Plaque development, vessel curvature, and wall shear stress in coronary arteries assessed by X-ray angiography and intravascular ultrasound

Abstract

The relationships among vascular geometry, hemodynamics, and plaque development in the coronary arteries are complex and not yet well understood. This paper reports a methodology for the quantitative analysis of in vivo coronary morphology and hemodynamics, with particular emphasis placed on the critical issues of image segmentation and the automated classification of disease severity. We were motivated by the observation that plaque more often developed at the inner curvature of a vessel, presumably due to the relatively lower wall shear stress at these locations. The presented studies are based on our validated methodology for the three-dimensional fusion of intravascular ultrasound (IVUS) and X-ray angiography, introducing a novel approach for IVUS segmentation that incorporates a robust, knowledge-based cost function and a fully optimal, three-dimensional segmentation algorithm. Our first study shows that circumferential plaque distribution depends on local vessel curvature in the majority of vessels. The second study analyzes the correlation between plaque distribution and wall shear stress in a set of 48 in vivo vessel segments. The results were conclusive for both studies, with a stronger correlation of circumferential plaque thickness with local curvature than with wall shear stress. The inverse relationship between local wall shear stress and plaque thickness was significantly more pronounced (p<0.025) in vessel cross sections exhibiting compensatory enlargement (positive remodeling) without luminal narrowing than when the full spectrum of disease severity was considered. The inverse relationship was no longer observed in vessels where less than 35% of vessel cross sections remained without luminal narrowing. The findings of this study confirm, in vivo, the hypothesis that relatively lower wall shear stress is associated with early plaque development.

Fig. 1

Development of atherosclerotic plaque: lumen – light gray, plaque/intima – mid gray, media – dark gray; (a) vessel without any stenosis; (b) compensatory enlargement; (c) luminal narrowing; (d) after treatment with PTCA and stenting; (e) IVUS image with (1) catheter, (2) lumen/ plaque, and (3) media/adventitia borders.

Fig. 2

Processing of the data from acquisition over segmentation to the generation of the plain model, followed by quantitative analyses used to annotate the 3-D/4-D model.

Fig. 3

(a) “Unfolding” an IVUS image frame using a polar transform; (b) this process is applied to the IVUS pullback, so that the detection of the cylindrical surfaces of varying radius is transformed to the detection of an elevation map of varying height.

Fig. 4

Learned border patterns from a set of training images that have been segmented manually are examined: An accumulator represents a range of patterns; its entries corresponding to border patterns are increased with every incidence of that border pattern in the training set.

Fig. 5

Segmentation stage using the learned accumulator values of Fig. 4: The accumulator values are used to assign the likelihood of each pattern in the new image being a border pattern; the result is a cost image that contains the likelihood of each pixel being a border pixel.

Fig. 6

Definition of (a) normal and tangent vectors, (b) the circumferential curvature index k_idx derived from the local curvature k and the projected normal vector n⃗ for a specific IVUS frame; positive values indicate “inner” and negative values “outer” curvature.

Fig. 7

Plaque thickness vs. curvature: (a) angiogram of a left anterior descending artery with the IVUS catheter inserted; (b) 3-D model with lumen and adventitia borders from fusion, where the volume between the red and green surfaces represents the vessel wall; (c) plaque thickness annotation derived from the model shown in (b), where blue color indicates low and red color high wall thickness; (d) curvature-index annotation derived from (b), blue color marks “outer” and red “inner” curvature; (e) after classification into regions correlating the data from (c) and (d), with the branch segment removed from analysis as indicated by the red dotted line – see Section 2.6.1 for the definition of the regions.

Fig. 8

One of the angiograms used for fusion, showing the IVUS catheter path (dotted line) and the lumen of a right coronary artery; the inset shows the corresponding tetrahedral mesh of the lumen at the stenotic vessel segment used for CFD analysis.

Fig. 9

Results from 60 analyzed vessels, analyzed as illustrated in Fig. 7, with means and standard deviations per curvature threshold; a value r_PC > 0.5 indicates that our hypothesis was satisfied.

Fig. 10

IVUS frames of an untreated vessel segment with slight stenosis and after stent placement at a location with heavy disease.

Fig. 11

Index r_PC for the vessel shown in Fig. 10 over the full vessel (gray) and with stented subsegments excluded (black); r_PC > 0.5 is only satisfied after exclusion of the diseased segment as compared to the overall vessel.

Fig. 12

Vessel and segment grouping for the definition of the sets described in Section 3.4.1, with two example vessels of different disease severity.