Lattice Boltzmann Method Simulations Of Blood Flowing In Elastic Tube

Since 1990, the lattice Boltzmann method (LBM) based on single relaxation time has attracted more and more attention. Because of its intristically parallel dynamics, and absence of statistical noise, this method is exspecially suited for parallel computation on PC-cluster or Internet grid computation. Considering simplicity of program and convenience of boundary condition, LBM has been accepted as an alternate hydrodynamic computational method, and its accuracy and robustness has been broadly confirmed throught numerical simulations of turbulent flows, two-phase flows, reaction-diffusion processes, granular and suspended particles. Anyway, this mesoscopic model can perform large-scale computational simulation with relatively low cost. The blood circular system is a typical complex biological system consisting of heart, blood, vessel and capillary with deformable boundaries. In fact, the blood flow involves two factors mainly, wich are the artery pressure produced by heart periodical beats and the counterforce from the elastic vessel to the blood. In this article, we will focus on the later factor to investigate blood flowing throught the elastic vessel by LBM. The content includes the following three parts:(1) We study the influence on the blood flux in arteries exerted by vessl elasticity under the condition of steady and unsteady input flow. The vessel is discretized intomany equilength segments, which are limited moving along axial direction of the vessel based on the fact that the constraint of the vessel along axial direction is very strong. Inoder to study the influence on the vessel exerting by blood, we simulate the radial movement of the elastic vessel under the action of blood pressure. A long and thin distensible tube in two dimensions is discretized many segments adjacent fluid of which is simulated by a lattice Boltzmann method. It is found that the volume-flow rate increases considerably when the compliance constant of the vessel is below a critical value; otherwise, the volume-flow rate is insensible to the change of the compliance. Moreover, there is a range of the compliance constant within which the volume-flow rate is dramatically varied like chaos. A harmonic perturbation of the pressure does not change the behavior of the average volume-flow rate meanwhile the harmonic wave attenuates very quickly along the tube when the resonant period is close to that of the input wave. The model, together with the simulation results, is expected to be helpful to understand the mechanism of blood volume-flow rate related to the compliance constant of the vessel, especially, the dependence of the flux of human vessel on weather condition. This model may have medical significance to human body.(2) We propose a lattice Boltzmann scheme to study the hemodynamics of an artery with an aneurysm. Throught the study of the growing procedure of the aneurysm simulated by our scheme, we find that an aneurysm may occur if the pathological changes take place on the arterial wall resulting in some place of the wall becoming so soft as to lose its structural integrity under the action of the pulsatileintraluminal pressure. Abdominal aorta whose diameter ranges from 15mm to 20mm is one of the primary arteries of the body that supplies the lower half of the body with blood. The aorta may dilate into a balloon like bulge referred to as an abdominal aortic aneurysm (AAA). Here, we suppose that somewhere of the arterial wall becomes soft. In oder to balance the blood pressure inside the atery, the atery must expand its local skin to get enough elastic force. So an aneurysm has grown up when the balance between blood flow and the wall is reached. Under low Reynolds numbers condition, we calculated the distribution of shear stress on an aneurysm wall by stress-integration. The results indicate that shear stress exerting on the wall decreases greatly because of the existence of recirculation vortex, and the average magnitude in the recirculation zone is about thirty times less than that in the entrance tube. Both wall shear stress and wall normal stress profiles exhibit lots of peaks near the joint strap on the twig of the aneurysm. Our simualtion shows that the wall near the twig of the aneurysm would risk rupture and hemorrhage. Our results agree with other conclusions in vitro experiments and numerical calculations very well.(3) In order to investigate the influence of temprature distribution on blood flow we proposed a 13-speed thermal lattice Bhatnagar-Gross-Krook model on hexagonal lattice. Throught an adjustable parameter λ , the Prandtl number is tunable now. Despite this model is very simple, but it can capture the thermal conduction and convection of the blood flow. As a preliminary exploration, we simulate a lid-driven flow in a square cavity at a wide range of Reynolds numbers. Simulations of the natural convection flow in a square cavity are also implemented. Our simulationsshow that this model agree with conventional numerical methods very well in a wide range of Raleigh number spaning from 10~3 to 10~6 .