基于数值与随机统计方法的光学成像光传输问题研究
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摘要
作为一种新兴的成像技术，分子成像在近十年来获得了飞速的发展，并已经在疾病诊断、肿瘤检测和药物研发中获得了广泛的应用。这种技术可以在分子和细胞水平上实现对生物体生理病理变化的实时、无创、动态的成像，为研究特定基因功能、生物生长发育、疾病发生发展过程、药物治疗效果等提供了获取信息的有效手段。在分子成像的各种模态中，光学分子成像技术拥有高灵敏度、高性价比和高安全性等独特优势，因此成为近年来本领域中的研究热点。
光学分子成像的核心问题之一是如何对光在生物组织中的传输情况进行准确建模和快速求解。本文的研究工作即主要围绕这一问题而展开，通过分析各种光传输模型的特点，利用数值方法与随机统计方法对光学分子成像中的光传输问题进行了深入的研究。涉及的主要研究内容包括：
1.由于光学分子成像的真实实验非常昂贵、复杂和耗时，作者提出了一种通过光学分子仿真软件平台（molecular optical simulation evironment, MOSE）来对光学分子成像中的光传输问题进行研究的方法。所提出的方法不但可以为逆向断层重建算法的研究提供实验数据，还可以为真实实验系统搭建过程中的设备选择提供参考依据。其中蒙特卡洛方法（Monte Carlo, MC）被用来模拟光在生物组织中的传输过程。由于MC方法计算量大、比较耗时，本文提出了一种基于中央处理器(central processing unit, CPU)并行计算的方法对MC方法进行加速。这种方法将MC方法中光子包的仿真按比例分配给几台通过局域网连接的PC机进行并行计算，有效地降低了并行计算系统的成本。由于具有高分辨率的优势，非接触式成像成为了目前光学分子成像中探测系统的主流，这需要对光在自由空间中的传输进行研究。作者以前面MC方法提供的生物体表面光强分布数据作为输入，通过混合辐射度学理论对非接触式光学探测系统进行了研究，并设计了一系列的模拟仿真与真实实验来验证所提出方法的有效性。
2.提出了一种基于点加权最小二乘无网格法（point weighted least-squaresMeshless, PWLS）的生物组织光传输数值求解方法。由于较小的计算量与特定条件下可以接受的计算精度，漫射方程是目前光学分子成像中应用最广泛的生物组织光传输模型。漫射方程通常采用有限元等数值方法进行求解。但是有限元方法过分依赖于整个求解域的网格剖分，而对于类似生物组织这种形状极不规则的求解域的网格剖分是非常困难的，甚至昂贵的商业软件也难以很好的处理。本文所使用的PWLS无网格方法只需要在求解域内布置一系列规则分布的配点即可进行数值求解，从而可以避免有限元方法中困难而又耗时的网格剖分工作。此外，这种方法通过最小化控制方程和边界条件在每个配点上产生的残差加权平方和，来建立光源功率密度和光子流率密度之间的关系，不需要进行任何数值积分运算，非常适合应用于非规则求解域的求解。基于数字鼠模型的数值仿真实验和基于仿体的真实实验验证了该方法的准确性和有效性。
3.提出了一种基于图形处理器（graphic processing unit, GPU）并行计算加速的辐射传输方程（radiative transport equation, RTE）数值求解方法。RTE方程被公认为最为准确的生物组织光传输模型，离散坐标法（discrete ordinate method, SN）是目前最为常用的RTE方程数值求解方法。通过将光子辐射率的连续角度分布离散化，SN方法将RTE方程转化为了一系列的离散坐标方程，然后通过源迭代方法（source iteration, SI）进行求解。虽然SN方法非常精确且易于实现，然而其求解过程极为耗时。SI每步迭代的巨大计算量是造成SN方法时间代价大的主要原因之一。本文通过充分构造和寻找每一步SI迭代中所存在的计算独立性，通过GPU并行计算来减少其所消耗的时间。两个层次的计算独立性被用于进行并行计算：第一个层次是离散坐标方程层次，第二个层次是空间离散单元层次。通过使用前一次迭代的光子辐射率来近似计算边界反射，所提出的方法构造了离散坐标方程层次的计算独立性；由于计算独立性并不对任意的两个空间离散单元成立，一种单元扫描（element sweeping, ES）策略被提出来寻找存在计算独立性的特定空间单元。一种被称为通用计算设备架构（compute unified device architecture,CUDA）的GPU并行计算框架为本文的工作提供了一种高性能且低成本的并行计算解决方案。在NVIDIAGTX260显卡及Intel Xeon处理器W3505上进行的仿真对比实验验证了所提出方法的加速效果。
Molecular imaging is a promising and rapidly developing biomedical researchfield, which enables the visualization of the cellular function and the follow-up of themolecular process in living organisms noninvasively, and can be applied to the earlydisease diagnosis, tumor cell detection and drug improvement. Among molecularimaging modalities, optical molecular has become a research focus over the past yearsbecause of its significant advantages in sensitivity, cost-effectiveness and non-ionizingradiation.
The study of photon transport is one of the most important research contents inoptical imaging and our work is focused on this issue. According to the analysis on theactual demand of optical imaging and the characters of the different light transportmodels, we employed the numerical and random statistic methods to research thephoton transport issue of optical imaging. The main work of this dissertation can besummarized as follows:
1. Since the physical experiment is usually complicated and expensive for theoptical imaging, research methods based on simulation platforms have obtainedextensive attention. We developed a simulation method to research optical imagingthrough a soft platform named Molecular Optical Simulation Environment (MOSE). Inthis method, Monte Carlo (MC) method was used to simulate photon transport inbiological tissues. A central processing unit (CPU) parallelization strategy wasemployed to improve the computational efficiency of MC method. In this strategy, thephoton packages which need to be simulated in MC method were distributed to severalPCs which are connected by LAN with proper proportion, so the cost of the parallelcomputation system could be reduced. For the character of high resolution, thenon-contact imaging system has become quite popular recently, so the research for thephoton progress in free space is necessary. With the photon flux distribution on thesurface of the tissues which produced by MC method, we employed the hybridradiosity-radiance theorem to simulate the non-contact measurement mode of opticalimaging. A serial of simulated and physicial experiments were used to varify theefficiency of the proposed method.
2. A point weighted least-squares (PWLS) meshless method is proposed to obtainthe numerical solution of the light transport in tissues. For its acceptable accuracy inthe case of high scattering and small computation cost, the diffusion equation (DE) wasthe most popular photon transport model in optical imaging. The numerical solution of DE is usually obtained by the finite element method (FEM). However, theeffectiveness of FEM is heavily affected by the finite element mesh which is used todiscretize the domain of interested and construct the approximation function.Unfortunately, the generation of high quality mesh for the three-dimensional irregulardomain with complex geometrical structure is still a challenging and time-consumingtask. The proposed method does not need any mesh to construct the approximationfunction, so that complicated and time-consuming mesh generation can be avoid.Moreover, the linear relationship between source distribution and photon flux densitywas established by minimizing the weighted residuals quadratic sum of all collocationpoints for governing equation and boundary condtion, so no numerical integral isneeded. This proposed method is suitable to be applied to the domain with complexstructure because of the pre mentioned characters. The performance of the proposedmethod was dementrate by the experiments with phantom and numerical mouse.
3. A graphic processing unit (GPU) parallel accelerated algorithm was proposed toobtain the numerical solution for the radiative equation (RTE). RTE is considered asthe most accurate model for light transport in tissues. The discrete is a widely usedmethod to obtain the numerical solution of RTE. The discrete ordinates reduce the RTEto a serial of differential equations which can be solved by source iteration (SI).However, the tremendous time consumption of SI, which is partly caused by theexpensive computation of each SI step, limits its applications. Utilizing the calculationindependence on the levels of the discrete ordinate equations and spatial elements, theproposed method reduces the time cost of each SI step by parallel calculation. Thephoton reflection at the boundary was calculated based on the results of the last SI stepto ensure the calculation independence on the level of the discrete ordinate equation.An element sweeping strategy was proposed to detect the calculation independence onthe level of the spatial element. A GPU parallel frame called the compute unifieddevice architecture (CUDA) was employed to carry out the parallel computation. Thesimulation experiments, which were carried out with a PC of GTX260graphic cardand Xoen CPU, indicated that the time cost of each SI step can be reduced by morethan two orders of magnitudes with the proposed method.
光学分子成像的核心问题之一是如何对光在生物组织中的传输情况进行准确建模和快速求解。本文的研究工作即主要围绕这一问题而展开，通过分析各种光传输模型的特点，利用数值方法与随机统计方法对光学分子成像中的光传输问题进行了深入的研究。涉及的主要研究内容包括：
1.由于光学分子成像的真实实验非常昂贵、复杂和耗时，作者提出了一种通过光学分子仿真软件平台（molecular optical simulation evironment, MOSE）来对光学分子成像中的光传输问题进行研究的方法。所提出的方法不但可以为逆向断层重建算法的研究提供实验数据，还可以为真实实验系统搭建过程中的设备选择提供参考依据。其中蒙特卡洛方法（Monte Carlo, MC）被用来模拟光在生物组织中的传输过程。由于MC方法计算量大、比较耗时，本文提出了一种基于中央处理器(central processing unit, CPU)并行计算的方法对MC方法进行加速。这种方法将MC方法中光子包的仿真按比例分配给几台通过局域网连接的PC机进行并行计算，有效地降低了并行计算系统的成本。由于具有高分辨率的优势，非接触式成像成为了目前光学分子成像中探测系统的主流，这需要对光在自由空间中的传输进行研究。作者以前面MC方法提供的生物体表面光强分布数据作为输入，通过混合辐射度学理论对非接触式光学探测系统进行了研究，并设计了一系列的模拟仿真与真实实验来验证所提出方法的有效性。
2.提出了一种基于点加权最小二乘无网格法（point weighted least-squaresMeshless, PWLS）的生物组织光传输数值求解方法。由于较小的计算量与特定条件下可以接受的计算精度，漫射方程是目前光学分子成像中应用最广泛的生物组织光传输模型。漫射方程通常采用有限元等数值方法进行求解。但是有限元方法过分依赖于整个求解域的网格剖分，而对于类似生物组织这种形状极不规则的求解域的网格剖分是非常困难的，甚至昂贵的商业软件也难以很好的处理。本文所使用的PWLS无网格方法只需要在求解域内布置一系列规则分布的配点即可进行数值求解，从而可以避免有限元方法中困难而又耗时的网格剖分工作。此外，这种方法通过最小化控制方程和边界条件在每个配点上产生的残差加权平方和，来建立光源功率密度和光子流率密度之间的关系，不需要进行任何数值积分运算，非常适合应用于非规则求解域的求解。基于数字鼠模型的数值仿真实验和基于仿体的真实实验验证了该方法的准确性和有效性。
3.提出了一种基于图形处理器（graphic processing unit, GPU）并行计算加速的辐射传输方程（radiative transport equation, RTE）数值求解方法。RTE方程被公认为最为准确的生物组织光传输模型，离散坐标法（discrete ordinate method, SN）是目前最为常用的RTE方程数值求解方法。通过将光子辐射率的连续角度分布离散化，SN方法将RTE方程转化为了一系列的离散坐标方程，然后通过源迭代方法（source iteration, SI）进行求解。虽然SN方法非常精确且易于实现，然而其求解过程极为耗时。SI每步迭代的巨大计算量是造成SN方法时间代价大的主要原因之一。本文通过充分构造和寻找每一步SI迭代中所存在的计算独立性，通过GPU并行计算来减少其所消耗的时间。两个层次的计算独立性被用于进行并行计算：第一个层次是离散坐标方程层次，第二个层次是空间离散单元层次。通过使用前一次迭代的光子辐射率来近似计算边界反射，所提出的方法构造了离散坐标方程层次的计算独立性；由于计算独立性并不对任意的两个空间离散单元成立，一种单元扫描（element sweeping, ES）策略被提出来寻找存在计算独立性的特定空间单元。一种被称为通用计算设备架构（compute unified device architecture,CUDA）的GPU并行计算框架为本文的工作提供了一种高性能且低成本的并行计算解决方案。在NVIDIAGTX260显卡及Intel Xeon处理器W3505上进行的仿真对比实验验证了所提出方法的加速效果。
Molecular imaging is a promising and rapidly developing biomedical researchfield, which enables the visualization of the cellular function and the follow-up of themolecular process in living organisms noninvasively, and can be applied to the earlydisease diagnosis, tumor cell detection and drug improvement. Among molecularimaging modalities, optical molecular has become a research focus over the past yearsbecause of its significant advantages in sensitivity, cost-effectiveness and non-ionizingradiation.
The study of photon transport is one of the most important research contents inoptical imaging and our work is focused on this issue. According to the analysis on theactual demand of optical imaging and the characters of the different light transportmodels, we employed the numerical and random statistic methods to research thephoton transport issue of optical imaging. The main work of this dissertation can besummarized as follows:
1. Since the physical experiment is usually complicated and expensive for theoptical imaging, research methods based on simulation platforms have obtainedextensive attention. We developed a simulation method to research optical imagingthrough a soft platform named Molecular Optical Simulation Environment (MOSE). Inthis method, Monte Carlo (MC) method was used to simulate photon transport inbiological tissues. A central processing unit (CPU) parallelization strategy wasemployed to improve the computational efficiency of MC method. In this strategy, thephoton packages which need to be simulated in MC method were distributed to severalPCs which are connected by LAN with proper proportion, so the cost of the parallelcomputation system could be reduced. For the character of high resolution, thenon-contact imaging system has become quite popular recently, so the research for thephoton progress in free space is necessary. With the photon flux distribution on thesurface of the tissues which produced by MC method, we employed the hybridradiosity-radiance theorem to simulate the non-contact measurement mode of opticalimaging. A serial of simulated and physicial experiments were used to varify theefficiency of the proposed method.
2. A point weighted least-squares (PWLS) meshless method is proposed to obtainthe numerical solution of the light transport in tissues. For its acceptable accuracy inthe case of high scattering and small computation cost, the diffusion equation (DE) wasthe most popular photon transport model in optical imaging. The numerical solution of DE is usually obtained by the finite element method (FEM). However, theeffectiveness of FEM is heavily affected by the finite element mesh which is used todiscretize the domain of interested and construct the approximation function.Unfortunately, the generation of high quality mesh for the three-dimensional irregulardomain with complex geometrical structure is still a challenging and time-consumingtask. The proposed method does not need any mesh to construct the approximationfunction, so that complicated and time-consuming mesh generation can be avoid.Moreover, the linear relationship between source distribution and photon flux densitywas established by minimizing the weighted residuals quadratic sum of all collocationpoints for governing equation and boundary condtion, so no numerical integral isneeded. This proposed method is suitable to be applied to the domain with complexstructure because of the pre mentioned characters. The performance of the proposedmethod was dementrate by the experiments with phantom and numerical mouse.
3. A graphic processing unit (GPU) parallel accelerated algorithm was proposed toobtain the numerical solution for the radiative equation (RTE). RTE is considered asthe most accurate model for light transport in tissues. The discrete is a widely usedmethod to obtain the numerical solution of RTE. The discrete ordinates reduce the RTEto a serial of differential equations which can be solved by source iteration (SI).However, the tremendous time consumption of SI, which is partly caused by theexpensive computation of each SI step, limits its applications. Utilizing the calculationindependence on the levels of the discrete ordinate equations and spatial elements, theproposed method reduces the time cost of each SI step by parallel calculation. Thephoton reflection at the boundary was calculated based on the results of the last SI stepto ensure the calculation independence on the level of the discrete ordinate equation.An element sweeping strategy was proposed to detect the calculation independence onthe level of the spatial element. A GPU parallel frame called the compute unifieddevice architecture (CUDA) was employed to carry out the parallel computation. Thesimulation experiments, which were carried out with a PC of GTX260graphic cardand Xoen CPU, indicated that the time cost of each SI step can be reduced by morethan two orders of magnitudes with the proposed method.
引文
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