Grassmann Space-based Vascular Reconstruction And Blood Flow Analysis

Vascular disease is one of the serious threats to human health.Direct observation and exploration of blood vessels can help doctors better understand the patient’s condition.3D reconstruction is a core technology of computer vision and medical image analysis.The processes can be divided into three main steps: blood vessel segmentation,skeleton line extraction and surface modeling.The application of this technique to vascular disease has a broad prospect in clinical virtual surgery simulation.However,the diversity of vascular structure brings great challenges to vascular reconstruction.The 3D reconstruction of blood vessels based on reality and the simulation of blood flow in virtual surgery need to be solved urgently.In allusion to the demand of 3D vascular reconstruction and blood flow numerical analysis on the medical image section in virtual surgery simulation,we introduce recurrence graph method to Grassmann space.We propose an accurate and efficient 3D digital modeling method for blood vessels and an algorithm for blood flow structure analysis.The proposed method can simplify the problem of parameter constraint in rational complex recurrence graph.In addition,LCSF algorithm is proposed to analyze particle fluid structure for studying blood flow status and predicting vascular diseases.The main research contents of this thesis are as follows:(1)Firstly,for the issue of complex parameter constraints in the expression of recurrence curve and surface,Grassmann space is introduced.In this thesis,Grassmann space is compared with common mathematical space(i.e.geometric space,vector space,affine space,etc.),and the properties of Grassmann space and the expressions of the recursive curvesurface algorithm are studied and analyzed.It lays a foundation for 3D modeling of blood vessel surface and force analysis of blood flow particles.(2)In this thesis,a precise 3D modeling method for blood vessels is proposed,and the vascular tissue in three-dimensional computed tomography(CT)images is segmented using the regional growth method.Then,the centerline was extracted by the etching method,and the topological expression of the vascular tree was constructed.On the research of work(1),a 3D recurrence graph algorithm was proposed,and the contour interpolation method was used to reconstruct the surface of blood vessels.Finally,the bifurcated vessels were spliced and fused.Experimental results show that the modeling method is accurate and efficient,and can provide reliable guidance for virtual surgery planning.(3)In this thesis,a blood flow numerical simulation analysis method is proposed,which converts the blood flow process into the motion equation of particles in fluid motion.By abstracting the vessel model into the container wall spring model,the vessel function model with physical characteristics was established.In addition,we proposed the LCSF algorithm,which can be used to analyze the fluid structure of blood flow particles in blood vessels,and can be helpful in the study of cases such as vascular dynamic deformation,blood flow analysis and surface pressure analysis.