) = 0.74 log(V) + 1.45

. Discussion

The methodology presented has enabled the analysis ofhe volumetric micro-CT dataset of a swine heart. A previ-us study has reported a technique to analyze the micro-CTf a rat heart [23]. However, this study was limited in recon-tructing all branches in different generations of the coronaryrterial tree. In the current technique, the reconstruction of theoronary arterial tree was improved by using of a 3D mor-hological filter to enhance the vessels before segmentation.urthermore, the current technique was used to quantify coro-ary arterial length and lumen volume and relating them toegional myocardial mass. This study represents an applica-ion of various well-established image processing algorithmsor the purpose of extracting the coronary arterial tree infor-ation from micro-CT data and validating the morphological

elationships. Our aim was to determine the sequence of imagerocessing algorithms that can be easily implemented in ordero extract information from a CT dataset accurately. In thisegard, the four primary algorithms that were chosen were region

rowing, 3D topological thinning, voxel-based tree tracking andhortest-distance tissue voxel assignment. The results of theorphological relationships showed that these methods accu-

ately extracted parameters such as lengths and diameters from

t

bw

es of the LAD (a), LCX (b) and RCA (c). The fits are log(L) = 0.76 log(V) + 1.46.98) for (a), (b) and (c), respectively. L = crown length; V = crown volume.

he 3D dataset. However, there are more sophisticated imagerocessing techniques that can potentially improve upon theurrent methods of data analysis [35,36]. Specifically, improve-ents can be made to segment the tree down to the scanner’s

esolution and to assign the myocardial voxel to the supply-ng arterial branch more accurately. Segmentation of the vesselss the most critical step because all subsequent vessel process-ng steps depend on its quality. Region growing is an efficient

ethod for segmenting a large dataset with fairly uniform imageegions, but it cannot segment complex volumes. For this study, aocally adaptive method was used, and the region growing algo-ithm could segment vessels as small as 400 �m. A limitationf the region growing method is its inability to compensate forhe roughness of the anatomical surface caused by image noisend artifacts. Because the skeletonization entirely depends onhe quality of the initial segmentation, rough surfaces cause thelgorithm to produce spurious branches. Compensating for theurface imperfections requires the use of deformable contoursor segmentation [36]. These contours, or snakes, are given var-ous constraints to deform until their shapes coincide to that of

he vessel.

The assignment of tissue voxels to the supplying arterialranch is straightforward but not as intuitive. Since the vesselsere not segmented to the pre-capillary arterioles, it is difficult

H. Le et al. / Computerized Medical Imaging and Graphics 32 (2008) 488–501 497

F asses( (R =d

tbitaitacsssmtvlt

lpklbfi

sswogha

wlA[pctlst0u

ig. 7. Relationships between the total distal branch lengths and myocardial mR = 0.78), log(L) = 0.82 log(M) + 0.06 (R = 0.77) and log(L) = 0.85 log(M) + 0.05ial mass.

o assign tissue voxel to the arterial branch that supplies it withlood. If the locations of pre-capillary arterioles are known, thent is more accurate to assume that the myocardial mass closesto a particular arteriole is supplied by the corresponding parentrterial branch. This mass region can be determined by comput-ng the voronoi polyhedra surrounding the arterioles [10]. Withhe tree truncated at 400 �m, the alternative is to computation-lly grow the tree to the pre-capillary level with a set of statisticalonstraints and mathematical rules [37]. Subsequently, the tis-ue assignment can proceed naturally with the knowledge of thepatial coordinates of all terminating arterioles. The relation-hips between total distal volumes and lengths versus regionalyocardial mass can potentially improve with a tree grown to

he pre-capillary level. Implementation of more sophisticatedessel extraction techniques, tree-growing to the pre-capillaryevel and assignment of mass based on voronoi polyhedra arehe subjects of future investigations.

The computation of branch properties such as diameters andengths using volumetric micro-CT data were validated withhantoms. The validation showed good agreement with the

nown diameters and lengths. The best method for choosing theow-threshold value in the region growing algorithm, as revealedy the diameter validation results, was utilization of both therst and second derivative where the outer maximums of the

ttmv

of the LAD (a), LCX (b) and RCA (c). The fits are log(L) = 0.73 log(M) + 0.090.87) for (a), (b) and (c), respectively. L = crown length; M = dependent myocar-

econd derivative were used. For length computations, cubicmoothing B-spline improved the results. Computed lengthsithout B-spline smoothing were often overestimated. More-ver, longer branches with higher degrees of curvature have areater probability of deviating from the true medial axis andaving their lengths overestimated if B-spline smoothing is notpplied.

Previous studies have shown that regional myocardial massas closely and linearly related to the total coronary branch

ength distal to any point in the coronary arterial tree [6,38].linear relation between length and mass were found in dogs

6]. However, a recent report [34] has indicated that there is aower law relationship between length and mass. Specifically,rown length is proportional to the total perfused mass raised tohe power of 0.75. The present study also found a 0.75 poweraw between crown length and regional myocardial mass inwine—the average value of the exponents for the three coronaryrees was βV = 0.76. Previous studies [15,33] have also found a.75 power relationship between crown length and crown vol-me. Accordingly, the current investigation closely agrees with

hese past results with an average value of βM = 0.80. Sincehe crown length is related to the crown volume and dependent

yocardial mass with the same power law exponent, the crownolume should be linearly proportional to the dependent myocar-

498 H. Le et al. / Computerized Medical Imaging and Graphics 32 (2008) 488–501

F asses( .10 (Rm

daiortitdaaf3ttwdmtvcTtav

ithe user to draw a region of interest around an arterial tree orsubtree, and then the obtained lumen volume distal to the steno-sis can be used to estimate the amount of myocardium at risk.

ig. 8. Relationships between the total distal vessel volumes and myocardial mR = 0.81), log(V) = 1.02 log(M) − 1.79 (R = 0.78) and log(V) = 1.17 log(M) − 2yocardial mass.

ial mass. Indeed, this is the case according to our results of theverage of βVM = 1.04. These findings suggest that quantitativenformation on the myocardial area at risk can potentially bebtained from coronary angiograms by measuring the total arte-ial lengths or lumen volumes of a crown that belongs to the stemhat has segmental stenosis. By analyzing clinical angiographs, its possible to categorize patients according to different prognos-ic indications suggested by the area at risk. However, it can beifficult to measure the lengths of arterial branches on coronaryngiograms [39]. Tracing the tree manually is time consumingnd tracking it automatically is limited by image noise, arti-acts and anatomical background [40]. For biplane angiography,D reconstruction based on geometrical methods can be usedo obtain the lengths [41–44]. However, the method requireshe user to define corresponding points in the biplane images,hich is also time-consuming. In the current findings, the totalistal lumen volumes can also be used to estimate the regionalyocardial mass at risk, which supports the theoretical deriva-

ion of the volume-mass relation by West et al. [9]. The lumenolume of an arterial tree can be readily obtained from digitaloronary angiogram by using a densitometry technique [45,46].

he densitometry technique is more robust than the geometric

echniques because it is independent of the projection anglesnd makes no assumption as to the cross-section of the coronaryessels. An iodine calibration phantom is used for converting

FcR

of the LAD (a), LCX (b) and RCA (c). The fits are log(V) = 0.93 log(M) − 1.66= 0.82) for (a), (b) and (c), respectively. V = crown volume; M = dependent

ntegrated gray level into volume. The implementation requires

ig. 9. Comparison of βV and its errors for different levels of diameter trun-ations. The bottom, middle and top graphs correspond to the LAD, LCX andCA, respectively.

H. Le et al. / Computerized Medical Imaging and Graphics 32 (2008) 488–501 499

FcR

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FcR

Fig. 12. Comparison of log(kV) and its errors for different levels of diameterta

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ig. 10. Comparison of βM and its errors for different levels of diameter trun-ations. The bottom, middle and top graphs correspond to the LAD, LCX andCA, respectively.

The morphological relationships were examined at differ-nt levels of diameter truncations to investigate if a truncatedoronary tree can still be used to assign regional myocardialass accurately. Although branches with diameters of 400 �mere detected, the analysis was performed for truncation values

tarting at 600 �m to insure uniform diameters at the terminalessels. The errors in βM and βVM increased as the trunca-ion diameter increased since there were fewer data points forarger truncations. But values of approximately 0.75 and 1 (0.80nd 1.04, average for the three trees) were still found for βMnd βVM at a truncation diameter of 1400 �m with maximum

rrors of 12.74% and 10.59%, respectively. βV errors remainedow (1.13–1.98%) and did not increase with truncation diameterecause truncation affects both length and volume calculations.hen the trees were truncated at a certain diameter, both the

ig. 11. Comparison of βVM and its errors for different levels of diameter trun-ations. The bottom, middle and top graphs correspond to the LAD, LCX andCA, respectively.

dtre

Fta

runcations. The bottom, middle and top graphs correspond to the LAD, LCXnd RCA, respectively.

ength and the volume of the vessels were cut off proportionately.imilar to βM and βVM the errors in kM and kVM increased as

he truncation diameter increased because of fewer data points.owever, the errors for kV decreased slightly for larger trunca-

ions because smaller arteries, which are usually associated witharger length and volume measurement errors, were excluded.hese results indicated that the parameters of the morphological

elationships could be faithfully extracted for trees with trunca-ion diameter as large as 1400 �m. On the other hand, βM andVM is dependent on regional mass assignment, which can incur

ncreased error due to the truncation. Mass assignment was vali-

ated by weighing the three main perfusion beds and comparinghem to the values obtained from CT. The CT mass errors wereelatively lower for truncations of 600–1000 �m (1.01–6.43%rrors) than for truncations of 1200 and 1400 �m (5.10–29.03%

ig. 13. Comparison of log(kM) and its errors for different levels of diameterruncations. The bottom, middle and top graphs correspond to the LAD, LCXnd RCA, respectively.

500 H. Le et al. / Computerized Medical Imagi

Fta

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ig. 14. Comparison of log(kVM) and its errors for different levels of diameter

runcations. The bottom, middle and top graphs correspond to the LAD, LCXnd RCA, respectively.

rrors). The maximum errors were 18.34% and 29.03% for trun-ations of 1200 and 1400 �m, respectively. These errors indicatehat regional myocardial mass at risk cannot be reliably obtainedrom these two truncation levels. The maximum error for theower three truncation levels was 6.43%. Therefore, relativelyccurate regional masses supplied by the LAD, LCX and RCAould be deduced from coronary arterial branches as large as000 �m in diameter.

An important mediating factor for coronary artery diseasehat was not considered in this study is collateral circulation50]. Collaterals serve as bridges between coronary arteries torovide an alternate blood source to ischemic myocardial beds.

ardiac vulnerability depends on the patient’s ability to developoronary collaterals. The current study utilized normal swineearts; therefore collaterals were not visualized. By not includ-ng the collaterals, the myocardial mass at risk predicted by the

ig. 15. Errors of the CT computed masses for different levels of diameterruncations. The bottom, middle and top graphs correspond to the LAD, LCXnd RCA, respectively.

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ng and Graphics 32 (2008) 488–501

orphological relationships would be overestimated since col-ateral perfusion is ignored. However, the effects of collateralsn the exponents and slopes of the L versus M and V versus Melationships require further investigation.

Despite the various improvements that can be made on theurrent methodology, results from this study provide insightsnto the coronary arterial tree and its perfusion bed that canotentially be clinically useful. Future studies might involvehe aforementioned improvements in the methodology that canmprove the accuracy of the computed branch parameters. More-ver, in combination with current advances in coronary CTngiography [47], the reported method can be used to obtainhe lumen volume–mass and length–mass relationships as theatients undergo non-invasive coronary CT angiography. Thus,his additional information can potentially provide a guide forntervention.

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uy Le received his BS degree in Computer Engineering and MS degree iniomedical Engineering at the University of California, Irvine. He is currentlyn MD/PhD candidate at the same university. His research interests include CTmage processing in applications toward coronary artery diseases.

erry Wong received his BS and MS degrees in Chemistry from Stanford Uni-ersity, California. He is currently an MD/PhD candidate at the University ofalifornia, Irvine. His research interests include medical imaging and coronaryhysiology.

abee Molloi received his BS in chemistry and physics from Minnesota State

niversity. He received his Masters and PhD in medical physics from Universityf Wisconsin-Madison. His primary research interest is in the area of medical-ray imaging. He is presently Professor in Departments of Radiological Sci-

nces, Medicine (Cardiology) and Biomedical Engineering. He is a member ofmerican Association of Physicist in Medicine (AAPM).