A mathematical model for estimating the axial stress of the common carotid artery wall from ultrasound images.

Clarifying the complex interaction between mechanical and biological processes in healthy and diseased conditions requires constitutive models for arterial walls. In this study, a mathematical model for the displacement of the carotid artery wall in the longitudinal direction is defined providing a satisfactory representation of the axial stress applied to the arterial wall. The proposed model was applied to the carotid artery wall motion estimated from ultrasound image sequences of 10 healthy adults, and the axial stress waveform exerted on the artery wall was extracted. Consecutive ultrasonic images (30 frames per second) of the common carotid artery of 10 healthy subjects (age 44 ± 4 year) were recorded and transferred to a personal computer. Longitudinal displacement and acceleration were extracted from ultrasonic image processing using a block-matching algorithm. Furthermore, images were examined using a maximum gradient algorithm and time rate changes of the internal diameter and intima-media thickness were extracted. Finally, axial stress was estimated using an appropriate constitutive equation for thin-walled tubes. Performance of the proposed model was evaluated using goodness of fit between approximated and measured longitudinal displacement statistics. Values of goodness-of-fit statistics indicated high quality of fit for all investigated subjects with the mean adjusted R-square (0.86 ± 0.08) and root mean squared error (0.08 ± 0.04 mm). According to the results of the present study, maximum and minimum axial stresses exerted on the arterial wall are 1.7 ± 0.6 and -1.5 ± 0.5 kPa, respectively. These results reveal the potential of this technique to provide a new method to assess arterial stress from ultrasound images, overcoming the limitations of the finite element and other simulation techniques.

A novel non-invasive ultrasonic method to assess total axial stress of the common carotid artery wall in healthy and atherosclerotic men.

In the present study, developing a new non-invasive method independent from blood flow, we estimated and compared the total axial stress of the common carotid artery wall in healthy and atherosclerotic subjects. Consecutive ultrasonic images of the common carotid artery of 48 male subjects including healthy, with less and more than 50% stenosis in carotid artery were recorded. Longitudinal displacement and acceleration was extracted from ultrasonic image processing using a block matching algorithm. Furthermore, images were examined using a maximum gradient algorithm and time rate changes of the internal diameter and intima-media thickness were extracted. Finally, axial stress was estimated using an appropriate constitutive equation. Statistical analysis results showed that with stenosis initiation and its progression, axial acceleration and stress increase significantly. According to the results of the present study, maximum axial stress of the arterial wall is 1.713±0.546, 1.993±0.731 and 2.610±0.603 (kPa) in normal, with less and more than 50% stenosis in carotid artery respectively. Whereas minimum axial stress is -1.714±0.676, -1.982±0.663 and -2.593±0.661 (kPa) in normal, with less and more than 50% stenosis in carotid artery respectively. Moreover, internal diameter and intima-media thickness of the artery also increase significantly with stenosis initiation and its progression. In this study, the feasibility of axial wall stress computation for human common carotid arteries based on non-invasive in vivo clinical data is concluded. We found a strong and graded association between axial stress and severity of carotid stenosis, which might be used to discriminate healthy from atherosclerotic arteries.

Carotid Artery Wall Motion Estimation from Consecutive Ultrasonic Images: Comparison between Block-Matching and Maximum-Gradient Algorithms.

BACKGROUND: Radial movement of the arterial wall is a well-known indicator of the mechanical properties of arteries in arterial disease examinations. In the present study, two different motion estimation methods, based on the block-matching and maximum-gradient algorithms, were examined to extract the radial displacement of the carotid artery wall. METHODS: Each program was separately implemented to the same axial consecutive ultrasound images of the carotid artery of 10 healthy men, and the radial displacement waveform of this artery was extracted during two cardiac cycles. The results of the two methods were compared using the linear regression and Bland-Altman statistical analyses. The maximum and mean displacements traced by the block-matching algorithm were compared with the same parameters traced by the maximum-gradient algorithm. The frame numbers in which the maximum displacement of the wall occurred were compared too. RESULTS: There were no significant differences between the maximum and the mean displacements traced by the block-matching algorithm and the same parameters traced by the maximum-gradient algorithm according to the pair t-test analysis (p value > 0.05). There was a significant correlation between the radial movement of the common carotid artery measured with the block-matching and maximum-gradient methods (with a correlation coefficient of 0.89 and p value < 0.05). The Bland-Altman analysis results confirmed a good agreement between the two methods in measuring the radial movement, with a mean difference and limits of agreement of 0.044 ± 0.038. The results showed that both methods found the maximum displacement occurring in the same frame. CONCLUSION: Both block-matching and maximum-gradient algorithms can be used to extract the radial displacement of the carotid artery wall and in addition, with respect to the pixel size as error, the same results can be obtained.

Differentiation of mild and severe stenosis with motion estimation in ultrasound images.

Doppler ultrasound technique is now recognized as the best noninvasive screening test for carotid artery stenosis. Ultrasound does not calculate directly the degree of arterial narrowing, but relies on extrapolating the changes in blood flow parameters to an anatomical stenosis. This paper deals with the estimation of the stiffness indices of mild and severe stenosis of common carotid artery by motion estimation algorithm, focusing on their changes with the progression of atherosclerosis. 145 men with the mean age of 55 +/- 12 y who were healthy or had mild stenosis or severe stenosis were studied. For each ultrasound examination, matching longitudinal views of the common carotid artery were located, the frames were grabbed and processed with motion estimation algorithm and then diameter, cross-section changes and intima-media thickness of the right common carotid artery were estimated. The blood pressure was recorded in the right brachial artery using a semiautomatic device. The arterial diameter and cross-section changes and intima-media thickness were used together with the blood pressure measurements to estimate standard arterial stiffness indices. Relative diameter changes in carotid arteries with mild and severe stenosis were decreased by 22% to 48%, respectively, compared with healthy carotid artery. Systolic blood pressure in mild stenosis was approximately 4.4% lower and in severe stenosis was 2.0% higher compared with the healthy carotid. The stiffness indices were significantly different in the group of patients with severe stenosis (p-value < 0.05) compared with the healthy and mild stenosis subjects. It is concluded that, regarding the influence of atherosclerosis on the stiffness indices of right common carotid artery, we can differentiate mild and severe stenosis in carotid artery, through processing the sequential color Doppler ultrasound images by optical flow tracking algorithm.