A bilinear stress–strain relationship for arteries

Zhang, Wei; Kassab, Ghassan S.

doi:10.1016/j.biomaterials.2006.10.022

Cited by 14 publications

(18 citation statements)

References 25 publications

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“…The strain energy function has been widely used to characterize the passive mechanical properties of blood vessels (5,8). For large epicardial coronary arteries, extensive mechanical measurements and analysis were carried out in the passive state (18,19,23,30,33,34).…”

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confidence: 99%

Biaxial vasoactivity of porcine coronary artery

Huo¹,

Cheng²,

Zhao³

et al. 2012

American Journal of Physiology-Heart and Circulatory Physiology

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The passive mechanical properties of blood vessel mainly stem from the interaction of collagen and elastin fibers, but vessel constriction is attributed to smooth muscle cell (SMC) contraction. Although the passive properties of coronary arteries have been well characterized, the active biaxial stress-strain relationship is not known. Here, we carry out biaxial (inflation and axial extension) mechanical tests in right coronary arteries that provide the active coronary stress-strain relationship in circumferential and axial directions. Based on the measurements, a biaxial active strain energy function is proposed to quantify the constitutive stress-strain relationship in the physiological range of loading. The strain energy is expressed as a Gauss error function in the physiological pressure range. In K ϩ -induced vasoconstriction, the mean Ϯ SE values of outer diameters at transmural pressure of 80 mmHg were 3.41 Ϯ 0.17 and 3.28 Ϯ 0.24 mm at axial stretch ratios of 1.3 and 1.5, respectively, which were significantly smaller than those in Ca 2ϩ -free-induced vasodilated state (i.e., 4.01 Ϯ 0.16 and 3.75 Ϯ 0.20 mm, respectively). The mean Ϯ SE values of the inner and outer diameters in no-load state and the opening angles in zero-stress state were 1.69 Ϯ 0.04 mm and 2.25 Ϯ 0.08 mm and 126 Ϯ 22°, respectively. The active stresses have a maximal value at the passive pressure of 80 -100 mmHg and at the active pressure of 140 -160 mmHg. Moreover, a mechanical analysis shows a significant reduction of mean stress and strain (averaged through the vessel wall). These findings have important implications for understanding SMC mechanics.contraction; constitutive equation; stress-strain relation; vessel mechanics VASOACTIVITY OF LARGE EPICARDIAL coronary arteries is affected by cardiovascular diseases such as diabetes (14, 15), hypertension (14, 20), atherosclerosis (11), vasospasm (10, 32), and aneurysm (26), which are major risk factors for angina pectoris or myocardial infarction in patients. The constitutive passive and active stress-strain relationships can characterize the vasoactivity and are fundamental for understanding the mechanical behaviors of vascular smooth muscle cell (SMC) in health and disease (5). The strain energy function has been widely used to characterize the passive mechanical properties of blood vessels (5,8). For large epicardial coronary arteries, extensive mechanical measurements and analysis were carried out in the passive state (18,19,23,30,33,34).The active mechanical properties of coronary arteries are much known. To date, there are only uniaxial active constitutive length-tension relationships in the circumferential direction of coronary arteries (1, 2, 24, 31). Although some multi-axial active models have been proposed, those have been of theoretical forms not rooted in experimental measurements (25, 36). Clearly, there is a need for multi-axial active mechanical measurements and experimentally determined multi-dimensional active strain energy functions for coronary arteries.The objective ...

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confidence: 99%

Biaxial vasoactivity of porcine coronary artery

Huo¹,

Cheng²,

Zhao³

et al. 2012

American Journal of Physiology-Heart and Circulatory Physiology

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“…It was found that a bilinear stress-strain relation represents the two-dimensional (2D) Fung model very well [7]. This paper extends the same notion to the threedimensional (3D) stress-strain relationship.…”

Section: Introductionmentioning

confidence: 85%

“…(6)) is more general and rigorous than the previously defined strains [7], but the strain measure is now coupled in the 3D space. A fixed stretch ratio in one direction does not necessarily mean a constant strain along that direction (except for zero strains, see Fig.…”

Section: Model Advantages and Limitationsmentioning

confidence: 98%

“…It has been discussed [7] that linear model parameters are easier to determine from experiments because linear least square fits are more definitive than nonlinear fits. Moreover, constants in the generalized Hooke's law have clearer physical meanings; i.e., n characterizes the material nonlinearity, c's are elastic moduli with respect to the log-exp strains defined by n, and the material anisotropy is revealed by the moduli in various directions.…”

Section: Model Advantages and Limitationsmentioning

confidence: 99%

“…To overcome some of the shortcomings of nonlinear constitutive models, Zhang and Kassab [7] proposed the definition of a strain measure with an adjustable parameter to absorb the nonlinearity of stress-strain relationship and hence reduce the nonlinearity of the constitutive equation. It was found that a bilinear stress-strain relation represents the two-dimensional (2D) Fung model very well [7].…”

Section: Introductionmentioning

confidence: 99%

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