基于格子Boltzmann方法的个体化颅内动脉瘤几何重建及其数值模拟

发布时间：2018-08-25 14:48

【摘要】：颅内动脉瘤是危害人类健康的最危险和最常见疾病之一,而血流动力学作为影响颅内动脉瘤产生、发展、破裂和治疗的主要因素,受到国内外学者的广泛关注。在临床治疗方面,血流转向支架和弹簧圈栓塞的血管内部介入治疗手段取得了好的疗效,但支架和弹簧圈的工业设计仍需要理论和实验的进一步改善。但是传统的临床实验面临风险大、周期长、成本高的困境。目前基于医学图像的个体化颅内动脉瘤数值实验受到青睐。现有的数值研究方法大多采用各种计算流体力学(CFD)软件,在使用过程中受到血管复杂几何结构、血液流动特性、低计算效率等诸多问题的限制。近年来,格子Boltzmann方法(LBM)因其在计算流体力学方面的快速发展越来越备受瞩目。在模型的通用性、处理复杂边界的能力和计算的效率上,LB方法有其天然的优势,适合用于颅内动脉瘤血流动力学的模拟和分析。此外,很多学者已将LB方法作为一种有效的数值方法用于求解各种偏微分方程,如：对流扩散方程、反应扩散方程、泊松方程等。目前,基于LBM的动脉瘤血流动力学数值模拟已有一些研究工作,但是在动脉瘤几何模型上已有的工作大多基于二维的模型或者圆柱加圆球组合的理想三维模型,缺乏个体化病人的研究；在病人个体化数据的研究中,数值模拟的进出口边界条件仍需要讨论。在此基础上,本文以LBM为主要的数值手段研究个体化颅内动脉瘤血流动力学模拟的整个过程：从临床采集的三维断层医学影像数据出发,通过发展多种格子Boltzmann模型,并借助图形处理器(GPU)并行计算设备完成个体病人血管图像分割、几何重建、LBM计算网格处理和血流动力学模拟。论文的工作主要包括两个方面：个体化动脉瘤几何外形的重建和复杂边界的血流动力学数值模拟。在几何外形重建和计算网格方面： (1)本文通过对格子Boltzmann方法求解方程的特点和基于偏微分方程的图像去噪、边缘检测、图像分割模型特点的研究,提出一种能高效解决图像去噪,边缘检测和图像分割的LB模型,并将此模型运用于个体化颅内动脉瘤断层CT图像数据处理之中,能够准确的完成个体化动脉瘤三维几何模型的图像分割。该模型不仅仅能运用于医学图像,对于更为复杂的自然图片的轮廓检测和图像分割也具有良好的效果。 (2)为了达到格子Boltzmann方法计算网格和临床研究的需求,我们对几何模型做了进一步改进,使得几何模型更加合理。基于图像分割的结果,我们提出血管中心线方法,重建载瘤血管和血管支架。一方面,使得载瘤血管更加光滑,更接近实际情况；另一方面,可以根据研究需要随意取舍动脉瘤附近分支血管。通过与传统CFD软件重建的三维模型的对比,本文提出的几何模型处理结果更为合理,且满足各种类型血管支架的设计。在复杂边界的血流动力学数值模拟方面： (1)在血管几何模型的基础上,我们发展基于复杂边界的格子Boltzmanr模型,以此求解描述血流动力学的Navier-Stokes方程。同时也探讨个体化颅内动脉瘤进出口条件。研究发现采用速度进口,压力出口条件更适合各种个体化颅内动脉瘤几何模型的需求。此外,在速度进口与压力出口的边界条件下,讨论了脉动速度进口与定常速度进口的区别,发现采用脉动速度均值和脉动峰值的平均值作为定常速度进口可以近似模拟血流脉动峰值时刻的流动状态。 (2)结合临床治疗中的问题,我们对多例颈动脉瘤病人数据的进行了数值模拟。针对血管支架的设计问题,本文研究了不同疏密和类型的血管支架置入载瘤血管后瘤内血流动力学变化。发现支架置入之后动脉瘤内部流线形态发生明显变化,血流速度明显减小,且随着支架密度的增大而减小得更显著,同样疏密的螺旋网状支架比单螺旋支架更能抑制瘤内速度；研究了动脉瘤附近支血管对瘤内血流动力学的影响,并通过对瘤内部速度大小和流态的分析得出当载瘤血管与支血管直径比较大或者分支血管距离动脉瘤较远时,瘤内流场差异较小。在数值研究中可以根据需要去除这部分分支血管。总之,本文以格子Boltzmann方法为主要数值手段,建立了个体化颅内动脉瘤血流动力学模拟的整套方案,并在GPU高性能并行平台下完成了LB算法的设计,相比CPU程序得到近两个数量级的加速比,大大提高了数值模拟算法的效率。与此同时,本文针对临床病例开展数值研究,分析了各种几何模型对于血流动力学的影响,并通过临床的对比得到了定性上的验证。为进一步探索动脉瘤治疗手段,本文将两种螺旋支架数字化置入个体化病人动脉瘤几何模型中,一方面通过数值模拟对临床治疗给出了理论上的解释,另一方面对临床血管支架置入选择和置入位置给予了指导。
[Abstract]:Intracranial aneurysms are one of the most dangerous and common diseases that endanger human health. Hemodynamics, as a major factor affecting the generation, development, rupture and treatment of intracranial aneurysms, has attracted wide attention of scholars both at home and abroad. In clinical treatment, interventional therapy with blood flow diversion stent and coil embolization has been achieved. However, the traditional clinical trials are faced with the difficulties of high risk, long cycle and high cost. At present, individual numerical experiments based on medical images are favored. Most of the existing numerical methods use various computational flows. Body mechanics (CFD) software is limited by the complex geometry of blood vessels, the characteristics of blood flow and the low computational efficiency.
In recent years, lattice Boltzmann method (LBM) has attracted more and more attention because of its rapid development in computational fluid dynamics. LB method has its natural advantages in the generality of models, the ability to deal with complex boundaries and the efficiency of computation. It is suitable for the simulation and analysis of intracranial aneurysm hemodynamics. As an effective numerical method, the method is used to solve various partial differential equations, such as convection-diffusion equation, reaction-diffusion equation and Poisson equation.
At present, there are some research work on the numerical simulation of aneurysm hemodynamics based on LBM, but most of the work on the geometric model of aneurysm is based on the two-dimensional model or the ideal three-dimensional model combined with cylinder and sphere, lacking of individual patient research; in the study of individual patient data, the import and export of numerical simulation. On this basis, the whole process of individualized hemodynamic simulation of intracranial aneurysms is studied by using LBM as the main numerical means: starting from the clinical acquired three-dimensional tomographic medical image data, a variety of lattice Boltzmann models are developed and implemented with the help of a graphics processor (GPU) parallel computing device. Individual patient's blood vessel image segmentation, geometric reconstruction, LBM computational grid processing and hemodynamics simulation.
The work of this paper includes two aspects: reconstruction of the geometric shape of aneurysm and numerical simulation of hemodynamics with complex boundary.
(1) By studying the characteristics of the lattice Boltzmann method and the image denoising, edge detection and image segmentation model based on PDE, this paper proposes a LB model which can efficiently solve image denoising, edge detection and image segmentation, and applies this model to the computed tomography image of intracranial aneurysms. In principle, the 3D geometric model of individual aneurysms can be accurately segmented. The model can not only be applied to medical images, but also has a good effect on contour detection and image segmentation of more complex natural images.
(2) In order to meet the needs of grid computing and clinical research, we have further improved the geometric model to make the geometric model more reasonable. Based on the results of image segmentation, we propose a vascular center line method to reconstruct tumor-bearing vessels and vascular stents. On the other hand, the branches near the aneurysms can be freely removed according to the needs of the study. Compared with the three-dimensional models reconstructed by traditional CFD software, the geometric model presented in this paper is more reasonable and can meet the design of various types of vascular stents.
In the numerical simulation of complex boundary hemodynamics,
(1) Based on the vascular geometry model, we developed a lattice Boltzmanr model with complex boundary to solve the Navier-Stokes equations describing hemodynamics. We also discussed the individualized inlet and outlet conditions of intracranial aneurysms. In addition, under the boundary conditions of the velocity inlet and the pressure outlet, the difference between the pulsatile velocity inlet and the steady velocity inlet is discussed. It is found that the flow state at the peak time of the pulsatile flow can be approximately simulated by using the mean value of the pulsatile velocity and the mean value of the pulsatile peak value as the steady velocity inlet.
(2) Combining with the problems in clinical treatment, we simulated the data of several patients with carotid aneurysms. Aiming at the design of stents, we studied the hemodynamic changes in aneurysms after implantation of different dense and different types of stents. With the increase of stent density, the same dense spiral mesh stent can inhibit the intratumoral velocity more effectively than single spiral stent. The effect of the branches near the aneurysm on the intratumoral hemodynamics was studied, and the velocity and flow pattern inside the aneurysm were analyzed. The flow field in the aneurysm is smaller when the diameter of the branch is larger or the branch is farther away from the aneurysm.
In a word, this paper takes the lattice Boltzmann method as the main numerical means, establishes the whole scheme of individual intracranial aneurysm hemodynamics simulation, and completes the design of LB algorithm under the high performance parallel platform of GPU. Compared with the CPU program, the acceleration ratio of nearly two orders of magnitude is obtained, which greatly improves the efficiency of numerical simulation algorithm. In order to further explore the treatment of aneurysms, two kinds of spiral stents were digitally implanted into the geometric models of individual patients with aneurysms. On the one hand, the numerical models were used. This paper provides a theoretical explanation for the clinical treatment, on the other hand, it provides guidance for the selection and placement of clinical vascular stents.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TP391.41;R739.41

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