Fast retrieval of calcification from sequential intravascular ultrasound gray-scale images

1.1. Backgrounds and medical context

Cardiac vessel disease is caused by atheromatous plaques that build up along the tunica intima (inner layer) of coronary arterial walls. Detection, tissue-typing, and description of the accumulated plaques are essential to diagnose and plan an interventional treatment of coronary artery diseases [1].

Intravascular ultrasound (IVUS) imaging is currently the most sensitive methodology that invasively detects and measures advanced atheroma within living individuals [2]. Owing to different absorption and reflection properties of different wall tissues, the morphometry and composition of vessel walls, including possible plaques, are visible with different gray scales on echo images [3] (see Fig. 1).

Retrieval of key IVUS frames, including plaques, and discrimination between components of plaques are invaluable in predicting plaque progression and regression. In clinic, IVUS tissue characterization tends to be performed by manual labeling and interpretation because of the relatively low resolution, high speckle noises, non-uniform luminance, and random presence of various artifacts within the images [4]. However, frame-by-frame visual analysis is a complicated, subjective, and tedious process that depends highly on the specialist.

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Fig. 1.

Typical IVUS gray-scale images.

Automated retrieval of IVUS data sets to identify plaque tissues and determine their composition can provide objective, quantitative, and reproducible measures of plaques. Thus far, two types of methods have been proposed according to the source data: radio frequency (RF)-based and image-based.

Raw backscattered RF signals are better data sources than reconstructed gray-scale images for tissue characterization due to the higher resolution of unprocessed data, especially for fatty and fibrotic plaques [5–10]. Recently, three different IVUS tissue characterization software systems based on the analysis of RF signals, namely, virtual histology (VH)-IVUS (Volcano Therapeutics, Inc., Rancho Cordova, CA, USA), integrated backscatter (IB)-IVUS (YD Co., Ltd, Nara, Japan), and iMap (Boston Scientific, MA, USA), became commercially available [11,12]. Methods to characterize tissues through the analysis of textural features during the reconstruction of gray-scale images from RF signals were also proposed in [13–17]. However, one limitation of RF-based methods relates to their dependence on electrocardiogram (ECG)-gated acquisition [4]. The RF signals are acquired according to the R-R wave amplitude of recorded ECG signals during catheter pullback. When ECG signals are not available or R-wave amplitude is too low, the RF-based techniques cannot be used to analyze coronary atherosclerotic plaques. Moreover, they need a large storage to save the IVUS backscattered signals of every subject. Standard outputs of most currently used IVUS equipment in clinic are also routine gray-scale images satisfying the DICOM (Digital Imaging and Communications in Medicine) standard, and raw data are not always available [3]. Related hardware of these IVUS devices should be improved to use RF-based techniques. Another limitation is that RF analysis cannot characterize the areas with acoustic shadows (e.g., calcium and guidewires) as image-based methods can [18].

Methods based on computerized image analysis adopt conventional gray-scale images, which are relatively easier to acquire than RF signals, to characterize plaques. Almost all image-based methods have adopted textural features as quantitative indices [4] combined with priori knowledge about plaque features to identify and classify plaques. For example, in [19], a semi-automated plaque characterization method based on the extraction of texture, intensity-based, and geometrical features as well as feature classification was presented. The method requires accurate detection of the media-adventitia and lumen borders. In [20], a method was presented to classify plaque regions into three classes: soft plaque, hard plaque, or hard plaque shadow. In [21], the performance of five statistical texture analysis techniques (i.e., first-order statistics, Haralick’s method, Laws’ texture energies, neighborhood gray-tone difference matrices, and texture spectrum method) in distinguishing plaques from IVUS images were evaluated. In [22], a detailed summary of the previous study on IVUS tissue characterization adopting textural feature analysis was given. A conclusion that textural descriptors alone are not suitable to distinguish mixed plaques in IVUS gray-scale images was finally drawn. In [23], a context-based framework built on a global object context and on mutual positions of local descriptors was proposed to retrieve IVUS images according to their vascular morphology. In [4], a combination of gray-scale-based features and textural descriptors (LBP, modified run-length, and neighboring gray-level) was adopted to extract IVUS textural features. Support vector machine (SVM) and ECOC classifier were then employed to classify feature vectors. In [24], tissue echomorphology was modeled by means of a mixture of Rayleigh distributions, and model parameters were estimated with the expectation maximization algorithm. The aforementioned methods are based on the extraction and classification of image textural features. They can be used to discriminate plaque compositions in an individual IVUS frame. However, their direct applications in sequential image retrieval are limited due to high computation cost and low automation.

Dense calcium, the most unusual kind of plaque tissue, is characterized by the high echoreflectivity and absorption of the emitted pulse from an ultrasonic transducer and a deep acoustic shadow behind the tissue in echo images. Gray-scale IVUS imaging features both high sensitivity and specificity in detecting calcium [19]. One kind of method for detecting calcification from IVUS images is to locate the calcified region after extracting the lumen and media-adventitia borders [25] based on the snake model or geometric deformable model [26]. A limitation of this kind of method is that it requires the accurate segmentation of inner and outer borders of the vessel wall in each frame. However, such segmentation is difficult to achieve, especially for IVUS images that include calcification. Another kind of method is to directly detect calcification by automatic thresholding of gray-scale images. The acoustic shadow that usually follows calcification regions is used as a discriminant of other bright regions of the image [27,28]. For example, the acoustic shadow was enhanced and recognized using an adaptive threshold method in [29]. In [30,31], calcium quantification was performed through an adaptive thresholding segmentation based on Otsu’s method combined with an analysis of the acoustic shadow regime. The 2-D Renyi’s entropy was used to adaptively threshold the IVUS image that includes calcifications in [32]. In [33], Rayleigh mixture model and Markov random field were adopted to coarsely detect calcified plaques.

1.3. Objectives of the work

This paper presents a novel four-step coarse-to-fine strategy that retrieves calcification rapidly without context information from routinely acquired sequential IVUS gray-scale images: (1) original images are filtered to reduce noise, (2) radial gray-scale variation curves (RGVC) are extracted from each filtered polar view, (3) an automatic thresholding scheme based on the jump features of RGVCs is employed to coarsely detect the location of calcified plaques, and (4) coarse query results are refined to remove pseudo calcified plaques by checking the gray-level features of neighboring pixels. For validation, we evaluate the correlation between the calcification detected by our method with the calcified tissues obtained by experienced physicians and by VH-IVUS.

The rest of this paper is organized as follows: Section 2 discusses the proposed method, including image pre-filtering, detection of RGVCs, coarse retrieval of calcified plaques, and refinement and location of calcified plaques. Section 3 lists the experimental results and discussions are given in Section 4. Finally, Section 5 summarizes and concludes this study.

2.1. Pre-filtering

The original IVUS images are first filtered with speckle-reducing anisotropic diffusion (SRAD) [34] to reduce speckle noises without blurring or removing the edges or details of calcifications. First, the diffusion coefficient c ( q ) of an IVUS image I is obtained: (1) c ( q ) = 1 1 + q 2 − q 0 2 ( t ) q 0 2 ( t ) [ 1 + q 0 2 ( t ) ] .

In Eq. (1), q is the instantaneous coefficient of variation determined by (2) q = 1 2 ( | ∇ I | I ) 2 − 1 4 2 ( | ∇ 2 I | I ) 2 [ 1 + 1 4 ( | ∇ 2 I | I ) ] 2 , where ∇ and ∇ 2 are the gradient operator and Laplacian operator, respectively. In Eq. (1), q 0 ( t ) is the local variance coefficient of the homogeneous regions of the image, which is determined by (3) q 0 ( t ) = var ( z ( t ) ) z ( t ) ‾ , where z ( t ) ‾ and var ( z ( t ) ) are, respectively, the intensity mean and variance over a homogeneous area at t. Then, we obtain the temporary result image I ˜ according to c ( q ) and I: (4) I ˜ = I + Δ t 4 [ div ( c ( q ) ) · ∇ I ] , where div is the divergence operator, and Δ t denotes the time step. We set Δ t as 1.

The first and second step are repeated for P times until the final result image I ˆ is obtained.

2.2. Extraction of radial gray-scale variation curves

Dense calcification blocks the transmission of ultrasound waves and is thus seen as a very bright area with black acoustic shadows behind in ultrasonic images. The intensities of normal wall tissues and soft plaques are relatively low because ultrasound waves can pass through these tissues. In consequence, the gray scales along the angular direction within the calcified plaque are obviously different from those within non-calcified regions in polar coordinates of the IVUS image.

To model the difference, each filtered IVUS image f ( x , y ) is transformed from the Cartesian domain to the polar domain centered on the image center (i.e., catheter center) to obtain its polar view f ¯ ( ρ , θ ) , where ρ and θ are the polar radius and angle respectively. The maximum intensity curve is defined in Definition 1.

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Fig. 2.

RGVCs of an IVUS image. (a) Original image. (b) Filtered image with SRAD. (c) RGVCs along radii 1 and 2 in (a). (d) RGVCs and their slope profiles along the radius 1 and 2 in (b).

As shown in Fig. 2(d), the RGVC along radius 1 changes more abruptly at the interface between the calcification and the acoustic shadow compared with that along radius 2, which belongs to the non-calcified region. The maximal slope of each RGVC is compared with a threshold ε to coarsely retrieve calcification: (5) f ¯ ′ ( : , θ ) = f ¯ ( : , θ ) , max θ > ε , 0 , else , where f ¯ ′ ( : , θ ) and f ¯ ( : , θ ) ( θ = 1 , 2 , … , 360 ) are, respectively, gray levels of the θth column of pixels in the preliminary result and the filtered polar view; and max θ is the maximal slope of the RGVC of f ¯ ( : , θ ) . If max θ is larger than ε, those pixels along the angular direction θ in the filtered polar view are preliminarily determined to belong to the calcified region, and their gray levels are preserved in the preliminary result. Otherwise, the gray-levels of the pixels along the angle θ are set as 0 in the preliminary result.

The threshold ε is adaptively selected for each IVUS frame. The detailed steps are as follows:

First, for a filtered polar view f ¯ ( ρ , θ ) , a total of 360 RGVCs are obtained. The maximal slopes of these RGVCs are calculated and denoted as a sequence S = { S 1 , S 2 , … , S 360 } .

Second, the elements of S are ordered down, thus obtaining S ′ = { S 1 ′ , S 2 ′ , … , S 360 ′ } . S ′ is separated into two parts by T : S ′ ( 1 ) = { S 1 ′ , S 2 ′ , … , S T ′ } and S ′ ( 2 ) = { S T + 1 ′ , S T + 2 ′ , … , S 360 ′ } .

Third, the sum of the variances of S ′ ( 1 ) and S ′ ( 2 ) is defined as (6) σ T 2 = 1 T ∑ i = 1 T [ S i ′ − μ 1 ] 2 + 1 360 − T ∑ i = T + 1 360 [ S i ′ − μ 2 ] 2 , where (7) μ 1 = 1 T ∑ i = 1 T S i ′ and (8) μ 2 = 1 360 − T ∑ i = T + 1 360 S i ′ are the mean of S ′ ( 1 ) and S ′ ( 2 ) respectively. When T = 1 , 2 , … , 359 , a total of 359 sums of the variances are obtained and denoted as { σ 1 2 , σ 2 2 , … , σ 359 2 } . We find the T corresponding to the minimal sum of the variances and take S T ′ as the threshold ε.

2.4. Retrieval refinement

Several incorrectly detected bright regions may be included in the preliminary result. To refine the query and improve the robustness, the intensity features of successive N columns of pixels are checked in the preliminary query result. If a column of pixels as well as successive N columns within their neighborhood are determined to belong to the calcified region, these pixels within this neighborhood are identified as the calcification; otherwise, they are non-calcification. The frames that include calcification are finally retrieved and calcified regions are located. Obviously, N should be properly selected to obtain robust retrieval. The dependence of retrieval accuracy on the parameter will be discussed in Section 4 according to experiments with in vivo image data.

4.1. Comparison to texture analysis methods

To quantitatively evaluate our method, three automated methods were compared: our method and two texture analysis methods. The first texture-based method proposed in [35] adopts low-level statistics [i.e., one-order statistics (including mean, standard deviation, coefficient of variation, skew, kurtosis, and entropy of histogram)] and a co-occurrence matrix to describe the image gray-level distribution and an SVM classifier to classify tissue features. This method is called gray-level method for short. Another method proposed in [36] uses K–L transformation to extract classification information and an SVM classifier to determine plaque type. It is called K–L method for short. Calcifications in all the images were traced and labeled manually by experienced physicians to serve as the ground truth for comparison.

Table 1 summarizes the results of three in vivo image sequences with automated methods and the manual operation. In the table, the processing time does not include the time cost for reading and displaying images. We can see that automated processing is much faster than manual operation. The accuracy of our method is higher than that of the gray-level method but is similar to the K–L method. However, the K–L method extracts multi-features of images for classifying through K–L transformation and designs an SVM model to classify image features. In our method, the existence of a calcification is determined only according to the jump features of RGVCs without image segmentation, feature extraction, and feature classification. Therefore, the complexity of our method is much lower than that of the K–L method. These experimental results demonstrate that our method is valid, simple, and fast in the retrieval and location of calcification.

We constructed a receiver operating characteristic (ROC) curve to compare the performance of our method and the K–L method. The horizontal axis of a ROC curve denotes the false positive rate (FPR), while the vertical axis represents the true positive rate (TPR). The role of calcification retrieval is to classify the pixels in an IVUS image into two categories: calcified (positive) and non-calcified (negative). TPR, also defined as sensitivity, refers to the ratio of correctly classified pixels based on the automated method for calcification to the total pixels correctly classified by the golden standard. On the other hand, FPR, which is equivalent to (1-specificity), defines non-calcified pixels incorrectly detected as calcified ones among all the non-calcifications. As illustrated in Fig. 6, the area under the ROC curve is 0.906 for the proposed method and 0.863 for the K–L method, suggesting that our method performs better.

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Fig. 6.

ROC curves: in red solid line, the proposed method; in green dashed line, the K–L method.

Our method was also applied to in vivo IVUS gray-scale images acquired with a commercially available 2.9F 64-element 20 MHz phased-array IVUS catheter (Eagle Eye, Volcano Therapeutics, Rancho Cordova, CA, USA), and our results were compared with corresponding VH-IVUS images for further validation. Through color-coded VH-IVUS maps, atheromatous tissues were classified into four categories and color coded as green (fibrotic, FT), yellow–green (fibro-fatty, FF), white (dense calcium, DC), or red (necrotic core, NC) [37].

Our experimental data sets consist of IVUS image sequences acquired from five patients. Frames that include calcification were retrieved from the sequential gray-scale images, and the calcified regions were labeled with our method. Characterized images were then validated by their corresponding VH-IVUS images. Figure 7 shows an application of our method in two IVUS frames. The calcified plaques were clearly detected similarly by VH-IVUS and by our method. The correlation coefficient between the calcification detected by our method and the calcified plaques detected by VH-IVUS is 0.661, with p < 0.001 .

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Fig. 7.

Two cross-sectional IVUS images and corresponding VH-IVUS frames characterizing a calcified plaque.

The size of detected calcified regions depends on N. A large N may result in some small calcified regions to be neglected. We experimentally chose N as 6 according to experimental results with a large amount of in vivo images. This number means that the small calcified points whose width in an IVUS polar view is smaller than 6 pixels cannot be detected with our method.