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Coronary artery disease (CAD) is the most common type of heart disease in western countries. Early detection and diagnosis of CAD is quintessential to preventing mortality and subsequent complications. We believe hemodynamic data derived from patient-specific computational models could facilitate more accurate prediction of the risk of atherosclerosis. We introduce a semiautomated method to build 3D patient-specific coronary vessel models from 2D monoplane angiogram images. The main contribution of the method is a robust segmentation approach using dynamic programming combined with iterative 3D reconstruction to build 3D mesh models of the coronary vessels. Results indicate the accuracy and robustness of the proposed pipeline. In conclusion, patient-specific modelling of coronary vessels is of vital importance for developing accurate computational flow models and studying the hemodynamic effects of the presence of plaques on the arterial walls, resulting in lumen stenoses, as well as variations in the angulations of the coronary arteries.

Coronary heart disease (CHD), also called coronary artery disease (CAD), is globally the leading cause of death and is predicted to remain so for the next 20 years. In 2020, it is estimated that this disease will be responsible for a total of 11.1 million deaths globally [

The most common cause of CAD is atherosclerosis, which is caused by the presence of plaques growing in the coronary arteries until the blood flow to the heart’s muscle is limited, resulting in lumen stenosis. If the clot becomes large enough, it can mostly or completely block the flow of oxygen-rich blood to the part of the heart muscle fed by the artery. This can lead to angina, myocardial infarction, or necrosis [

Computational fluid dynamics (CFD) allows for efficient and accurate computations of hemodynamic features of both normal and abnormal situations in the cardiovascular system and in vivo simulations of coronary artery flow changes [

In certain circumstances, treatment of coronary disease can be achieved without surgery. Angioplasty is a nonsurgical procedure, which is often used to open blocked coronary arteries. Despite the high resolution images obtained in cardiovascular imaging using powerful imaging techniques, such as Multislice Computed Tomography (CT) [

The 2D nature of the images further complicates the process, as it is, in general, difficult to assess overlapping and parallel vessels. Furthermore, other important anatomical characteristics of the arterial tree such as vessel curvature, torsion, and bifurcation take-off angles may not be reliably assessed using only 2D angiographic images. As discussed previously, these latter parameters may be important for the study of hemodynamic factors related to atherosclerosis [

There have been a number of studies in the literature for the quantitative determination of the 3D representation of the coronary tree based on angiographic views [

In this research, we introduce a semiautomatic method for reconstruction of coronary vessels in 3D from two monoplane angiogram images. The proposed approach incorporates a new robust edge extraction algorithm, where the user can choose any pair of start and end points along a vessel in order to obtain its 3D reconstructed volume, using the iterative 3D reconstruction approach, proposed previously by our group [

We present a methodology for reconstructing realistic topologies from arterial trees using accurate vessel wall positions from two conventional monoplane angiograms. The proposed method involves four main steps: (a) automatic centreline extraction, (b) a novel automatic edge detection method, (c) an iterative method for 3D centreline reconstruction, which results in an accurate representation of the main components of the arterial tree, namely, Left Anterior Descending (LAD) or Left Circumflex Artery (LCX), and finally (d) vessel surface reconstruction using vessel diameter information and intrinsic coordinates. The end result is a 3D surface representation of the arterial tree, which can subsequently be meshed using suitable Finite Element mesh generation software and used in computational fluid dynamics (CFD) simulations for hemodynamic assessment in cardiology applications.

The images were acquired using a Philips Integris 3000H X-Ray C-arm unit with an under couch tube/over couch image intensifier configuration. The projections obtained during routine coronary intervention of 5 stenotic patients using pulsed fluoroscopy (12.5 p/s) were LAO, 30° LAO caudal, 30° LAO cranial, anteroposterior with cranial and caudal angulations, RAO, 30° RAO caudal, and 30° RAO cranial and left lateral. As the image acquisition process is ECG-gated, the phase of the heart cycle for each frame can be determined. Other gantry information, such as the focal spot to image intensifier distance (SID), field of view (FOV), and gantry orientation, was automatically recorded and stored with each image file and included in DICOM 3.0 image format. All procedures were performed in accordance with institutional guidelines, and all patients gave informed consent before PCI.

The multistage 3D centreline reconstruction procedure consists of the following steps: (1) vessel enhancement, (2) hysteresis thresholding, (3) skeletonization, (4) bifurcation and end point detection, and finally (5) 3D centreline reconstruction. We use an automatic approach similar to the one proposed by the authors [

The algorithm uses a multiscale vessel enhancement method based on the eigenvalues of the Hessian matrix of the angiogram images in order to enhance the arterial tree and following the application of morphological operations, the final centreline, bifurcation, and end points are automatically extracted from the angiogram image. A sample centreline extraction of a patient angiogram is shown in Figure

Automatic coronary vessel skeletonization: (a) angiogram image, (b) vessel enhanced model, (c) binarized arterial tree, and (d) skeletonization followed by bifurcation and end point detection for arterial tree branch labelling.

Vessel centreline selection: (a) the user selects points on the arteries on both projections; (b) the corresponding centreline segments are extracted and are spline-interpolated to yield the final centrelines.

Once the centrelines of interest are obtained, a 3D representation of the centreline is generated using the concept of epipolar geometry [

The final reconstructed arterial tree is obtained by connecting the various arterial branches, as shown in Figure

3D vessel reconstruction. (a) Reconstructed 3D vessel centrelines from left and right 2D projections, (b) 3D reconstructed coronary tree alongside an inside view of the reconstructed vessel at three orthogonal planes. The stenosis can be clearly observed in the middle image as a sudden reduction in vessel diameter.

Once the coronary vessel centreline points are reconstructed in 3D, knowledge of the vessel lumen diameter is required in order to construct the 3D vessel lumen surface. The common method is to use information about the catheter size and scale accordingly for the diameter of the vessels. However, foreshortening may affect the vessel’s diameter on the projected planes. In what follows, we discuss a novel edge extraction method to address this.

In order to find the vessel walls, starting at the initial centreline point, we build normals to the centreline, comprised of 10 points of equal spacing on each side of the centreline. This ensures that the vessel walls are covered within this range. The latter gridding is depicted in Figure

Edge extraction: (a) normals (blue) to the centreline (yellow) are drawn, (b) an edge as a directed graph.

We approach the problem of edge curve extraction in the angiogram images from a graph theory point of view. In our approach, the generation of a vessel wall curve from a start point

The vessel surface reconstruction is based on using intrinsic coordinates by estimating the Frenet frames along the curve at each centreline point, using the central difference approximation of the derivative among the interior points and forward/backward differences at the ends. As the geometry of the centreline trajectory is known, we can, therefore, calculate the directions of the tangent (

At each centreline point

Simulations were run under Matlab R2010a using an Intel Xeon 5130, 2.00 GHZ processor with 8 GB of RAM. Edge detection was performed on all the branches selected in the centreline extraction stage. Based on the results of multiple simulations, the hyperparameter

Effect of the

Vessel edge extraction using the proposed dynamic programming method: (a) LAD edge extraction 1st and 2nd projections, left and right, respectively, and (b) LCX vessel edge extraction 1st and 2nd projections, left and right, respectively.

In order to validate the accuracy of the edge extraction results, the results were compared to ground truth segmentations. However, obtaining ground truth results is not an easy task and has been known to be a hard problem in image analysis and pattern recognition systems [

A solution is to use redundancy not only for identifying the correct vessel annotations for each angiogram image but also for evaluating the labelling quality of the experts. We use the method proposed in [

When using the latter method, we iterate the algorithm until convergence, following two steps: (1) estimate the correct label for each vessel branch on each projection, using labels assigned by three radiologists (1 for edge and 0 for nonedge), and (2) estimate the quality of the radiologists’ labelling capabilities by comparing the submitted annotations to the inferred correct answers. The final output is a set of (estimated) correct vessel edges for each branch on every projection and a confusion matrix for each radiologist, listing the error probabilities for each of them. From the confusion matrix, we can directly measure the overall error rate for each labeller as the sum of the nondiagonal elements of the confusion matrix (appropriately weighted by priors). This results in a single, scalar value as the quality score for each radiologist. In our studies, the first radiologist turned out to provide the most accurate annotations. The ROC generated from the described algorithm is shown in Figure

ROC comparison for the three expert annotators.

It is easy to verify that the first curve stretching almost into the top left corner represents the performance of the superior model (for a TPR = 0.9, the method commits virtually no false positives). Next, having obtained the best labeller, its corresponding labelled edge curves need to be compared with the extracted curves using the proposed method. In order to compare the distance between the vessel edge extraction results to that of the 1st annotator (i.e., ground truth), we use the Hausdorff distance between the curves to evaluate the difference. The Hausdorff distance is defined as

Discrepancies between ground truth and extracted vessel walls.

Patient | Average Hausdorff distance to ground truth | |||
---|---|---|---|---|

LAD 1st proj. | LAD 2nd proj. | LCX 1st proj. | LCX 2nd proj. | |

1 | 0.0039 | 0.0041 | 0.0035 | 0.0037 |

2 | 0.0032 | 0.0039 | 0.0031 | 0.0031 |

3 | 0.0041 | 0.0038 | 0.0039 | 0.0042 |

4 | 0.0029 | 0.0031 | 0.0029 | 0.0029 |

5 | 0.0034 | 0.0037 | 0.0033 | 0.0035 |

As it can be observed from Table

In order to have another comparison to an existing state-of-the-art vessel wall delineation method, we compared the proposed method to the automated vessel contour detection with manual correction methodology performed with QCA-CMS version 6.0 (Medis, Leiden, The Netherlands). The calibration procedure is initiated by the user defining start and end points in the catheter segment, which are connected using the Wavepath algorithm [

Discrepancies between the proposed method and QCA.

Patient | Average Hausdorff distance QCA and the proposed method | |||
---|---|---|---|---|

LAD 1st proj. | LAD 2nd proj. | LCX 1st proj. | LCX 2nd proj. | |

1 | 0.0068 | 0.0043 | 0.0052 | 0.0054 |

2 | 0.0051 | 0.0035 | 0.0069 | 0.0057 |

3 | 0.0059 | 0.0045 | 0.0050 | 0.0053 |

4 | 0.0034 | 0.0037 | 0.0035 | 0.0037 |

5 | 0.0062 | 0.0047 | 0.0063 | 0.0047 |

Vessel edge extraction comparison using the proposed dynamic programming method and QCA-CMS 6.0, left and right, respectively: (a) LAD, (b) LCX.

Having obtained the 2D projected vessel wall point coordinates (i.e., edge curves), the next step is to reconstruct the vessel walls in three dimensions. As we are only using two image projections, we assume a circular vessel cross section at each centreline point. In order to build the vessel surface in 3D, we proceed as follows. First, we use the 3D centreline reconstruction algorithm [

In this research, we introduced a new edge detection method for accurate reconstruction of coronary vessel walls in three dimensions from two monoplane angiogram images. The multistage approach offers a new automatic paradigm to reconstruct angiogram images from 2D projections. One of the main features of the proposed method is the novel robust edge extraction algorithm for the extraction of vessel edges using dynamic programming. The latter method is insensitive to the presence of bifurcation and branching points, which is a major problem in coronary vessels edge extraction. The user clicks on the desired segments of vessels and the process thereafter is fully automatic requiring no user interaction. The results show the robustness of the approach and its potential use in coronary image-guided interventions.

We introduced a pipeline for generation of patient-specific 3D models of coronary vessels using anatomical information from angiograms. Further work is in progress on the Finite Element (FEM) mesh models of the resulting reconstructions by adding boundary and material properties, with the ultimate goal of creating realistic vessel models. The resulting vessel models could be further coupled with the method of [

None of the authors have any conflict of interests.

The authors would like to thank Ioannis Pantos from the Department of Radiology, Medical School, University of Athens, Rimini 1, Chaidari, 1246 Athens, Greece, for providing the QCA-CMS edge extraction results.