时域扩散荧光层析技术基本原理与系统研究
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摘要
近红外扩散荧光层析成像技术(Fluorescence diffuse optical tomography, FDOT)作为一种最有前景的小动物成像手段渐渐突显出来。其目的是在特异性荧光探针的指引下,通过测量规则组织边界溢出的荧光信号,对生物体内部生理、病理过程在细胞或分子水平上实现在体动态观察。扩散层析成像技术能够对于目标区域进行全三维定位,并对其所聚集荧光探针的浓度进行量化的分析。时域技术的潜在优势在于通过解析激光脉冲激励下产生的荧光信号而直接获取荧光寿命信息,且能够同时重建荧光产率和寿命以及进行多组分分析。
本文提出了对于常用的无限平板透射模式及圆域层析模式的时域FDOT的成像重建算法,并且对算法进行了详细的描述。通过数值模拟验证对于算法的空间分辨率及噪声鲁棒性等方面进行了准确的评估。又设计相关实验系统,进一步通过实验验证结果证明算法的可行性。本文提出的时域FDOT算法是利用基于耦合扩散方程拉氏变换的广义脉冲谱技术和基于玻恩比的归一化逆问题模型,从而实现无限平板透射及圆柱层析模式下的图像重建。该方法采用外推边界条件下无限平板和二维圆域结构的扩散方程解析解。为了解决线性求逆过程中的病态问题,采用了代数重建技术进行相应的线性求逆。并通过引入一对实数拉氏变换因子,可实现荧光产率和寿命的同时重建。
尽管基于CCD相机的连续FDOT测量系统已被广泛接收,但光纤式系统具有的超高灵敏度和皮秒级别的时间分辨能力,使其在时域FDOT领域备受关注。如时间相关单光子计数(TCSPC)系统已经成功地在时域扩散光层析系统中得到了广泛地应用。本文针对提出的多维TCSPC系统,采用了基于时间分辨反透射测量技术的混浊介质光学参数重构方法,准确地测量了固态仿体和液态仿体的光学参数。
本文利用多通道的时间相关单光子计数系统对于透射模式及圆域层析模式的时域FDOT重建算法的可靠性及可行性进行实验验证。其中所用平板型及圆柱型实验仿体中的荧光靶向区域由荧光试剂及1%的类脂肪乳的混合溶液构成。实验中采用了已被广泛的应用于生物学和生物医学研究中的生物组织荧光标记物-Cy5.5和吲哚菁绿。实验结果表明提出的重建算法对于目标体的位置和形状都进行了较准确的重建。但为了提高时域FDOT技术的成像效果,在系统优化,算法开发方及实验量化等方面仍存在大量的工作需要完成。
Near-infrared Fluorescent Diffuse Optical Tomography (FDOT) is emerging as a promising tool for small animal imaging. The modality, with the aid of specific fluorescent probes, aims at in vivo visualizing interior cellular and molecular events from fluorescence signals measured on boundary of an intact tissue. FDOT enables both three-dimensional localization of the targeted areas and quantization of the local concentration of the fluorochromes. The time domain technique offers the potential advantages of directly extracting the lifetime information through temporally resolving the fluorescence responses to a pulsed excitation, and has additionally the favorite performances of simultaneously recovering fluorescent yield and lifetime distributions, as well as resolving multiple components.
This thesis presents the methodology of time-domain FDOT for slab and circular geometries that are commonly used in practice, involving image reconstruction algorithm, numerical simulations, instrumentation of a multi-channel time-resolved imaging system, and experimental validations. The algorithm is based on a linear generalized pulse spectrum technique that employs the analytical solution to the Laplace-transformed time-domain photon diffusion equation to construct a Born normalized inverse model, which can overcome the impact of the instrumental response function and therefore eliminate the requirement for calibrating the time-origins and the coupling factors of the system. The resultant linear inversions are solved using an algebraic reconstruction technique. A pair of real domain transform-factors is introduced to separate the fluorescent yield and lifetime images.
Despite the wide adoption of a CCD camera to continuous-wave FDOT, a fiber-based instrumentation is attractive in time-domain FDOT regime since it can make full use of well-established ultra-high sensitive and ps time-resolved detection techniques, such as a time-correlated single photon counting (TCSPC) technique that have been widely used in time-domain diffuse optical tomography with a great success. Based on the proposed multi-channel TCSPC system, a method for determining the optical properties of turbid medium is developed using time-resolved reflection and transmission measurements, and validated on solid and liquid phantoms.
The feasibility and reliability of the time-domain FDOT methodology are experimentally validated with the multi-channel TCSPC system, on slab and cylinder phantoms, each embedding one or two fluorescent targets made from mixture of 1%-Intralipid solution and Cy5.5 or Indocyanine green (ICG) agent, the two fluorescent agents widely used in biological and biomedical studies. The results show that the approach retrieves the positions and shapes of the targets with a reasonable accuracy. Nevertheless, an investigation must be made in depth on system optimization of the measurement system, modification of the image reconstruction methodology and assessment of FDOT quantification.
本文提出了对于常用的无限平板透射模式及圆域层析模式的时域FDOT的成像重建算法,并且对算法进行了详细的描述。通过数值模拟验证对于算法的空间分辨率及噪声鲁棒性等方面进行了准确的评估。又设计相关实验系统,进一步通过实验验证结果证明算法的可行性。本文提出的时域FDOT算法是利用基于耦合扩散方程拉氏变换的广义脉冲谱技术和基于玻恩比的归一化逆问题模型,从而实现无限平板透射及圆柱层析模式下的图像重建。该方法采用外推边界条件下无限平板和二维圆域结构的扩散方程解析解。为了解决线性求逆过程中的病态问题,采用了代数重建技术进行相应的线性求逆。并通过引入一对实数拉氏变换因子,可实现荧光产率和寿命的同时重建。
尽管基于CCD相机的连续FDOT测量系统已被广泛接收,但光纤式系统具有的超高灵敏度和皮秒级别的时间分辨能力,使其在时域FDOT领域备受关注。如时间相关单光子计数(TCSPC)系统已经成功地在时域扩散光层析系统中得到了广泛地应用。本文针对提出的多维TCSPC系统,采用了基于时间分辨反透射测量技术的混浊介质光学参数重构方法,准确地测量了固态仿体和液态仿体的光学参数。
本文利用多通道的时间相关单光子计数系统对于透射模式及圆域层析模式的时域FDOT重建算法的可靠性及可行性进行实验验证。其中所用平板型及圆柱型实验仿体中的荧光靶向区域由荧光试剂及1%的类脂肪乳的混合溶液构成。实验中采用了已被广泛的应用于生物学和生物医学研究中的生物组织荧光标记物-Cy5.5和吲哚菁绿。实验结果表明提出的重建算法对于目标体的位置和形状都进行了较准确的重建。但为了提高时域FDOT技术的成像效果,在系统优化,算法开发方及实验量化等方面仍存在大量的工作需要完成。
Near-infrared Fluorescent Diffuse Optical Tomography (FDOT) is emerging as a promising tool for small animal imaging. The modality, with the aid of specific fluorescent probes, aims at in vivo visualizing interior cellular and molecular events from fluorescence signals measured on boundary of an intact tissue. FDOT enables both three-dimensional localization of the targeted areas and quantization of the local concentration of the fluorochromes. The time domain technique offers the potential advantages of directly extracting the lifetime information through temporally resolving the fluorescence responses to a pulsed excitation, and has additionally the favorite performances of simultaneously recovering fluorescent yield and lifetime distributions, as well as resolving multiple components.
This thesis presents the methodology of time-domain FDOT for slab and circular geometries that are commonly used in practice, involving image reconstruction algorithm, numerical simulations, instrumentation of a multi-channel time-resolved imaging system, and experimental validations. The algorithm is based on a linear generalized pulse spectrum technique that employs the analytical solution to the Laplace-transformed time-domain photon diffusion equation to construct a Born normalized inverse model, which can overcome the impact of the instrumental response function and therefore eliminate the requirement for calibrating the time-origins and the coupling factors of the system. The resultant linear inversions are solved using an algebraic reconstruction technique. A pair of real domain transform-factors is introduced to separate the fluorescent yield and lifetime images.
Despite the wide adoption of a CCD camera to continuous-wave FDOT, a fiber-based instrumentation is attractive in time-domain FDOT regime since it can make full use of well-established ultra-high sensitive and ps time-resolved detection techniques, such as a time-correlated single photon counting (TCSPC) technique that have been widely used in time-domain diffuse optical tomography with a great success. Based on the proposed multi-channel TCSPC system, a method for determining the optical properties of turbid medium is developed using time-resolved reflection and transmission measurements, and validated on solid and liquid phantoms.
The feasibility and reliability of the time-domain FDOT methodology are experimentally validated with the multi-channel TCSPC system, on slab and cylinder phantoms, each embedding one or two fluorescent targets made from mixture of 1%-Intralipid solution and Cy5.5 or Indocyanine green (ICG) agent, the two fluorescent agents widely used in biological and biomedical studies. The results show that the approach retrieves the positions and shapes of the targets with a reasonable accuracy. Nevertheless, an investigation must be made in depth on system optimization of the measurement system, modification of the image reconstruction methodology and assessment of FDOT quantification.
引文
[1] T. F. Massoud, S. S. Gambhir, Molecular imaging in living subjects: seeing fundamental biological processes in a new light, Genes Dev., 2003, 17(5): 545-580.
[2] R. Weissleder, Molecular imaging: Exploring the next frontier, Radiology, 1999, 212(3): 609-614.
[3] R. weissleder, U. Mamood, Molecular Imaging, Radiology , 2001, 219(2): 316-333
[4] G. D. Lucker, D. Piwnica-Worms, Molecular imaging in vivo with PET and SPECT, Acad.Radiol, 2001, 8: 4-14.
[5] R. Weissleder, Scaling down imaging: Molecular mapping of cancer in mice, Nature Reviews Cancer, 2002, 2(1): 11-18.
[6] H. R. Herschman, Molecular imaging: looking at problems, seeing solutions, Science, 2003, 302(5645): 605-608.
[7] J. K. Willmann, N. V. Bruggen, L. M. Dinkelborg, et al, Molecular imaging in drug development, Nature Reviews Drug Discovery, 2008, 7(7): 591-607.
[8] E. M. C. Hillman, A. Moore, All-optical anatomical co-registration for molecular imaging of small animals using dynamic contrast, Nature photonics, 2007, 1: 526-530.
[9] V. Ntziachristos, J. Ripoll, L.V. Wang, et al. Looking and listening to light: the evolution of whole-body photonic imaging, Nature Biotechnology, 2005, 23(3): 313-320.
[10]章鲁,陈瑛等,分子成像及医学图像分析,上海:科学技术出版社,2009.30-40。
[11] R. Weissleder, Mikael J. Pittet, Imaging in the era of molecular oncology, Nature, 2008, 452(3): 580-589.
[12] G. Strangman, D.A. Boas, J.P. Sutton, Non-invasive neroimaging using near-infrared Light, Biol. Psychiatry, 2002, 52: 679-693.
[13] A. Zaheer, R. E. Lenkinski, et al, In vivo near-infrared fluorescence imaging of osteoblastic activity, Nature biotechnology , 2001, 19: 1148-1154.
[14] Umar Mahmood, Ralph Weissleder, Near-infrared optical imaging of proteases in cancer, Molecular cancer therapeutics, 2003, 2: 489-496.
[15] S. R. Arridge, M. Schweiger, D. T. Delpy, Iterative reconstruction of near-infrared absorption images, Proceedings of SPIE, 1992, 1767: 372-383.
[16] R. J. Grable, D.P. Rohle, K. L. A. Sastray, Optical tomography breast imaging, Proc. SPIE, 2004, 2979: 197-210.
[17] H. Dehghani, B. W. Pogue, S. P. Poplack, et al, Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom and clinical results, Appl. Opt. ,2003, 42: 135-145
[18] J. C. Hebden, et al, Three-dimensional optical tomography of the premature infant brian, Phys. Med. Bol., 2002,47:.4155-4166.
[19] A. P. Gibson , T. Austin, N. L. Everdell, et al, Three-dimensional whole–head optical tomography of passive motor evoked responses in the neonate, Neuroimage, 2006,30: 521-528.
[20] J. C. Hebden, A. Gibson, T. Austin, et al, Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography, Phys. Med. Biol. , 2004, 49: 1117-1130.
[21] R. Weissleder, C. H. Tung, et al, In vivo imaging of tumors with protease- activated near-infrared fluorescent probes, Nature Biotechnology, 1999, 17:375-378.
[22] E. M. Sevick-Muraca, J. P. Houston, M. Gurfinkel, Fluorescence-enhanced near infrared diagnostic imaging with contrast agent, Curr. Opin. Chem. Biol., 2002, 6: 642-650.
[23] A. B. Milstein, S. Oh, K. J. Webb, et al, Fluorescence optical diffusion tomography, Appl. Opt., 2003,42: 3081-3094.
[24] A. Corlu, R. Choe, T. Durduran, et al, Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans, 2007, 15(11): 6696-6716.
[25] V. Ntziachristos, C. H. Tung, C. Bremer, et al, Fluorescence molecular tomography resolves protease activity in vivo, Nature Med., 2002, 8: 757-760.
[26] V. Ntziachristos, C. Bremer, R. Weissleder, Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging, European Radiology, 2003, 13: 195-208.
[27] A. D. Klose, U. Netz, J. Beuthan, et al, Optical tomography using the time independent equation of radiative transfer. Part 1: forward model, Journal of quantitative spectroscopy & radiative transfer, 2002, 72: 691-713.
[28] A. D. Klose, A. H. Hieischer, Optical tomography using the time-independent equation of radiative transfer. Part 2: inverse model, Journal of quantitative spectroscopy & radiative transfer, 2002, 72: 715-732.
[29]徐可欣,高峰,赵会娟.生物医学光子学.北京:中国科学出版社,2007
[30] R. C. Haskell, L.O. Svaasand, T. T. Tsay, et al, Boundary conditions for the diffusion equation in radiative transfer, J. Opt. Soc. Am., 1994, 11: 2727-2741.
[31]盛剑霓,工程电磁场的数值分析,西安:西安交通大学出版社,1991。
[32]李开泰,黄艾香,黄庆怀,有限元方法及其应用,西安:西安交通大学出版社,1992。
[33]曾余庚,刘京生,张雪阳,有限元法与边界元法,西安:西安电子科技大学出版社,1991。
[34]高峰,牛憨笨,张焕文,超短激光脉冲作用下生物组织体光学响应的时域和频域分析-Dirichlet边界条件和无向点激励源,光子学报,1997,26:865-876。
[35] X. Y. Lin, Y. M. Chen., A. generalized pulse-spectrum technique (GPST) for determininge quations, SIAM J .Sci. Stat. Comput., 1987, 8(1): 436-445.
[36] Y. M. Chen, Generalized pulse-spectrum technique, Geophysics, 1985, 50: 1664-1675.
[37]韩波,刘家琦等,广义脉冲谱技术的一个新形式及其应用,计算物理,1995, 12(3): 349-354.
[38] F. Gao, H. J. Zhao, Y. Yamada, et al. Time-resolved diffuse optical tomography using a modified generalized Pulse Spectrum Technique, IEICE Trans. Inform. & Syst., 2002, 85(1): 133-142.
[39] F. Gao, H. J. Zhao, Y. Yamada, A linear, featured-data scheme for image reconstruction in time-domain fluorescence molecular tomography, Opt. Exp., 2006, 14(16): 7109-7124.
[40] L. M. Zhang, F. Gao, H. Y. He, H. J. Zhao, Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors, Opt. Exp., 2008 , 16(10): 7214-7223.
[41] V. Ntziachristos, R. Weissleder, Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation, Opt. Lett., 2001, 26(12): 893-895.
[42] A. Soubret, J. Ripoll and V. Ntziachristos, Accuracy of Fluorescent Tomography in the presence of heterogeneities: study of the normalized Born Ratio, IEEE Tans. Med. Imaging, 2005, 24(10): 1377-1386.
[43] D. Hyde, E. Miller, D. H. Brooks, et al , A statistical approach to inverting the Born Ratio, IEEE Tans. Med. Imaging, 2007, 26(7): 893-905.
[44] R. Gordon, R. Bender, G.T. Herman, Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography, J.theor. Biol, 1970, 29: 471-481.
[45] K.T. Ladas, A. J. Devaney, Generalized ART algorithm for diffraction tomography, Inverse Problems, 1991, 7: 109-125.
[46] G. T.赫尔曼,由投影重建图像-CT的理论基础,北京:科学出版社,1985。
[47] F. Gao, P. Poulet,Y. Yamada, Simultaneous mapping of absorption and scattering coefficients from a three-dimensional model of time-resolved optical tomography, App. Opt. , 2001, 39(31): 5898-5910.
[48] A. T. N. Kumar, J. Skoch, B. J. Bacskai, Fluorescent-lifetime-based tomography for turbid media, Opt. Lett., 2005, 30(24): 3347-3349.
[49]王竹溪,郭敦仁等,特殊函数概论,北京:科学出版社,1979。
[50] W. Becker,屈军乐,高峰,高级时间相关单光子计数技术,北京:科学出版社,2009。
[51]高峰,和慧园,马烝,基于时间分辨反射测量的混浊介质光学参数计算方法,天津大学学报,2008, 41(6): 757-761.
[52] M. S. Patterson, B. Chance, B. C. Wilson, Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties, App. Opt., 1989, 28(12): 2331-2336.
[53] H. J. Staveren, J. M. Christian, et al, Light scattering in Intralipid-10% in the wavelength range of 400-1100nm, Appl. Opt., 1991, 30(31): 4507-4514.
[54] S. T. Flock, S. L. Jacques, B. C. Wilson, et al. Optical properties of Intralipid: A phantom medium for light propagation studies, Lasers in Surgery and Medicine, 1992, 12(5): 510-519.
[55] I. Texier, J. Razkin, et al, Activatable probes for non- invasive small animal fluorescence imaging, Nuclear instruments and methods in physics research , 2007, 571: 165-168.
[2] R. Weissleder, Molecular imaging: Exploring the next frontier, Radiology, 1999, 212(3): 609-614.
[3] R. weissleder, U. Mamood, Molecular Imaging, Radiology , 2001, 219(2): 316-333
[4] G. D. Lucker, D. Piwnica-Worms, Molecular imaging in vivo with PET and SPECT, Acad.Radiol, 2001, 8: 4-14.
[5] R. Weissleder, Scaling down imaging: Molecular mapping of cancer in mice, Nature Reviews Cancer, 2002, 2(1): 11-18.
[6] H. R. Herschman, Molecular imaging: looking at problems, seeing solutions, Science, 2003, 302(5645): 605-608.
[7] J. K. Willmann, N. V. Bruggen, L. M. Dinkelborg, et al, Molecular imaging in drug development, Nature Reviews Drug Discovery, 2008, 7(7): 591-607.
[8] E. M. C. Hillman, A. Moore, All-optical anatomical co-registration for molecular imaging of small animals using dynamic contrast, Nature photonics, 2007, 1: 526-530.
[9] V. Ntziachristos, J. Ripoll, L.V. Wang, et al. Looking and listening to light: the evolution of whole-body photonic imaging, Nature Biotechnology, 2005, 23(3): 313-320.
[10]章鲁,陈瑛等,分子成像及医学图像分析,上海:科学技术出版社,2009.30-40。
[11] R. Weissleder, Mikael J. Pittet, Imaging in the era of molecular oncology, Nature, 2008, 452(3): 580-589.
[12] G. Strangman, D.A. Boas, J.P. Sutton, Non-invasive neroimaging using near-infrared Light, Biol. Psychiatry, 2002, 52: 679-693.
[13] A. Zaheer, R. E. Lenkinski, et al, In vivo near-infrared fluorescence imaging of osteoblastic activity, Nature biotechnology , 2001, 19: 1148-1154.
[14] Umar Mahmood, Ralph Weissleder, Near-infrared optical imaging of proteases in cancer, Molecular cancer therapeutics, 2003, 2: 489-496.
[15] S. R. Arridge, M. Schweiger, D. T. Delpy, Iterative reconstruction of near-infrared absorption images, Proceedings of SPIE, 1992, 1767: 372-383.
[16] R. J. Grable, D.P. Rohle, K. L. A. Sastray, Optical tomography breast imaging, Proc. SPIE, 2004, 2979: 197-210.
[17] H. Dehghani, B. W. Pogue, S. P. Poplack, et al, Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom and clinical results, Appl. Opt. ,2003, 42: 135-145
[18] J. C. Hebden, et al, Three-dimensional optical tomography of the premature infant brian, Phys. Med. Bol., 2002,47:.4155-4166.
[19] A. P. Gibson , T. Austin, N. L. Everdell, et al, Three-dimensional whole–head optical tomography of passive motor evoked responses in the neonate, Neuroimage, 2006,30: 521-528.
[20] J. C. Hebden, A. Gibson, T. Austin, et al, Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography, Phys. Med. Biol. , 2004, 49: 1117-1130.
[21] R. Weissleder, C. H. Tung, et al, In vivo imaging of tumors with protease- activated near-infrared fluorescent probes, Nature Biotechnology, 1999, 17:375-378.
[22] E. M. Sevick-Muraca, J. P. Houston, M. Gurfinkel, Fluorescence-enhanced near infrared diagnostic imaging with contrast agent, Curr. Opin. Chem. Biol., 2002, 6: 642-650.
[23] A. B. Milstein, S. Oh, K. J. Webb, et al, Fluorescence optical diffusion tomography, Appl. Opt., 2003,42: 3081-3094.
[24] A. Corlu, R. Choe, T. Durduran, et al, Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans, 2007, 15(11): 6696-6716.
[25] V. Ntziachristos, C. H. Tung, C. Bremer, et al, Fluorescence molecular tomography resolves protease activity in vivo, Nature Med., 2002, 8: 757-760.
[26] V. Ntziachristos, C. Bremer, R. Weissleder, Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging, European Radiology, 2003, 13: 195-208.
[27] A. D. Klose, U. Netz, J. Beuthan, et al, Optical tomography using the time independent equation of radiative transfer. Part 1: forward model, Journal of quantitative spectroscopy & radiative transfer, 2002, 72: 691-713.
[28] A. D. Klose, A. H. Hieischer, Optical tomography using the time-independent equation of radiative transfer. Part 2: inverse model, Journal of quantitative spectroscopy & radiative transfer, 2002, 72: 715-732.
[29]徐可欣,高峰,赵会娟.生物医学光子学.北京:中国科学出版社,2007
[30] R. C. Haskell, L.O. Svaasand, T. T. Tsay, et al, Boundary conditions for the diffusion equation in radiative transfer, J. Opt. Soc. Am., 1994, 11: 2727-2741.
[31]盛剑霓,工程电磁场的数值分析,西安:西安交通大学出版社,1991。
[32]李开泰,黄艾香,黄庆怀,有限元方法及其应用,西安:西安交通大学出版社,1992。
[33]曾余庚,刘京生,张雪阳,有限元法与边界元法,西安:西安电子科技大学出版社,1991。
[34]高峰,牛憨笨,张焕文,超短激光脉冲作用下生物组织体光学响应的时域和频域分析-Dirichlet边界条件和无向点激励源,光子学报,1997,26:865-876。
[35] X. Y. Lin, Y. M. Chen., A. generalized pulse-spectrum technique (GPST) for determininge quations, SIAM J .Sci. Stat. Comput., 1987, 8(1): 436-445.
[36] Y. M. Chen, Generalized pulse-spectrum technique, Geophysics, 1985, 50: 1664-1675.
[37]韩波,刘家琦等,广义脉冲谱技术的一个新形式及其应用,计算物理,1995, 12(3): 349-354.
[38] F. Gao, H. J. Zhao, Y. Yamada, et al. Time-resolved diffuse optical tomography using a modified generalized Pulse Spectrum Technique, IEICE Trans. Inform. & Syst., 2002, 85(1): 133-142.
[39] F. Gao, H. J. Zhao, Y. Yamada, A linear, featured-data scheme for image reconstruction in time-domain fluorescence molecular tomography, Opt. Exp., 2006, 14(16): 7109-7124.
[40] L. M. Zhang, F. Gao, H. Y. He, H. J. Zhao, Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors, Opt. Exp., 2008 , 16(10): 7214-7223.
[41] V. Ntziachristos, R. Weissleder, Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation, Opt. Lett., 2001, 26(12): 893-895.
[42] A. Soubret, J. Ripoll and V. Ntziachristos, Accuracy of Fluorescent Tomography in the presence of heterogeneities: study of the normalized Born Ratio, IEEE Tans. Med. Imaging, 2005, 24(10): 1377-1386.
[43] D. Hyde, E. Miller, D. H. Brooks, et al , A statistical approach to inverting the Born Ratio, IEEE Tans. Med. Imaging, 2007, 26(7): 893-905.
[44] R. Gordon, R. Bender, G.T. Herman, Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography, J.theor. Biol, 1970, 29: 471-481.
[45] K.T. Ladas, A. J. Devaney, Generalized ART algorithm for diffraction tomography, Inverse Problems, 1991, 7: 109-125.
[46] G. T.赫尔曼,由投影重建图像-CT的理论基础,北京:科学出版社,1985。
[47] F. Gao, P. Poulet,Y. Yamada, Simultaneous mapping of absorption and scattering coefficients from a three-dimensional model of time-resolved optical tomography, App. Opt. , 2001, 39(31): 5898-5910.
[48] A. T. N. Kumar, J. Skoch, B. J. Bacskai, Fluorescent-lifetime-based tomography for turbid media, Opt. Lett., 2005, 30(24): 3347-3349.
[49]王竹溪,郭敦仁等,特殊函数概论,北京:科学出版社,1979。
[50] W. Becker,屈军乐,高峰,高级时间相关单光子计数技术,北京:科学出版社,2009。
[51]高峰,和慧园,马烝,基于时间分辨反射测量的混浊介质光学参数计算方法,天津大学学报,2008, 41(6): 757-761.
[52] M. S. Patterson, B. Chance, B. C. Wilson, Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties, App. Opt., 1989, 28(12): 2331-2336.
[53] H. J. Staveren, J. M. Christian, et al, Light scattering in Intralipid-10% in the wavelength range of 400-1100nm, Appl. Opt., 1991, 30(31): 4507-4514.
[54] S. T. Flock, S. L. Jacques, B. C. Wilson, et al. Optical properties of Intralipid: A phantom medium for light propagation studies, Lasers in Surgery and Medicine, 1992, 12(5): 510-519.
[55] I. Texier, J. Razkin, et al, Activatable probes for non- invasive small animal fluorescence imaging, Nuclear instruments and methods in physics research , 2007, 571: 165-168.