肿瘤生长过程形态模拟及相关技术研究
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摘要
随着计算机科学的飞速发展和学科之间交叉研究频频出现,计算机应用技术已经渗透到各个学科的研究。虚拟手术、虚拟人等项目便是在计算机科学与医学相结合的产物。用计算机模拟肿瘤生长也逐渐受到研究者们的关注和重视,它融合了计算机技术、计算几何、科学计算可视化、计算机图形学、生物力学、现代医学等多学科知识。用计算机模拟肿瘤生长将有助于人们了解肿瘤发生和发展的机理以及理解人体肿瘤作为自组织系统和动态演化系统的特征,对提高我国的肿瘤诊断和防治水平具有一定的意义。
论文以模拟肿瘤在颅底(内耳附近)的有血管等组织的复杂环境生长为背景,综述了模拟肿瘤生长的结构和构成模块,并对模拟系统的关键技术进行了深入研究和探索：
1)论文在深入研究基于方向包围盒的碰撞检测算法基础上,提出了基于近似凸包的方向包围盒(OBB:Oriented Bounding Box)构造算法和基于1-范数预判的包围盒相交测试算法。基于近似凸包的包围盒构造算法基本思想是根据近似凸包的思想提取出部分模型表面顶点集,然后对提取出的点集构造OBB包围盒。基于简单测度的包围盒相交测试算法的基本思想是在构造包围盒层次结构时,对每个包围盒,增加两条记录分别记录包围盒中心点到包围盒顶点距离的最大值和最小值,这里的距离是1-范数意义下的距离。在包围盒相交测试时,首先判断当前两个待判断包围盒的中心之间的距离是否比两个包围盒的最小记录之和小,如果条件成立,则判定两个包围盒相交,否则进一步判断包围盒中心之间的距离是否比两个包围盒的最大记录大,如果条件满足,则可判定两个包围盒不相交,如果前面两个条件都不满足,则按分离轴的方法分别在15个轴上进行投影判断。为了避免乘方和开方以提高预判速度,包围盒的最大值、最小值记录和包围盒中心的距离采用每个1-范数计算。
2)提出了基于隐式曲面和惩罚力的碰撞响应算法。首先通过A、B两模型的碰撞检测得到B模型相交基本几何元素集,将B模型的这些基本几何元素中的代表模型表面的顶点构造隐式曲面。根据A模型顶点的隐函数值将A模型的顶点分为两类,碰撞点集和非碰撞点集。对每一个碰撞点集的点,计算其梯度向量并单位化,然后乘以该点的隐函数值得到点的深度向量。根据深度向量计算力向量,最后通过相应的力学模型计算A物体顶点的位移,从而得物体形变结果。
3)为了给肿瘤模型建立以四面体为基本单元的元胞有限元力学模型,以便肿瘤模型在生长过程中肿瘤模型和组织器官模型能表现出真实的行为,提出了如何将以六面体为基本单元的细胞自动机空间的肿瘤模型网格转化为以四面体为单元的网格。由于以四面体为单元的有限元力学分析比以六面体为单元的有限元力学分析更为准确,所以要将元胞自动机空间(CA：Cellular Automata)肿瘤模型进一步划分为以四面体为基本单元的网格。对于每一个六面体,首先标志出8个顶点中不属于肿瘤模型的顶点和属于肿瘤模型的顶点。然后把属于肿瘤模型的顶点根据顶点到最近非肿瘤模型顶点的最短路径的大小进行分类,最后根据本文第5章5.4部分的划分策略将属于肿瘤模型的顶点划分为互不交叉四面体。对肿瘤模型所占的每个细胞进行同样的处理,得到以四面体为基本单元网格模型。另一方面,针对用细胞自动机得到的肿瘤模型的特殊性,论文提出一种提取肿瘤模型表面顶点和提取表面三角形面片集的方法,计算顶点的法向量,并用隐式曲面对肿瘤体模型进行渲染。
4)针对从人体切片重建模型中提取的血管模型形态的不准确性,及其对血管力学性质的影响造成力学分析的不准确的情况,论文提出了一种血管模型形态纠正算法。基本思想是：利用拾取技术对一段血管拾取两个点,从而计算一条近似的血管中轴,然后根据血管段顶点到中轴的距离统计情况,对满足一定条件的点沿着血管截面半径方向向外或向内移动顶点。
With the development of the computer science and the continual appearance of the cross-discipline researches, computer application technology has been used widely in multitudes of subjects'researches. The virtual operation and virtual human are the products in combination with computer science and medicine. The simulation of the tumor growth using computers attracts the attentions of many researchers. This technology involves computer application, computational geometry, and visualization in scientific computing, computer graphics, biomechanics and medicine. The simulation of tumor growth using computers can help people to explore the mechanism of the tumor generation and growth and then to understand the characteristics of tumor as a self-organizing system and a dynamic evolvement system, which in turn has great significance for the diagnosis of tumor prevention and cure.
The dissertation firstly sets its background in the tumor growth simulation in vein complex environment located at the skull base, then summarizes the structure of the simulation system and studies the crucial technology of simulating system.
1) With the thorough research of the collision detection algorithm based on oriented bounding box, a new construct algorithm using approximate convex hull and a new test algorithm using 1-norm pre-judgment are presented in the dissertation. The constructing algorithm of OBB basing on approximate convert hull is divided into two stages. Firstly, extract the vertices near the model surface to construct OBB by way of the approximate convex hull algorithm. Secondly, constructing OBB using the extracted vertices set. The basic idea of the test algorithm on simple measure OBB is that add 2 records to record the maximum and minimum distances from the center of OBB to the vertices of bounding box when constructing the hierarchical structure. First of all, judge whether the centre distance between the two bounding boxes is less than the sum of the two bounding boxes' minimum distance. The two bounding boxes are judged whether they are overlapped when the centers'distance of the two OBBs is less than the sum of the two minimum records. Then consider whether the distance of the centers between the two bounding boxes is greater than the sum of the max records. If the condition is satisfied, the bounding boxes are not considered overlapped, otherwise, project boxes to 15 axes by way of separating axis to judge whether the two OBB are overlapped. To speed up pre-judging process, the max record, the min record and the centers distance are computed by 1-norm.
2) The thesis presents a collision response algorithm basing on punishment force and implicit surface. First, obtain the intersected set of the geometrical element of model B by the collision detection between model A and model B. Then construct implicit surface using the surface vertices extracted from intersected vertices of Model B. According to the implicit function value of vertices in the model A, the vertices sets of Model A are classified into two groups:the set of collision and the set of non-collision. For the vertices involved in the set of the collision, compute gradient vector of every vertex and then normalized them. Then multiply the results derived from the previous process with the value of implicit function. And finally, the depth vector is used to compute the force vectors, the result of shape change can be obtained by means of computing the displacement of the vector of A.
3) The paper proposes a method to convert a hexahedron CA mesh into a new tetrahedron CA mesh in order to construct accurate force model which helps simulate the interaction process between tumor model and tissue model. The FEM analysis of tetrahedron mesh is more accurate than the FEM analysis of hexahedron mesh, so we should convert the hexahedron mesh into tetrahedron mesh. For every hexahedron, first label the vertices belonging to tumor model and the vertices which do not belong to tumor model. Then classify the vertices according to minimum distance to vertex not belonging to tumor model, finally based on the strategies proposed in the 5.4 part of the dissertation, divide the tumor model into tetrahedron which in not overlapped. Deal with every cell of the tumor model with the same method to get tetrahedron mesh. On the other hand, with regard to the specialties of tumor model obtained from CA model, the thesis proposes an algorithm to abstract the surface vertices and surface triangles, which will make computing the normal vectors apply in rendering tumor volume model with implicit surface.
4) Since the vessel model extracted by reconstructed model is inaccurate and the inaccurateness will lead to the inaccurateness of force analysis, the dissertation puts forward an algorithm on rectifying the vessel model. The basic idea of the algorithm is:computing an approximate vessel axis by extracting 2 points; then according to the statistics of the distance between the vertices and the axis, moving the vertices inwardly or outwardly along the vessel's radius direction.
论文以模拟肿瘤在颅底(内耳附近)的有血管等组织的复杂环境生长为背景,综述了模拟肿瘤生长的结构和构成模块,并对模拟系统的关键技术进行了深入研究和探索：
1)论文在深入研究基于方向包围盒的碰撞检测算法基础上,提出了基于近似凸包的方向包围盒(OBB:Oriented Bounding Box)构造算法和基于1-范数预判的包围盒相交测试算法。基于近似凸包的包围盒构造算法基本思想是根据近似凸包的思想提取出部分模型表面顶点集,然后对提取出的点集构造OBB包围盒。基于简单测度的包围盒相交测试算法的基本思想是在构造包围盒层次结构时,对每个包围盒,增加两条记录分别记录包围盒中心点到包围盒顶点距离的最大值和最小值,这里的距离是1-范数意义下的距离。在包围盒相交测试时,首先判断当前两个待判断包围盒的中心之间的距离是否比两个包围盒的最小记录之和小,如果条件成立,则判定两个包围盒相交,否则进一步判断包围盒中心之间的距离是否比两个包围盒的最大记录大,如果条件满足,则可判定两个包围盒不相交,如果前面两个条件都不满足,则按分离轴的方法分别在15个轴上进行投影判断。为了避免乘方和开方以提高预判速度,包围盒的最大值、最小值记录和包围盒中心的距离采用每个1-范数计算。
2)提出了基于隐式曲面和惩罚力的碰撞响应算法。首先通过A、B两模型的碰撞检测得到B模型相交基本几何元素集,将B模型的这些基本几何元素中的代表模型表面的顶点构造隐式曲面。根据A模型顶点的隐函数值将A模型的顶点分为两类,碰撞点集和非碰撞点集。对每一个碰撞点集的点,计算其梯度向量并单位化,然后乘以该点的隐函数值得到点的深度向量。根据深度向量计算力向量,最后通过相应的力学模型计算A物体顶点的位移,从而得物体形变结果。
3)为了给肿瘤模型建立以四面体为基本单元的元胞有限元力学模型,以便肿瘤模型在生长过程中肿瘤模型和组织器官模型能表现出真实的行为,提出了如何将以六面体为基本单元的细胞自动机空间的肿瘤模型网格转化为以四面体为单元的网格。由于以四面体为单元的有限元力学分析比以六面体为单元的有限元力学分析更为准确,所以要将元胞自动机空间(CA：Cellular Automata)肿瘤模型进一步划分为以四面体为基本单元的网格。对于每一个六面体,首先标志出8个顶点中不属于肿瘤模型的顶点和属于肿瘤模型的顶点。然后把属于肿瘤模型的顶点根据顶点到最近非肿瘤模型顶点的最短路径的大小进行分类,最后根据本文第5章5.4部分的划分策略将属于肿瘤模型的顶点划分为互不交叉四面体。对肿瘤模型所占的每个细胞进行同样的处理,得到以四面体为基本单元网格模型。另一方面,针对用细胞自动机得到的肿瘤模型的特殊性,论文提出一种提取肿瘤模型表面顶点和提取表面三角形面片集的方法,计算顶点的法向量,并用隐式曲面对肿瘤体模型进行渲染。
4)针对从人体切片重建模型中提取的血管模型形态的不准确性,及其对血管力学性质的影响造成力学分析的不准确的情况,论文提出了一种血管模型形态纠正算法。基本思想是：利用拾取技术对一段血管拾取两个点,从而计算一条近似的血管中轴,然后根据血管段顶点到中轴的距离统计情况,对满足一定条件的点沿着血管截面半径方向向外或向内移动顶点。
With the development of the computer science and the continual appearance of the cross-discipline researches, computer application technology has been used widely in multitudes of subjects'researches. The virtual operation and virtual human are the products in combination with computer science and medicine. The simulation of the tumor growth using computers attracts the attentions of many researchers. This technology involves computer application, computational geometry, and visualization in scientific computing, computer graphics, biomechanics and medicine. The simulation of tumor growth using computers can help people to explore the mechanism of the tumor generation and growth and then to understand the characteristics of tumor as a self-organizing system and a dynamic evolvement system, which in turn has great significance for the diagnosis of tumor prevention and cure.
The dissertation firstly sets its background in the tumor growth simulation in vein complex environment located at the skull base, then summarizes the structure of the simulation system and studies the crucial technology of simulating system.
1) With the thorough research of the collision detection algorithm based on oriented bounding box, a new construct algorithm using approximate convex hull and a new test algorithm using 1-norm pre-judgment are presented in the dissertation. The constructing algorithm of OBB basing on approximate convert hull is divided into two stages. Firstly, extract the vertices near the model surface to construct OBB by way of the approximate convex hull algorithm. Secondly, constructing OBB using the extracted vertices set. The basic idea of the test algorithm on simple measure OBB is that add 2 records to record the maximum and minimum distances from the center of OBB to the vertices of bounding box when constructing the hierarchical structure. First of all, judge whether the centre distance between the two bounding boxes is less than the sum of the two bounding boxes' minimum distance. The two bounding boxes are judged whether they are overlapped when the centers'distance of the two OBBs is less than the sum of the two minimum records. Then consider whether the distance of the centers between the two bounding boxes is greater than the sum of the max records. If the condition is satisfied, the bounding boxes are not considered overlapped, otherwise, project boxes to 15 axes by way of separating axis to judge whether the two OBB are overlapped. To speed up pre-judging process, the max record, the min record and the centers distance are computed by 1-norm.
2) The thesis presents a collision response algorithm basing on punishment force and implicit surface. First, obtain the intersected set of the geometrical element of model B by the collision detection between model A and model B. Then construct implicit surface using the surface vertices extracted from intersected vertices of Model B. According to the implicit function value of vertices in the model A, the vertices sets of Model A are classified into two groups:the set of collision and the set of non-collision. For the vertices involved in the set of the collision, compute gradient vector of every vertex and then normalized them. Then multiply the results derived from the previous process with the value of implicit function. And finally, the depth vector is used to compute the force vectors, the result of shape change can be obtained by means of computing the displacement of the vector of A.
3) The paper proposes a method to convert a hexahedron CA mesh into a new tetrahedron CA mesh in order to construct accurate force model which helps simulate the interaction process between tumor model and tissue model. The FEM analysis of tetrahedron mesh is more accurate than the FEM analysis of hexahedron mesh, so we should convert the hexahedron mesh into tetrahedron mesh. For every hexahedron, first label the vertices belonging to tumor model and the vertices which do not belong to tumor model. Then classify the vertices according to minimum distance to vertex not belonging to tumor model, finally based on the strategies proposed in the 5.4 part of the dissertation, divide the tumor model into tetrahedron which in not overlapped. Deal with every cell of the tumor model with the same method to get tetrahedron mesh. On the other hand, with regard to the specialties of tumor model obtained from CA model, the thesis proposes an algorithm to abstract the surface vertices and surface triangles, which will make computing the normal vectors apply in rendering tumor volume model with implicit surface.
4) Since the vessel model extracted by reconstructed model is inaccurate and the inaccurateness will lead to the inaccurateness of force analysis, the dissertation puts forward an algorithm on rectifying the vessel model. The basic idea of the algorithm is:computing an approximate vessel axis by extracting 2 points; then according to the statistics of the distance between the vertices and the axis, moving the vertices inwardly or outwardly along the vessel's radius direction.
引文
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