摘要
正电子断层发射成像(Positron Emission Tomography, PET)和弥散光学层析成像(Diffuse Optical Tomography, DOT)都是能够对生物组织进行定量功能成像的医学成像方式。前者借助放射性核素标记的分子探针对活体生物体内的生化过程进行显像；后者则利用人体对近红外光的透射窗,通过内在生色团获取组织光学参数的分布进而得到血氧代谢情况。
混合成像是当前医学成像领域发展的热点,不同成像方式的组合为科研和临床应用带来诸多益处。PET和DOT硬件系统能够较为方便的结合,图像可互相验证,互相补充,PET高分辨图像还可作为DOT先验信息。本文在对这两种成像方法分别研究的基础上,结合混合成像前沿研究方向,分别在硬件构建和图像重建算法方面的一些关键问题做了研究工作,主要内容和贡献如下。
硬件构建方面：
1.构建了适用于PET/DOT混合成像的小型平板PET系统,利用锗酸铋晶体配合新型位置灵敏型光电倍增管作为探测单元,给出了点源、线源等性能测试结果,还对小鼠进行了静态和动态成像实验。
2.开发适用于混合成像的高速数据采集系统：利用现场可编程门阵列(Field Programmable Gate Array,FPGA)技术处理位置分析电路输出的数字信号,进行各种控制和判断；利用光纤和标准并化、串化模块实现FPGA模块之间的高速通信；充分利用FPGA和光纤通信技术带来的性能提高,研究了适合特定系统的环状符合判断系统架构；研究了适用于特定系统的时钟同步方式。
3.对于DOT,根据混合成像需要,实现了时域信号转换到频域并进行校正的过程,制作固体体模进行实验。提供了一种新的实验方案,为方便的进行多频率成像提供了工作基础。
图像重建算法方面：
4.传统PET图像重建方法中都没有考虑系统矩阵的不确定性,不符合实际应用情况,影响了重建图像的质量。本文开创性的在PET图像重建过程中针对系统矩阵和采集过程中的不确定性,建立不确定性惩罚加权最小二乘估计框架,使用最小最大误差方法求解状态空间体系中的目标函数,得到系统扰动下的稳定解。在优化PET重建图像质量的同时,也能为DOT提供更加精确的先验信息。
5.在DOT图像重建中,为模拟光子在任意形状组织内的传输,传统上使用有限元方法将成像区域离散表达为节点和单元的组合来计算。本文引入无网格方法中的无网格伽辽金法,仅仅用节点来表达成像区域,避免了有限元方法繁杂的网格划分和调整过程,且方便根据需要随时调整节点分布。计算结果也表明该方法能够得到更精确的正问题解。
6.在利用无网格方法精确求解正问题的基础上,使用第二重自适应稀疏节点阵列作为重建基,求解DOT逆问题。给出了状态空间体系下优化表达式和重建策略。同时引入自适应算法,根据迭代过程中图像更新变化量自动调整稀疏节点阵列分布,在保证重建图像质量的同时,尽量减少了计算量,以适应当前计算机的计算能力。给出了无网格方法应用于DOT图像重建的表达式和参数的选择方式和具体结果,以仿真模型和实物体模实验为例,定量比较了无网格方法和有限元方法的计算时间和内存消耗与图像质量的关系。为进一步应用中采用数值方法的策略给出了参考。
Positron emission tomography (PET) and diffuse optical tomography (DOT) are quantitative functional medical imaging modalities. The former employs radio isotope labeled tracers and track their distribution and concentration in living tissues to get information about physiological metabolisms; the later utilizes the transmitting band of tissue to near infrared light to get optical parameter's distribution image and oxygen saturation.
Hybrid imaging is thoroughly researched all over the world recently. Different imaging modalities are combined to supply more information for research and clinical applications. Among them, the system of PET and DOT can be easily corporated, PET image with high resolution can be adopted as a priory information for DOT image reconstruction; moreover, the images of the two modalities are complementary in some cases, and can also validate each other in certain applications. This paper workes on the two modalities and tries to combine them. The main content and contributions of this paper are as followed.
System construction and experiments:
1. Construct planar PET system which is proper for hybrid imaging. BGO crystal is employed with flat panel position sensitive photo multiplier tube to construct the gamma ray detection unit. Initial tests are held, including point source test, line source test and mouse experiments.
2. Develop high speed coincidence detection and data acquisition unit basing on FPGA and fiber communication modules. The system is designed with circle shaped protocol, which can be easily corporate with new units.
3. For the purpose of hybrid imaging, use Hamamatsu TRS system to get time domain signals measured from self made solid phantoms, transform the data into frequency domain for reconstruction.
Reconstruction algorithms:
4. The consumption that the system probability matrix is exactly known in most statistical PET image reconstruction algorithms are not true and may influence the quality of reconstructed images. We propose an algorithm for PET image reconstruction for the real world case where the PET system model is subject to uncertainties. The method counts PET reconstruction as a regularization problem and the image estimation is achieved by means of an uncertainty weighted least squares framework. The performance of our work is evaluated with the Shepp-Logan simulated and real phantom data, which demonstrates significant improvements in image quality over the least squares reconstruction efforts. Finely reconstructed images can be used as a priory information for DOT image reconstruction.
5. Employ element free Galerkin method (EFG, one of mesh free methods) to simulate photon transport process in tissues, discretize imaging domain with a set of nodes, avoid the burdensome mesh generation and adjusting work in finite element method (FEM) and the node set can be easily adjusted. The forward calculation results are validated with Green's function.
6. Basing on mesh free representation of imaging domain, employ self-adopted sparse node set as reconstruction basis for DOT image reconstruction. The state space reconstruction formulas are given. Self-adopted algorithm promises the reconstruction quality and calculation consumption proper for contemporary computer servers. Compare FEM and EFG method in calculation consumption and image quality aspects, give advices on the choice of numerical methods in future applications.
引文
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