## Three-dimensional bioluminescence tomography with model-based reconstruction

Optics Express, Vol. 12, Issue 17, pp. 3996-4000 (2004)

http://dx.doi.org/10.1364/OPEX.12.003996

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### Abstract

A model-based image reconstruction method, bioluminescence tomography (BLT), is described. BLT has the potential to spatially resolve bioluminescence associated with gene expression in vivo, thus, offering a tomographic molecular imaging method. The three-dimensional spatial map of reporter genes is recovered using a diffusion equation model-based, finite element reconstruction algorithm. The imaging method is demonstrated using both numerical simulations and phantom experiments.

© 2004 Optical Society of America

## 1. Introduction

1. S. Bhaumik and S. Gambhir, “Optical imaging of *Renilla* luciferase reporter gene express in living mice,” Proc. Natl. Acad. Sci. *USA* **99**, 377–382 (2002). [CrossRef]

3. S. Mandl, C. Schimmelpfennig, M. Edinger, R. Negrin, and C. Contag, “Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,” J. Cellular Biochem. Suppl. **39**, 239–248 (2002). [CrossRef]

2. C. Contag and M. Bachmann, “Advances in *in vivo* bioluminescence imaging of gene express,” Annu. Rev. Biomed. Eng. **4**, 235–260 (2002). [CrossRef] [PubMed]

## 2. Methods and materials

### 2.1 Reconstruction algorithm

4. A. Yodh and B. Chance, “Spectroscopy and imgaing with diffusing light,” Phys. Today **48**, 34–40 (1995). [CrossRef]

*x*,

*y*,

*z*) is the photon density; D and µ

_{a}are the diffusion and absorption coefficients, respectively;

*S*(

*x*,

*y*,

*z*) is the source distribution of gene expression.

5. R. Haskell, L. Svaasand, T. Tsay, T. Feng, M. McAdams, and B.J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A **11**, 2727–2741 (1994). [CrossRef]

6. H. Jiang, K. Paulsen, U. Osterberg, B. Pogue, and M. Patterson, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A **13**, 253–266 (1996). [CrossRef]

7. K. Paulsen and H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. **22**, 691–702 (1995). [CrossRef] [PubMed]

8. Y. Xu, X. Gu, T. Khan, and H. Jiang, “Absorption and scattering images of heterogeneous scattering media can be simultaneously reconstructed by use of dc data,” Appl. Opt. **41**, 5427–5437 (2002). [CrossRef] [PubMed]

_{ij}=〈-D∇ϕ

_{j}·∇ϕ

_{i}-µ

_{a}ϕ

_{j}ϕ

_{i}〉 and b

_{i}=〈

_{k}ϕ

_{k}ϕ

_{i}〉 where 〈 〉 indicates integration over the problem domain and N is the total number of nodes in the finite element mesh used; ϕ

_{i}, ϕ

_{j}and ϕ

_{k}are locally spatially varying Lagrangian basis functions at nodes i, j and k, respectively; ℑ is the Jacobian matrix that should be formed by ∂Φ/∂S at the boundary measurement sites; ΔS=(ΔS

_{1},ΔS

_{2},⋯,ΔS

_{N})

^{T}is the update vector for the light source profile; Φ

^{(m)}=(

^{(c)}=(

### 2.2 Simulations

^{-1}, respectively. One or two approximate cylindrical targets (7.0mm in diameter and 10mm in height) were embedded 7.2mm off-center in the background to simulate the gene expression. In the target volumes, the source coefficient (S

_{k}) was 1.0, whereas it was zero in the background volume. A 3D finite-element mesh with 1749 nodes and 7440 tetrahedral elements was used for the reconstruction results presented. All the reconstructions were results of 50 iterations, after which no noticeable improvement was observed. The computations were conducted in a 2.6 GHz Pentium IV PC.

### 2.3 Experiments

^{®}recombinant luciferase (Promega, Milwaukee, WI), a standard firefly luciferase with a peak emission at 560nm, was used as the source of enzyme, while a luciferase assay system (Promega, Milwaukee, WI) provided luciferin, magnesium, ATP and other co-factors for generating high total light output with a half life of 10 minutes. Quantilum

^{®}recombinant luciferase was diluted 10

^{6}-fold in 1 x cell culture lysis reagent (supplied by the luciferase assay system) and 1mg/ml acetylated BSA (Sigma-Aldrich, St Louis, MO). The luciferase assay substrate was dissolved into luciferase assay buffer to obtain luciferase assay reagent. Light was generated when combining the diluted luciferase (350µl) with the luciferase assay reagent (350µl).

## 3. Results and discussion

*et al*. [9

9. B.W. Rice, M. Cable, and M. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. **6**, 432–440 (2001). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | S. Bhaumik and S. Gambhir, “Optical imaging of |

2. | C. Contag and M. Bachmann, “Advances in |

3. | S. Mandl, C. Schimmelpfennig, M. Edinger, R. Negrin, and C. Contag, “Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,” J. Cellular Biochem. Suppl. |

4. | A. Yodh and B. Chance, “Spectroscopy and imgaing with diffusing light,” Phys. Today |

5. | R. Haskell, L. Svaasand, T. Tsay, T. Feng, M. McAdams, and B.J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A |

6. | H. Jiang, K. Paulsen, U. Osterberg, B. Pogue, and M. Patterson, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A |

7. | K. Paulsen and H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. |

8. | Y. Xu, X. Gu, T. Khan, and H. Jiang, “Absorption and scattering images of heterogeneous scattering media can be simultaneously reconstructed by use of dc data,” Appl. Opt. |

9. | B.W. Rice, M. Cable, and M. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. |

**OCIS Codes**

(110.6960) Imaging systems : Tomography

(170.3010) Medical optics and biotechnology : Image reconstruction techniques

(170.6280) Medical optics and biotechnology : Spectroscopy, fluorescence and luminescence

**ToC Category:**

Research Papers

**History**

Original Manuscript: July 20, 2004

Revised Manuscript: August 9, 2004

Published: August 23, 2004

**Citation**

Xuejun Gu, Qizhi Zhang, Lyndon Larcom, and Huabei Jiang, "Three-dimensional bioluminescence tomography with model-based reconstruction," Opt. Express **12**, 3996-4000 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-17-3996

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### References

- S. Bhaumik, S. Gambhir, �??Optical imaging of Renilla luciferase reporter gene express in living mice,�?? Proc. Natl. Acad. Sci. USA 99, 377-382 (2002). [CrossRef]
- C. Contag, M. Bachmann, �??Advances in in vivo bioluminescence imaging of gene express,�?? Annu. Rev. Biomed. Eng. 4, 235-260 (2002). [CrossRef] [PubMed]
- S. Mandl, C. Schimmelpfennig, M. Edinger, R. Negrin, C. Contag, �??Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,�?? J. Cellular Biochem. Suppl. 39, 239-248 (2002). [CrossRef]
- A. Yodh, B. Chance, �??Spectroscopy and imgaing with diffusing light,�?? Phys. Today 48, 34-40 (1995). [CrossRef]
- R. Haskell, L. Svaasand, T. Tsay, T. Feng, M. McAdams, B.J. Tromberg, �??Boundary conditions for the diffusion equation in radiative transfer,�?? J. Opt. Soc. Am. A 11, 2727-2741 (1994). [CrossRef]
- H. Jiang, K. Paulsen, U. Osterberg, B. Pogue, M. Patterson, �??Optical image reconstruction using frequencydomain data: simulations and experiments," J. Opt. Soc. Am. A 13, 253-266 (1996) [CrossRef]
- K. Paulsen, H. Jiang, �??Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,�?? Med. Phys. 22, 691-702 (1995). [CrossRef] [PubMed]
- Y. Xu, X. Gu, T. Khan, H. Jiang, �??Absorption and scattering images of heterogeneous scattering media can be simultaneously reconstructed by use of dc data,�?? Appl. Opt. 41, 5427-5437 (2002). [CrossRef] [PubMed]
- B.W. Rice, M. Cable, M. Nelson, �??In vivo imaging of light-emitting probes,�?? J. Biomed. Opt. 6, 432-440 (2001). [CrossRef] [PubMed]

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