Numerical simulation of the flow in model skeletal muscle ventricles
Until recently, the only realistic form of treatment available to patients in end stage heart failure was transplantation. In the last few years, the possibility of diverting skeletal muscle from its normal function to perform a cardiac assist role has emerged as a potential alternative to transplant surgery. The introduction of an Skeletal Muscle Ventricle (SMV) to the circulation is a potential long-term hazard, as the patient's blood comes into contact with the non-endothelialised surfaces of the wall of the new ventricle and the connecting conduits. This may trigger a cascade of events leading to deposition of thrombus, whose formation is dependent on the nature of the blood flow. The potential problem of haemostasis may arise in the apex of the artificial ventricle, where little mixing and large residence times may occur. There is therefore a strong need for carrying out flow analysis studies to address in detail the questions of haemostasis and thrombogenesis and in this context to evaluate possible candidate SMV configurations. Research on the dynamics of the flow inside model SMVs has been carried out on physical and numerical models with the objective of aialysing the effect of the size and shape of the ventricle and inlet/outlet orientation of the duct. Due to the physiological limit on the power available to pump the blood out of the ventricle, the efficiency of these potential assistance devices has to be maximized. It is also necessary to minimize the risks of haemolysis and thrombogenesis, which are both related, in different ways, to the level of shear stress on the wall and within the flow. A common feature of these flows is the formation of vortex rings. Vortices enhance mixing, and this is a useful process to encourage in an SMV, as it could assist in the mixing of the blood components and in the reduction of apical residence time. Being able to predict accurately the dynamics of the vortices is therefore important, as this will affect the prediction of residence times and shear stresses at the wall and within the flow. It is also very important to know whether numerical codes can predict vortex ring dynamics from both qualitative and quantitative points of view. In order to study the dynamics of the formation of these vortices, first, mathematical models were studied. The general purpose CFDS-FLOW3D code was used in all numerical simulations. Initial investigations of this research project concerned a progressive validation of the numerical solution predicted by the code when the domain where the flow is calculated had moving boundaries. Firstly, comparisons were made with the analytical solution for expanding/contracting pipes. An adapted compliant SMV model was then generated with a truncated apex using sinusoidally prescribed motion of the wall. With this model, two vortex rings could be predicted as in the experiments. The spherical-end model also gave good agreement with experimental flow patterns (ludicello et al., 1994). Frequency-dependent studies were carried out over the range of cardiac values using single- and multi-block versions of the code. A further validation exercise involved the use of sigmoidal filling curves in the in vitro models (Shortland et a!., 1994). Experimental data provided by such studies were used to drive the wall motion in the numerical simulations, and parametric studies of several simulation parameters were carried out. Flow field features and trajectories of the vortex paths were compared with the experiments for different filling curves, with reasonable agreement. However, because shear stress discontinuities occurred in the predictions a strict volume-defined analytical model was constructed for wall movement with smooth spatial and temporal behaviour reproducing experimental filling curves. Numerical predictions showed not only an improvement in the qualitative features of the flow compared with the experiments, but also a quantitative improvement in the prediction of the vortex core paths. Also the shear stress discontinuities were no longer evident. In order to be able to estimate residence times, instantaneous streamlines and particle tracks were produced. Analysis of shear stresses in the fluid and generation of particle pathlines for residence calculation in 3-D geometries will be carried out in the next feature for model candidates for the final SMV design. Some of the material published during the course of the project is included in APPENDIX 1. In this thesis, attention is paid to the SMV fluid dynamics. However, SMV behaviour is a coupled fluid-solid problem. Future work will be carried out in the muscle modelling. To this end, a careful review has been carried out, and is included in the thesis. Implications for future work are also discussed.