Biaxial incremental homeostatic elastic moduli of coronary artery: two-layer model

A bilinear stress-strain relationship for arteries

A comprehensive understanding of the mechanical properties of blood vessels is essential for vascular physiology, pathophysiology and tissue engineering. A well-known approach to study the elasticity of blood vessels is to postulate a strain energy function such as the exponential or polynomial forms. It is typically difficult to fit experimental data to derive material parameters for blood vessels, however, due to the highly nonlinear nature of the stress-strain relation. In this work, we generalize the strain definition to absorb the elastic nonlinearity and then propose a two-dimensional bilinear stress-strain relation between second Piola-Kirchhoff stress and the new strain measure. The model is found to represent the Fung's exponential model very well. The novel linearized constitutive relation simplifies the determination of material constants by reducing the nonlinearity and provides a clearer physical interpretation of the model parameters. The limitations of the constitutive model and its implications for vascular mechanics are discussed.

Three-dimensional mechanical properties of porcine coronary arteries: a validated two-layer model

The normal coronary artery consists of two mechanically distinct layers: intima-media and adventitia. The objective of this study is to establish a two-layer three-dimensional (3-D) stress-strain relation of porcine coronary arteries. Experimental measurements were made by a series of biaxial tests (inflation and axial extension) of intact coronary arteries and, subsequently, their corresponding intima-media or adventitia layer. The Fung-type exponential strain energy function was used to describe the 3-D strain-stress relation for each layer and the intact wall. A genetic algorithm was used to determine the material constants in the Fung-type constitutive equation by curve fitting the experimental data. Because one layer must be sacrificed before the other layer can be tested, the material property of the missing layer was computed from the material constants of the intact vessel and the tested layer. A total of 20 porcine hearts were used: one group of 10 hearts for the left anterior descending artery and another group of 10 hearts for the right coronary artery. Each group was further divided into two subgroups of five specimens tested for the intact wall and the intima-media layer and for the intact wall and the adventitia layer. Our results show statistically significant differences in the material properties of the two layers. The mathematical model was validated by experimental stress-strain data for individual layers. The validated 3-D constitutive model will serve as a foundation for formulation of layer-specific boundary value problems in coronary physiology and cardiology.

Structural and Drug Diffusion Models of Conventional and Auxetic Drug-Eluting Stents

Most balloon angioplasty procedures include the insertion of tiny cylindrical wire mesh structures, called cardiovascular stents, into the artery to prevent the elastic recoil that follows arterial dilatation. The scaffolding characteristics of the stent provide strength to the artery wall. However, vascular injury during stent deployment and∕or recognition of the stent as a foreign material triggers neointimal hyperplasia, causing re-closure, or restenosis, of the artery. A recent advancement to counteract restenosis is to employ drug-eluting stents to locally deliver immunosuppressant and antiproliferative drugs. In this project, Fick’s law of diffusion was used to model drug diffusion from the stent matrix into the adjacent arterial tissue. An analytical procedure was also developed to estimate the circumferential and the flexural stiffnesses of stents. Furthermore, a unique auxetic (negative Poisson’s ratio) stent structure was proposed that exhibits high circumferential strength in its expanded configuration and low flexural rigidity in its crimped configuration. Results generated with the analytical diffusion model, developed in this project, compare favorably with previously published clinical and experimental data. The circumferential and flexural stiffnesses estimated using the analytical procedure developed in this project compare favorably with the results from rigorous finite element analyses and previously published experimental data.

Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling

At autopsy, 13 nonstenotic human left anterior descending coronary arteries [71.5 +/- 7.3 (mean +/- SD) yr old] were harvested, and related anamnesis was documented. Preconditioned prepared strips (n = 78) of segments from the midregion of the left anterior descending coronary artery from the individual layers in axial and circumferential directions were subjected to cyclic quasi-static uniaxial tension tests, and ultimate tensile stresses and stretches were documented. The ratio of outer diameter to total wall thickness was 0.189 +/- 0.014; ratios of adventitia, media, and intima thickness to total wall thickness were 0.4 +/- 0.03, 0.36 +/- 0.03, and 0.27 +/- 0.02, respectively; axial in situ stretch of 1.044 +/- 0.06 decreased with age. Stress-stretch responses for the individual tissues showed pronounced mechanical heterogeneity. The intima is the stiffest layer over the whole deformation domain, whereas the media in the longitudinal direction is the softest. All specimens exhibited small hysteresis and anisotropic and strong nonlinear behavior in both loading directions. The media and intima showed similar ultimate tensile stresses, which are on average three times smaller than ultimate tensile stresses in the adventitia (1,430 +/- 604 kPa circumferential and 1,300 +/- 692 kPa longitudinal). The ultimate tensile stretches are similar for all tissue layers. A recently proposed constitutive model was extended and used to represent the deformation behavior for each tissue type over the entire loading range. The study showed the need to model nonstenotic human coronary arteries with nonatherosclerotic intimal thickening as a composite structure composed of three solid mechanically relevant layers with different mechanical properties. The intima showed significant thickness, load-bearing capacity, and mechanical strength compared with the media and adventitia.

Biaxial elastic material properties of porcine coronary media and adventitia

The importance of mechanical stresses and strains has become well recognized in vascular physiology and pathology. To compute the stress and strain on the various components of the vessel wall, we must know the constitutive equations for the different layers of the vessel wall. The objective of the present study is to determine the constitutive equation of the coronary artery treated as a two-layer composite: intima-media and adventitial layers. Twelve hearts were obtained from a local slaughterhouse, and the right coronary artery and left anterior descending artery were dissected free from the myocardium. The vessel wall was initially mechanically tested biaxially (inflation and axial extension) as a whole (intact wall) and subsequently as intima-media or adventitial layer. A Fung-type exponential strain energy function was used to curve fit the experimental data for the intact wall and individual layers for the right coronary artery and left anterior descending artery. Two methods were used for the determination of material constants, including the Marquardt-Levenberg nonlinear least squares method and the genetic algorithm method. Our results show that there were no statistically significant differences in the material constants obtained from the two methods and that either set of elastic constants results in good fit of the data. Furthermore, at an in vivo value of axial stretch ratio, we find that the stiffness is as follows: intima-media > intact > adventitia. These results underscore the composite nature of coronary arteries with different material properties in each layer. The present results are necessary for analysis of coronary artery mechanics and to provide a fundamental understanding of vessel physiology.

Transmural strain distribution in the blood vessel wall

The transmural distributions of stress and strain at the in vivo state have important implications for the physiology and pathology of the vessel wall. The uniform transmural strain hypothesis was proposed by Takamyzawa and Hayashi (Takamizawa K and Hayashi K. J Biomech 20: 7–17, 1987; Biorheology 25: 555–565, 1988) as describing the state of arteries in vivo. From this hypothesis, they derived the residual stress and strain at the no-load condition and the opening angle at the zero-stress state. However, the experimental evidence cited by Takamyzawa and Hayashi ( J Biomech 20: 7–17, 1987; and Biorheology 25: 555–565, 1988) to support this hypothesis was limited to arteries whose opening angles (θ) are <180°. It is well known, however, that θ > 180° do exist in the cardiovascular system. Our hypothesis is that the transmural strain distribution cannot be uniform when θ is >180°. We present both theoretical and experimental evidence for this hypothesis. Theoretically, we show that the circumferential stretch ratio cannot physically be uniform across the vessel wall when θ exceeds 180° and the deviation from uniformity will increase with an increase in θ beyond 180°. Experimentally, we present data on the transmural strain distribution in segments of the porcine aorta and coronary arterial tree. Our data validate the theoretical prediction that the outer strain will exceed the inner strain when θ > 180°. This is the converse of the gradient observed when the residual strain is not taken into account. Although the strain distribution may not be uniform when θ exceeds 180°, the uniformity of stress distribution is still possible because of the composite nature of the blood vessel wall, i.e., the intima-medial layer is stiffer than the adventitial layer. Hence, the larger strain at the adventitia can result in a smaller stress because the adventitia is softer at physiological loading.

Imaging coronary artery microstructure using second-harmonic and two-photon fluorescence microscopy

The microstructural basis for the mechanical properties of blood vessels has not been directly determined because of the lack of a nondestructive method that yields a three-dimensional view of these vascular wall constituents. Here, we demonstrate that multiphoton microscopy can be used to visualize the microstructural basis of blood vessel mechanical properties, by combining mechanical testing (distension) of excised porcine coronary arteries with simultaneous two-photon excited fluorescence and second-harmonic generation microscopy. Our results show that second-harmonic generation signals derived from collagen can be spectrally isolated from elastin and smooth muscle cell two-photon fluorescence. Two-photon fluorescence signals can be further characterized by emission maxima at 495 nm and 520 nm, corresponding to elastin and cellular contributions, respectively. Two-dimensional reconstructions of spectrally fused images permit high-resolution visualization of collagen and elastin fibrils and smooth muscle cells from intima to adventitia. These structural features are confirmed by coregistration of multiphoton microscopy images with conventional histology. Significant changes in mean fibril thickness and overall wall dimension were observed when comparing no load (zero transmural pressure) and zero-stress conditions to 30 and 180 mmHg distension pressures. Overall, these data suggest that multiphoton microscopy is a highly sensitive and promising technique for studying the morphometric properties of the microstructure of the blood vessel wall.