Sami Qorchi

Didier Vray

Maciej Orkisz
email: maciej.orkisz@creatis.insa-lyon.fr

Estimating Arterial Wall Deformations from Automatic Key-Point Detection and Matching

Keywords: Ultrasound, Carotid artery, Arterial wall motion, Motion estimation

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Diseases such as atherosclerosis and arteriosclerosis are known to modify biomechanical properties of the arterial wall, and particularly of its intima and/or media layers [START_REF] Van Popele | Association between arterial stiffness and atherosclerosis: the Rotterdam Study[END_REF][START_REF] Wilkinson | Arteriosclerosis and atherosclerosis : guilty by association[END_REF]. Therefore, assessing arterial wall motion and deformations may reveal pathological alterations in these properties and thus contribute to the detection of vascular disease onset. Ultrasound (US) is an appropriate imaging modality for screening such alterations in carotid arteries (CA), as US-image sequences allow the observation of CA wall motion with adequate spatial and temporal resolution. Many methods have been developed to estimate temporal changes in artery diameter during the heart beat, mainly based on segmentation of the blood-wall interface; see [START_REF] Loizou | A review of ultrasound common carotid artery image and video segmentation techniques[END_REF] for a survey. Similarly, segmentation of lumen-intima (LI) and media-adventitia (MA) interfaces allows the assessment of wall thickness (actually intima-media thickness, IMT) and its temporal variations to measure the wall compression [START_REF] Molinari | A state of the art review on intimamedia thickness (IMT) measurement and wall segmentation techniques for carotid ultrasound[END_REF][START_REF] Nilsson | A method for measuring the variation of intima-media thickness during the entire cardiac cycle using B-Mode images[END_REF][START_REF] Ilea | Fully automated segmentation and tracking of the intima media thickness in ultrasound video sequences of the common carotid artery[END_REF][START_REF] Menchon-Lara | Automatic detection of the intima-media thickness in ultrasound images of the common carotid artery using neural networks[END_REF][START_REF] Zahnd | Simultaneous extraction of carotid artery intima-media interfaces in ultrasound images: assessment of wall thickness temporal variation during the cardiac cycle[END_REF]. Advances in US-image quality have enabled the visualization and assessment of the wall-motion component parallel to the blood stream, called longitudinal motion; see [START_REF] Rizi | Carotid wall longitudinal motion in ultrasound imaging: An expert consensus review[END_REF] for a thorough overview.

Most of the methods use various versions of the block-matching approach, called speckle tracking, to estimate two-dimensional displacements of manually selected points, e.g.: [START_REF] Persson | A new non-invasive ultrasonic method for simultaneous measurements of longitudinal and radial arterial wall movements: first in vivo trial[END_REF]; [START_REF] Stoitsis | Analysis and quantification of arterial wall motion from B-mode ultrasound images -comparison of blockmatching and optical flow[END_REF]; Gas-tounioti et al. (2013); [START_REF] Zahnd | Evaluation of a Kalman-based block matching method to assess the bi-dimensional motion of the carotid artery wall in B-mode ultrasound sequences[END_REF]; [START_REF] Yli-Ollila | Axial and radial waveforms in common carotid artery: An advanced method for studying arterial elastic properties in ultrasound imaging[END_REF]; [START_REF] Albinsson | Improved tracking performance of lagrangian block-matching methodologies using block expansion in the time domain: In silico, phantom and in vivo evaluations[END_REF]; [START_REF] Gao | Motion estimation of common carotid artery wall using a H ro filter based block matching method[END_REF]; [START_REF] Tat | Carotid atherosclerotic plaque alters the direction of longitudinal motion in the artery wall[END_REF]; [START_REF] Qorchi | Kalmanbased carotid-artery longitudinal-kinetics estimation and pattern recognition[END_REF]. Estimating the longitudinal motion of points located at various depths from LI has enabled the assessment of shearing within the wall [START_REF] Cinthio | Longitudinal movements and resulting shear strain of the arterial wall[END_REF][START_REF] Nilsson | A method to measure shear strain with high spatial resolution in the arterial wall non-invasively in vivo by tracking zero-crossings of B-mode intensity gradients[END_REF][START_REF] Au | Cardiac and haemodynamic influence on carotid artery longitudinal wall motion[END_REF], while differences in longitudinal motion magnitude between points placed at the same depth but at different longitudinal locations have evidenced artery stretching [START_REF] Zahnd | Progressive attenuation of the longitudinal kinetics in the common carotid artery: Preliminary invivo assessment[END_REF]. Recently, arguing that speckle decorrelation may lead to progressive disappearance of the initially selected salient patterns, some authors relaxed the need for manually selecting specific points and tracking them across the entire sequence.

Instead, one method jointly estimates frame-to-frame displacements of blocks densely redistributed in each frame within the previously segmented intima-media complex (IMC) regardless the salience of their contents [START_REF] Zahnd | Dynamic block matching to assess the longitudinal component of the dense motion field of the carotid artery wall in B-mode ultrasound sequences -association with coronary artery disease[END_REF]. Another approach relies on automatically detecting multiple salient speckle patterns, called key-points, in each frame, and then matching them frame-to-frame, while handling the appear-ing/disappearing key-points [START_REF] Scaramuzzino | Longitudinal motion assessment of the carotid artery using speckle tracking and scale-invariant feature transform[END_REF][START_REF] Riha | Analysis of carotid artery transverse sections in long ultrasound video sequences[END_REF][START_REF] Dorazil | Feature drift resilient tracking of the carotid artery wall using unscented Kalman filtering with data fusion[END_REF]. The latter approach, referred to as feature matching, is particularly appealing but seems to remain underexploited. Indeed, all individual displacements estimated for key-points located within a given layer are averaged to assess the common longitudinal motion of this layer as though each layer was a rigid object [START_REF] Scaramuzzino | Longitudinal motion assessment of the carotid artery using speckle tracking and scale-invariant feature transform[END_REF] or, alternatively in cross-sectional US-image sequences, the key-point displacements are exploited to assess across time only two parameters: artery radius and center [START_REF] Riha | Analysis of carotid artery transverse sections in long ultrasound video sequences[END_REF][START_REF] Dorazil | Feature drift resilient tracking of the carotid artery wall using unscented Kalman filtering with data fusion[END_REF].

We conjectured that the approach using automatic detection and matching of key-points can allow the simultaneous assessment of all the parameters of interest separately addressed in literature: radial and longitudinal displacements, wall shear, stretching, and compression. The objective of the work herein presented was to verify the feasibility of such strategy. The main contribution of the proposed method is the introduction of a robust estimator based on an affine transformation model to assess frame-to-frame motion explaining at best the key-point matches and reject outliers. Realistic simulated B-mode US-image sequences representing carotid-artery longitudinal view were used to evaluate the accuracy and robustness of the method.

The method was also successfully applied on clinical image sequences.

Materials and Methods

Motion Estimation

The description hereafter is given for two consecutive frames

{ } n+1 ( ; I ) I, 0,..., 1 , n I n N ∈ ∈
-, where N is the number of frames in a sequence I; the same processing is repeated all along the sequence. As per the above-mentioned feature-matching approach, the proposed method first detects key-point sets Pn, Pn+1

from the considered frames, then these points are matched. The set of matched points

( ) { } 1 , k l n n M P P + =
is fed to the algorithm representing the core of our proposal (Fig. 2). The subsequent sections will first discuss the choice of key-point detector along with the matching strategy; then the actual robust estimation algorithm will be described.

Key-point Detection and Matching. In the work herein presented, we assumed that one detector providing a large number of stable key-points may suffice. Salient speckle patterns usually selected for motion-tracking purposes have blob-like shapes.

Points centered on blobs correspond to local extrema of second derivatives and can be localized using invariants of the Hessian matrix calculated at several scales to allow detecting blobs of different sizes. This is the case of key-point detectors used by [START_REF] Scaramuzzino | Longitudinal motion assessment of the carotid artery using speckle tracking and scale-invariant feature transform[END_REF], namely SIFT [START_REF] Lowe | Object recognition from local scale-invariant features[END_REF][START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF] and SURF [START_REF] Bay | Speeded-up robust features (SURF)[END_REF], as well as of a detector called KAZE [START_REF] Alcantarilla | KAZE features[END_REF]. We also tested the Harris detector [START_REF] Harris | A combined corner and edge detector[END_REF], as it has been successfully used by [START_REF] Riha | Analysis of carotid artery transverse sections in long ultrasound video sequences[END_REF] and [START_REF] Dorazil | Feature drift resilient tracking of the carotid artery wall using unscented Kalman filtering with data fusion[END_REF]

′ + + ′ ′ - ∈ ⇔ ∀ ≠ < .
Otherwise, the match is considered as unreliable and is rejected. Figure 1 shows an example of matches retained for keypoints detected by KAZE algorithm within a region restricted to the arterial wall.

SIFT, SURF, and KAZE come with descriptors built of features fj based on derivatives calculated at the detection stage. As Harris detector comes without its native descriptor, we used the descriptor proposed by [START_REF] Alahi | FREAK: Fast Retina Keypoint[END_REF], in order to compare different detectors and retain the one consistently providing the largest number of matched points. This comparison will be described in Section Evaluation Methodology.

Deformation Model. The wall tissue-motion parameters of interest are: radial compression cy (thickness changes), longitudinal stretching cx and shearing sx. All these can be described by affine transformation T:

( )

:
, with A= and B= ,

xx xy k k k n n n x y yx yy T P T P P A B t t ε ε ε ε     → = +       (1)
B representing a translation vector. The linear map A can be written as matrix product of compression C, shearing S, and rotation R, A = CSR, so cx, cy, and sx are hidden in εxx through εyy (see Eq. 2). Their retrieval requires a polar decomposition of A [START_REF] Chandrasekharaiah | Continuum Mechanics[END_REF]. Actual rotation is not expected, but estimating R is useful to compensate the possible tilt of the artery in the images and thus decompose the remaining parameters into longitudinal and radial.

Estimation Algorithm. As the point-matching strategy does not restrict the spatial distance between k n P and 1 l n P + , the set of matches M may contain erroneous pairs having similar descriptors (see Figure 1). These pairs can be eliminated and motion of the remaining points can be robustly estimated if one assumes that all the keypoints located within a given layer, or rather in its small piece encompassed by an US image, undergo displacements consistent with the above-described affine model.

Under this assumption, the intima-media layer can be automatically delineated using the method developed by [START_REF] Zahnd | Simultaneous extraction of carotid artery intima-media interfaces in ultrasound images: assessment of wall thickness temporal variation during the cardiac cycle[END_REF]. The external boundary of the adventitia layer being much more difficult to localize, it can be approximated by moving the MA boundary outwards by an amount proportional to the estimated IMT.

Figure 2 summarizes the algorithm proposed to estimate T within a region of interest (ROI), typically a layer, with M restricted to key-point pairs such that Pn falls into the ROI in In. It builds on the well-known RANSAC algorithm, more specifically on its MSAC version [START_REF] Torr | MLESAC: A new robust estimator with application to estimating image geometry[END_REF], which differs by the cost-function used.

In each of imax iterations: 1) a tentative T transformation is estimated based on a small subset of randomly drawn points, and 2) this transformation is applied to all points, and the corresponding cost is calculated in order to retain T generating the smallest total error e. in which the point clouds Pn and Pn+1 are first normalized by putting them in the same reference system related to their centroids, second the transformation is calculated using total least squares, eventually it is de-normalized [START_REF] Hartley | Multiple view geometry in computer vision[END_REF].

Image Data

To create ground truth for the evaluation of the proposed method, we simulated sequences of realistic B-mode US images with controlled deformations and variable speckle-decorrelation degree. The method was also applied onto clinical image sequences, for which true deformations were unknown. 1) without rotation, so that: , and ˆˆ100 x y t t m µ = = (see Fig. 4). Please note that the compression and stretching parameters have different behavior than the remaining ones: they are equal to 1 when deactivated (unchanged thickness/length), and 1 c + when activated (relative change in thickness/length equal to ĉ ), while the others are equal to 0 when deactivated.

Simulated

0 1 0 1 A=CSR= 0 1 0 x y x c c s                (
Their activation followed the Gray code, so one single value changed at a time. For each of the 2 5 combinations, the scatterers were re-sampled ten times to assess the method's robustness against speckle decorrelation; thus, each sequence contained 320 frames. For each frame, the transformation parameters were estimated with respect to the initial frame, where all parameters were deactivated. A total of nine sequences was generated, using three different real images of variable quality, curvature, and tilt as initial model (see Fig. 3 as an example) and three different speckle-decorrelation levels (m = 0%, 5%, and 10%).

Clinical Data. We used B-mode US-image sequences from a previous study (Zahnd F et al., 2015) approved by an ethics committee (Comite de Protection des Personnes Sud-Est IV, 2009/12/10), containing data from fifty healthy controls and 75 at-risk patients from whom informed consent was obtained. One third of these sequences was randomly drawn for training, and was namely used to select the best key-point detector. This subset contained a total of 3321 frames (115 ± 33 frames per sequence), i.e., 3193 consecutive-frame pairs.

Evaluation Methodology

Selecting a key-point detector used three criteria: high number of detected points, high number of matches, and its stability over the cardiac cycle. The candidate detectors were used with parameter settings from literature.

For each simulated sequence, the transformations were calculated twice: within the intima-media complex (IMC) alone (depth equal to 1IMT from lumen), and in the entire arterial wall approximated by the depth of 2 IMT. To assess the distance between the simulated transformations T and their estimated counterpart T % , we calculated the Frobenius norm ( )

, F d T T T T = = % %
but also the one-to-one differences ( )

Results

Selection of the Key-point Detector

Mean values and standard deviations of the detected-and matched-point numbers are reported in Table 1. Harris detector found substantially more key-points than SURF and SIFT, but less than half of them were matched, while KAZE not only detected the largest number of points, but most of them were then successfully matched. KAZE detector also was stable across the cardiac cycle: although the number of key-points detected by each detector dropped in systole, the average max/min ratio was smaller than 1.5 for KAZE, while it was larger than 3.7 for

Harris. Based on these results, KAZE detector was retained for further experiments.

Simulated Sequences

The results were dependent on the quality of the model image: the best estimates were obtained in medium-quality sequences with clearly perceptible speckle texture rather than in smooth and highly-contrasted images. Figure 4 displays an example of results obtained in a synthetic sequence. As this sequence was simulated without scatterer re-sampling, speckle decorrelation was weak, so the observed variability may be partly due to the stochastic nature of the RANSAC algorithm.

Comparing the distance between ground-truth and estimated transformations for sequences with different levels of speckle decorrelation, clear tendencies were observed: ( ) , d T T % increased by 4.6 on average (from 0.6% to 2.6% of the groundtruth value F T ) between sequences with low and intermediate decorrelation, and anew by 2.2 (up to 5.7% of F T ) for the highest decorrelation level. This distance also was larger, by an average factor of 4.4, when T % was estimated within IMC, as compared with the estimates in the entire arterial wall: 4.8% vs. 1.1% of For the stretching parameter cx, the mean value of the errors d(cx) was within -1.0% of the ground-truth value 1 , but the mean value of absolute differences (MAD) |d(cx)| was equal to 7.1% of this value in the entire wall, and 13.1% for estimates restricted to IMC. On average, MAD was equal to 1.9%, 9.6%, and 18.8% of the ground truth at increasing levels of speckle decorrelation. The mean errors for the compression parameter cy were comparable with those of cx in the entire wall, but they reached -6.0% on average in IMC, and the respective MADs were 14.1% and 66.9% of the ground-truth value. On average, MAD for cy was equal to 5.6%, 34.6%, and 81.4% of the ground truth at increasing levels of speckle decorrelation. The worst results were obtained for the shearing parameter. Although the mean value of the errors d(sx) was 0.7% and 3.4% of the ground-truth value in the entire wall and in IMC respectively, but the corresponding MADs were as large as 34.3% and 154.7%.

Average MADs for sx were 18.7%, 83.1%, and 181.0% of the ground truth at increasing levels of speckle decorrelation. For each parameter, the mean value was calculated taking into account both activated and deactivated states, but the percentage was obtained with respect to the ground-truth magnitude, i.e., difference between the activated and deactivated state. decorrelation (0%, 5%, 10%). Each MAD value is represented as a percentage of the corresponding parameter's ground-truth magnitude.

The translation parameters tx and ty were overall slightly underestimated: mean errors in the longitudinal direction ( ) 4.7

x d t m µ = -
and in the radial direction d(ty) = -1.5 µm respectively, i.e., -4.7% and -1.5% of the 100 pm magnitude. These mean values remained almost independent of wall-depth used to estimate T and of speckledecorrelation level, but MADs of tx and ty respectively increased from 19.1 to 29.6, and from 4.9 to 7.4pm between the entire wall and IMC. On average, MAD of tx increased from 7.5 to 26.3 and 39.3 pm for increasing decorrelation levels. The corresponding MAD increase for ty was from 1.7 to 6.4 and 10.3 pm. Figure 5 represents MAD values calculated for the parameters cx,cy,sx,tx,ty in the entire wall.

For more details the interested reader may refer to the Supplementary Material. An example of estimated transformation-parameter evolution across a clinical image sequence corresponding to five heart beats is displayed in Figure 6. Here, Ttransformation parameters were estimated between consecutive frames and the curves represent the components of accumulated transformations, i.e.:

, 1 1, 2 1,0 ,

n n n n n T T T T - -- = % % % o oLo , where , 1 n n T - %
is the transformation estimated from frame n-1 to frame n. Please note that, in this example, periodic variations were estimated for the parameter εxy, while no vertical shearing was expected. This is probably due to the curvature of the artery observed in this sequence (Fig. 3).

Figure 7 displays corresponding elongation, compression and shearing curves obtained by polar decomposition, along with the respective results obtained for the simulated sequence from Figure 4. As expected, cx and cy were very close to εxx and εyy, respectively. In this example real sequence, elongation magnitude (≈ 1%) was substantially smaller than in the simulated sequences, whereas compression (≈ 5%)

and shearing angle (≈ 5 deg.) magnitudes were comparable.

Total processing time per image pair was of 0.66 seconds, on average (range 0.61 -0.76). The major part of this time was spent on detecting the key-points and calculating their descriptors, average 0.64 seconds (range 0.60 -0.76), while estimating the transformation took on average 0.02 seconds (range 0.01 -0.07).

Discussion

The objective of the work herein presented was to verify the feasibility of simultaneously assessing carotid-artery wall radial and longitudinal displacements, wall shear, stretching, and compression, using an approach based on automatic detection and matching of key-points. To this purpose, we simulated sequences of realistic US images with controlled speckle-decorrelation levels. Most results remained acceptable up to a substantial decorrelation level obtained by re-sampling 5% of scatterers, which was the maximum used by [START_REF] Dorazil | Feature drift resilient tracking of the carotid artery wall using unscented Kalman filtering with data fusion[END_REF]. Our results also showed that beyond this level only the estimates of radial and longitudinal displacements (translations), and of longitudinal stretching remain exploitable, provided that they are calculated using the full thickness of the wall. Estimating motion parameters within IMC is challenging because of the small thickness of this region and a small number of key-points detected therein. The difficulty was particularly high for the wall-compression and shearing parameters, as the detected blobs were mainly located along the center-line of IMC layer, so the equation system likely was poorly conditioned. For this reason, our a posteriori conclusion is that the selection of a single detector (KAZE) probably was not the optimal solution.

Combining KAZE with another detector to increase the number of points located near the IMC boundaries could improve the system conditioning. Although Harris detector might seem a good candidate, as it tends to detect key-points on blob boundaries, the number of its detections and particularly the number of resulting matches dramatically decreased in systole. Therefore, a better candidate still needs to be sought, keeping in mind that adding a detector is likely to substantially increase the processing time. Another perspective might be to exploit the prediction of estimation errors, as made within RANSAC algorithm, in order to warn the user in case of unreliable results.

The method herein proposed relies on the assumption that the motion of arterial tissues encompassed by an US image can be modeled by an affine transformation. While this assumption might not hold in diseased arteries with plaque, it is explicitly or implicitly made in state-of-the-art approaches addressing motion of arteries without plaque, which separately assess shearing, stretching, and elongation. Our method shares with these approaches another limitation: it attempts to assess motion that actually occurs in 3D, using information from 2D images, and thus the results depend on probe orientation. Sonographers do their best to hold the probe aligned on the artery central axis, but the success depends not only on their experience but also on the patient's arterial 3D geometry and on the complexity of the actual motion patterns. Namely, no current method accounts for possible out-of-plane motion.

We reported results for three simulated speckle-decorrelation levels, and those obtained at the highest level were hardly exploitable. This shows that the sequences are to be acquired with sufficiently high frame rate, to limit decorrelation.

Nevertheless, usual clinical frame rates (≥25 fps) seem to be adequate, and the simulations reported in literature do not go beyond our intermediate decorrelation level. The number of real images used as model for simulated sequences was not sufficient to fully assess the sensitivity of the method to various levels of image quality and to such geometric characteristics as artery tilt and curvature. While tilt is expected to be compensated by the polar decomposition, curvature may lead to incorrect estimates, e.g., unexpected vertical shearing was estimated in clinical sequences. As this phenomenon in likely due to the artery curvature, one solution might be artery flattening based on IMC segmentation [START_REF] Zahnd | Simultaneous extraction of carotid artery intima-media interfaces in ultrasound images: assessment of wall thickness temporal variation during the cardiac cycle[END_REF].

Results obtained on clinical sequences seem consistent with the findings reported in literature. Maximum shearing angles reported by [START_REF] Cinthio | Longitudinal movements and resulting shear strain of the arterial wall[END_REF] varied from 5 to 50 degrees from one patient to another and the magnitude of this parameter in the example from Figure 7 was in the order of 5 degrees. Similarly, wallcompression magnitude observed in this example was in the order of 5%, to be compared with 13±5% reported by [START_REF] Zahnd | A fully-automatic method to segment the carotid artery layersin ultrasound imaging: Application to quantify thecompressiondecompression pattern of the intima-media complex during the cardiac cycle[END_REF]. Also, approximately 1% elongation magnitude can be compared to 1.7 ± 1.6% that can be deduced from the attenuation in longitudinal motion reported by [START_REF] Zahnd | Progressive attenuation of the longitudinal kinetics in the common carotid artery: Preliminary invivo assessment[END_REF]. In general, parameters estimated by our method were close to the lower bounds of the previous findings, which is likely due to averaging over the whole thickness of the wall, while methods separately estimating different parameters use more localized supports.

The strength of our method, inherited from the key-point detection and matching approach [START_REF] Scaramuzzino | Longitudinal motion assessment of the carotid artery using speckle tracking and scale-invariant feature transform[END_REF][START_REF] Riha | Analysis of carotid artery transverse sections in long ultrasound video sequences[END_REF][START_REF] Dorazil | Feature drift resilient tracking of the carotid artery wall using unscented Kalman filtering with data fusion[END_REF], is its independence of manually selected points. Key-points are not required to remain salient all throughout the sequence; they may disappear and new ones may appear at detectors within the intima-media complex (depth 1IMT) and within the entire wall approximately (depth 2IMT).

Detector

Figure 2 :

 2 Figure 2: Flowchart of the proposed robust algorithm estimating an affine transformation T between point sets Pn and Pn+1 matched between frames n and n +1. The input

  Sequences. Simulating an US image requires a cloud of scatterers. For the first frame I1 of a sequence, scatterer locations were drawn from a uniform distribution ensuring sufficient spatial density, and their retro-diffusion coefficients were assigned according to the method proposed by Alessandrini et al. (2015), which samples gray-levels of a real US image 0 r I (model) and inverts the logarithmiccompression equation used in US scanners. For subsequent frames In, a fixed percentage m of scatterers (up to 10%) was randomly re-sampled from the were displaced according to an affine transformation T (Eq.

  was simulated using SIMUS[START_REF] Shahriari | Meshfree simulations of ultrasound vector flow imaging using smoothed particle hydrodynamics[END_REF]. Parameter values varied across the sequence according to binary (absent/present) combinations with magnitudes in the order of clinically observed largest frame-to-frame variations: ˆ0.

Figure 3 :

 3 Figure 3: Example of medium-quality US image, with slight tilt and curvature, used as model (left) and a frame from the corresponding simulated sequence (right).

Figure 4 :

 4 Figure 4: Example of estimated transformation parameters (red asterisks) vs. ground truth (solid lines) in a synthetic sequence with binary variations of these parameters. The dotted lines on the translation plots (tx,ty) indicate the limits of onepixel errors

Figure 5 :

 5 Figure 5: Mean absolute differences (MAD) between preset parameters of the transformation T and their counterpart estimated within the full depth of the wall, along with the Frobenius norm of the differences between the respective entire transformations. Labels specify image quality (good, medium, poor) and speckle

Figure 6 :

 6 Figure 6: Estimated variations of the transformation parameters in an example clinical sequence corresponding to the image from Figure 3 left.

Figure 7 :

 7 Figure 7: Elongation, compression and shearing obtained by polar decomposition and corresponding (left) to the simulated sequence from Figure 4, and (right) to the clinical sequence from Figure 6. A second scale of the ordinate in graphs representing sx displays the values of shearing angle in degrees calculated as arctan(sx).

  any moment. We made a step beyond the limitations of the seminal work by incorporating a robust estimation algorithm devised to simultaneously assess several parameters of tissue deformation. In this way, information carried by key-point matches is exploited more thoroughly without the need for resorting to several methods specialized in estimating different parameters of interest. This advantage was experimentally confirmed for elongation and 2D translation parameters, for which different key-points likely carried complementary information. Conversely, the estimates of compression and shearing probably suffered from a lack of such complementarity. For these parameters, the state-of-the-art methods respectively based on contour extraction and on careful manual selection of salient points may be more accurate. Nevertheless, as previously mentioned, we expect an improved accuracy of our method by adding a complementary key-point detector.Additionally, our method may be particularly useful to assess wall compression, in weak-contrast image sequences, where contour-based methods may fail. Assessing as many kinematic parameters as possible may contribute to a better understanding of the bio-mechanical and pathological phenomena occurring within the arterial wall and, ultimately, to the definition, validation, and transfer from research to the clinic of cardiovascular disease markers accessible through the analysis of US-image sequences.ConclusionsAutomatic detection and matching of key-points, combined with a robust algorithm estimating the parameters of the underlying transformation model, can simultaneously assess the radial and longitudinal displacements, wall shear, stretching, and compression of the arterial wall, from US-image sequences representing the carotid artery longitudinal section. Estimating the wall shear and compression requires key-points distributed all throughout the thickness of the considered layers, and is therefore difficult when restricted to the IMC layer alone.The results might be improved by combining the key-point detector retained in this study, which tends to extract points close to IMC centerline, with another detector favoring points closer to the IMC edges. Future research also should address the limitations related to the presence of artery curvature and plaque.

Acknowledgements

This work was performed within the framework of the LABEX PRIMES (ANR-11-LABX-0063) of Universite de Lyon, within the program "Investisse-ments d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). The authors are grateful to Pr P. Moulin and Dr A. Serusclat who provided the clinical data.