Modeling and Simulation of Valve Cycle in Vein Using an Immersed Finite Element Method

A vein model was established to simulate the periodic characteristics of blood flow and valve deformation in blood-induced valve cycles.Using an immersed finite element method which was modified by a ghost fluid technique,the interaction between the vein and blood was simulated.With an independent solid solver,the contact force between vein tissues was calculated using an adhesive contact method.A benchmark simulation of the normal valve cycle validated the proposed model for a healthy vein.Both the opening orifice and blood flow rate agreed with those in the physiology.Low blood shear stress and maximum leaflet stress were also seen in the base region of the valve.On the basis of the healthy model,a diseased vein model was subsequently built to explore the sinus lesions,namely,fibrosis and atrophy which are assumed stiffening and softening of the sinus.Our results showed the opening orifice of the diseased vein was inversely proportional to the corresponding modulus of the sinus.A drop in the transvalvular pressure gradient resulted from the sinus lesion.Compared to the fibrosis,the atrophy of the sinus apparently improved the vein deformability but simultaneously accelerated the deterioration of venous disease and increased the risk of potential fracture.These results provide understandings of the normal/abnormal valve cycle in vein,and can be also helpful for the prosthesis design.

Numerical study of opposed zero-net-mass-flow jet-induced erythrocyte mechanoporation

With the advantages of biosafety and efficiency,increasing attention has been paid to the devices for gene and macromolecular drug delivery based on mechanoporation.The transient pore formation on the cell membrane allows cargo transportation when the membrane areal strain is beyond the critical pore value and below the lysis tension threshold.Based on this principle,we propose a method to apply the proper fluid stress on cells moving in a microchannel under the action of zero-net-mass-flux(ZNMF)jets.In this study,an immersed finite element method(IFEM)is adopted to simulate the interaction between the cells and the fluid fields so as to investigate the cell movement and deformation in this mechanoporation system.To evaluate the efficiency of the cargo delivery,a pore integral is defined as the mean pore rate when the cell passes through the jet region.By analyzing the effects of the parameters,including the pressure gradient along the microchannel,the jet amplitude,and the jet frequency,on the pore integrals,a group of optimized parameters for cargo delivery efficiency are obtained.Additionally,the stability and safety of this system are analyzed in detail.These results are helpful in designing the mechanoporation devices and improving their efficiency of drug delivery.

Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions

In this paper,we propose an immersed finite volume element method for solving the semi-linear elliptic interface problems with non-homogeneous jump conditions.Furthermore,two-grid techniques are used to improve the computational efficiency.In this way,we only need to solve a non-linear system on the coarse grid,and a linear system on the fine grid.Numerical results illustrate that the proposed method can solve the semi-linear elliptic interface problems efficiently.Approximate secondorder accuracy for the solution in the L¥norm can be obtained for the considered examples.

A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems

This article extends the finite element method of lines to a parabolic initial boundary value problem whose diffusion coefficient is discontinuous across an interface that changes with respect to time.The method presented here uses immersed finite element(IFE)functions for the discretization in spatial variables that can be carried out over a fixedmesh(such as a Cartesianmesh if desired),and this featuremakes it possible to reduce the parabolic equation to a system of ordinary differential equations(ODE)through the usual semi-discretization procedure.Therefore,with a suitable choice of the ODE solver,this method can reliably and efficiently solve a parabolic moving interface problem over a fixed structured(Cartesian)mesh.Numerical examples are presented to demonstrate features of this new method.

Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver

This article is to discuss the bilinear and linear immersed finite element(IFE)solutions generated from the algebraic multigrid solver for both stationary and moving interface problems.For the numerical methods based on finite difference formulation and a structured mesh independent of the interface,the stiffness matrix of the linear system is usually not symmetric positive-definite,which demands extra efforts to design efficient multigrid methods.On the other hand,the stiffness matrix arising from the IFE methods are naturally symmetric positive-definite.Hence the IFE-AMG algorithm is proposed to solve the linear systems of the bilinear and linear IFE methods for both stationary and moving interface problems.The numerical examples demonstrate the features of the proposed algorithms,including the optimal convergence in both L 2 and semi-H1 norms of the IFE-AMG solutions,the high efficiency with proper choice of the components and parameters of AMG,the influence of the tolerance and the smoother type of AMG on the convergence of the IFE solutions for the interface problems,and the relationship between the cost and the moving interface location.

Fluid-structure interaction simulation of pathological mitral valve dynamics in a coupled mitral valve-left ventricle model

Background Understanding the interaction between the mitral valve(MV)and the left ventricle(LV)is very important in assessing cardiac pump function,especially when the MV is dysfunctional.Such dysfunction is a major medical problem owing to the essential role of the MV in cardiac pump function.Computational modelling can provide new approaches to gain insight into the functions of the MV and LV.Methods In this study,a previously developed LV-MV model was used to study cardiac dynamics of MV leaflets under normal and pathological conditions,including hypertrophic cardiomyopathy(HOCM)and calcification of the valve.The coupled LV-MV model was implemented using a hybrid immersed boundary/finite element method to enable assessment of MV haemodynamic performance.Constitutive parameters of the HOCM and calcified valves were inversely determined from published experimental data.The LV compensation mechanism was further studied in the case of the calcified MV.Results Our results showed that MV dynamics and LV pump function could be greatly affected by MV pathology.For example,the HOCM case showed bulged MV leaflets at the systole owing to low stiffness,and the calcified MV was associated with impaired diastolic filling and much-reduced stroke volume.We further demonstrated that either increasing the LV filling pressure or increasing myocardial contractility could enable a calcified valve to achieve near-normal pump function.Conclusion The modelling approach developed in this study may deepen our understanding of the interactions between the MV and the LV and help in risk stratification of heart valve disease and in silico treatment planning by exploring intrinsic compensation mechanisms.