Concise biomarker for spatial–temporal change in three-dimensional ultrasound measurement of carotid vessel wall and plaque thickness based on a graph-based random walk framework: Towards sensitive evaluation of response to therapy

Highlights

• A graph-based sensitive metric quantifying the change of carotid vessel-wall-plus-plaque thickness (VWT-Change) distribution is proposed.

• The Weighted Cosine (WCos) function was tailored for the quantification of responsiveness to therapy.

• The WCos-based biomarker was 14 times more sensitive than the mean VWT-Change in discriminating responsive and unresponsive subjects.

Abstract

Rapid progression in total plaque area and volume measured from ultrasound images has been shown to be associated with an elevated risk of cardiovascular events. Since atherosclerosis is focal and predominantly occurring at the bifurcation, biomarkers that are able to quantify the spatial distribution of vessel-wall-plus-plaque thickness (VWT) change may allow for more sensitive detection of treatment effect. The goal of this paper is to develop simple and sensitive biomarkers to quantify the responsiveness to therapies based on the spatial distribution of VWT-Change on the entire 2D carotid standardized map previously described. Point-wise VWT-Changes computed for each patient were reordered lexicographically to a high-dimensional data node in a graph. A graph-based random walk framework was applied with the novel Weighted Cosine (WCos) similarity function introduced, which was tailored for quantification of responsiveness to therapy. The converging probability of each data node to the VWT regression template in the random walk process served as a scalar descriptor for VWT responsiveness to treatment. The WCos-based biomarker was 14 times more sensitive than the mean VWT-Change in discriminating responsive and unresponsive subjects based on the p-values obtained in T-tests. The proposed framework was extended to quantify where VWT-Change occurred by including multiple VWT-Change distribution templates representing focal changes at different regions. Experimental results show that the framework was effective in classifying carotid arteries with focal VWT-Change at different locations and may facilitate future investigations to correlate risk of cardiovascular events with the location where focal VWT-Change occurs.

Introduction

Stroke is among the leading causes of death and disability worldwide, with a prevalence of 33 millions and 16.9 millions suffering a stroke in 2013 [1]. Over two-thirds of stroke deaths occurred in the developing countries [2]. China, as the most populous developing country, has an annual stroke mortality of 1.6 million [3], and the mortality rate is more than 7 times higher than in the United States [4]. As atherosclerosis is a complex disease that involves the interaction of many factors, such as genetic factors, cells of the arterial wall, blood chemistry and hemodynamics, rapid progression may occur despite intensive treatment of traditional risk factors [5]. The progression of plaque despite treatment are associated with higher stroke risk [6], [7], [8]. Therefore, these subjects should be identified early so that more intensive treatment strategies could be administered sooner. Objective identification of non-responders to treatments requires the development of sensitive quantitative biomarkers of carotid atherosclerosis.

Although ultrasound measurement of carotid intima-media thickness (IMT) (Fig. 1a) measured from 2D B-mode ultrasound has been widely used in clinical studies [9], [10] and has been shown to correlate with the risk of cardiovascular events [11], the rate of change of IMT is typically small (0.01–0.03 mm/year) and large sample and long duration of observation are required to identify statistically significant changes [12].

Direct measurements of plaque have been developed to improve the sensitivity for detecting therapy response and stratify vascular risk. Patients with progression in total plaque area (TPA) (Fig. 1b) [6] were found to have higher risk of vascular events compared to those with no change and regression in TPA. 2D B-mode ultrasound was used to quantify plaque textural features, which were able to discriminate symptomatic and asymptomatic patients [13], [14]. However, 2D ultrasound images were difficult to reproduce due to the requirement to localize a 2D image plane in each scanning; for this reason, 2D ultrasound was not optimal in monitoring plaque changes in a longitudinal study. 3D carotid ultrasound has been developed to address this issue [15], [16]. Wannarong et al. [8] reported that progression in total plaque volume (TPV) measured from 3D ultrasound (Fig. 1c) was more able to predict stroke than TPA. Egger et al. [17] introduced the use of vessel wall volume (VWV) to assess carotid atherosclerosis (Fig. 1c). VWV measurements incorporate both vessel wall and plaque without the need of isolating plaques from the vessel wall and were associated with higher intra-observer and inter-scan reproducibility than TPV. Although these biomarkers provide rich information regarding progression or regression on global plaque and vessel wall dimensions, the localized nature of carotid atherosclerosis suggests that biomarkers considering local change in plaque or vessel wall thickness may be more sensitive, thereby allowing more proof-of-principle studies to be conducted over a shorter duration that involves fewer subjects. To quantify the 3D distribution of vessel wall thickness change, our group measured vessel-wall-plus-plaque-thickness (VWT) (Fig. 1d) and VWT difference between baseline and follow-up scanning sessions [18] on a point-by-point basis and generated a 3D map that allows for the visualization and quantification of the VWT-Change distribution (Fig. 2c).

However, the shape and size of 3D VWT-Change maps constructed for different arteries are highly subject-specific, precluding quantitative comparisons between VWT-Change distributions of different arteries. We developed a technique to flatten 3D VWT-Change maps of different arteries onto a rectangular 2D standardized map [19] (Fig. 2d) to adjust for the inter-subject variability in carotid geometry. Since the VWT-Change distributions for all subjects could be mapped to a standardized 2D coordinate frame, the average VWT-Change maps for the atorvastatin and the placebo groups could be generated, thereby allowing group-wise comparison of VWT-Change distributions in these two treatment arms.

Although the 2D standardized VWT-Change maps adjust for the variability in arterial geometry and allow for quantitative comparison of local VWT-Change distributions, clinical conclusions are difficult to be drawn based on the complex distribution represented by thousands of VWT-Change data points per artery. In Chiu et al. [19], a biomarker was developed to quantify the effect of the atorvastatin treatment. The biomarker was developed based on a feature selection algorithm and was effective in identifying regions of interest (ROI) where the atorvastatin subjects experienced regression and the placebo subject experienced progression. Subject-based average VWT-Change computed over the ROI was more sensitive than that computed over the whole 2D map in identifying the effect of atorvastatin. However, the biomarker based on selected regions described above is less capable of identifying subjects with rapid focal progression despite treatment. In regions where atorvastatin subjects experienced rapid progression, the placebo subjects may also progress by various degrees. The difference in VWT-Change at these regions was not strong enough for them to be selected and included in the computation of the region-based biomarker. Moreover, the feature selection algorithm is a forward sequential searching algorithm that adds features one at a time without an objectively defined stopping criterion. To address this issue, we chose the size of the ROI selected by the algorithm to be the one that produces an average VWT-Change that discriminated the atorvastatin and placebo groups with greatest sensitivity within the searching range of 10–50% of the area of the entire 2D standardized map [19]. The rationale in choosing these upper and lower thresholds was to select regions that is large enough to detect “representative” patterns, while small enough so that we were still focusing on “local” instead of “global” patterns. Admittedly, the line between local and global patterns was hard to draw and the choices of these thresholds were based on empirical observation of the data. For these reasons, instead of considering selected ROI exclusively, a better biomarker would involve the whole distribution but be able to emphasize regional progression or regression. As subjects with rapid progression are exposed to higher stroke risk [6], [7], [8], there is a requirement of a metric that can identify subjects with rapid progression in an early stage so that alternative treatment plan can be made.

This motivated us to introduce a graph-based random walk framework in this paper to assign a score serving as a biomarker to quantify the degree of VWT regression or response based on the entire 2D VWT-Change distribution of each subject. The random walk framework considered the VWT-Change map of each patient as a node with transition probabilities to other nodes in a graph derived from their similarity. Although this problem was related to discriminating patients into those with VWT regression and progression, a more important requirement was to come up with a score to quantify the degree of VWT-Change. For this reason, the random walk framework was more appropriate than graph-based clustering techniques, such as spectral clustering.

In this work, we introduce a novel similarity metric that considered the similarity of the sign as well as the magnitude of point-wise VWT-Change at the corresponding location in each pair of 2D maps. In other words, each point contributed a weight in the similarity measurement and the whole VWT-Change distribution was involved. With the transition probabilities available, the probabilities of each VWT-Change map converging to the exemplary progression and the regression distributions (Fig. 4) in the random walk process were computed without iteration [20]. These two probabilities summed to unity for each VWT-Change map. Thus, one of these probabilities could be used as a metric to quantify to what extent the VWT has progressed or regressed. The sensitivity of this metric to VWT responsiveness was evaluated in this study.

In addition to providing an index that characterizes degrees of progression or regression, because the random walk framework could accommodate more than two exemplary distributions or templates, the proposed framework can be extended to quantify where progression or regression occurs by appropriately defining the templates. The location where focal VWT change occurs could be quantified by the converging probability to each template representing focal progression or regression at different regions of interest (Fig. 8). Although sudden focal plaque progression identified based on TPA and IMT measurements has been shown to associate with an elevated risk of vascular event [6], [7], no study has been performed to correlate risk of vascular events with the location where focal VWT change occurs. The quantification of the location of focal VWT changes would make such clinical studies possible.