Arterial Wall Mechanics in Conscious Dogs

Abstract

Abstract To evaluate arterial physiopathology, complete arterial wall mechanical characterization is necessary. This study presents a model for determining the elastic response of elastin (ς E , where ς is stress), collagen (ς C ), and smooth muscle (ς SM ) fibers and viscous (ς η ) and inertial (ς M ) aortic wall behaviors. Our work assumes that the total stress developed by the wall to resist stretching is governed by the elastic modulus of elastin fibers (E E ), the elastic modulus of collagen (E C ) affected by the fraction of collagen fibers (f C ) recruited to support wall stress, and the elastic modulus of the maximally contracted vascular smooth muscle (E SM ) affected by an activation function (f A ). We constructed the constitutive equation of the aortic wall on the basis of three different hookean materials and two nonlinear functions, f A and f C : \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[{\varsigma}{=}{\varsigma}_{E}{+}{\varsigma}_{C}{+}{\varsigma}_{SM}{+}{\varsigma}_{{\eta}}{+}{\varsigma}_{M}{=}E_{E}\ {\cdot}\ ({\varepsilon}{-}{\varepsilon}_{0E}){+}E_{C}\ {\cdot}\ f_{C}\ {\cdot}\ {\varepsilon}{+}E_{SM}\ {\cdot}\ f_{A}\ {\cdot}\ {\varepsilon}\] \end{document} \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[{+}{\eta}\ {\cdot}\ \frac{d{\varepsilon}}{dt}{+}M\ {\cdot}\ \frac{d^{2}{\varepsilon}}{dt^{2}}\] \end{document} where ε is strain and ε 0E is strain at zero stress. Stress-strain relations in the control state and during activation of smooth muscle (phenylephrine, 5 μg · kg −1 · min −1 IV) were obtained by transient occlusions of the descending aorta and the inferior vena cava in 15 conscious dogs by using descending thoracic aortic pressure (microtransducer) and diameter (sonomicrometry) measurements. The f C was not linear with strain, and at the onset of significant collagen participation in the elastic response (break point of the stress-strain relation), 6.02±2.6% collagen fibers were recruited at 23% of stretching of the unstressed diameter. The f A exhibited a skewed unimodal curve with a maximum level of activation at 28.3±7.9% of stretching. The aortic wall dynamic behavior was modified by activation increasing viscous (η) and inertial (M) moduli from the control to active state (viscous, 3.8±1.3×10 4 to 7.8±1.1×10 4 dyne · s · cm −2 , P <.0005; inertial, 61±42 to 91±23 dyne · s 2 · cm −2 , P <.05). Finally, the purely elastic stress-strain relation was assessed by subtracting the viscous and inertial behaviors.