[Modeling of elastic deformation and vascular resistance of arterial and venous vasa vasorum].

As in most living tissues, a network of nutritional vessels, the so-called vasa vasorum, irrigates the vessel wall under physiological conditions. An alteration or obstruction of this network can induce severe lesions. Most normal arteries and veins are irrigated by a vasa vasorum network located mainly in the adventice. They essentially supply oxygen to the outer layers of the vascular wall, the inner layer being mainly oxygenated by direct diffusion from bloodstream. Vasa vasorum responds to vasomotor stimuli and can even regress, e.g., after vascularization of arterial grafts. Their pathophysiological importance for arteries is now established. Indeed, it is known that an infusion disorder or vasa vasorum alteration may induce or promote early atherosclerotic lesions, fibrodysplasia or even media necrosis. From a mechanical point of view, and considering the three layers as a unique material, the vessel shows non-isotropic linear elastic and incompressible (v = 0.5) behaviour in the case of minimal or moderate deformation. But in the case of major deformation, the vessel displays a non-linear behaviour. The interaction between vasa vasorum supply and the mechanical properties of the arterial vascular wall can promote the occurrence of aneurysms as soon as vasa vasorum irrigation decreases. Some authors have hypothesized that these microvessels could fulfil the same function in the venous wall. It appears also that microcirculation flow rates are lower in varicose veins than in healthy ones and that partial oxygen pressure, already low in a healthy vein media, is even lower in a varicose vein. All these facts underline the importance of supply by the vasa vasorum network and its determining role in maintaining vascular wall integrity. In addition, the influence of vessel non-linear properties and their pathological changes on microcirculation would partially explain media necrosis in arteries and veins. Studying vascular wall deformation under the influence of intraluminal pressure revealed that an initially circular vasa vasorum rapidly takes on an elliptical shape which results more from crosswise circumferential stretching of the wall than from radial crushing. This induces increased hydraulic resistance. Thus permanent overpressure reduces vascular wall irrigation. Once the wall has been devascularized, it will loose its elasticity, harden and retain its maximal deformation. A vicious circle is then created. This phenomenon, noticeable in arteries, could be more serious in veins because their walls are thinner and elasticity modulus is lower. For example, for an intraluminal overpressure of 100 mmHg in an artery and 10 mmHg in a vein the ellipticity of the vasa vasorum becomes 1.2 and 3 respectively. Based on the hypothesis of a linear elastic behaviour and a periodical intraluminal overpressure, the ratio of the two axis of an arterial vasa vasorum B/A varies from 1.13 to 1.28 for Pa = 100 + 30 sin (2 pi t) mmHg, and from 1.24 to 1.44 for Pa = 160 + 40 sin (2 pi t) mmHg. In this case, the ratio of hydraulic resistances R(ellipse)/R(circle) changes little (less than 1, the ratio of the axis varies from 1.1 to 2.6 for Pa = 5 + 5 sin (2 pi t) mmHg) and from 1.8 to 5.8 for Pa = 10 + 5 sin (2 pi t) mmHg). Thus the ratio of hydraulic resistance varies from 1 to 1.5 and from 1.2 to 2.8 respectively. In practice Young's modulus increases in parallel with luminal pressure by limiting vascular wall and vasa vasorum deformation. If we consider the non-linear behaviour of the vessel wall and suppose the same conditions of intraluminal pressure, the ratio of the axis of the venous vasa vasorum in a hypertensive patient varies from 1.6 to 2.6 (instead of 1.8 to 5.8 in the case of linear model). This ratio is higher than that of the healthy subject which is less than 1.7. So the vascular structure in physiological conditions itself reacts to the pressure increases which may jeopardize vasa vasorum irrigation by delaying mural transfor