多光谱生物发光断层成像的光源形状重建
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摘要
生物发光断层成像(bioluminescence tomography,BLT)是一种利用生物体表面光强测量值重建内部光源分布的光学分子影像技术,为研究常用光传输模型对BLT重建光源形状的影响,该文在相同的模拟测量值条件下,对比研究了辐射传输方程的三阶简化球谐近似(third-order simplified spherical harmonics,SP3)模型和扩散近似(diffusion approxima-tion,DA)模型对光源形状的拟合能力。此外,为了减小重建问题的不适定性,重建中结合了多光谱测量数据和稀疏正则化方法。数字鼠模型上的仿真实验结果表明,基于SP3模型的多光谱BLT重建方法,在不同深度下的不同尺寸的单、双光源重建中均可以更为准确地重建光源的中心位置和形状。
Bioluminescence tomography is an optical molecular imaging technique that can retrieve the spatial distribution of internal sources from the surface intensity measurements. For investigating the influence of commonly used optical transmission models on the shape of reconstructed light source,a comparison study on the shape-fitting ability between the third-order simplified spherical harmonics model of radiation transfer equation and the diffusion equation was made with the same simulated measurements. Besides,multispectral data and sparse regularization were combined to reduce the ill-posedness of the BLT reconstruction problem. Simulation results on digital mouse models demonstrate that the proposed reconstruction method for multispectral BLT based on the SP3 model produced more accurate reconstruction results in center position and shape of the light source under different source settings including source numbers,sizes and depths.
Bioluminescence tomography is an optical molecular imaging technique that can retrieve the spatial distribution of internal sources from the surface intensity measurements. For investigating the influence of commonly used optical transmission models on the shape of reconstructed light source,a comparison study on the shape-fitting ability between the third-order simplified spherical harmonics model of radiation transfer equation and the diffusion equation was made with the same simulated measurements. Besides,multispectral data and sparse regularization were combined to reduce the ill-posedness of the BLT reconstruction problem. Simulation results on digital mouse models demonstrate that the proposed reconstruction method for multispectral BLT based on the SP3 model produced more accurate reconstruction results in center position and shape of the light source under different source settings including source numbers,sizes and depths.
引文
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[15]LIU K,YANG X,LIU D,et al.Spectrally resolved three-dimensional bioluminescence tomography with a level-set strategy[J].JOSA A,2010,27(6):1413-1423.
[16]YU J J,LI Q Y,WANG H Y.Source reconstruction for bioluminescence tomography via L1/2 regularization[J].Journal of Innovative Optical Health Sciences,2018,11(2):1750014.
[17]YU J J,LIU F,WU J,et al.Fast source reconstruction for bioluminescence tomography based on sparse regularization[J].IEEE Transactions on Biomedical Engineering,2010,57(10):2583-2586.
[18]GAO H,ZHAO H K.Multilevel bioluminescence tomography based on radiative transfer equation Part 2:Total variation and l1 datafidelity[J].Optics Express,2010,18(3):2894-2912.
[19]LIU K,LU Y J,TIAN J,et al.Evaluation of the simplified spherical harmonics approximation in bioluminescence tomography through heterogeneous mouse models[J].Optics Express,2010,18(20):20988-21002.
[20]HAN W M,CONG W X,WANG G.Mathematical study and numerical simulation of multispectral bioluminescence tomography[J].International Journal of Biomedical Imaging,2006(2006):1-10.
[21]CHAUDHARI A J,DARVAS F,BADING J R,et al.Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging[J].Physics in Medicine&Biology,2005,50(23):5421-5441.
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[23]WRIGHT S J,NOWAK R D,FIGUEIREDO M A T.Sparse reconstruction by separable approximation[J].IEEE Transactions on Signal Processing,2009,57(7):2479-2493.
[24]HE X W,LIANG J M,WANG X R,et al.Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method[J].Optics Express,2010,18(24):24825-24841.
[25]CHEN D M,ZHU S P,YI H J,et al.Cone beam xray luminescence computed tomography:A feasibility study[J].Medical Physics,2013,40(3):031111.
[26]DOGDAS B,STOUT D,CHATZIIOANNOU A F,et al.Digimouse:A 3D whole body mouse atlas from CTand cryosection data[J].Physics in Medicine&Biology,2007,52(3):577-587.
[27]ALEXANDRAKIS G,RANNOU F R,CHATZIIOAN-NOU A F.Tomographic bioluminescence imaging by use of a combined optical-PET(OPET)system:Acomputer simulation feasibility study[J].Physics in Medicine&Biology,2005,50(17):4225-4241.
[28]CHEN X L,ZHANG Q T,YANG D F,et al.Hybrid radiosity-SP3 equation based bioluminescence tomography reconstruction for turbid medium with low-and non-scattering regions[J].Journal of Applied Physics,2014,115(2):024702.
[29]GUO H B,YU J J,HE X W,et al.Improved sparse reconstruction for fluorescence molecular tomography with L1/2 regularization[J].Biomedical Optics Express,2015,6(5):1648-1664.
[2]LIU J T,WANG Y B,QU X C,et al.In vivo quantitative bioluminescence tomography using heterogeneous and homogeneous mouse models[J].Optics Express,2010,18(12):13102-13113.
[3]CHEHADE M,SRIVASTAVA A K,BULTE J W M.Co-registration of bioluminescence tomography,computed tomography,and magnetic resonance imaging for multimodal in vivo stem cell tracking[J].Tomography:A Journal for Imaging Research,2016,2(2):159-165.
[4]QIN C H,FENG J C,ZHU S P,et al.Recent advances in bioluminescence tomography:Methodology and system as well as application[J].Laser&Photonics Reviews,2014,8(1):94-114.
[5]JENKINS D E,OEI Y,HORNIG Y S,et al.Bioluminescent imaging(BLI)to improve and refine traditional murine models of tumor growth and metastasis[J].Clinical&Experimental Metastasis,2003,20(8):733-744.
[6]LIU K,TIAN J,QIN C H,et al.Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models[J].Journal of Biomedical Optics,2011,16(4):046016.
[7]YU J J,ZHANG B,IORDACHITA I I,et al.Systematic study of target localization for bioluminescence tomography guided radiation therapy[J].Medical Physics,2016,43(5):2619-2629.
[8]杨明洁.基于多光谱信息的高质量生物发光断层成像重建算法研究[D].北京:北京工业大学,2015.
[9]KLOSE A D,LARSEN E W.Light transport in biological tissue based on the simplified spherical harmonics equations[J].Journal of Computational Physics,2006,220(1):441-470.
[10]YANG D F,CHEN X L,CAO X,et al.Performance investigation of SP3 and diffusion approximation for three-dimensional whole-body optical imaging of small animals[J].Medical&Biological Engineering&Computing,2015,53(9):805-814.
[11]LU Y J,DOURAGHY A,MACHADO H B,et al.Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation[J].Physics in Medicine&Biology,2009,54(21):6477-6493.
[12]金晨,郭红波,侯榆青,等.基于变量分离近似稀疏重构和简化球谐近似的生物发光断层成像[J].光学学报,2014,34(6):197-205.
[13]HE X W,GUO H B,YU J J,et al.Effective and robust approach for fluorescence molecular tomography based on Co Sa MP and SP3 model[J].Journal of Innovative Optical Health Sciences,2016,9(6):1650024.
[14]李维,易黄建,张岐坦,等.简化球谐近似与拉普拉斯正则化的FMT成像方法[J].西安电子科技大学学报,2015,42(1):82-85.
[15]LIU K,YANG X,LIU D,et al.Spectrally resolved three-dimensional bioluminescence tomography with a level-set strategy[J].JOSA A,2010,27(6):1413-1423.
[16]YU J J,LI Q Y,WANG H Y.Source reconstruction for bioluminescence tomography via L1/2 regularization[J].Journal of Innovative Optical Health Sciences,2018,11(2):1750014.
[17]YU J J,LIU F,WU J,et al.Fast source reconstruction for bioluminescence tomography based on sparse regularization[J].IEEE Transactions on Biomedical Engineering,2010,57(10):2583-2586.
[18]GAO H,ZHAO H K.Multilevel bioluminescence tomography based on radiative transfer equation Part 2:Total variation and l1 datafidelity[J].Optics Express,2010,18(3):2894-2912.
[19]LIU K,LU Y J,TIAN J,et al.Evaluation of the simplified spherical harmonics approximation in bioluminescence tomography through heterogeneous mouse models[J].Optics Express,2010,18(20):20988-21002.
[20]HAN W M,CONG W X,WANG G.Mathematical study and numerical simulation of multispectral bioluminescence tomography[J].International Journal of Biomedical Imaging,2006(2006):1-10.
[21]CHAUDHARI A J,DARVAS F,BADING J R,et al.Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging[J].Physics in Medicine&Biology,2005,50(23):5421-5441.
[22]BECK A,TEBOULLE M.A fast iterative shrinkagethresholding algorithm for linear inverse problems[J].SIAM Journal on Imaging Sciences,2009,2(1):183-202.
[23]WRIGHT S J,NOWAK R D,FIGUEIREDO M A T.Sparse reconstruction by separable approximation[J].IEEE Transactions on Signal Processing,2009,57(7):2479-2493.
[24]HE X W,LIANG J M,WANG X R,et al.Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method[J].Optics Express,2010,18(24):24825-24841.
[25]CHEN D M,ZHU S P,YI H J,et al.Cone beam xray luminescence computed tomography:A feasibility study[J].Medical Physics,2013,40(3):031111.
[26]DOGDAS B,STOUT D,CHATZIIOANNOU A F,et al.Digimouse:A 3D whole body mouse atlas from CTand cryosection data[J].Physics in Medicine&Biology,2007,52(3):577-587.
[27]ALEXANDRAKIS G,RANNOU F R,CHATZIIOAN-NOU A F.Tomographic bioluminescence imaging by use of a combined optical-PET(OPET)system:Acomputer simulation feasibility study[J].Physics in Medicine&Biology,2005,50(17):4225-4241.
[28]CHEN X L,ZHANG Q T,YANG D F,et al.Hybrid radiosity-SP3 equation based bioluminescence tomography reconstruction for turbid medium with low-and non-scattering regions[J].Journal of Applied Physics,2014,115(2):024702.
[29]GUO H B,YU J J,HE X W,et al.Improved sparse reconstruction for fluorescence molecular tomography with L1/2 regularization[J].Biomedical Optics Express,2015,6(5):1648-1664.