脑血管疾病是在世界范围内都普遍存在的一种流行病学，具有发病率高、死亡率高的特点，对人们的身心健康造成了极大的危害。相关研究表明，其发生多与脑血管几何形态的变异相关，所以对脑血管几何形态变化和特定疾病之间关联关系的研究具有重要意义，但是获得这种关联关系的前提是实现对脑血管上几何特征的定量表征和分析。随着医学图像技术的发展，越来越多高分辨率的三维图像被应用于临床诊疗，医生可以方便地在图像中对自己感兴趣的部位进行手动测量，但这种方式耗时长且测量精度不高，所以提出一种可以对脑血管上几何特征进行准确定量计算的方法有重要意义。

基于此，本文提出了一种脑血管几何特征自动定量计算方法，实现了对脑血管上任意采样点处几何特征的定量计算，之后基于获得的定量数据对脑血管分支的形态变化规律进行了研究分析，挖掘出了一些潜在的医学知识。文中研究工作的主要创新点如下：

1）提出了基于球B样条的脑血管几何特征自动定量计算方法。本文使用球B样条理论对离散的脑血管数据进行了拟合，获得了连续的参数曲线，有效实现了对脑血管任意位置处几何特征的自动定量计算，完成从个体样本到群体样本的定量计算方法提升。

2）在大样本真实人群数据集上验证了方法的可行性。本文首先对计算获得的脑血管直径数据和医生手动测量的直径数据进行了双盲一致性检验，之后对本文基于客观定量数据预测得到的相关疾病诊断结果和对应的医生人工诊断结果间的一致性进行了检验，两类检验结果均表现出良好的一致性，为之后的工作奠定了坚实的数据基础。

3）提出了基于定量几何特征的脑血管形态变化规律挖掘方法。本文通过构建假设检验获得了同血管不同特征量和不同血管相同特征量间的相关规律，之后针对基底动脉延长扩张疾病进行了影响因素分析，在广义数据层面明确了各特征量对该疾病的影响价值，最后对大脑动脉环中其他血管分支各几何特征量在该疾病样本集和正常样本集间的差异进行了统计分析，挖掘了基底动脉段变异对其他脑血管分支形态的影响。

关于方法的可行性和定量计算结果的有效性，本文在协和医院顺义区的1093套脑血管图像数据上进行了相关实验，计算了脑血管的长度、半径、曲率和挠率，并和医院的测量金标准进行了双盲一致性检验，结果表明数据一致性良好；关于脑血管分支的形态变化规律，实验结果显示，几何特征间的强相关性多出现在大脑动脉环的对称结构中；此外，血管扩张是造成基底动脉延长扩张疾病的主要原因，且基底动脉的延长扩张会导致大脑动脉环中远端主要分支的长度和半径变大。以上实验结果均可为相关脑血管疾病的预防、诊断及治疗工作提供帮助，具有重要应用价值。

Cerebrovascular disease is a kind of epidemiology that is widespread all over the world. It has the characteristics of high morbidity and high mortality, which has caused great harm to people's physical and mental health. Relevant studies have shown that its occurrence is mostly related to the variation of cerebrovascular geometry, so it is of great significance to study the relationship between the changes of cerebrovascular geometry and the specific disease. However, the prerequisite for obtaining this relationship is to achieve the quantitative characterization and analysis of geometric characteristics on the cerebrovascular. With the development of medical imaging technology, more and more high-resolution three-dimensional images are used in clinical diagnosis and treatment. Doctors can conveniently measure the interesting parts in the images manually, but this method is time-consuming and not accurate. So it is important to propose a method that can accurately and quantitatively calculate the geometric features of the cerebrovascular.

Hence, this paper proposes an automatic quantitative calculation method for cerebrovascular geometric features, which effectively realizes the quantitative calculation of geometric features at any sampling point on the cerebrovascular,.Then, based on the obtained quantitative data, this paper studies and analyzes the morphological changes of cerebrovascular branches, and excavates some potential medical knowledge. The main innovations of this paper are as follows:

1) An automatic quantitative calculation method of cerebrovascular geometric features based on spherical B-spline is proposed. In this paper, the discrete cerebrovascular data are fitted by ball B-spline and the continuous parameter curve is obtained, which can effectively realize the automatic quantitative calculation of geometric features at any position of the cerebrovascular, completing the improvement of quantification calculation methods from individual samples to group samples.

2) The feasibility of the method is verified on a large-sample real population data set. This paper first conducts a double-blind consistency test on the calculated cerebrovascular diameter data by this method and the diameter data manually measured by the doctor, and then the consistency between the relevant disease diagnosis results predicted by the paper based on objective quantitative data and the corresponding doctor's manual diagnosis results is tested. The results of the two types of consistency test experiments showed good consistency, which lays a solid data foundation for the future work.

3) A method for mining the morphological changes of cerebral blood vessels based on quantitative geometric features is proposed. In this paper, by constructing a hypothesis test, we have obtained the correlation law between different characteristic quantities of the same blood vessel and the same characteristic quantity of different blood vessels, and then analyzed the influencing factors of the cerebrovascular prolongation and expansion disease, and clarified the impact of each feature on the disease at the broad data level. Finally, the statistical analysis is carried out on the difference between the geometrical characteristics of other blood vessel branches in the circle of Willis between the disease sample set and the normal sample set, and the medical knowledge of the variation of the Basilar Artery and the morphological changes of other blood vessel branches is discovered.

Regarding the feasibility of the method and the validity of the quantitative calculation results, this article conducted experiments on 1093 sets of cerebrovascular image data in Shunyi District of Union Hospital. The length, radius, curvature and torsion of the cerebrovascular are calculated, and the double-blind consistency test is carried out between the calculation results and the gold standard of the hospital. The results show that the data is in good agreement. As for the morphological changes of cerebrovascular branches, the experimental results shows that the strong correlation between geometric features mostly occurs in the symmetrical structure of the cerebral arterial circle. In addition, vascular dilatation is the main cause of vertebrobasilar dolichoectasia(VBD), and VBD will lead to the increase of the length and radius of the main branches in the cerebral arterial circle. The above experimental results can provide help for the prevention, diagnosis and treatment of related cerebrovascular diseases, and have important application value.