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

The incidence of subarachnoid haemorrhage (SAH) is stable, at around six cases per 100 000 patient years. Any apparent decrease is attributable to a higher rate of CT scanning, by which other haemorrhagic conditions are excluded. Most patients are <60 years of age. Risk factors are the same as for stroke in general; genetic factors operate in only a minority. Case fatality is approximately 50% overall (including pre-hospital deaths) and one-third of survivors remain dependent. Sudden, explosive headache is a cardinal but non-specific feature in the diagnosis of SAH: in general practice, the cause is innocuous in nine out of 10 patients in whom this is the only symptom. CT scanning is mandatory in all, to be followed by (delayed) lumbar puncture if CT is negative. The cause of SAH is a ruptured aneurysm in 85% of cases, non-aneurysmal perimesencephalic haemorrhage (with excellent prognosis) in 10%, and a variety of rare conditions in 5%. Catheter angiography for detecting aneurysms is gradually being replaced by CT angiography. A poor clinical condition on admission may be caused by a remediable complication of the initial bleed or a recurrent haemorrhage in the form of intracranial haematoma, acute hydrocephalus or global brain ischaemia. Occlusion of the aneurysm effectively prevents rebleeding, but there is a dearth of controlled trials assessing the relative benefits of early operation (within 3 days) versus late operation (day 10-12), or that of endovascular treatment versus any operation. Antifibrinolytic drugs reduce the risk of rebleeding, but do not improve overall outcome. Measures of proven value in decreasing the risk of delayed cerebral ischaemia are a liberal supply of fluids, avoidance of antihypertensive drugs and administration of nimodipine. Once ischaemia has occurred, treatment regimens such as a combination of induced hypertension and hypervolaemia, or transluminal angioplasty, are plausible, but of unproven benefit.

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Subarachnoid haemorrhage: diagnosis, causes and management

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 =...

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

Mechanical properties of the adventitia are largely determined by the organization of collagen fibers. Measurements on the waviness and orientation of collagen, particularly at the zero-stress state, are necessary to relate the structural organization of collagen to the mechanical response of the adventitia. Using the fluorescence collagen marker CNA38-OG488 and confocal laser scanning microscopy, we imaged collagen fibers in the adventitia of rabbit common carotid arteries ex vivo. The arteries were cut open along their longitudinal axes to get the zero-stress state. We used semi-manual and automatic techniques to measure parameters related to the waviness and orientation of fibers. Our results showed that the straightness parameter (defined as the ratio between the distances of endpoints of a fiber to its length) was distributed with a beta distribution (mean value 0.72, variance 0.028) and did not depend on the mean angle orientation of fibers. Local angular density distributions revealed four axially symmetric families of fibers with mean directions of 0°, 90°, 43° and −43°, with respect to the axial direction of the artery, and corresponding circular standard deviations of 40°, 47°, 37° and 37°. The distribution of local orientations was shifted to the circumferential direction when measured in arteries at the zero-load state (intact), as compared to arteries at the zero-stress state (cut-open). Information on collagen fiber waviness and orientation, such as obtained in this study, could be used to develop structural models of the adventitia, providing better means for analyzing and understanding the mechanical properties of vascular wall.

/pdf/experimental-investigation-of-collagen-waviness-and-35sv8tu15v.pdf

Experimental investigation of collagen waviness and orientation in the arterial adventitia using confocal laser scanning microscopy.

Measurements on the directional organization of collagen are necessary for relating the structure and mechanical function of blood vessels The birefringent optical property of collagen has enabled us

Three-Dimensional Collagen Organization of Human Brain Arteries at Different Transmural Pressures

Background and Purpose—Unruptured saccular aneurysms are relatively common, occurring in 4% to 9% of autopsies. Their development at the apex region of brain artery bifurcations is attributed to a combination of structural factors and the effect of blood pressure. Collagen is a primary tension-bearing fabric of the vessel wall, and our purpose was to examine its 3-dimensional alignment at arterial branches. Methods—Sixteen segments of arteries from the circle of Willis, including bifurcations, were pressure distended, fixed, and sectioned in 1 of 3 orthogonal planes. We measured the 3-dimensional organization of collagen at the flow divider by using the polarized light microscope. An electron microscopy study performed in tandem provided measurements on the collagen fibril diameters and packing density. Results—Orientation data of the collagen fabric were obtained from sections from 3 different cutting planes. The tunica media of all bifurcations had an alignment that was primarily circumferential, and th...

Collagen Organization in the Branching Region of Human Brain Arteries

With the long term goal of improving our understanding of the mechanisms involved in coronary artery spasm, we have undertaken a two part study of the artery structure. We have made a comparison of the relative proportions of the different layers in proximal and distal regions of the main coronary arteries, and have quantitatively assessed their three dimensional structural fabric. Major coronary arteries from nine hearts were prepared for histological examination after fixation at a transmural pressure of 120 mm Hg. Measurements from 14 proximal and distal pairs of the cross sectioned arteries showed a dominant subendothelial layer, which diminished in thickness distally, with a small fraction of muscle cells interspersed with collagen. Three dimensional orientation measurements of the collagen and muscle components, which are birefringent, were obtained from one pair of segments from each of the left anterior descending, circumflex and right coronary arteries, using the polarising light microscope and Universal stage. Findings showed (1) a single circumferential order of adventitial collagen, with a mean circular standard deviation (CSD) of 22.3 degrees; (2) very highly ordered medial smooth muscle, mean CSD of 5.0 degrees (both findings are quantitatively similar between proximal and distal segments of artery, and between arteries); and (3) a multilayered fabric of collagen in the subendothelium in all vessel segments. The principal contributor to functional differences between proximal and distal regions may be the prominent and structurally varied subendothelial layer of the coronary arteries.

Measurements from light and polarised light microscopy of human coronary arteries fixed at distending pressure.

Objectives: To report quantitatively on the three-dimensional layered organization of the collagen and smooth muscle component of the two most successful vessels for coronary bypass—the internal mammary artery (IMA) and the long saphenous vein (SV). Our aim was to provide an explanation for the differential structural stiffness of these two vessels (both functioning at arterial pressures in their new environment), and how they might be susceptible to endothelial thickening. Methods: Eleven human saphenous veins and 23 internal mammary arteries were fixed at arterial distending pressure of 110 mmHg, and were sectioned in cross-section at 7 μm thickness. A subset of these was also sectioned tangentially. Measurements of the three-dimensional alignment of collagen and smooth muscle fibers within the vessel wall were made using polarized light microscopy and the universal stage attachment. Data were plotted and analysed using circular statistics. Results: The IMA, structured like an elastic artery, is dominated by a media with discrete lamellae of wavy collagen and smooth muscle, aligned nearly circumferentially, with a low variability of alignment (mean circular SD 12°). The SV is more variable in its size and structure, characteristically with a narrow circumferential media comprised mostly of collagen which is straightened and highly aligned at arterial pressures (mean circular SD 9°). Circumferential collagen in the vein was often adjacent to longitudinal bundles of smooth muscle and collagen. Conclusions: The strikingly aligned structure of the SV complements the known high mechanical stiffness of this vessel when at arterial distending pressure. The high fraction of longitudinal muscle, in addition to the circumferential muscle cells in the SV make it vulnerable to any pre-implant surgical preparation, and to the cyclical luminal pressures and longitudinal strains characteristic for epicardial arteries.

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Contrasting structure of the saphenous vein and internal mammary artery used as coronary bypass vessels

Intravascular bridges, resulting from developmental anomalies of brain arteries, are now better known as arterial fenestrations. Their tendency to develop aneurysms, similar to arterial bifurcations, makes their anatomy and microstructure important for study.Six segments of artery, each including a fenestration (five from the vertebrobasilar junction and one from the middle cerebral artery), were pressure distended, fixed, and sectioned. We made three-dimensional orientation measurements of smooth muscle and collagen, stained to enhance their birefringence, using the polarized light microscope.The general contour of the fenestrations is streamlined with a thickened layered subendothelium at the trailing or distal edge, structurally similar to the region of convergence of major brain arteries. Defects of the medial layer were found at both proximal and distal edges of all the fenestrations. Results included regional mean orientations of individual layers, with circular SDs. The medial layer was found to be...

Helen M. Finlay

Papers

Three-Dimensional Collagen Organization of Human Brain Arteries at Different Transmural Pressures

Collagen Organization in the Branching Region of Human Brain Arteries

Measurements from light and polarised light microscopy of human coronary arteries fixed at distending pressure.

Contrasting structure of the saphenous vein and internal mammary artery used as coronary bypass vessels

The layered fabric of cerebral artery fenestrations.