Research On The Immersed Transitional-Interface Finite Element Method And Its Applications To The Pathlological Behavior Of Vein Valve

Veins and venous valves are essential parts of the human cardiovascular system.Understanding the normal and abnormal physiological behaviors of veins and venous valves can help medical researchers to better know the pathogenesis in veins,and design the therapeutic treatments such as vein graft and bioprostheses,as well as prevent the onset or progression of the vein diseases.However,the interaction between veins and blood is essentially a fluid-structure interaction(FSI)problem which is highly nonlinear.In the interaction,vein and venous valves are flexible bodies with the large deformation,and the blood is a typical non-Newtonian viscous fluid.Especially,this interaction is simultaneously accompanied by valve closure and valve-wall contact,thus it is a big challenge to simulate the interaction process in veins.Although one type of immersed finite element method(IFEM)has been successfully applied to studying the FSI characteristics in the aortic valve,some disadvantages still exist in the existing IFEMs owing to the basic assumptions.For example,the support domain of a solid contains part of the real fluid.The error induced by the fictitious fluid will "contaminate" the solution of the real fluid via the transmission of the FSI variables(velocity and traction),in case of solving the Navier-Stokes(N-S)equations and interpolating the FSI variables.Thus,based on the IFEM,an immersed transitional interface finite element method(ITI-FEM)was proposed by introducing modifications into the original IFEM.Then,the vein model was built using the ITI-FEM.The pathological vein models were further proposed and employed to explore the effect of two venous lesions on the dynamic behavior of the vein.The primary research contents and results are listed as follows:1.Implementation of the original IFEM program.Based on the original IFEM theory,the finite element formulations of the governing equations were derived.According to the framework of the finite element program,we coded the original IFEM program in FORTRAN90.The program was verified by comparing the results calculated by the ITI-FEM with those calculated by the original IFEM for several examples.2.Theory and finite element program of the proposed ITI-FEM.Based on the original IFEM,a ghost domain and transitional interface were introduced along with a momentum balance scheme.We also employed a Newmark-? based solid solver and integrated the Adhesive Contact Method(ACM)into it,then the so-called ITI-FEM was proposed.To understand its theory,the governing equations and corresponding weak forms were derived.Because the fluid module,solid module and FSI module in the program varied after those modifications,we redesigned the framework and structure of the ITI-FEM program and coded it.The feasibility and validation of the program were verified by several numerical examples,including the flow over a circular cylinder,a free drop of a circular disk in the water,and aeroelasticity of a leaflet in a channel,and so on.Comparison with the existing numerical and experimental results demonstrated that the ITI-FEM are more accurate and efficient.3.Establishment of the FSI model with the vein interacting with blood.According to the anatomical structure of a vein sample,the geometric model was built.Based on the reported properties information of veins and blood,we established the hyperelastic constitutive model for the vein and the Newtonian viscous fluid model for the blood.The distensions and contractions of the valve,wall and sinus were considered,so as to capture the dynamic characteristics of the vein and blood in the FSI model.4.Dynamic analysis of the venous valve cycle.On the basis of the above work,the physiological behavior of the vein was studied,and the motion and deformation fields of the vein and the flow fields of the blood were calculated.To validate the numerical vein model,the dynamic characteristics of the vein and the blood were compared with the existing physiological ones,including the geometric orifice area,venous volume and wall shear stress.Then the dynamic behavior of the healthy vein was further analyzed,which leads to a better understanding of the valve closure mechanism and the vein functioning,such as preventing the venous reflux and adjusting the blood flow.5.Analyzing effect of the venous lesions on the dynamic behavior of the vein and the blood.According to the existing physiology research,the pathological elasticities of the valve and wall were employed as two kinds of the venous lesion.The abnormal behaviors of the venous valve and blood under different pathological states(different position and degrees of the lesions)were studied.The calculated results showed that the valve atrophy will lead to vein incompetency,and the valve fibrosis may decrease the transportation capability of the transvalvular blood flow.The wall lesion had a less influence than the valve lesion,while its effect on the wall shear stress was relatively more apparent.