Research On Erythrocyte Mechanical Damage Based On The Stress Of Cellular Membrane

In this dissertation,the mechanical damage of red blood cells induced by the flow was studied based on the stress state of the cell membrane.Firstly,the red blood cells were mathematically modeled,and the finite element method was used to simulate the red blood cell movement.The red blood cell model was validated and the membrane reference state and other parameters were determined.The interaction between the cell membrane and fluid was coupled by the immersed boundary method.An explicit algorithm was proposed to ensure cell volume conservation.Secondly,using the above red blood cell model and numerical method,the red blood cell dynamics and the membrane stress state in pure shear flow and planar extensional flow were studied,and the effects of fluid normal stress and shear stress on red blood cell damage were revealed.Limitations of scalar shear stress in the existing literature were also shown.A red blood cell in vitro shear test system was established to investigate red blood cell damage in the complex flow field.The red blood cell shape and damage were studied qualitatively when the fluid normal stress and shear stress were considered simultaneously.Finally,a multi-scale model was established,including cell membrane tension differential equation,hemoglobin release differential equation,and macroscopic hemodynamic equation.The effect of turbulence on red blood cells was described by using the turbulent energy dissipation rate.The evaluation results of red blood cell damage by the multi-scale model and exponential model were compared numerically and the validity of the multi-scale model was verified.The contents of this dissertation are as follows:(1)Research on red blood cell modeling and membrane reference stateThe mathematical model of red blood cells was established by the continuum model,and the parameterization of membrane reference state was given.The finite element method was used to simulate the red blood cell motion.On this basis,the equilibrium shape,optical tweezers stretching tests,and shape memory of red blood cells were simulated,and the influence of the membrane reference state was studied.The correctness of the red blood cell mathematical model and the numerical method was verified by comparison with the experimental and numerical results in the existing literature,and the membrane reference state used in the subsequent research was confirmed,which established the basis for the subsequent studies.(2)Research on volume-conserving immersed boundary methodBased on the original immersed boundary method,an explicit algorithm for ensuring cell volume conservation was proposed.The volume conservation was achieved by correcting the position of Lagrangian grid points along the normal direction of the cell membrane.The algorithm was validated using multiple examples,such as passive advection and shear deformation of spherical cells,and compared with algorithms in the existing literature.The results show that the proposed algorithm improved computational efficiency under the premise of accuracy.In addition,the proposed algorithm was used to simulate the movement of red blood cells in the shear flow.The trilobe and quadralobe observed in the literature were successfully reproduced,which further proved the correctness and necessity of the proposed algorithm.(3)Research on red blood cell dynamics under strong fluid stressBased on the red blood cell model and numerical method proposed in this dissertation,the red blood cell dynamics and membrane stress state in pure shear flow and planar extensional flow were studied.The results show that as the fluid stress increases,the red blood cells are gradually elongated and tend to a certain extreme shape.During the stretching process,the tension and shear stress of the membrane also increases.When the critical tension or yield stress is reached,the membrane may get ruptured or yield from the middle.The planar extensional flow is more likely to cause membrane rupture than the pure shear flow when the scalar shear stresses are the same.The above studies also pointed out that the scalar shear stress in the existing literature can not reflect the stress state of the membrane,and therefore is not suitable as an estimation index of red blood cell damage.In addition,the effect of turbulence on red blood cells was studied by sinusoidal shear flow.It was pointed out that when the frequency of turbulence was lower than the elastic characteristic frequency of the membrane,the membrane could fully respond to turbulence.(4)In vitro shear experiments of red blood cellsAn experimental system for observing the damage of red blood cells in complex flow fields was established.The rotor impeller was used to generate the spatially varying flow field,and the red blood cell dynamics were observed by solidifying red blood cells during loading or unloading.The experimental results show that with the increase of the rotational speed,the red blood cells are gradually stretched;after the unloading,the red blood cells can not return to the normal state in a short time,and the shrinkage occurs.Further numerical simulations show that the fluid stress is dominated by the turbulent stress,which causes the damage of red blood cells.The shape of red blood cells is the result of the interaction of fluid normal stress and shear stress.When the magnitude of normal stress and shear stress are of the same order,the effect of normal stress is more significant.(5)Research on a multi-scale model of red blood cell damageA multi-scale model based on membrane tension and hemoglobin release process was proposed to evaluate the mechanical damage of red blood cells caused by flow.At the cell scale,the differential equation of membrane tension was established to describe the effect of flow on the cell membrane.The process of hemoglobin release from red blood cells was divided into diffusion hemolysis and rupture hemolysis,and the diffusion equations were established respectively.At the macroscopic scale,the Lagrangian or Eulerian method was used to calculate the hemoglobin concentration in plasma,and the turbulent energy dissipation rate is used to describe the effect of turbulence on the membrane tension.On the basis of the above model,the numerical simulation results were used to fit the parameters of the membrane tension differential equation,and the parameters of the hemoglobin release equation were fitted by the exponential model.The multi-scale model and the exponential model were compared by numerical simulation.The results show that the multi-scale model can more accurately predict the red blood cell damage and hemolysis process.