光谱差分策略在扩散近似模型和简化球谐近似模型中的应用

Application of spectral differential strategy in diffusion approximation model and simplified spherical harmonic approximation model

生物发光断层成像(Bioluminescence Tomography,BLT)是一种很有前途的在体分子成像工具,可以在细胞和分子水平上对生理和病理过程进行无创监测。BLT的重建精度受光传输模型误差和逆问题病态性影响,针对此问题,受高阶光传输模型可提高模型精度、多光谱方法可降低逆问题病态性的启发,本文将光谱差分理论和多光谱方法结合构建的光谱差分策略分别应用到基于扩散近似方程(Diffusion approximation Equation,DE)和三阶简化球谐近似方程(3rd Simplified spherical harmonic approximation equation,SP3)建立的光传输模型。首先,对这两种辐射传输方程(Radiative Transfer Equation,RTE)近似产生的误差进行分析,对比了光谱差分策略对两种光传输模型误差的衰减作用。前向仿真实验结果表明光谱差分策略能有效地减少DE和SP3的模型误差,对DE模型采用光谱差分,能够获得接近SP3模型的传输精度,并且降低高阶近似对运算时间和存储空间的高要求。在此基础上,将光谱差分策略分别应用到DE和SP3光传输模型进行光源重建。实验结果表明光谱差分策略在提高两种光传输模型精度的同时,缓解了BLT中逆问题的病态性,使光源重建的位置误差小于1 mm,在目标定位、形状恢复和图像对比度等方面取得了更准确的效果。相比于SP3模型平均耗时约1525 s,DE模型结合光谱差分策略平均耗时仅为34 s左右,较好地兼顾了重建精度和重建速率。

Bioluminescence tomography(BLT)is a promising in vivo molecular imaging tool that allows non-invasive monitoring of physiological and pathological processes at the cellular and molecular levels.The reconstruction accuracy of BLT is affected by the optical transmission model error and the ill-posedness of the inverse problem.The higher-order optical transmission model was able to improve the precision,while the multi-spectral method was able to alleviate the ill-posedness of the inverse problem.In this study,the spectral differential strategy,combining the spectral differential theory and multi-spectral method,was applied on the optical transmission model based on the diffusion approximation equation(DE)and third simplified spherical harmonic approximation equation(SP3).First,errors in these two radiative transfer equations(RTE)approximations were analyzed,and the attenuation effect on the error was compared when the spectral differential strategy was applied on two types of optical transmission models.The forward simulation experiment results showed that the spectral differential strategy can effectively reduce the model error of the DE and SP3models.The spectral differential strategy resulted in the transmission accuracy of the DE model resembling that of the SP3model,and decreased the high requirements on computing time and storage space of high-order approximation.On this basis,the spectral differential strategy was applied on the DE and SP3optical transmission models for light source reconstruction.The experimental results showed that the spectral differential strategy not only improves the accuracy of the two light transmission models,but also alleviates the ill-condition of the inverse problem in BLT,yields a location error of reconstructed source within 1 mm,and improves the accuracy of the light source reconstruction in target location,shape restoration,and image contrast.The average time required by the SP3model was approximately 1525 s.In contrast,the DE model combined with spectral differential strategy had an average time consumption of only approximately 34 s,resulting in balanced reconstruction accuracy and speed.