A local angle compensation method based on kinematics constraints for non-invasive vascular axial strain computations on human carotid arteries

Abstract

Non invasive vascular elastography (NIVE) was developed to highlight atherosclerotic plaque constituents. However, NIVE motion estimates are affected by artifacts, such as an underestimation of deformations due to projected movement angles with respect to the ultrasound beam, movements of the operator or of the patient during image acquisition. The main objective of this work was to propose a local angle compensation method within small measurement windows for the axial strain based on kinematics constraints, and to introduce a filtering process on the strain time-varying curve to reduce as much as possible the impact of motion artifacts. With such preprocessing, we successfully quantified the strain behavior of near and far walls in longitudinal images of internal carotid arteries without (n = 30) and with (n = 21) significant atherosclerotic disease (greater than 50% stenosis). Maximum strain rates of 4.49% s⁻¹ for the healthy group and of 2.29% s⁻¹ for the atherosclerotic group were calculated on the far wall of internal carotid arteries; significant differences were found between these values (p = 0.001). The minimum strain rates, also on the far wall of internal carotid arteries, of −3.68% s⁻¹ for the healthy group and of −1.89% s⁻¹ for the atherosclerotic group were significantly different as well (p = 8 ×10⁻⁴). The mean systolic, diastolic and cumulated axial strains could also distinguish the two groups after normalization by the pressure gradient between acquired images. To conclude, the proposed techniques allowed to differentiate healthy and atherosclerotic carotid arteries and may help to diagnose vulnerable plaques.

Introduction

Stroke is the third leading cause of death and the first cause of morbidity in western countries [1]. Mainly due to atherosclerosis, 60% of all cerebral infarctions are linked to the rupture of a vulnerable plaque [2]. Carotid stenosis has long been the primary marker of vulnerability. However, it has been shown that calcified plaques are less prone to rupture than non calcified plaques [3] and are thus more stable. A vulnerable plaque can be characterized by a soft necrotic core embedded in the wall under a thin fibrous cap [4]. In fact, plaque vulnerability is multifactorial and depends mainly on its tissue composition (fibrotic, calcified and lipidic) and the biomechanical properties of its components. The studies [5], [6], and later [7], [8], have shown that circumferential stress, more specifically the “peak cap stress” (PCS), is a strong mechanical indicator of vulnerability. The PCS mainly depends on the fibrous cap thickness, lipid core Young modulus and blood pressure. In this context, it is relevant to assess plaque morphology, composition and biomechanical properties to prevent stroke events. Mechanical properties of the arterial wall have been the subject of numerous researches and various tools have been developed using ultrasound imaging to measure compliance, distensibility, stiffness [9], [10], [11], [12], and elasticity [13], [14], [15], [16], [17].

Elastography is an ultrasound imaging technique for estimating elastic properties of tissues [18]. It has been extensively studied for the diagnosis of breast, liver, prostate and thyroid [17]. In the context of diagnosis of arterial vascular diseases, the pioneer work in intravascular elastography by [19], [20], [21], [22] using intravascular ultrasound (IVUS) catheter has shown the ability to distinguish between fiber, fibro fatty and fatty plaque components based on the radial strain. Later, different components of the full strain tensor were proposed and studied [23], [24], [25], [26], [27], [28], [29], [30], [31], [32] in the context of human coronary and carotid arteries. More recently, IVUS elastography has led to a promising tool known as modulography [13], [16], [33], [34], [35], [36], [37], [38], which aims at computing the Young modulus mapping of the arterial wall. Although IVUS imaging provides a higher spatial resolution than external echography, the main modality used for superficial vessels, such as the carotid artery, is external echography due to its non-invasiveness. Elastography studies have been performed on human carotid arteries using cross-correlation algorithms [39], [40], [41], [42] and the Lagrangian speckle model estimator (LSME) [43], [44], [45], [46], which allows the computation of the complete 2D strain tensor. Thus, the LSME gives access from a single optimization to axial and lateral strains and shears. These studies have shown a potential for non-invasive vascular elastography (NIVE) to evaluate arterial stiffness and plaque morphology based on strain and shear maps. In both IVUS and NIVE elastography, the natural pulsation of the blood flow induces vessel motion and deformation, which are detected by ultrasound speckle tracking applied on either B-mode or radio-frequency (RF)-mode data.

Noninvasive vascular imaging techniques still present challenges. Due to the low lateral resolution of external echography using standard beamforming, the lateral components of the displacement gradient matrix are less reliable than the axial ones [47], [48], [49], thus limiting the evaluation of the strain tensor to the axial strain and shear components. In this context, one would prefer a longitudinal analysis of the artery to a cross-sectional one, since displacements and deformations will then mainly occur in the axial direction. Moreover, it has been shown, with IVUS elastography [50], [51] and NIVE [52], that the strain tensor depends on the coordinate system and needs to be corrected for a reliable interpretation. In IVUS, due to the catheter eccentricity, the strain tensor needs to be transformed towards the vessel coordinate system. Similarly, in external elastography, the strain tensor can be compensated for the local wall deformation direction.

The first goal of this paper is to provide a new local compensation method based on the plane strain condition in the context of NIVE. Previous angle correction methods for the strain estimate were presented to obtain a compounded strain image or to determine the normal strain tensor, in the context of beam-steered data [53], [54], [55], [56], [57]. However, the beam-steering approaches consider angles (for each direction of the beam-steering) that are global to the image. As far as we know, this is a difference with our proposed angle compensation method, where the angle is computed locally on measurement windows. The effect of the angle compensation on the axial strain time-varying curves was also investigated. Moreover, the resulting temporal strain rate evolution – a parameter that was previously described for cardiac strain application [58], [59], [60], [61], [62], [63], [64] – is presented and discussed in this work. In order to compute the strain rate, a filtering method that keeps the principal frequency components close to the heartbeat frequency is introduced. It is shown that the strain rate computed on the filtered axial strain curves is able to differentiate normal from atherosclerotic carotid walls, with or without the angle compensation.