In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia (the solid mechanically relevant layers in healthy tissue). Each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component of the material and symmetrically disposed with respect to the cylinder axis. The resulting constitutive law is orthotropic in each layer. Fiber orientations obtained from a statistical analysis of histological sections from each arterial layer are used. A specific form of the law, which requires only three material parameters for each layer, is used to study the response of an artery under combined axial extension, inflation and torsion. The characteristic and very important residual stress in an artery in vitro is accounted for by assuming that the natural (unstressed and unstrained) configuration of the material corresponds to an open sector of a tube, which is then closed by an initial bending to form a load-free, but stressed, circular cylindrical configuration prior to application of the extension, inflation and torsion. The effect of residual stress on the stress distribution through the deformed arterial wall in the physiological state is examined. The model is fitted to available data on arteries and its predictions are assessed for the considered combined loadings. It is explained how the new model is designed to avoid certain mechanical, mathematical and computational deficiencies evident in currently available phenomenological models. A critical review of these models is provided by way of background to the development of the new model.

https://hal.archives-ouvertes.fr/hal-01297725/document

A new constitutive framework for arterial wall mechanics and a comparative study of material models

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

Protein–protein interactions have a key role in most biological processes, and offer attractive opportunities for therapeutic intervention. Developing small molecules that modulate protein–protein interactions is difficult, owing to issues such as the lack of well-defined binding pockets. Nevertheless, there has been important progress in this endeavour in recent years. Here, we use illustrative examples to discuss general strategies for addressing the challenges inherent in the discovery and characterization of small-molecule inhibitors of protein–protein interactions.

Small-molecule inhibitors of protein–protein interactions: progressing towards the dream

Background Central aortic pressures and waveform convey important information about cardiovascular status, but direct measurements are invasive. Peripheral pressures can be measured noninvasively, and although they often differ substantially from central pressures, they may be mathematically transformed to approximate the latter. We tested this approach, examining intersubject and intrasubject variability and the validity of using a single averaged transformation, which would enhance its applicability. Methods and Results Invasive central aortic pressure by micromanometer and radial pressure by automated tonometry were measured in 20 patients at steady state and during hemodynamic transients (Valsalva maneuver, abdominal compression, nitroglycerin, or vena caval obstruction). For each patient, transfer functions (TFs) between aortic and radial pressures were calculated by parametric model and results averaged to yield individual TFs. A generalized TF was the average of individual functions. TFs varied among patients, with coefficients of variation for peak amplitude and frequency at peak amplitude of 24.9% and 16.9%, respectively. Intrapatient TF variance with altered loading (>20% variation in peak amplitude) was observed in 28.5% of patients. Despite this, the generalized TF estimated central arterial pressures to ≤0.2±3.8 mm Hg error, arterial compliance to 6±7% accuracy, and augmentation index to within −7% points (30±45% accuracy). Individual TFs were only marginally superior to the generalized TF for reconstructing central pressures. Conclusions Central aortic pressures can be accurately estimated from radial tonometry with the use of a generalized TF. The reconstructed waveform can provide arterial compliance estimates but may underestimate the augmentation index because the latter requires greater fidelity reproduction of the wave contour.

Estimation of Central Aortic Pressure Waveform by Mathematical Transformation of Radial Tonometry Pressure Validation of Generalized Transfer Function

The vascular myogenic response refers to the acute reaction of a blood vessel to a change in transmural pressure. This response is critically important for the development of resting vascular tone, upon which other control mechanisms exert vasodilator and vasoconstrictor influences. The purpose of this review is to summarize and synthesize information regarding the cellular mechanism(s) underlying the myogenic response in blood vessels, with particular emphasis on arterioles. When necessary, experiments performed on larger blood vessels, visceral smooth muscle, and even striated muscle are cited. Mechanical aspects of myogenic behavior are discussed first, followed by electromechanical coupling mechanisms. Next, mechanotransduction by membrane-bound enzymes and involvement of second messengers, including calcium, are discussed. After this, the roles of the extracellular matrix, integrins, and the smooth muscle cytoskeleton are reviewed, with emphasis on short-term signaling mechanisms. Finally, suggestions are offered for possible future studies.

https://www.physiology.org/doi/pdf/10.1152/physrev.1999.79.2.387

Signaling mechanisms underlying the vascular myogenic response

Passive mechanics and connective tissue composition of canine arteries

Background Human growth hormone is an anabolic agent that attenuates injury-induced catabolism and stimulates protein synthesis. Recombinant human growth hormone (rhGH) administered therapeutically to patients with massive burns has been shown to increase the rate of skin graft donor site healing. It has been postulated that growth hormone affects wound healing and tissue repair by stimulating the production of insulin-like growth factor-1 (IGF-1) by the liver to increase circulating IGF-1 concentrations. The mechanism by which it improves wound healing, however, remains in question. The authors hypothesize that rhGH up-regulates IGF-1 receptors and IGF-1 levels both systemically and locally in the wound site to stimulate cell mitosis and increase synthesis of laminin, collagen types IV and VII, and cytokeratin. This hypothesis was tested in nine patients with burns covering >40% of total body surface area. Objective The authors assessed the efficacy of rhGH in promoting several major building materials in the donor site of patients with massive burns. Methods Ten massively burned patients with full-thickness burns covering more than 40% of total body surface area were participants in a placebo-controlled prospective study to determine the efficacy of 0.2 mg/kg/day rhGH on donor site wound healing and to identify some of the major components involved in wound healing and its integrity. Results Donor sites in burn patients receiving rhGH showed an increased coverage by the basal lamina of 26% for placebo to 68% coverage of the dermal-epidermal junction. Insulin-like growth factor-1 receptors and laminin, types IV and VII collagen, and cytokeratin-14 all increased significantly. Healing times of the donor sites were significantly decreased compared with patients receiving placebo. Conclusion Results indicate that growth hormone or its secondary mediators may directly stimulate the cells of the epidermis and dermis during wound healing to produce the structural proteins and other components needed to rebuild the junctional structures.

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Characterization of growth hormone enhanced donor site healing in patients with large cutaneous burns

The diameters of small arteries and arterioles are tightly regulated by the dynamic interaction between Ca(2+) and K(+) channels in the vascular smooth muscle cells. Calcium influx through voltage-gated Ca(2+) channels induces vasoconstriction, whereas the opening of K(+) channels mediates hyperpolarization, inactivation of voltage-gated Ca(2+) channels, and vasodilation. Three types of voltage-sensitive ion channels have been highly implicated in the regulation of resting vascular tone. These include the L-type Ca(2+) (Ca(L)) channels, voltage-gated K(+) (K(V)) channels, and high-conductance voltage- and Ca(2+)-sensitive K(+) (BK(Ca)) channels. Recently, abnormal expression profiles of these ion channels have been identified as part of the pathogenesis of arterial hypertension and other vasospastic diseases. An increasing number of studies suggest that high blood pressure may trigger cellular signaling cascades that dynamically alter the expression profile of arterial ion channels to further modify vascular tone. This article will briefly review the properties of Ca(L), K(V), and BK(Ca) channels, present evidence that their expression profile is altered during systemic hypertension, and suggest potential mechanisms by which the signal of elevated blood pressure may result in altered ion channel expression. A final section will discuss emerging concepts and opportunities for the development of new vasoactive drugs, which may rely on targeting disease-specific changes in ion channel expression as a mechanism to lower vascular tone during hypertensive diseases.

New expression profiles of voltage-gated ion channels in arteries exposed to high blood pressure.

Anisotropic properties of the canine carotid artery in vitro

We demonstrate, using reverse transcriptase-polymerase chain reaction, that, whereas abdominal aorta from rabbit consists almost entirely of myosin heavy chain (MHC) mRNA with no insert at the 5'-t...

Robert H. Cox

Papers

Passive mechanics and connective tissue composition of canine arteries

Characterization of growth hormone enhanced donor site healing in patients with large cutaneous burns

New expression profiles of voltage-gated ion channels in arteries exposed to high blood pressure.

Anisotropic properties of the canine carotid artery in vitro

NH2-terminal-inserted myosin II heavy chain is expressed in smooth muscle of small muscular arteries.