New experiments on shear modulus of elasticity of arteries

Deng, Shiqiang; Tomioka, Jun; Debes, Jack C.; Fung, Y. C.

doi:10.1152/ajpheart.1994.266.1.h1

Cited by 80 publications

(76 citation statements)

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“…Shear was studied by Deng et al (24), but was zero in the present study, hence a 3 and b 3 are irrelevant in the present experiment. When the strains E and E zz and stresses S , S zz were calculated from the experimental data on one hand and formulas Eqs.…”

Section: Methodsmentioning

confidence: 66%

“…After examining the application of the formula to experimental data on skin, Tong and Fung (28) concluded that the third order terms contribute little to the improvement of accuracy of the stress-strain law, and recommended dropping them in further mathematical modeling of soft tissue mechanics. The shear term has been shown to be correct in representing the results of torsion experiments of blood vessels by Deng et al (24), who used the results to evaluate the shear modulus, G, of the arterial wall. On specializing the formula in (28) to blood vessel and emphasizing the linear and nonlinear terms, we get Eq.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

The degree of nonlinearity and anisotropy of blood vessel elasticity

Zhou

Fung

1997

Proc. Natl. Acad. Sci. U.S.A.

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151

126

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Blood vessel elasticity is important to physiology and clinical problems involving surgery, angioplasty, tissue remodeling, and tissue engineering. Nonlinearity in blood vessel elasticity in vivo is important to the formation of solitons in arterial pulse waves. It is well known that the stress-strain relationship of the blood vessel is nonlinear in general, but a controversy exists on how nonlinear it is in the physiological range. Another controversy is whether the vessel wall is biaxially isotropic. New data on canine aorta were obtained from a biaxial testing machine over a large range of finite strains referred to the zero-stress state. A new pseudo strain energy function is used to examine these questions critically. The stress-strain relationship derived from this function represents the sum of a linear stress-strain relationship and a definitely nonlinear relationship. This relationship fits the experimental data very well. With this strain energy function, we can define a parameter called the degree of nonlinearity, which represents the fraction of the nonlinear strain energy in the total strain energy per unit volume. We found that for the canine aorta, the degree of nonlinearity varies from 5% to 30%, depending on the magnitude of the strains in the physiological range. In solving any surgical problems of a blood vessel, physicians need to know the mechanical properties of the blood vessels. In devising any strategy to heal or remodel an artery, we must know the stress and strain in the vessel (1-8). To determine the stress and strain, we must know the constitutive equations of the materials (1,4,5,7,9). To determine the constitutive equation, we must know the zero-stress state of the material (10, 11). The constitutive equation of the blood vessel wall has been studied by Bergel, Patel, Vaishnav, Fung, Hayashi and many others (see refs. 1, 2, 5, 8, and 12 and references therein). Conventionally, tests were done on cannulated excised straight segments of blood vessels by longitudinal stretching and circumferential distension with internal pressure. Fung (13,14) summarized the experimental viscoelastic results by describing the arterial wall as pseudo-elastic, which has the characteristics that its hysteresis is essentially independent of frequency over a wide range of 5 to 6 decades. This pseudo-elasticity is explained by a stress-relaxation function that has a continuous relaxation spectrum. For pseudo-elastic bodies, the loading and unloading curves are repeatable in cyclic testing, hence each can be treated as an elastic curve. Aorta is pseudo-elastic, and its hysteresis is small (ϳ5%). Until 1983, however, it was not known that the zero-stress state of the aorta (or more precisely, the state of zero stress-resultants and stressmoments) is not an unloaded tube, but is an open sector (10, 11). Thus, all pre-1983 data and most newer ones were not referred to the correct zero-stress state. On the other hand, newer data that refer to the zero-stress state have been limited to uniaxial strain va...

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Section: Methodsmentioning

confidence: 66%

Section: Discussionmentioning

confidence: 99%

The degree of nonlinearity and anisotropy of blood vessel elasticity

Zhou

Fung

1997

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

151

126

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show abstract

“…A common set of special problem features that leads to simplifying models includes "small" vessel wall thickness allowing a reduction from three-dimensional models to two-dimensional shell models, and cylindrical geometry of a section of an artery where no branching is present allowing the use of cylindrical shell models. Neglecting bending rigidity of arteries, studied in [18,21], reduces the shell model to a membrane model. Further simplifications include axial symmetry of the loading exerted by the blood flow to the vessel walls in the approximately straight cylindrical sections, leading to axially symmetric models with a potential of further reduction to one-dimensional models.…”

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confidence: 99%

Modeling Viscoelastic Behavior of Arterial Walls and Their Interaction with Pulsatile Blood Flow

Čanić¹,

Tambača²,

Guidoboni³

et al. 2006

SIAM J. Appl. Math.

109

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Abstract. Fluid-structure interaction describing wave propagation in arteries driven by the pulsatile blood flow is a complex problem. Whenever possible, simplified models are called for. One-dimensional models are typically used in arterial sections that can be approximated by the cylindrical geometry allowing axially symmetric flows. Although a good first approximation to the underlying problem, the one-dimensional model suffers from several drawbacks: the model is not closed (an ad hoc velocity profile needs to be prescribed to obtain a closed system) and the model equations are quasi-linear hyperbolic (oversimplifying the viscous fluid dissipation), typically producing shock wave solutions not observed in healthy humans. In this manuscript we derived a simple, closed reduced model that accounts for the viscous fluid dissipation to the leading order. The resulting fluid-structure interaction system is of hyperbolic-parabolic type. Arterial walls were modeled by a novel, linearly viscoelastic cylindrical Koiter shell model and the flow of blood by the incompressible, viscous Navier-Stokes equations. Kelvin-Voigt-type viscoelasticity was used to capture the hysteresis behavior observed in the measurements of the arterial stress-strain response. Using the a priori estimates obtained from an energy inequality, together with the asymptotic analysis and ideas from homogenization theory for porous media flows, we derived an effective model which is an 2 -approximation to the three-dimensional axially symmetric problem, where is the aspect ratio of the cylindrical arterial section. Our model shows two interesting features of the underlying problem: bending rigidity, often times neglected in the arterial wall models, plays a nonnegligible role in the 2 -approximation of the original problem, and the viscous fluid dissipation imparts long-term viscoelastic memory effects on the motion of the arterial walls. This does not, to the leading order, influence the hysteresis behavior of arterial walls. The resulting model, although two-dimensional, is in the form that allows the use of one-dimensional finite element method techniques producing fast numerical solutions. We devised a version of the Douglas-Rachford time-splitting algorithm to solve the underlying hyperbolic-parabolic problem. The results of the numerical simulations were compared with the experimental flow measurements performed at the Texas Heart Institute, and with the data corresponding to the hysteresis of the human femoral artery and the canine abdominal aorta. Excellent agreement was observed. 1. Introduction. The study of flow of a viscous incompressible fluid through a compliant tube is of interest to many applications. A major application is blood flow through human arteries. Understanding wave propagation in arterial walls, local hemodynamics, and temporal wall shear stress gradient is important in understanding the mechanisms leading to various complications in the cardiovascular function. Many clinical treatments can be studied in detail only if a r...

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“…In vivo tests on rabbit mesenteric arteries by Gorisch and Boergen (4) showed no contraction under 75°C, and Deng et al (1) found that temperatures between 25 and 37°C had a small effect on the shear modulus of rat aortas under multiaxial loading. Herrera et al (7) reported contradictory effects of temperature on isometric tests performed in the range of 5-37°C, where a rise of temperature induced contraction in rat aortas while relaxing pig renal arteries.…”

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confidence: 99%

Thermomechanical behavior of human carotid arteries in the passive state

Guinea¹,

Atienza²,

Elices³

et al. 2005

American Journal of Physiology-Heart and Circulatory Physiology

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Localized heating or cooling is expanding the clinical procedures used to treat cardiovascular diseases. Advantageous implementation and development of these methods are linked indissolubly to a deeper understanding of the arterial response to combined mechanical and thermal loads. Despite this, the basic thermomechanical behavior of human blood vessels still remains largely unknown, primarily due to the lack of appropriate experimental data. In this work, the influence of temperature on the passive behavior of human carotid arteries was studied in vitro by means of inflation tests. Eleven carotid segments were tested in the range 0 -200 mmHg at four different temperatures of 17, 27, 37, and 42°C. The results show that the combined change of temperature and stress has a dramatic effect on the dilatation coefficient of the arterial wall, which is shifted from negative to positive depending on the stress state, whereas the structural stiffness of the arterial wall does not change appreciably in the range of temperatures tested. blood vessels; inflation tests; thermal dilatation coefficient; mechanical properties; structural stiffness QUANTITATIVE KNOWLEDGE of the thermomechanical behavior of human arteries is fundamental for a better understanding of the physiology of the cardiovascular system and for the development of treatment methods and techniques for cardiovascular diseases, such as angioplasty, stent, or bypass surgery. Although much has been written on arterial mechanics (see Ref.9 and the references herein), thermomechanical experiments on human blood vessels are scarce, and in most cases only physiological temperatures (35-37°C) are considered. Nearly all the data available on the combined response of blood vessels to mechanical and thermal loading come from tests on mammalians such as rabbits, pigs, or dogs.The thermomechanical behavior of arteries, however, is not a secondary issue in cardiovascular research because many cardiac surgical procedures are performed at nonphysiological temperatures; coronary artery bypass surgeries are ordinarily performed in conditions of hypothermia (26 -31°C) (13), and hyperthermia over 50°C is routinely used in thermal balloon angioplasty (3,10,16,22).Still today, a lot of efforts are devoted to understanding the effects of changes in temperature on the final results of the treatments and the quality of life of the patients (13, 16). Also, the influence of temperature on vascular properties is important in situations like organ preservation, because modifications of temperature could affect intrarenal vasodilatation, bypass surgery, and extracorporeal circulation.In addition, thermomechanical experimental data are needed for the development of appropriate constitutive equations for the arterial wall (9, 18) implemented in numerical models, which are proving to be a useful tool for surgical procedures as well as for other clinical cardiovascular issues such as the assessment of plaque vulnerability (9).The first study on the effect of temperature on human blood vessels ...

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New experiments on shear modulus of elasticity of arteries

Cited by 80 publications

References 0 publications

The degree of nonlinearity and anisotropy of blood vessel elasticity

The degree of nonlinearity and anisotropy of blood vessel elasticity

Modeling Viscoelastic Behavior of Arterial Walls and Their Interaction with Pulsatile Blood Flow

Thermomechanical behavior of human carotid arteries in the passive state

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