Dynamic Active Contour Model for

Size Independent Blood Vessel Lumen

Segmentation and Quantification in

High-Resolution Magnetic Resonance Images

Catherine Desbleds-Mansard1, Alfred Anwander1, Linda Chaabane2,Maciej Orkisz1, Bruno Neyran1, Philippe C. Douek1, Isabelle E. Magnin1

1 CREATIS, CNRS Research Unit (UMR 5515) affiliated to INSERM, Lyon, France2 Laboratory RMN, CNRS Research Unit (UMR 5012) , Lyon, FranceCorrespondence address: CREATIS, INSA de Lyon, bat. Blaise Pascal,

7 rue J. Capelle, 69621 Villeurbanne cedex, Francecatherine.mansard@creatis.insa-lyon.fr

.The final version of the paper is available from:http://link.springer.com/chapter/10.1007%2F3-540-44692-3 33

Abstract. We are presenting a software tool developed for the purposeof atherosclerotic plaque study in high resolution Magnetic ResonanceImages. A new implementation of balloon-type active contour model usedfor segmentation and quantification of blood vessel lumen is described.Its originality resides in a dynamic scaling process which makes the influ-ence of the balloon force independent of the current size of the contour.The contour can therefore be initialized by single point. Moreover, sys-tem matrix inversion is performed only once. Hence computational costis strongly reduced. This model was validated in ex vivo vascular imagesfrom Watanabe heritable hyperlipidaemic rabbits. Automatic quantifica-tion results were compared to measurements performed by experts. Meanquantification error was smaller than average intra-observer variability.

1 Introduction

Atherosclerosis is a disease of the vascular wall, which can cause hemodynamictroubles and acute accidents due to rupture of the atherosclerotic plaque. Itstwo well known manifestations are stroke (acute cerebrovascular disease) andmyocardial infarction (acute manifestation of cardiac ischaemia). There is agrowing field of investigation dealing with the atherosclerotic plaque identifi-cation and characterization before plaque rupture and severe lumen obstruction.Animal models of pathologies met in humans are used to evaluate both thetherapeutic methods and exploration techniques, Magnetic Resonance Imaging(MRI) in our case. Watanabe heritable hyperlipidaemic (WHHL) rabbit was de-scribed as a well suited model for the atherosclerosis. Characterization of theplaque structure and composition has been performed by means of in vitro high

2 CAIP’2001, Springer-Verlag, Lecture Notes in Computer Science

resolution MRI. These studies have shown good correlation with histology [1]- [5] (fig.1). Among other tasks, such studies require quantification of the vas-cular lumen and of the plaque in numerous images. This tedious task needs tobe computer-assisted. First-level assistance is an interactive region drawing andautomatic calculation of the corresponding areas, diameters and perimeters. Thesecond level is a user-initialized automatic segmentation, with eventual interac-tive corrections in difficult cases where the user disagrees with the automaticallyfound outlines. The objective of the hereafter presented work was to realize anassistance tool with a maximum degree of automation, so as to save the user’stime and to improve the reproducibility of the results.

Fig. 1. Histological section (left) and in vitro MR image (right) of a human artery witha large atheroscerotic plaque. Expert hand-drawn regions representing different plaquecomponents in the histological section were simply superimposed on the MR image.Slight differences are mostly due to tearing of the artery during manipulations

One of the main functionalities of this tool is an automatic extraction of thevessel lumen contour. In medical images, smooth closed boundaries are expectedin most cases, in particular in the case of the vascular lumen, while simple edgedetection often leads to discontinuous lines with gaps and protrusions, becauseof contrast variations and noise. One of the methods suggested to obtain smoothcontinuous contours is based on the minimum-cost path search formalism [6].However, the technique most used today in the medical image processing, isbased on deformable models (see [7] for a survey) or on deformable templates[8]. This technique consists in using an initial form (curve, surface . . . ), providedwith certain properties of flexibility and elasticity, which is gradually deformedto coincide with the boundaries present in the image. The deformations occurunder influence of external forces which attract the form towards image pointsthe likely to belong to a boundary (typically maximum of the gradient), and ofinternal forces which attract it towards an expected reference form. Since thevery first implementation of planar deformable models called active contoursor snakes [9] many improvements have been proposed in order to make theresult initialization-independent. We proposed an original implementation calledDynamic Active Contour (DAC) which only needs a single initialization point

IAPR Int. Conf. Comput. Anal. Images & Patterns, Warsaw (PL), sept.2001 3

inside the object [10] and which can propagate on a whole sequence of imagesrepresenting contiguous cross-sections. The algorithm was implemented withina user-friendly graphical interface nicknamed ATHER.

This paper describes a validation of this tool applied to the vessel lumenquantification in ex vivo MR images from WHHL rabbits. In the sequel, firstlythe animals and the image acquisition protocol will be described. Then the DACmodel, the features of the software and the validation method will be detailed.Lastly, the obtained results will be presented and discussed.

2 Animals

The entire study includes six WHHL rabbits, three homozygous and three het-erozygous, two of which had a lipid-rich diet. First, two kinds of in vivo MRimages were acquired: one set of images focused on the vascular wall, the otherone used a contrast agent in order to highlight the vessel lumen. Then the animalswere sacrificed at age between 13 and 18 months. Their entire aorta with heartand kidneys were removed after fixation under perfusion with paraformaldehyde.

3 Images

In vitro MR imaging was performed with a 2 T horizontal Oxford magnet and aSMIS console. The specimens were placed on a half-birdcage RF coil of 25 mmdiameter working at 85.13 MHz. High resolution axial images of the thoracicand abdominal aorta were taken using a multislice 2D spin-echo sequence witha 256× 128 matrix. Slice thickness was 0.8 to 1 mm and the pixel size was 58 to78 m. T1 and T2 weighted images were obtained with TR/TE = 600/21 ms and1800/50 ms respectively. Six territories have been explored from the aortic archdown to the iliac bifurcation. The acquired images were organized into series,one per territory (fig.2).

4 Dynamic Active Contours

Let us first remind some fundamentals on active contours. A deformable contourmodel is defined by a parametric curve ν(s, t) = (x(s, t), y(s, t))T , which evolvesin time t and space, and by its energy, E(ν) = Eint(ν) + Eext(ν). The energyEint(ν), corresponding to internal forces, imposes constraints on the first andsecond derivatives of the curve:

E(ν) = Eelast(ν) + Eflex(ν) = α

∫

1

0

∣

∣

∣

∣

∂ν(s, t)

∂s

∣

∣

∣

∣

2

ds+ β

∫

1

0

∣

∣

∣

∣

∂2ν(s, t)

∂s2

∣

∣

∣

∣

2

ds , (1)

where α controls its elasticity while β controls its flexibility and s ∈ [0, 1] isthe arc length. There are two kinds of external forces represented by a potential

4 CAIP’2001, Springer-Verlag, Lecture Notes in Computer Science

Fig. 2. Examples of high resolution cross-sectional MR images of a rabbit aorta. Longi-tudinal section with lines showing the positions of cross sections from the correspondingseries (left). Cross-sectional images weighted T1 and T2 (right). Vessel lumen appearsin black, surrounded by a thick vessel wall layer (media), which appears in grey (betterdelineated on top). Atherosclerotic plaque is perceptible as an additional layer betweenthe media and the vessel lumen in the right part of each image (arrow). In fact, theplaque is a pathological thickening of a thin internal vessel wall layer (intima).

energy Eext(ν) =∫

1

s=0P (ν(s, t))ds : image forces and a balloon force. The link

between potentials Pi(ν) and forces is given by : Fi(ν) = −∇Pi(ν). The imageforces are usually designed to attract the snake toward strong intensity gradients.One can also use prior knowledge about the vessel outline as function of theintensity, so that the potential energy function has a minimum at the vesselboundary. With an initialization far from any edge, the active contour wouldcollapse. One solution consists in adding an external balloon force Fb [11], whichacts like an inflating pressure, and makes the active contour model move withoutany image gradient. It is expressed as Fb = bn(s, t), where n(s, t) is the normalunitary vector oriented outward at the point ν(s, t), and b is a coefficient whichcontrols the inflation. The total external force Fext(ν) is a weighted sum of theseforces.

The parametric curve ν(s) is fitted to the image by minimization of the energyE(ν). The minimization is a temporal and spatial discrete process, using a finitenumber N of snake points ν(i, k) that approximate the snake as a polygon. Thepartial derivatives in (1) are approximated by finite differences ∂ν(s, t)/∂s ≈(ν((i+1), k)−ν((i−1), k)/2h, with h the discretization step of the snake pointson the contour. The snake is iteratively deformed, explicitly using the externalforces Fext(ν) at each point of the snake, while implicitly minimizing the internalenergy. The new position ν(i, k) at time step k is computed by solving theassociated Euler equations. These equations can be solved by matrix inversion :

ν(i, k) = [γI+A]−1 · [γ · ν(i, k − 1)] + Fext (ν(i, k − 1))] . (2)

This equation is referred to as the evolution equation of the snake. The ma-trix A represents a discretized formulation of the internal energy. The dampingparameter γ controls the snake deformation magnitude at each iteration.

IAPR Int. Conf. Comput. Anal. Images & Patterns, Warsaw (PL), sept.2001 5

The discretization step h depends on the number of snake points N and,initially, is equal to the distance between the snake points. The evolution equa-tion (2) is only valid if the snake points are equally spaced and the step h isunchanged. After each iteration however, the length of a snake grows due toexternal force, and h does not correspond to the real distance between the snakepoints. In conventional implementations of the active contours, the internal en-ergy, especially the term Eelast(ν) associated with the contour’s tension, growswith the snake length and may stop the snake before the boundary is reached.This is particularly annoying if the initialization is far from the final position.In this case, the model needs to be resampled with a new (higher) number ofsnake points N , or/and a new step h. The N by N matrix [γI +A], as well asits inverse have to be recomputed. This is a time-consuming task which limitsthe classical snake model application in many cases.

In order to make the snake scale-independent and allow an initialization by asingle pixel in the image, we proposed [10] a new numerical scheme for the snakeenergy minimization. It was designed to preserve the validity of the equation (2)in spite of the evolution of the snake’s size. It only needs a single computation ofthe matrices [γI+A] and [γI+A]−1, and uses a fixed number of points for allthe iterations. The snake size is scaled at each iteration, in order to normalizethe internal energy of the model with a fixed discretization step h′ = 1. Thescaled snake ν′(i, k− 1) has a normalized length equal to N . It is obtained fromthe actual snake and the average distance hk−1 between its points:

ν′(i, (k − 1)) = ν(i, k − 1)/hk−1 . (3)

The scaled snake is deformed according to the evolution equation (2), usingthe external forces Fext from the non-scaled snake. Hence, the new (scaled)positions for the snake points ν′(i, k) are:

ν′(i, k) = [γI+A]−1 · [γ · ν′(i, k − 1)] + Fext (ν(i, k − 1))] . (4)

Let △ν′(i, k) be the snake deformation vectors for each snake point:

△ν′(i, k) = ν′(i, k)− ν′(i, k − 1) . (5)

The deformation vectors are computed with a normalized internal energy,and the deformation is directly applied onto the non-scaled snake △ν(i, k) =△ν′(i, k). Therefore, the new position of the snake, after the normalized defor-mation is:

ν(i, k) = ν(i, k − 1) +△ν(i, k) . (6)

In this new position, the snake points are redistributed along the polygonaloutline, to ensure equal distances hk for the next iteration.

5 Graphical Interface: ATHER

ATHER stands for Atherosclerosis MR image visualization and quantificationsoftware. It displays one entire image series at a time. Each slice can be zoomed,

6 CAIP’2001, Springer-Verlag, Lecture Notes in Computer Science

its histogram can be interactively stretched and signal to noise ratio as well asthe standard deviation of noise can be measured in user-selected regions. Ves-sel lumen contours can both be manually drawn and automatically extracted,with a possibility of interactive refinement if necessary. The automatic contourextraction needs no parameter tuning, since the parameters of the DAC modelhave been experimentally optimized for the available vascular images. Firstly,we set the parameters of the general shape of the boundary, i.e. weighting co-efficients of the flexibility and elasticity terms. Secondly, we set the coefficientsof the image force (gradient) term and of the stop criterion. We thus obtaineda class-of-image dependent model. The same set of parameters is applicable forexample to MRI of rabbits (in vitro and in vivo) and to human MR angiogra-phy of aorta and carotid arteries. Hence, the only necessary user interaction is adouble-click in the vessel lumen in the selected slice. For further speed-up, thecontour extraction can be performed in the entire series. The extracted contour’sgravity center becomes the starting point for the contour extraction in the nextslice and so on. This method is applicable because each series represents a short,approximately straight, portion of the aorta (fig.2). Quantitative results (area,perimeter and diameter) are displayed and stored in a computer file. ATHERalso features such functionalities as automatic extraction of the external contourof the vessel wall, as well as semi-automatic plaque quantification (fig.3). Theywill not be detailed in this paper, because their validation is still ongoing.

Fig. 3. Left: cross-section of an artery with internal (dots) and external contours (line)of the vessel wall superimposed and plaque delineated. Right: schematic representationexplaining the image structure.

6 Measurement Protocol

Validation of the DAC model was performed on a subset of three from six rabbits.The measurements were done on 121 slices subdivided into series correspondingto different territories (contiguous slices).

IAPR Int. Conf. Comput. Anal. Images & Patterns, Warsaw (PL), sept.2001 7

Quantitative validation was based on area measurement. The areas of the au-tomatically extracted contours were compared with the areas of the contours pre-viously drawn by two experts using Osiris software (University Hospital GenevaSwizterland). Let us note that Osiris also offers the possibility of an automaticcontour extraction. However, it needs to be done in each slice separately, afteran interactive selection of a region of interest and an adjustment of a toleranceparameter (percentage of image dynamics). In practice, the experts used thisautomatic extraction and stored the result only when, in their opinion, the con-tour perfectly fit the boundary. Otherwise they drew it manually. In order toquantify intra-observer variability of the measurements, one expert re-measuredthe areas in 45 slices, 6 months later. Inter-observer variability was calculatedfor the same set of 45 slices. ATHER’s intra-variability was calculated after ap-plying the automatic contour extraction twice to all the data set. The user wasauthorized to change the initialization point in single images within a series butnot to modify the resulting contours.

For a qualitative comparison between ATHER and the experts, contours’forms were visually inspected. However, distances between contours could notbe measured except for a couple of slices for which the contours hand-drawn bythe experts were stored as curves. All the other results of the expert-performedmeasurements were only stored as area values.

7 Results

The contours automatically extracted using the DAC model are very close tothe experts’ ones. For the available (stored as curves) experts’ contours, themaximum distance was about one pixel (fig. 4).

Fig. 4. Qualitative comparison between the contours drawn by ATHER and by theExpert. Maximum distance is about one pixel. The curves’ thickness, in this picture,is 1/3 of the pixel size.

This qualitative result (see also fig.5) agrees with the quantitative compari-son. Average absolute difference between the experts’ measurements and ATHERmeasurements, calculated over the slices i:

µ = mean

[

|AreaATHER(i)−Areaexpert(i)|

Areaexpert(i)

]

× 100 , (7)

8 CAIP’2001, Springer-Verlag, Lecture Notes in Computer Science

was equal to 4% for the entire set of data. It is to be compared with the variabilityof the expert-performed measurements calculated in a similar way. The intra-observer variability was as large as 6,4% and the inter-variability between thetwo experts was equal to 4%. The high intra-observer variability, compared tothe inter-observer variability, can be explained by the very long delay betweenthe two measures and by the fact the the second series of expert’s measurementswas carried out on a different screen.

Fig. 5. Examples of results obtained with the DAC model in different territories (wenote the variable quality (signal to noise ratio) of images).

However, the maximum difference between ATHER and the experts was aslarge as 19%. Large errors like this occurred in a few images of particularly poorquality (high level of noise) and in case of images with residual quantities offormol in the vessel lumen (fig.6). In the latter case, even an experienced humaneye is sometimes unable to distinguish the boundary between these residues andthe vessel wall. As confirmed by the second expert, human diagnosis based onthese images cannot be reliable. We also calculated the intra-variability of theresults obtained with ATHER. This variability was not more than 1,2%. Whenthe images are of good quality, the automatic contour gives very good results andis very insensitive to the position of the initialization point. The error increasesmoderately for reasonable noise levels. In one of the rabbits, the measurementerror increased by 2.8%, as the noise standard deviation increased from 0 to 6%of the image dynamics.

Let us underline time savings obtained with ATHER. The experts used ap-proximately 1 hour to obtain the measurements for 45 slices, with their usualoperating mode. It is to be compared with execution time by ATHER, e.g.: fora series of 17 slices, all the operations from image file opening to 3D surfacerendering of the automatically extracted contours, took 30 s on the same PC.

8 Discussion and Conclusion

The main characteristics of our active contour implementation are fast computa-tion and results stability with different starting points within the vessel lumen.The latter characteristic reduces to minimum the user interaction. In particular,when propagating the boundary extraction from one slice to another, the previ-ous contour’s center can be used as starting point. This is very useful when slice

IAPR Int. Conf. Comput. Anal. Images & Patterns, Warsaw (PL), sept.2001 9

Fig. 6. Example of image where the automatically extracted contour was significantlydifferent from the expert’s one, due to poor image quality and a residue of formol invessel lumen.

spacing is large and the contour forms may vary significantly between neigh-boring slices. In our study the slice spacing is large so as to coincide with thethickness of histological slices. However, with smaller spacing, the current con-tour can be initialized by the previous contour, slightly reduced. In this case, thecontour extraction is even faster and more robust. The extracted planar contoursare not only used for the purpose of quantification. They are also exploited forthe sake of 3D visualization. From the detected boundary points, ATHER gen-erates a shaded surface display (fig.7) which can be interactively animated. Thisis of great interest for visual assessment of the overall intraluminal morphologyof the plaque. The herein presented work is a part of a wider project. ATHERwill be validated on in vivo images from the same rabbits, also for the externalboundaries of the vessels. In parallel, the same model was implemented in an-other graphical interface, named MARACAS, specially designed for the studyof MR angiography images, i.e. images of the vascular lumen obtained after acontrast agent injection. It was already validated on images from phantoms [10].Now, it is applied to images from our rabbits and from patients.

Acknowledgements

This work is in the scope of the scientific topics of the GDR-PRC ISIS researchgroup of the French National Center for Scientific Research (CNRS). The au-thors are grateful to Emmanuelle Canet for her help in image acquisition andassessment.

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