Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress–strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech. Eng. 190, 4379–4403) and Holzapfel et al. (Holzapfel et al. 2000 J. Elast. 61, 1–48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2005.0073

Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

An important factor in the transition from an open to a closed circulatory system was a change in vessel wall structure and composition that enabled the large arteries to store and release energy during the cardiac cycle. The component of the arterial wall in vertebrates that accounts for these properties is the elastic fiber network organized by medial smooth muscle. Beginning with the onset of pulsatile blood flow in the developing aorta, smooth muscle cells in the vessel wall produce a complex extracellular matrix (ECM) that will ultimately define the mechanical properties that are critical for proper function of the adult vascular system. This review discusses the structural ECM proteins in the vertebrate aortic wall and will explore how the choice of ECM components has changed through evolution as the cardiovascular system became more advanced and pulse pressure increased. By correlating vessel mechanics with physiological blood pressure across animal species and in mice with altered vessel compliance, we show that cardiac and vascular development are physiologically coupled, and we provide evidence for a universal elastic modulus that controls the parameters of ECM deposition in vessel wall development. We also discuss mechanical models that can be used to design better tissue-engineered vessels and to test the efficacy of clinical treatments.

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Vascular Extracellular Matrix and Arterial Mechanics

Tissue-engineered grafts may be useful in myocardial repair; however, previous scaffolds have been structurally incompatible with recapitulating cardiac anisotropy. Here, we use microfabrication techniques to create an accordion-like honeycomb microstructure in poly(glycerol sebacate), which yields porous, elastomeric three-dimensional (3D) scaffolds with controllable stiffness and anisotropy. Accordion-like honeycomb scaffolds with cultured neonatal rat heart cells demonstrated utility through: (1) closely matched mechanical properties compared to native adult rat right ventricular myocardium, with stiffnesses controlled by polymer curing time; (2) heart cell contractility inducible by electric field stimulation with directionally dependent electrical excitation thresholds (p<0.05); and (3) greater heart cell alignment (p<0.0001) than isotropic control scaffolds. Prototype bilaminar scaffolds with 3D interconnected pore networks yielded electrically excitable grafts with multi-layered neonatal rat heart cells. Accordion-like honeycombs can thus overcome principal structural–mechanical limitations of previous scaffolds, promoting the formation of grafts with aligned heart cells and mechanical properties more closely resembling native myocardium. Construction of tissue-engineering scaffolds that mimic cardiac anisotropy is a challenge. Now, accordion-like honeycomb scaffolds have been created that can form tissue grafts with preferentially aligned heart cells, and with mechanical properties that closely resemble the anisotropy of native myocardium.

Accordion-like honeycombs for tissue engineering of cardiac anisotropy.

The invention provides tissue engineering compositions and methods wherein three-dimensional matrices for growing cells are prepared for in vitro and in vivo use. The matrices comprise biodegradable polymer fibers capable of the controlled delivery of therapeutic agents. The spatial and temporal distribution of released therapeutic agents is controlled by use of defined nonhomogeneous patterns of therapeutic agents in the matrices.

Drug releasing biodegradable fiber implant

Tumors generate physical forces during growth and progression. These physical forces are able to compress blood and lymphatic vessels, reducing perfusion rates and creating hypoxia. When exerted directly on cancer cells, they can increase cells' invasive and metastatic potential. Tumor vessels-while nourishing the tumor-are usually leaky and tortuous, which further decreases perfusion. Hypoperfusion and hypoxia contribute to immune evasion, promote malignant progression and metastasis, and reduce the efficacy of a number of therapies, including radiation. In parallel, vessel leakiness together with vessel compression causes a uniformly elevated interstitial fluid pressure that hinders delivery of blood-borne therapeutic agents, lowering the efficacy of chemo- and nanotherapies. In addition, shear stresses exerted by flowing blood and interstitial fluid modulate the behavior of cancer and a variety of host cells. Taming these physical forces can improve therapeutic outcomes in many cancers.

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The role of mechanical forces in tumor growth and therapy.

In the study of vascular elasticity the unloaded state (one with zero transmural pressure and zero axial load) is commonly used as the reference state in which stresses and strains are considered as zero everywhere. Strains at loaded states are defined with respect to this state. Stress-strain relationships are identified under the assumption that the vessel wall is stress-free at this unloaded state. Evidence of the existence of residual stresses in the arterial wall at the unloaded state is given in Fung [4]. With a longitudinal cut along the vessel wall the unloaded specimen springs open and its cross section becomes a sector. The opening angle of the vessel wall is time-dependent after the sudden relief of the initial residual stress. It shows that the artery is not stress-free at the unloaded state. It is important to identify the stress-free state. When we use pseudoelasticity [3] to characterize the arterial wall, we need a stress-free state as the reference state for strain measurements. Correspondingly, we also want to define stress with respect to this same reference state so that we can relate stresses to strains easily. Presence of the residual stress at the unloaded tube state will certainly affect the evaluation of stress distribution in the arterial wall due to actual loadings in the physiological range. In this note we present a method to describe the geometry of the opened-up stress-free state of the artery, which is taken to be the reference state. An algorithm is outlined for the identification of the stress-strain relationship of the arterial wall. Residual stresses, and strains in the unloaded tube are evaluated. With the consideration of residual stresses the stress distributions due to loadings in the physiological range are also evaluated.

/pdf/on-residual-stresses-in-arteries-2otkw9zueu.pdf

On Residual Stresses in Arteries

To facilitate bioprosthetic heart valve design, especially in the use of novel antimineralization chemical technologies, a thorough understanding of the multiaxial mechanical properties of chemically treated bovine pericardium (BP) is needed. In this study, we utilized a small angle light scattering based tissue pre-sorting procedure to select BP specimens with a high degree of structural uniformity. Both conventional glutaraldehyde (GL) and photo-oxidation (PO) chemical treatment groups were studied, with untreated tissue used as the control group. A second set of GL and PO groups was prepared by prestretching them along the preferred fiber direction during the chemical treatment. An extensive biaxial test protocol was used and the resulting stress-strain data fitted to an exponential strain energy function. The high structural uniformity resulted in both a consistent mechanical response and low variability in the material constants. For free fixed tissues, the strain energy per unit volume for GL treated BP was ∼ 2.8 times that of PO treated BP at an equibiaxial Green’s strain level of 0.16. Prestretched tissues exhibited a profound increase in both stiffness and the degree of anisotropy, with the GL treatment demonstrating a greater effect. Thus, structural control leads to an improved understanding of chemically treated BP mechanical properties. Judicious use of this knowledge can facilitate the design and enhanced long-term performance of bioprosthetic heart valves. © 1998 Biomedical Engineering Society.
 PAC98: 8790+y, 8745Bp, 8780+s

Orthotropic mechanical properties of chemically treated bovine pericardium

The biaxial mechanical properties of right ventricular free wall (RVFW) myocardium were studied. Tissue specimens were obtained from the sub-epicardium of potassium-arrested hearts and different stretch protocols were used to characterize the myocardium's mechanical response. To assess regional differences, we excised tissue specimens from the conus and sinus regions. The RVFW myocardium was found to be consistently anisotropic, with a greater stiffness along the preferred (or averaged) fiber direction. The anisotropy in the conus region was more pronounced than in the sinus region. A comparison with studies of left ventricle (LV) midwall myocardium revealed that, 1) the fiber direction stiffnesses are greater in the RVFW than in the LV, 2) the degree of anisotropy is greater in the RVFW than in the LV.

Cheng Jen Chuong

Papers

On Residual Stresses in Arteries

Orthotropic mechanical properties of chemically treated bovine pericardium

Biaxial mechanical properties of passive right ventricular free wall myocardium.

Biaxial mechanical properties of passive right ventricular free wall myocardium

An in vitro force measurement assay to study the early mechanical interaction between corneal fibroblasts and collagen matrix.