# A Liquid-Solid Coupling Hemodynamic Model with Microcirculation Load
## 1 Introduction  
A hemodynamic model is able to provide theoretical evidence for suitable selections of clinical treatment plan, and hence has important meanings. Take human physiology as an example: if the heart is regarded as a power source and the arteries at each level as transportation pipelines, the human microcirculation system can be seen as the system load. There is a complex coupling relationship between various components of the circulation system, which influence each other severely. A change in one factor can even cause a change in the environment of the entire circulation system. Complex phenomena in the human blood circulation system should be the properties produced by the coupling of various parts of the system, not only relying on the selection of boundary conditions. Therefore, a well-developed hemodynamic model must be able to show completely different components of the circulation system and their effects. Only in this way can it provide a correct simulation of the numerous phenomena of human blood flow, and provide evidence for research on producing and developing principles for dealing with some diseases. Nowadays, there are many studies on the hemodynamics model, but none of them is able to show the properties of the human circulation system. Though the hemodynamic model of a rigid tube wall [1; 2; 3; 4] has been widely utilized, it is not able to show the stress-strain properties of solids, which places severe limitations on clinical applications. The model of a flexible tube wall [5; 6; 7] is not only able to show the deformation of the solid, but also reflects the influence of solid deformation on flow field, which has great potential for application [8]. However, the model fails to show the complexpressure wave of physiology [9] and simulate the propagation of a pulse wave. In these studies, the outlet pressures were all set as a fixed value or a measured value, and it was assumed that these outlet conditions will not change with the change of the flow field. Since pressure influences the deformation of the tube wall, the change of outlet pressure conditions will have a profound influence on the flow field. Therefore, the results were not ideal in those studies relating to the adjustment process of the entire human circulation system [10]. In the study on myocardial bridge [11], [PERSON] observed the influence of changes of downstream flow field on the front-end flow field. It follows that changeable load condition is one of the most important components neglected in most hemodynamic models. Through analysis of the characteristics of a capillary microcirculation system and the flow properties of the kidney and other organs, it was found that the seepage in porous media is a load model that accords relatively well with the form of physiological changes. Therefore, this paper needs to add a load of porous media seepage in the classical bi-directional liquid-solid coupling model to completely simulate the human circulation system. Additionally, in order to make the load of porous media seepage accord with physiology, there are requirements for the tube length and other flow field factors. The human microcirculation system is located at the end of the human blood circulation system. Before arriving at the microcirculation system, the fluid will flow through the entire circulation system and experience severe changes. However in previous studies, the flow field was not long enough for the simulation of these changes, so the model requires a flow field that is equivalent to the actual physiology to simulate the physiological flow field correctly. In addition, the deformation of tube wall is an important factor influencing the flow field. Thus, in the calculating simulation of [PERSON] [12], as the influence of liquid-solid coupling was not considered, his simulation results were not very satisfying, though the load of porous media seepage was also selected.