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Performance investigation of SP3 and diffusion approximation for three-dimensional whole-body optical imaging of small animals

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Abstract

The third-order simplified harmonic spherical approximation (SP3) and diffusion approximation (DA) equations have been widely used in the three-dimensional (3D) whole-body optical imaging of small animals. With different types of tissues, which were classified by the ratio of µ s′/µ ɑ, the two equations have their own application scopes. However, the classification criterion was blurring and unreasonable, and the scope has not been systematically investigated until now. In this study, a new criterion for classifying tissues was established based on the absolute value of absorption and reduced scattering coefficients. Using the newly defined classification criterion, the performance and applicability of the SP3 and DA equations were evaluated with a series of investigation experiments. Extensive investigation results showed that the SP3 equation exhibited a better performance and wider applicability than the DA one in most of the observed cases, especially in tissues of low-scattering-low-absorption and low-scattering-high-absorption range. For the case of tissues with the high-scattering-low-absorption properties, a similar performance was observed for both the SP3 and the DA equations, in which case the DA was the preferred option for 3D whole-body optical imaging. Results of this study would provide significant reference for the study of hybrid light transport models.

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References

  1. Alexandrakis G, Rannou FR, Chatziioannou AF (2005) Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study. Phys Med Biol 50(17):4225–4241

    Article  PubMed Central  PubMed  Google Scholar 

  2. Arridge SR, Dehghani H, Schweiger M, Okada E (2000) The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions. Med Phys 27(1):252–264

    Article  CAS  PubMed  Google Scholar 

  3. Bassani M, Martelli F, Zaccanti G, Contini D (1997) Independence of the diffusion coefficient from absorption: experimental and numerical evidence. Opt Lett 22:853–855

    Article  CAS  PubMed  Google Scholar 

  4. Cao X, Zhang B, Wang X, Liu F, Liu K, Luo J, Bai J (2013) An adaptive Tikhonov regularization method for fluorescence molecular tomography. Med Biol Eng Comput 51(8):849–858

    Article  PubMed  Google Scholar 

  5. Chen X, Yang D, Qu X, Hu H, Liang J, Gao X, Tian J (2012) Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection. J Biomed Opt 17(6):066015

    Article  PubMed  Google Scholar 

  6. Chu M, Dehghani H (2009) Image reconstruction in diffuse optical tomography based on simplified spherical harmonics approximation. Opt Express 17(26):24208–24223

    Article  PubMed  Google Scholar 

  7. Chu M, Vishwanath K, Klose AD, Dehghani H (2009) Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations. Phys Med Biol 54(8):2493–2509

    Article  PubMed  Google Scholar 

  8. Cong WX, Wang G, Kumar D, Liu Y, Jiang M, Wang LV, Hoffman EA, McLennan G, McCray PB, Zabner J, Cong A (2005) Practical reconstruction method for bioluminescence tomography. Opt Express 13(18):6756–6771

    Article  PubMed  Google Scholar 

  9. Dehghani H, Delpy DT, Arridge SR (1999) Photon migration in non-scattering tissue and the effects on image reconstruction. Phys Med Biol 44:2897–2906

    Article  CAS  PubMed  Google Scholar 

  10. Dehghani H, Arridge SR, Schweiger M, Delpy DT (2000) Optical tomography in the presence of void regions. J Opt Soc Am A 17(9):1659–1670

    Article  Google Scholar 

  11. Gibson AP, Hebden JC, Arridge SR (2005) Recent advances in diffuse optical imaging. Phys Med Biol 50(4):R1–R43

    Article  CAS  PubMed  Google Scholar 

  12. Gorpas D, Andersson-Engels S (2012) Evaluation of a radiative transfer equation and diffusion approximation hybrid forward solver for fluorescence molecular imaging. J Biomed Opt 17(12):126010

    Article  PubMed  Google Scholar 

  13. Hayashi T, Kashio Y, Okada E (2003) Hybrid Monte Carlo-diffusion method for light propagation in tissue with a low-scattering region. Appl Opt 42(16):2888–2896

    Article  PubMed  Google Scholar 

  14. Hielscher AH, Alcouffe RE (1996) Non-diffusive photon migration in homogenous and heterogenous tissues. Proc SPIE 2925:22–30

    Article  CAS  Google Scholar 

  15. Jacques SL (2013) Optical properties of biological tissues: a review. Phys Med Biol 58(11):R37–R61

    Article  PubMed  Google Scholar 

  16. Kavuri VC, Lin Z, Tian F, Liu H (2012) Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography. Biomed Opt Express 3(5):943–957

    Article  PubMed Central  PubMed  Google Scholar 

  17. Klose AD, Larsen EW (2006) Light transport in biological tissue based on the simplified spherical harmonics equations. J Comput Phys 220(1):441–470

    Article  Google Scholar 

  18. Klose AD, Poschinger T (2011) Excitation-resolved fluorescence tomography with simplified spherical harmonics equations. Phys Med Biol 56(5):1443–1469

    Article  PubMed Central  PubMed  Google Scholar 

  19. Lee JH, Kim S, Kim YT (2004) Modeling of diffuse-diffuse photon coupling via a nonscattering region: a comparative study. Appl Opt 43(18):3640–3655

    Article  PubMed  Google Scholar 

  20. Lehtikangas O, Tarvainen T (2013) Hybrid forward-peaked-scattering-diffusion approximations for light propagation in turbid media with low-scattering regions. J Quant Spectrosc Radiat Transf 116:132–144

    Article  CAS  Google Scholar 

  21. Liao LD, Tsytsarev V, Delgado-Martínez I, Li ML, Erzurumlu R, Vipin A, Orellana J, Lin YR, Lai HY, Chen YY, Thakor NV (2013) Neurovascular coupling: in vivo optical techniques for functional brain imaging. Biomed Eng Online 12:38

    Article  PubMed Central  PubMed  Google Scholar 

  22. Liu K, Lu Y, Tian J, Qin C, Yang X, Zhu S, Yang X, Gao Q, Han D (2010) Evaluation of the simplified spherical harmonics approximation in bioluminescence tomography through heterogeneous mouse models. Opt Express 18(20):20988–21002

    Article  CAS  PubMed  Google Scholar 

  23. Lu Y, Douraghy A, Machado HB, Stout D, Tian J, Herschman H, Chatziioannou AF (2009) Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation. Phys Med Biol 54(21):6477–6493

    Article  PubMed Central  PubMed  Google Scholar 

  24. Lu Y, Zhu B, Darne C, Tan I, Rasmussen JC, Sevick-Muraca EM (2011) Improvement of fluorescence-enhanced optical tomography with improved optical filtering and accurate model-based reconstruction algorithms. J Biomed Opt 16(12):126002

    Article  PubMed Central  PubMed  Google Scholar 

  25. Nakai T, Nishimura G, Yamamoto K, Tamura M (1997) Expression of optical diffusion coefficient in high-absorption turbid media. Phys Med Biol 42:2541

    Article  CAS  PubMed  Google Scholar 

  26. Ntziachristos V, Ripoll J, Wang LHV, Weissleder R (2005) Looking and listening to light: the evolution of whole-body photonic imaging. Nat Biotechnol 23(3):313–320

    Article  CAS  PubMed  Google Scholar 

  27. Periyasamy V, Pramanik M (2014) Monte Carlo simulation of light transport in turbid medium with embedded object-spherical, cylindrical, ellipsoidal, or cuboidal objects embedded within multilayered tissues. J Biomed Opt 19(4):045003

    Article  PubMed  Google Scholar 

  28. Ren S, Chen X, Wang H, Qu X, Wang G, Liang J, Tian J (2013) Molecular optical simulation environment (MOSE): a platform for the simulation of light propagation in turbid media. PLoS One 8(4):e61304

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  29. Shi Z, Zhao H, Xu K (2011) Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain. J Biomed Opt 16(10):105002

    Article  PubMed  Google Scholar 

  30. Tarvainen T, Vauhkonen M, Kolehmainen V, Arridge SR, Kaipio JP (2005) Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions. Phys Med Biol 50(20):4913–4930

    Article  CAS  PubMed  Google Scholar 

  31. Tarvainen T, Kolehmainen V, Pulkkinen A, Vauhkonen M, Schweiger M, Arridge SR, Kaipio JP (2010) An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography. Inverse Probl 26:015005

    Article  Google Scholar 

  32. Tian J, Bai J, Yan XP, Bao SL, Li YH, Liang W, Yang X (2008) Multimodality molecular imaging. IEEE Eng Med Biol Mag 27(5):48–57

    Article  CAS  PubMed  Google Scholar 

  33. Yang D, Chen X, Peng Z, Wang X, Ripoll J, Wang J, Liang J (2013) Light transport in turbid media with non-scattering, low-scattering and high absorption heterogeneities based on hybrid simplified spherical harmonics with radiosity model. Biomed Opt Express 4(10):2209–2223

    Article  PubMed Central  PubMed  Google Scholar 

Download references

Acknowledgments

This work was partly supported by the Program of National Basic Research and Development Program of China (973) under Grant No. 2011CB707702, the National Natural Science Foundation of China under Grant Nos. 81090272, 81227901, 81101083, 81230033, the Open Research Project under Grant 20120101 from SKLMCCS, and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. Engineering Research Center of Molecular and Neuro Imaging of Ministry of Education, School of Life Science and Technology, Xidian University, Xi’an, 710071, Shaanxi, China

    Defu Yang, Xueli Chen, Xu Cao, Jimin Liang & Jie Tian

  2. Department of Nuclear Medicine, Xijing Hospital, Fourth Military Medical University, Xi’an, 710032, Shaanxi, China

    Jing Wang

  3. Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

    Jie Tian

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  1. Defu Yang
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  2. Xueli Chen
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  3. Xu Cao
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Correspondence to Xueli Chen.

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Yang, D., Chen, X., Cao, X. et al. Performance investigation of SP3 and diffusion approximation for three-dimensional whole-body optical imaging of small animals. Med Biol Eng Comput 53, 805–814 (2015). https://doi.org/10.1007/s11517-015-1293-8

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  • DOI: https://doi.org/10.1007/s11517-015-1293-8

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