A coupled left ventricle and systemic arteries model

QA Mathematics

Chen, Weiwei ; Hill, Nicholas A

University:University of Glasgow

关键词: Cardiovascular modelling, left ventricle, systemic circulation, computational fluiddynamics, fluid-structure interaction, vascular disease;   

Others  :  http://theses.gla.ac.uk/7037/7/2015ChenPhd.pdf

来源: University of Glasgow

【 摘 要 】

Mathematical modelling and computational simulation are effective tools in studyingthe function of the cardiovascular system and diagnosing the progress of diseases in this system, especially when clinical experiments or measurements are limited or not capable to proceed. A variety of models have been developed related to different segments in the cardiovascular system, such as the heart, the valves, the systemic arteries and the pulmonary arteries, etc. Among these studies, modelling the left ventricle (LV) and systemic arteries (SA) have drawn a great deal of attention in the last several decade due to the high pressure and high morbidity of the systemic circulation. The recent models range from lumped-parameter models, one-dimensional models to three-dimensional models,which expand our understanding of the function of the left ventricle and systemic arteries respectively, but few of them considered the interaction between two parts. Thus, the propose of this thesis is to develop a dynamic cardiac-vascular model to study the pressure and flow wave interactions in the systemic circulation.Here we employs two advanced models, a three-dimensional finite-strain structure-based LV, and a one-dimensional dynamic physiologically-based model for the systemic arteries, to complete a coupled LV-SA model. The LV model is based on Gao et al. [35]’s work. In this model, the fluid-structure interaction (FSI) is described by an Immersed Boundary (IB) approach, in which an incompressible solid is immersed in a viscous incompressible fluid, and solved by a Lagrangian Finite Element (FE) method [40]. The systemic circulation model is employed from Olufsen et al. [90]’s work, which consists of two groups of arteries, the large arteries and the small arteries or vascular beds. The large-arteries model uses a LaxWendroff scheme to compute the cross-sectional area-averaged flow and pressure based on physiological parameters of the arterial tree. The vascular beds are modelled as asymmetric structured tree, to provide outflow boundary conditions at the end of each terminal vessel in the network of large arteries. The coupling is achieved by matchingthe pressure and flow rate at the aortic root, i.e. the circulation model feeds back the pressure as a boundary condition to the LV model, and the flow rate from the LV is used as the inflow for the circulation model. The function of the aortic valve (AV) is modelled as follows: the AV opens when the pressure in the LV just exceeds the pressure in the proximal aorta adjacent to the valve; the AV closes when the flow rate is negative (referring to backflow) at the boundary plane in the LV proximal to the AV. The governing equations of the system is solved by a combined immersed boundary finite element (IB/FE) method, and the LaxWendroff scheme of Olufsen et al. [90].To investigate the cardio-vascular interactions under different conditions in the LV-SA system, this thesis first simulate a standard case defined by using parameters based on measurements of healthy LV and healthy systemic arteries from two healthy subjects, and then simulating four disease-related cases based on different pathological conditions in the LV-SA model, i.e. stiffening of the large arteries, functional rarefaction, increasing heart beat rate (by shortening the systemic diastolicphase) and varied end-of-diastolic pressure. The results of pathological cases are comparedwith the standard case to provide a more insightful change of the pressure/flow interaction, and the change of LV contractility. To better understand the cardiac-valvular-vascular interactions, a lumped-parameter AV model is coupled in the LV-SA model to further develop it into a more detailed LV-AV-SA model. Compared to the LV-SA model (no AV), when a normal AV condition is used in the coupled LV-AV-SA model, the active tension of the LV and the peak LV pressure at early systole slightly increases, but the peak flow rate and the cardiac output barely changed. While, when a mild stenosis AV condition is applied in the LV-AV-SA model, the LV function changes dramatically, especially a dramatically increase of the peak LV pressure and the peak active tension of the LV. This indicates that the valve condition is also important in studying cardiac-vascular interactions, especially for diseased valve conditions that the effects are huge and cannot be ignored.In order to study how the valvular region affects the cross-valve pressure difference, we reconstruct the valvular region in the LV based on the mid-systolic CMR images, which shows a 93% increaseof the cross-sectional area in the valvular region than early systole. The cross-valve pressuredrop decreases dramatically with a expanded valvular region compared with the narrower valvular region in previous LV-SA model. This indicates that the a local stenosis in the valvular region may have significant effects on the heart function, and a better description of modelling the expanding procedure of the valvular region is needed to predict more physiological results.This thesis is a step forward for studying the cardiac-valvular-vascular interactions in the systemic circulation, and can provide dynamic pressure and flow waveforms in the LV and long the systemic arteries. Moreover, this model not only verifies the effects of pethological conditions but also quantifies change of pressure, flow rate and ventricular inotropy in the LV-SA system, which is important progress and has barely been studied before. Further approach of this work is to develop a patient-specific model in the future to diagnose the progress of disease, as well as providing practical treatment strategy.