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      A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics

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          Abstract

          The strong coupling between the flow in coronary vessels and the mechanical deformation of the myocardial tissue is a central feature of cardiac physiology and must therefore be accounted for by models of coronary perfusion. Currently available geometrically explicit vascular models fail to capture this interaction satisfactorily, are numerically intractable for whole organ simulations, and are difficult to parameterise in human contexts. To address these issues, in this study, a finite element formulation of an incompressible, poroelastic model of myocardial perfusion is presented. Using high-resolution ex vivo imaging data of the coronary tree, the permeability tensors of the porous medium were mapped onto a mesh of the corresponding left ventricular geometry. The resultant tensor field characterises not only the distinct perfusion regions that are observed in experimental data, but also the wide range of vascular length scales present in the coronary tree, through a multi-compartment porous model. Finite deformation mechanics are solved using a macroscopic constitutive law that defines the coupling between the fluid and solid phases of the porous medium. Results are presented for the perfusion of the left ventricle under passive inflation that show wall-stiffening associated with perfusion, and that show the significance of a non-hierarchical multi-compartment model within a particular perfusion territory.

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          Most cited references23

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          Cross-talk between cardiac muscle and coronary vasculature.

          The cardiac muscle and the coronary vasculature are in close proximity to each other, and a two-way interaction, called cross-talk, exists. Here we focus on the mechanical aspects of cross-talk including the role of the extracellular matrix. Cardiac muscle affects the coronary vasculature. In diastole, the effect of the cardiac muscle on the coronary vasculature depends on the (changes in) muscle length but appears to be small. In systole, coronary artery inflow is impeded, or even reversed, and venous outflow is augmented. These systolic effects are explained by two mechanisms. The waterfall model and the intramyocardial pump model are based on an intramyocardial pressure, assumed to be proportional to ventricular pressure. They explain the global effects of contraction on coronary flow and the effects of contraction in the layers of the heart wall. The varying elastance model, the muscle shortening and thickening model, and the vascular deformation model are based on direct contact between muscles and vessels. They predict global effects as well as differences on flow in layers and flow heterogeneity due to contraction. The relative contributions of these two mechanisms depend on the wall layer (epi- or endocardial) and type of contraction (isovolumic or shortening). Intramyocardial pressure results from (local) muscle contraction and to what extent the interstitial cavity contracts isovolumically. This explains why small arterioles and venules do not collapse in systole. Coronary vasculature affects the cardiac muscle. In diastole, at physiological ventricular volumes, an increase in coronary perfusion pressure increases ventricular stiffness, but the effect is small. In systole, there are two mechanisms by which coronary perfusion affects cardiac contractility. Increased perfusion pressure increases microvascular volume, thereby opening stretch-activated ion channels, resulting in an increased intracellular Ca2+ transient, which is followed by an increase in Ca2+ sensitivity and higher muscle contractility (Gregg effect). Thickening of the shortening cardiac muscle takes place at the expense of the vascular volume, which causes build-up of intracellular pressure. The intracellular pressure counteracts the tension generated by the contractile apparatus, leading to lower net force. Therefore, cardiac muscle contraction is augmented when vascular emptying is facilitated. During autoregulation, the microvasculature is protected against volume changes, and the Gregg effect is negligible. However, the effect is present in the right ventricle, as well as in pathological conditions with ineffective autoregulation. The beneficial effect of vascular emptying may be reduced in the presence of a stenosis. Thus cardiac contraction affects vascular diameters thereby reducing coronary inflow and enhancing venous outflow. Emptying of the vasculature, however, enhances muscle contraction. The extracellular matrix exerts its effect mainly on cardiac properties rather than on the cross-talk between cardiac muscle and coronary circulation.
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            Inhibition of coronary blood flow by a vascular waterfall mechanism.

            The mechanism whereby systole inhibits coronary blood flow was examined. A branch of the left coronary artery was maximally dilated with an adenosine infusion, and the pressure-flow relationship was obtained for beating and arrested states. The pressure-flow curve for the arrested state was shifted toward higher pressures and in the range of pressures above peak ventricular pressure was linear and parallel to that for the arrested state. Below this range the curve for the beating state converged toward that for the arrested state and was convex to the pressure axis. These results were compared with a model of the coronary vasculature that consisted of numerous parallel channels, each responding to local intramyocardial pressure by forming vascular waterfalls. When intramyocardial pressure in the model was assigned values from zero at the epicardium to peak ventricular pressure at the endocardium, pressure-flow curves similar to the experimental ones resulted. Thus, we conclude that systole inhibits coronary perfusion by the formation of vascular waterfalls and that the intramyocardial pressures responsible for this inhibition do not significantly exceed peak ventricular pressure.
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              Diastolic-systolic coronary flow differences are caused by intramyocardial pump action in the anesthetized dog.

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                Author and article information

                Journal
                J Biomech
                J Biomech
                Journal of Biomechanics
                Elsevier Science
                0021-9290
                1873-2380
                15 March 2012
                15 March 2012
                : 45
                : 5
                : 850-855
                Affiliations
                [a ]Imaging Sciences & Biomedical Engineering Division, St Thomas' Hospital, King's College London, SE1 7EH, UK
                [b ]Department of Computer Science, Oxford OX1 3QD, UK
                [c ]Biomedical Engineering and Physics, Academic Medical Center, University of Amsterdam, 1105 AZ, The Netherlands
                Author notes
                [* ]Corresponding author. nicolas.smith@ 123456kcl.ac.uk
                [1]

                Joint first authors, listed alphabetically.

                Article
                BM5484
                10.1016/j.jbiomech.2011.11.026
                3334269
                22154392
                7475494e-7e13-4aaf-ae30-7f927d92c51c
                © 2012 Elsevier Ltd.

                This document may be redistributed and reused, subject to certain conditions.

                History
                : 4 October 2011
                Categories
                Article

                Biophysics
                incompressible poroelastic media,myocardial mechanics,multi-compartment,coronary perfusion,finite element method

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