Herbert Oertel Kathrin Spiegel Sven Donisi Modelling the Human Cardiac Fluid Mechanics 2nd edition universitätsverlag karlsruhe Herbert Oertel Kathrin Spiegel Sven Donisi Modelling the Human Cardiac Fluid Mechanic 2nd edition Modelling the Human Cardiac Fluid Mechanics von Herbert Oertel Kathrin Spiegel Sven Donisi 2nd edition Autoren Prof. Prof. e.h. Dr.-Ing. habil. Herbert Oertel, Ordinarius Dipl.-Ing. Kathrin Spiegel Dr. Ing. Sven Donisi Institut für Strömungslehre, Universität Karlsruhe (TH) Kaiserstr. 12, 76128 Karlsruhe 2nd edition Impressum Universitätsverlag Karlsruhe c/o Universitätsbibliothek Straße am Forum 2 D-76131 Karlsruhe www.uvka.de Dieses Werk ist unter folgender Creative Commons-Lizenz lizenziert: http://creativecommons.org/licenses/by-nc-nd/2.0/de/ Universitätsverlag Karlsruhe 2006 Print on Demand ISBN-13: 978-3-86644-087-6 ISBN-10: 3-86644-087-1 Modelling the Human Cardiac Fluid Mechanics H. Oertel ∗, K. Spiegel, S. Donisi Institute for Fluid Mechanics, University of Karlsruhe, D-76128 Karlsruhe, Germany Abstract In the second edition of the article a virtual heart model simulating the flow in the active left human ventricle and atrium is presented. Because in vivo myocardium data is not available, the movement of the active ventricle and its atrium is given by three-dimensional, time-dependent in vivo image data of a nuclear spin MRI tomograph. The passive part of the virtual heart model consists of a model aorta and of two-dimensionally modelled heart valves. As the flow is actively driven by the ventricle and atrium, a coupling of flow and structure is necessary to take into account the deviation of the aorta and the closing and opening of the heart valves. This coupling is replaced by the movement given by MRI tomograph and ultrasonic Doppler echocardiography, since we focus on the flow simulation in the left pumping ventricle. The flow simulation is performed by a validated commercial software package that uses the finite volume method. The flow resistance of the circulation through the body is taken into account with a simplified circulation model. The article shows how the virtual heart model can be used to predict flow losses and flow structures due to pathological ventricle contraction defects. It provides as an example the flow simulation of an unhealthy human ventricle with an aneurysm. The flow structure and flow losses are considered before and after surgery. ∗ Email address:
[email protected] (H. Oertel). URL: www-isl.mach.uni-karlsruhe.de (H. Oertel). 1 Introduction To predict the flow in the human heart, we need to model the time-dependent geometry of the ventricle, the atrium and the heart valves during one cardiac cycle. In literature many approaches to model the electro-mechanical pump behavior of the heart are found (Fung (1997)). The structure of the muscle fibers of the human heart has already been published by Robb and Robb (1942). Hunter et al. (1996), (1998), Nash and Hunter (2000) developed a finite elasticity theory and a finite element method for analyzing ventricular electro-mechanics during the filling phase of the cardiac cycle, when cardiac muscle cells are not actively contracting. The orthotropic properties of the passive tissue are described by a constitutive law whose parameters are derived from a model of collagen fibers and in vitro stress measurements on animal hearts. A model of the active tissue properties, based on isolated animal muscle experiments, is also introduced in order to predict distributions of principal strain at the end of the contraction phase of the cardiac cycle. The mathematical modellin