A Texture Matching Method Considering Geometric Transformations in Noninvasive Ultrasonic Measurement of Arterial Elasticity

Ultrasound in Med. & Biol., Vol. 38, No. 3, pp. 524–533, 2012 Crown Copyright Ó 2012 Published by Elsevier Inc on behalf of World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/$ - see front matter

doi:10.1016/j.ultrasmedbio.2011.12.010

d

Original Contribution A TEXTURE MATCHING METHOD CONSIDERING GEOMETRIC TRANSFORMATIONS IN NONINVASIVE ULTRASONIC MEASUREMENT OF ARTERIAL ELASTICITY LILI NIU, MING QIAN, RUIBO SONG, LONG MENG, XIN LIU, and HAIRONG ZHENG Paul C. Lauterbur Research Center for Biomedical Imaging, Institute of Biomedical and Health Engineering, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China (Received 16 June 2011; revised 12 November 2011; in final form 7 December 2011)

Abstract—Measurement of arterial elasticity can provide an important reference for understanding arterial wall changes that may occur in the early stages of atherosclerosis. Conventional correlation-based methods for evaluating arterial wall movements consider only the translation, ignoring the rotation and deformation, which limits the accuracy of measurement of arterial displacement and its biomechanical properties. This article proposes a novel texture matching method based on ultrasonic B-mode image considering geometric transformations to accurately measure arterial displacement and acquire arterial elasticity noninvasively. The method was validated by simulated images with rotation and deformation and further by measurements in vitro arterial phantom and in vivo common carotid arteries of 20 healthy volunteers. Simulation results demonstrate that the method can improve the accuracy of measurement of arterial displacement. Experimental results show that the elastic modulus of the arterial phantom agrees well with the results obtained from mechanical tests, deviating only 4.1%. The mean elastic modulus of the common carotid arteries is 361.7 ± 93.5 kPa. The texture matching method was shown to be able to measure the displacement and elasticity of the arterial wall with complex geometric transformations and may be clinically useful for early detecting and monitoring atherosclerosis. (E-mail: hr.zheng@siat. ac.cn) Crown Copyright Ó 2012 Published by Elsevier Inc on behalf of World Federation for Ultrasound in Medicine & Biology. Key Words: Ultrasound imaging, Arterial elasticity, Geometric transformations, Elasticity imaging, Atherosclerosis.

perceptible (Gronholdt 1999; Selzer et al. 2001). Therefore, measurement of arterial elasticity may serve as a valuable clinical tool for early detection and monitoring of atherosclerosis in individuals before appearance of clinical symptoms. Intravascular ultrasonography has been used for imaging the strain distribution of the arterial wall, proving the potential for the differentiation of regions with different strain values (Brusseau et al. 2001; de Korte et al. 1997). As a transcutaneous approach, the tissue Doppler imaging technique has been developed to measure the displacement and strain of the arterial wall (Long et al. 2004; Thrush et al. 2008). Furthermore, studies on noninvasive evaluation of arterial elasticity included using the Moens-Korteweg equation from measured pulse wave velocity (Benthin et al. 1991; Brands et al. 1998; Marque et al. 2000) and using local arterial stiffness from the change in geometric shape (Lanne et al. 1992; Laurent et al. 2006; Oliver et al. 2003). These methods only acquire

INTRODUCTION Steady increase in the incidence of cardiovascular diseases caused by atherosclerosis (Lee et al. 1991; Steinberger et al. 2009) demands efficient clinical tools for early diagnosis. Clinical ultrasound examination mainly relies on changes in hemodynamics (Cheng et al. 2006; Feaver et al. 2010) and intima-media thickness (Polak et al. 2010; Zanchetti et al. 2009) to characterize plaque and stenosis for patients with overt symptoms and routinely neglects arterial elasticity as an important diagnostic criterion. However, it is worth noting that changes in arterial elasticity may occur early in the atherosclerotic process, even before the anatomical changes of intima-media thickening become

Address correspondence to: Hairong Zheng, Ph.D., Paul C. Lauterbur Research Center for Biomedical Imaging, Institute of Biomedical and Health Engineering, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, 1068 Xueyuan Avenue, SZ University Town, Shenzhen, China, 518055. E-mail: [email protected] 524

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Fig. 1. The movements of the arterial model at four different stages of the pulse cycle.

a single elasticity value for the whole arterial wall and may be insufficient to understand overall changes in the arterial wall. Other methods were used to evaluate arterial elasticity from the distribution of the displacement gradient. The displacement of the arterial wall could be detected with approaches such as autocorrelation (Hoeks et al. 1985; Rabben et al. 2002), cross-correlation of radio-frequency data (Brands et al. 1997; De Jong et al. 1990) and B-mode images (Golemati et al. 2003; Zakaria et al. 2010) and phasetracking using complex-demodulated data (Kanai et al. 2003). In these methods, a correlation-based technique is used and only the translational displacement of the arterial wall is obtained. However, the movements of the arterial wall during the cardiac cycle are complex. They undergo not only translation but also rotation and deformation subjected to pulse pressure, transmural pressure and shear force (Holzapfel et al. 2000). A typical example of the movements of the arterial model at four different stages of the pulse cycle is shown in Figure 1. Thus, it is necessary to consider the complex geometric transformations (translation, rotation and deformation) of the arterial wall to obtain more accurate displacement estimates. This article proposes a novel texture matching method to accurately measure the displacement of the arterial wall with geometric transformations, thereby improving the measurement accuracy of arterial elasticity. The accuracy of the method to measure the displacement and elasticity of the arterial wall is demonstrated by simu-

lated images with rotation and deformation and further by measurements in vitro arterial phantom made of polyvinyl alcohol (PVA) cryogel and in vivo common carotid arteries of 20 young healthy volunteers. MATERIALS AND METHODS The texture matching method The procedure of the texture matching method is illustrated in Figure 2. Let f(1)(x, y),.., f(N)(x, y) denote a cineloop consisting of N images, where (x, y) correspond to the coordinates of a pixel in the image plane. In each image f(n)(x, y), a region-of-interest (ROI), g(n)(x, y), is selected. Thereafter, the comparison region g(n11)(x, y) is obtained in f(n11)(x, y), which is exactly the same region as the ROI in the succeeding frame. Each ROI is divided into a grid of small sections known as interrogation windows. Given an interrogation window in an image, matching consists in finding the most similar texture in the next image. The normalized crosscorrelation function corrected for the average values is used as the preferred matching criterion. It is defined as: PM 1 PN 1 x51 y 5 1 ðhðx; yÞ2hÞðkðx1p; y1qÞ2kÞ NCCðp; qÞ 5 dh dk (1) where h and k denote the gray intensity distribution over an interrogation window of size M1 3 N1. h and k are the average values of the functions h and k, respectively, and sh and sk are their standard deviations.

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Fig. 2. Block diagram of the texture matching method to measure the displacement for one interrogation window (IW) before (IW(n)) and after (IW(n11)) movement. NCC 5 normalized cross-correlation; SPM 5 sub-pixel method; FIM 5 filter and interpolation method; MIA 5 multiple iterative algorithm; SVEA 5 spurious vector elimination algorithm.

The two-dimensional (2-D) normalized crosscorrelation technique, which combines the sub-pixel method and the filter and interpolation method, is used to calculate the translational displacement of the texture of each interrogation window. Then, a multiple iterative algorithm uses the gradient of displacement to estimate rotation and deformation. Finally, the 2-D normalized cross-correlation technique is applied with a reduced interrogation window to obtain higher spatial resolution and a spurious vector elimination algorithm is used to obtain more accurate displacement estimates. A detailed description of these algorithms can be found in Niu et al. (2010). The texture matching method starts when n 51 and repeats with the same size ROI translated exactly the same distance as the estimated displacement, until n 5 N-1. The lateral and axial components of all displacement vectors are stored in three-dimensional (3-D) arrays, where the three dimensions are lateral and axial positions within an image and frame number. Elastic modulus evaluation From the estimated axial displacement v(x, y, n), the displacement gradient (strain) of each layer with a constant thickness of h0 is obtained as follows: Dεðx; y; nÞ 5 ðvðx11; y; nÞ2vðx; y; nÞÞ=h0 :

(2)

The maximum strain of each layer during one cardiac cycle is obtained by Dεmax ðx; yÞ 5 maxn jDεðx; y; nÞj. Assuming that the arterial wall is incompressible and the blood pressure is applied normal to each layer, the elastic modulus, E(x, y), is approximately given by Hasegawa et al. (2004):

  1 Ril L2x11 DP Eðx; yÞ 5 1 ; 2 h0 $L L Dεmax ðx; yÞ

(3)

where L and Ril are the number of layers and the inner radius of the l-th layer, respectively. ΔP is pulse pressure measured at the brachial artery. The following equation can be derived when the arterial wall is assumed to be homogeneous: 1 DP E 5 ðRi =d11Þ ; 2 Dh

(4)

where d and Ri are the wall thickness and the inner radius of the artery, respectively. Dh is the maximum displacement gradient between the proximal and distal wall during one cardiac cycle. Simulation study To simplify the simulation, geometric transformations are assumed to take place in the x-y plane (image plane) only. Thus, the transformations can be described by polar decomposition: 0 1 0 1 a cos q sin q 0 B C B C T 5 @ b A ; R 5 @ 2sin q cos q 0 A ; 0

0

1

a B S5@g

g b

0 C 0A ;

0

0

1

0

1 B D5@0

c 1

1 1 0 C 0A:

0

0

1

0

0

(5)

The first term T represents the translation. R, S and D describe the x-y plane rotation, scaling deformation and shear deformation, respectively. The eigenvectors of S

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Fig. 3. Experimental set-up was used to measure the elastic modulus of in vitro arterial phantom made of polyvinyl alcohol (PVA) cryogel using the texture matching method.

show the deformation main axis while the corresponding eigenvalues reflect the extent of the deformation. In the following simulations, only lateral and axial deformations are considered, which means that g 5 0. The incompressibility constraint for the movement is det(S) 5 ab 5 1. The eigenvectors of D mean pushing a geometric object in the x-direction with shearing factor c. The relationship between a point (x, y) and its new position (x0 , y0 ) can be expressed as follows: 0 01 0 1 x x2a 21 @ y0 A 5 ðRSDÞ @ y2b A: (6) z0 z A 2-D simulated tissue image was produced by the PIV-STD project (Okamoto et al. 2000) and then three groups of images were produced using Matlab software (version R2007b, The Mathworks Inc., Natick, MA). The first group was acquired by a 1-degree to 9-degree rotation around the simulated image center; the second group was obtained by a scaling deformation with lateral expansions of 1.1 to 1.9; the third group was acquired by a shear deformation in the negative x-direction with shearing factor of 0.02 to 0.18. In vitro study for arterial phantom model A closed-loop compression system was designed to pressurize an arterial phantom while simultaneously scanning with an ultrasound imaging system (Sonix RP; Ultrasonix Medical Corporation, Richmond, BC, Canada). Pulsatile pressure was created with a pulsatile pump (Model 55-3305; Harvard Apparatus, Holliston, MA, USA) and a compliance chamber was used to serve

as a cushioning function. A pressure transducer (HDP708; HeDi Sensor Instrument Co., Ltd., Foshan, Guangdong, China) was placed between the pump and the phantom to measure the intraluminal pressure. The general schematic of the system is shown in Figure 3. An aqueous solution of PVA undergoes a series of freeze-thaw cycles and the final product is referred to as PVA cryogel. The number of freeze-thaw cycles controls properties of PVA cryogel, including speed of sound and elasticity. Manufacture of an arterial phantom using PVA cryogel was described by Dineley et al. (2006). An arterial PVA phantom (6 freeze-thaw cycles; wall thickness: 3 mm; inner radius: 3 mm) was placed in a water tank connected to the flow path filled with degassed water. Pulsatile flow, which simulates the ventricular action of the heart, was produced from the pump at a heart rate of 70 beats/min. A L14-5W/60 linear array transducer (transmit frequency: 10 MHz) was connected to the Sonix RP system to image the longitudinal section of the arterial PVA phantom. A sequence of 2-D ultrasound B-mode images were acquired at a frame rate of 223 Hz using 128 ultrasound beams with a focal depth of 17 mm and field of view of 30 mm (depth) by 32 mm (width). Meanwhile, the intraluminal pressure over time was recorded by an oscilloscope (MSO7104A; Agilent Technologies UK Limited, Wokingham, Berkshire, UK). The experiment was repeated three times to obtain an average value for each data point. A final interrogation window of 32 3 8 (pixels2) was used with an overlap ratio of 0.5 for the texture matching analysis, corresponding to a spatial vector grid of 1.76 3 0.44 mm2 (lateral by axial).

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Table 1. Main characteristics of the subjects Parameters

Subjects (20)

Age, years Sex, M/F Height, cm Weight, kg Systolic blood pressure, mm Hg Diastolic blood pressure, mm Hg

24.6 6 3.3 13/7 167 6 10 60 6 11 111 6 9 76 6 6

In vivo study for common carotid artery An in vivo preliminary study was performed with measurements on the common carotid arteries of 20 young healthy volunteers with no history of hypertension, smoking or cardiovascular disease. All subjects gave their informed consent for examination and the protocol was approved by the institutional review board of Shenzhen Institutes of Advanced Technology. Characteristics of these subjects are given in Table 1. All records were performed on the subjects at rest in the supine position. Left common carotid arteries were imaged in longitudinal section to enable calculation of both axial and lateral movements using the Sonix RP system with the L14-5W/60 linear array transducer. B-mode images were continuously acquired over four cardiac cycles at a frame rate of 93 Hz. An echo depth range of 3 or 4 cm was used, depending on the individual differences. Blood pressure was measured over the brachial artery three times at 5-min intervals using a mercury sphygmomanometer. Care was taken during the examination to avoid undue physical stretching of the artery and to maintain a uniform temperature surrounding the artery. In this study, a final 16 3 4 (pixels2) interrogation window with an overlap ratio of 0.5 was used in texture matching analysis, which yields a spatial vector grid of 0.88 3 0.22 mm2.

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RESULTS Simulation study Figure 4 shows the assessment of the texture matching method on an image subjected to rotation. Figure 4a is the simulated tissue image. Figure 4b is the image subjected to 2-degree rotation. Figure 4c shows the displacement field computed from the two images. Figure 4d shows a comparison of the correlation index measured by the texture matching method and conventional correlation-based method (Chen et al. 1991) at different rotation angles. The texture matching method shows a better correlation than conventional method and the correlation index decreases exponentially as the rotation angle increases. It becomes more difficult to correlate the movement as the rotation angle gets larger. Figure 5 demonstrates the ability of the texture matching method to calculate an image undergoing scaling deformation. Figure 5a is the simulated tissue image and Figure 5b is the scaling deformed image with lateral expansion of 10% (b 5 1.1). Figure 5c shows the computed displacement field from the two images. Figure 5d shows the correlation index measured against lateral deformations with the two different methods. Similarly, the texture matching method shows a better correlation. At the beginning, the correlation index declines sharply until reaching a certain value and then decreases slowly. It can be seen that the image scaling deformation has a great influence on the correlation index. Furthermore, the texture matching method was applied to process an image suffered shear deformation. Figure 6a is the simulated tissue image and Figure 6b is the shear deformed image at c 5 0.02. Figure 6c shows computed displacement field and Figure 6d shows a comparison of the correlation index at different shearing factors. As can be seen from the figure, the

Fig. 4. (a) The simulated tissue image; (b) the image subjected to a rotation of 2-degree; (c) displacement vectors calculated using the texture matching method; (d) a comparison of the correlation index measured by the texture matching method and the conventional correlation-based method at different rotation angles.

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Fig. 5. (a) The simulated tissue image; (b) the image undergoing a lateral expansion of 10% (b 5 1.1); (c) displacement vectors calculated using the texture matching method; (d) a comparison of the correlation index measured by the texture matching method and the conventional correlation-based method at different scaling deformations.

texture matching method is more sensitive to shear deformation compared to rotation and scaling deformation. In vitro study for arterial phantom model Figure 7a shows the B-mode image of the PVA phantom and the rectangle indicates the ROI. Figure 7b and c show the axial strain and lateral strain as a function of time. It can be seen that the axial and lateral strain profiles exhibit a periodic pattern, following the pulse cycle of 70 beats/min. Figure 7d displays a graph obtained by plotting the axial strain against wall thickness. The strain decreases from 8.4% to 3.4% over only 3 mm. Taking the particular case of a hollow cylinder subjected to an inner pressure, even when isotropic and homogeneous, the propagation of the stress is not uniform, but decreases in amplitude across the wall thickness (Hearn 1997). The elastic modulus of the arterial PVA phantom was calculated as 343 kPa by eqn (4) when the pressure inside the phantom was 5.5 kPa measured by the pressure transducer.

The elastic modulus of the PVA phantom was also tested on an electronic universal material testing machine (CMT6104; New Sans Machinery Co., Ltd., Shenzhen, Guangdong, China) to validate the calculated elastic modulus using the texture matching method. Five cylindrical PVA samples (six freeze-thaw cycles) were tested on the CMT6104. The mean elastic modulus of five samples is 328.8 kPa, suggesting that there is a difference of 4.1% between the calculated value and the measured value. In vivo study for common carotid artery The texture matching method was applied to in vivo measurements of the common carotid arteries of 20 healthy volunteers. Arterial and mechanical parameters of common carotid artery (CCA) in the subjects are listed in Table 2. Figure 8 shows an example of axial and lateral strains and elasticity distribution on a normal CCA. Figure 8a shows the B-mode image of CCA and the rectangles indicate the ROIs. The axial and lateral strain

Fig. 6. (a) The simulated tissue image; (b) the image suffered a shear deformation with shearing factor of 0.02; (c) displacement vectors calculated using the texture matching method; (d) a comparison of the correlation index measured by the texture matching method and the conventional correlation-based method at different shearing factors.

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Fig. 7. (a) The B-mode image of the arterial polyvinyl alcohol (PVA) phantom and the rectangle indicates the region-ofinterest (ROI); (b) axial strain and (c) lateral strain computed over the ROI of the PVA phantom as a function of time; (d) a graph obtained by plotting the axial strain against the wall thickness.

profiles computed over the ROI (proximal wall) exhibit a periodic pattern following the cardiac cycle, as shown in Figure 8b and c. The elasticity distribution of the ROIs is color-coded and superimposed on the B-mode image as shown in Figure 8d. DISCUSSION A texture matching method based on B-mode image has been developed for measurement of the displacement and elasticity of the arterial wall with complex geometric transformations. The accuracy of the method is assessed by simulated tissue images and the results show obvious improvement on the correlation index. The validity of this method has also been demonstrated by an in vitro PVA phantom and in vivo common carotid arteries. The results show a difference of 4.1% between the calculated and measured elastic modulus values for the PVA phantom. Table 2. Arterial and mechanical parameters of common carotid artery in the subjects Parameters

Subjects (20)

Systolic internal diameter, mm Diastolic internal diameter, mm Radial strain, % Mean elastic modulus, kPa

6.6 6 0.8 5.8 6 0.7 563 361.7 6 93.5

Preliminary investigation of the common carotid arteries in 20 healthy subjects suggests a higher mean elastic modulus for the oldest man (35-year-old; 665.2 kPa) compared with the youngest man (21-year-old; 223.8 kPa), confirming a marked difference in age (Mitchell et al. 2004; Vaitkevicius et al. 1993). These results show that the texture matching method may be appropriate for clinical studies and may offer a valuable tool for detecting changes in arterial elasticity and identifying patients with atherosclerosis at the early stage. Previous studies have given mean elastic modulus of the CCA walls. In this study, by averaging the available elastic modulus over CCA walls of 20 subjects age 21 to 35 years, mean elastic modulus of 361.7 6 93.5 kPa was obtained. Riley et al. (1992) found the mean elastic modulus increasing from 701 kPa in women and 771 kPa in men in the 45-49-year-old age group to 965 and 983 kPa, respectively, in the 60- to 64-year-old age group. Blacher et al. (1998) indicated the mean elastic modulus of 600 6 300 kPa in 38- to 70-year-old age group. Using phase tracking method, Kanai et al. (2003) determined the mean elastic modulus of lipid of 816 40 kPa and that of a mixture of smooth muscle and collagen fiber of 1.0 6 0.63 MPa. Paini et al. (2007), who employed a noninvasive echo-tracking system, showed the mean elastic modulus of 677 6 427 kPa in 37 subjects age 25 to 76 years. More recently, Claridge et al. (2009) reported

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Fig. 8. Axial and lateral strain profiles and elasticity distribution of a normal common carotid artery (CCA) wall. (a) the B-mode image of CCA and the rectangles indicate the regions-of-interest (ROIs); (b) axial and (c) lateral strain profiles computed over the ROI (proximal wall) exhibit a periodic pattern following the cardiac cycle; (c) the elasticity distribution of the ROIs was color-coded and superimposed on B-mode image.

the mean elastic modulus of 744 6 102 kPa in 43 subjects aged 55 to 82 years. The elastic characteristics of the CCA walls are determined by both passive (elastin and collagen) and active factors. The absolute amounts of elastin and collagen, as well as their ratio, are important determinants of arterial elasticity (Bank et al. 1996; Brown et al. 1994; Danpinid et al. 2010). Differences in these passive components could account for a portion of the interindividual variation in elastic modulus. In addition, neural, hormonal and physical stimuli can activate smooth muscle cells, leading to a small change in arterial elasticity (Riley et al. 1986; Zulliger et al. 2004). There is no existing ‘‘gold standard’’ for measurement arterial elasticity yet and the ‘‘true’’ elastic modulus of the CCA walls can hardly be obtained noninvasively. The accuracy of the results was to be validated by comparing with published data. However, a credible comparison would have required a prospective investigation of the same subjects during the same imaging session with previous studies. The limited availability of these techniques and individual difference make the comparison difficult. Even so, preliminary application of the texture matching method in investigated subjects confirms that the elastic modulus changes with age (Mitchell et al. 2004; Vaitkevicius et al. 1993). Although the texture matching method initially shows its feasibility in vitro and in vivo studies, there are some limitations associated with the method that should be considered before the next clinical study:

First, the study on 20 young healthy volunteers can only be considered as a preliminary study. It has been realized that age, gender and other atherosclerosis risk factors can greatly influence arterial elasticity (Juonala et al. 2005, 2008). The data reported here may not represent the whole population and a further study would be carried out to investigate the arterial elasticity in patients with different atherosclerosis risk factors. Second, as discussed in Riley Jr et al. (1984), blood pressure measured in the brachial artery may not always accurately reflect blood pressure in the CCA. However, comparisons of intra-arterial pressure in the large vessels with brachial artery pressures determined with noninvasive oscillometric methods are generally in good agreement (Borow et al. 1982). Third, the matching procedure searches for the best matches with a final interrogation window of 16 3 4 pixels2 in vivo study. Thus, the maximum measurable displacement is 1.76 mm and 0.44 mm in the lateral and axial directions, respectively. This may not be large enough to cover the arterial displacement in the whole cardiac cycle, especially in cases of large or fast artery movement. According to the equations described by Bang et al. (2003), the frame rate above 76 Hz is necessary for proper analysis of the movement, for the given interrogation window of 0.44 mm and CCA wall velocity of 8.4 mm/s (Schmidt-Trucks€ass et al. 1998, 1999). Thus, frame rate of 93 Hz is adequate for displacement estimates in this study. However, when the frame rate is low, relatively large interrogation window is required to

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obtain accurate displacement estimates. However, Srinivasan et al. (2003) indicated that a small interrogation window can improve the spatial resolution. Therefore, the interrogation window should be a trade-off between the accuracy and the spatial resolution. The texture matching method was used to evaluate the movement of the arterial wall, considering not only the radial but also the longitudinal movements provided by movement of the aortic arch during the heart action, which might improve the ability to detect early abnormalities in arterial wall function. Increased knowledge of the longitudinal movement in the arterial wall may provide new information not only on the mechanical properties of arteries but might also provide new information on the mechanical forces, their type and pattern, acting on the arterial wall (Persson et al. 2003); information of fundamental importance for the study and evaluation of shear stress and endothelial function (Cinthio et al. 2006) and thus, for the study of atherosclerosis and vascular disease. CONCLUSION A novel texture matching method based on B-mode image was proposed to measure the displacement and elasticity of the arterial wall with complex geometric transformations. For investigation of the accuracy of the method, preliminary experiments were performed in simulated images, an in vitro arterial phantom made of PVA cryogel and in vivo common carotid arteries of 20 healthy volunteers. Simulation results show that the texture matching method has high accuracy. Results from in vitro validating experimental studies show good agreement with mechanical tests. Preliminary studies in vivo common carotid arteries show that the mean elastic modulus is 361.7 6 93.5 kPa. The texture matching method is found to be useful for measurement of arterial elasticity and may be a potential clinical tool for early detection of atherosclerosis. Acknowledgments—The work was supported by National Basic Research Program 973 (Grant Nos. 2010CB732600, 2010CB534914 and 2011CB707903) from Ministry of Science and Technology, China, and National Science Foundation Grants (Grant Nos. 81027006, 61020106008, 10904094, 11002152, 10904095, 61031003 and 61002001).

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