基于造影图像的冠状动脉三维重建和定量分析方法的研究
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摘要
冠状动脉造影图像是临床诊治冠心病的主要依据之一,被称为诊断冠心病的“金标准”,但基于二维造影图像的传统诊治方法存在很大的局限性。本文在二维血管提取的基础上,主要研究冠状动脉树的三维重建方法,并进行主干血管三维定量分析方法的研究,对于提高冠心病诊治的准确程度具有很高的临床应用价值。本论文研究课题受高等学校博士学科点专项科研基金的资助(“心血管造影图像中血管网的提取与三维重建”,20030056018),主要研究工作包括以下几个方面:
1.建立三维重建的理论模型
根据造影系统的运动特征建立透视投影的简化模型,并采用几何变换矩阵描述两幅图像的空间几何关系。在此基础上提出了空间点三维坐标的两种计算方法,即最小二乘解和几何解。
2.二维骨架树的分割和血管段的匹配
在二维血管提取的基础上,采用有向图、有向树和二叉树描述骨架树的拓扑结构。同时提出结点权值和相似结点的概念,实现两幅图像中血管段的匹配。
3.几何变换矩阵的优化
将几何变换矩阵表示为七元数的形式,提出利用分支点坐标、分支血管方向矢量和分支夹角三类数据优化几何变换矩阵的方法。
4.冠状动脉树骨架的三维重建
提出一种以B样条曲线为基元重建三维骨架的方法,采用B样条曲线拟合二维骨架,在B样条曲线透视不变性的假设下对三维控制点进行优化。
5.冠状动脉三维表面的重建
在假设血管为广义圆柱体的前提下,建立血管横截面的椭圆模型,并提出顶点融合技术很好地解决了相邻横截面相交的问题。同时分别采用球包络方法、三角形拼接法和NURBS曲面拟合方法重构血管的三维表面。
6.冠状动脉树的三维重建实验
分别采用计算机模拟图像、临床造影图像和实物模型造影图像进行三维重建实验,并对重建误差进行统计分析,验证本文重建方法的正确性。
7.冠状动脉的三维定量分析
在冠状动脉树三维重建的基础上,研究冠状动脉的三维定量分析方法。提出血管三维直径、分支夹角、血管段长度和体积的三维测量方法,并利用冠状动脉树实物模型进行三维定量分析实验,验证该方法的有效性和准确性。
Coronary angiography is regarded as the “gold standard” for the assessment of coronary artery disease. We are now carrying out a research project supported by the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) under the contract no. 20030056018. The project is entitled “2D extraction and 3D reconstruction of vessel net based on the angiograms”. The core of this dissertation is 3D reconstruction of coronary arterial tree and the 3D quantitative analysis of vessel. The main contents of this dissertation include seven parts as follows:
1. Theoretical Model of 3D reconstruction
We construct the simplified model of angiographic system according to its moving characters, and describe the transformation between the two angiograms using a rotation matrix and a translation vector. In addition, we present two methods to calculate 3D coordinate, which are Least Square Solution and Geometric Solution.
2. Segmentation of 2D tree and vessel-matching
After segmentation of 2D skeleton tree, we use Directed Graph, Directed Tree and Binary Tree to describe the topological structure of arterial tree. At the same time, Node Weight and Similar Node are defined, by which the vessels are matched successfully.
3. Optimization of transformation
Bifurcations, vessel vectors and branch angles are used to optimize the geometric transformation which is expressed as seven variables.
4. 3D reconstruction of coronary arterial tree’s skeleton
We propose a new method based on B-spline for reconstructing 3D skeleton. It mainly includes 2D B-spline curve fitting and optimization of 3D B-spline control points.
5. 3D reconstruction of vessel surface
On the assumption that vessel is generalized column, we establish the elliptical model of vessel’s cross-section and present vertex-merging method to solve the problem of neighboring cross-sections’ intersection. In addition, three methods are studied for 3D reconstruction of vessel surface, including Sphere Envelope, Triangularization and NURBS Surface Fitting.
6. Experiment of 3D reconstruction
The computer-simulated images, clinical angiograms and vessel phantom’s angiograms are respectively used for the experiment of 3D reconstruction. The performance of the method is validated by the statistic of reconstruction errors.
7. 3D quantitative analysis of coronary artery On the basis of 3D reconstruction, we study the 3D quantitative analysis of vessel, and propose a method to calculate the 3D values of diameter, length, and volume and branch angle. The method is validated by 3D quantitative analysis of vessel phantom.
1.建立三维重建的理论模型
根据造影系统的运动特征建立透视投影的简化模型,并采用几何变换矩阵描述两幅图像的空间几何关系。在此基础上提出了空间点三维坐标的两种计算方法,即最小二乘解和几何解。
2.二维骨架树的分割和血管段的匹配
在二维血管提取的基础上,采用有向图、有向树和二叉树描述骨架树的拓扑结构。同时提出结点权值和相似结点的概念,实现两幅图像中血管段的匹配。
3.几何变换矩阵的优化
将几何变换矩阵表示为七元数的形式,提出利用分支点坐标、分支血管方向矢量和分支夹角三类数据优化几何变换矩阵的方法。
4.冠状动脉树骨架的三维重建
提出一种以B样条曲线为基元重建三维骨架的方法,采用B样条曲线拟合二维骨架,在B样条曲线透视不变性的假设下对三维控制点进行优化。
5.冠状动脉三维表面的重建
在假设血管为广义圆柱体的前提下,建立血管横截面的椭圆模型,并提出顶点融合技术很好地解决了相邻横截面相交的问题。同时分别采用球包络方法、三角形拼接法和NURBS曲面拟合方法重构血管的三维表面。
6.冠状动脉树的三维重建实验
分别采用计算机模拟图像、临床造影图像和实物模型造影图像进行三维重建实验,并对重建误差进行统计分析,验证本文重建方法的正确性。
7.冠状动脉的三维定量分析
在冠状动脉树三维重建的基础上,研究冠状动脉的三维定量分析方法。提出血管三维直径、分支夹角、血管段长度和体积的三维测量方法,并利用冠状动脉树实物模型进行三维定量分析实验,验证该方法的有效性和准确性。
Coronary angiography is regarded as the “gold standard” for the assessment of coronary artery disease. We are now carrying out a research project supported by the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) under the contract no. 20030056018. The project is entitled “2D extraction and 3D reconstruction of vessel net based on the angiograms”. The core of this dissertation is 3D reconstruction of coronary arterial tree and the 3D quantitative analysis of vessel. The main contents of this dissertation include seven parts as follows:
1. Theoretical Model of 3D reconstruction
We construct the simplified model of angiographic system according to its moving characters, and describe the transformation between the two angiograms using a rotation matrix and a translation vector. In addition, we present two methods to calculate 3D coordinate, which are Least Square Solution and Geometric Solution.
2. Segmentation of 2D tree and vessel-matching
After segmentation of 2D skeleton tree, we use Directed Graph, Directed Tree and Binary Tree to describe the topological structure of arterial tree. At the same time, Node Weight and Similar Node are defined, by which the vessels are matched successfully.
3. Optimization of transformation
Bifurcations, vessel vectors and branch angles are used to optimize the geometric transformation which is expressed as seven variables.
4. 3D reconstruction of coronary arterial tree’s skeleton
We propose a new method based on B-spline for reconstructing 3D skeleton. It mainly includes 2D B-spline curve fitting and optimization of 3D B-spline control points.
5. 3D reconstruction of vessel surface
On the assumption that vessel is generalized column, we establish the elliptical model of vessel’s cross-section and present vertex-merging method to solve the problem of neighboring cross-sections’ intersection. In addition, three methods are studied for 3D reconstruction of vessel surface, including Sphere Envelope, Triangularization and NURBS Surface Fitting.
6. Experiment of 3D reconstruction
The computer-simulated images, clinical angiograms and vessel phantom’s angiograms are respectively used for the experiment of 3D reconstruction. The performance of the method is validated by the statistic of reconstruction errors.
7. 3D quantitative analysis of coronary artery On the basis of 3D reconstruction, we study the 3D quantitative analysis of vessel, and propose a method to calculate the 3D values of diameter, length, and volume and branch angle. The method is validated by 3D quantitative analysis of vessel phantom.
引文
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