Optimal source-modulation frequencies for transport-theory-based optical tomography of small-tissue volumes
Optics Express, Vol. 16, Issue 22, pp. 18082-18101 (2008)
http://dx.doi.org/10.1364/OE.16.018082
Acrobat PDF (2079 KB)
Abstract
In frequency-domain optical tomography (FDOT) the quality of the reconstruction result is affected by the choice of the source-modulation frequency. In general the accuracy of the reconstructed image should improve as the source-modulation frequency increases. However, this is only true for noise-free data. Experimental data is typically corrupted by noise and the accuracy is compromised. Assuming the validity of the widely used shot noise model, one can show that the signal-to-noise ratio (SNR) of the amplitude signal decreases with increasing frequency, whereas the SNR of the phase shift reaches peak values in the range between 400 MHz and 800 MHz. As a consequence, it can be assumed that there exists an optimal frequency for which the reconstruction accuracy would be highest. To determine optimal frequencies for FDOT, we investigate here the frequency dependence of optical tomographic reconstruction results using the frequency-domain equation of radiative transfer. We present numerical and experimental studies with a focus on small tissue volumes, as encountered in small animal and human finger imaging. Best reconstruction results were achieved in the 600–800 MHz frequency range.
© 2008 Optical Society of America
1. Introduction
1. K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comp. 28, 1463–89 (2006). [CrossRef]
4. A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Optics Express 15, 6696–6716 (2007). [CrossRef] [PubMed]
1. K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comp. 28, 1463–89 (2006). [CrossRef]
5. H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spec. Rad. Trans. 104, 24–39 (2007). [CrossRef]
9. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, R41–93 (1999). [CrossRef]
10. K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain,” Opt. Lett. 29, 578–580 (2004). [CrossRef] [PubMed]
11. A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998). [CrossRef] [PubMed]
12. A. H Hielscher, “Optical tomographic imaging of small animals,” Current Opinion in Biotechnology 16, 79–88 (2005). [CrossRef] [PubMed]
13. J. T. Wessels, A. C. Busse AC, J. Mahrt, C. Dullin, E. Grabbe, and G. A. Mueller, “In vivo imaging in experimental preclinical tumor research - A review,” Cytometry Part A 71A, 542–549 (2007). [CrossRef]
15. F.Y. Nilsson and V. Tolmachev, “Affibody (R) molecules: New protein domains for molecular imaging and targeted tumor therapy,” Current Opinion in Drug Discovery & Development 10, 167–175 (2007). [PubMed]
16. J. Masciotti, F. Provenzano, J. Papa, A. D. Klose, J. Hur, X. Gu, D. Yamashiro, J. Kandel, and A. H. Hielscher, “Monitoring tumor growth and treatment in small animals with magnetic resonance optical tomographic imaging,” Proc. SPIE 6081, 608105 (2006). [CrossRef]
17. A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. J. Netz, and J. Beuthan, “ Sagittal laser optical tomography for imaging of rheumatoid finger joints,” Phys. Med. Biol. 49, 1147 (2004). [CrossRef] [PubMed]
19. Q. Zhang and H. Jiang, “Three-dimensional diffuse optical tomography of simulated hand joints with a 64×64-channel photodiodes-based optical system,” J. Opt. A: Pure Appl. Opt. 7, 224–231 (2005). [CrossRef]
11. A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998). [CrossRef] [PubMed]
1. K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comp. 28, 1463–89 (2006). [CrossRef]
5. H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spec. Rad. Trans. 104, 24–39 (2007). [CrossRef]
6. G. S. Abddoulaev, K. Ren, and A.H. Hielscher, “Optical tomography as a PDE-constrained optimization problem,” Inverse Problems 21, 1507–1530 (2005). [CrossRef]
10. K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain,” Opt. Lett. 29, 578–580 (2004). [CrossRef] [PubMed]
22. V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain,” Opt. Express 11, 2117–729 (2003). [CrossRef]
23. X. Gu, K. Ren, and A. H. Hielscher, “Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer,” Appl. Opt. 46, 1624–32 (2007). [CrossRef] [PubMed]
2. Methods
2.1. Model of light propagation
1. K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comp. 28, 1463–89 (2006). [CrossRef]
5. H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spec. Rad. Trans. 104, 24–39 (2007). [CrossRef]
1. K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comp. 28, 1463–89 (2006). [CrossRef]
5. H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spec. Rad. Trans. 104, 24–39 (2007). [CrossRef]
24. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. 90, 70 (1941). [CrossRef]
7. A. D. Klose and A. H. Hielscher, “Quasi-newton methods in optical tomographic image reconstruction,” Inverse Problems 19, 309–87 (2003). [CrossRef]
1. K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comp. 28, 1463–89 (2006). [CrossRef]
6. G. S. Abddoulaev, K. Ren, and A.H. Hielscher, “Optical tomography as a PDE-constrained optimization problem,” Inverse Problems 21, 1507–1530 (2005). [CrossRef]
1. K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comp. 28, 1463–89 (2006). [CrossRef]
10. K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain,” Opt. Lett. 29, 578–580 (2004). [CrossRef] [PubMed]
29. H. Luo, J. D. Baum, and R. Löhner, “A fast matrix-free implicit method for compressible flows on unstructured grids,” J. Compt. Phys. 146, 664–690 (1998). [CrossRef]
30. B. W. Patton and J. P. Holloway, “Application of preconditioned GMRES to the numerical solution of the neutron transport equation,” Annals of Nuclear Energy 29, 109–136 (2002). [CrossRef]
2.2. Inverse model
22. V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain,” Opt. Express 11, 2117–729 (2003). [CrossRef]
23. X. Gu, K. Ren, and A. H. Hielscher, “Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer,” Appl. Opt. 46, 1624–32 (2007). [CrossRef] [PubMed]
1. K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comp. 28, 1463–89 (2006). [CrossRef]
5. H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spec. Rad. Trans. 104, 24–39 (2007). [CrossRef]
6. G. S. Abddoulaev, K. Ren, and A.H. Hielscher, “Optical tomography as a PDE-constrained optimization problem,” Inverse Problems 21, 1507–1530 (2005). [CrossRef]
3. Results
3.1. Numerical studies
3.1.1. Analysis of SNR values using numerical phantoms
22. V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain,” Opt. Express 11, 2117–729 (2003). [CrossRef]
23. X. Gu, K. Ren, and A. H. Hielscher, “Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer,” Appl. Opt. 46, 1624–32 (2007). [CrossRef] [PubMed]
3.1.2. Influence of SNR values on tomographic reconstruction results
7. A. D. Klose and A. H. Hielscher, “Quasi-newton methods in optical tomographic image reconstruction,” Inverse Problems 19, 309–87 (2003). [CrossRef]
3.2. Application to experimental data from general tissue phantoms
3.2.1. Frequency-domain imaging system
33. U. J. Netz, J. Beuthan, and A. H. Hielscher, “Multipixel system for gigahertz frequency-domain optical imaging of finger joints,” Rev. Sci. Instrum. 79, 034301 (2008). [CrossRef] [PubMed]
33. U. J. Netz, J. Beuthan, and A. H. Hielscher, “Multipixel system for gigahertz frequency-domain optical imaging of finger joints,” Rev. Sci. Instrum. 79, 034301 (2008). [CrossRef] [PubMed]
3.2.2. Square phantom
3.3. Finger phantom
17. A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. J. Netz, and J. Beuthan, “ Sagittal laser optical tomography for imaging of rheumatoid finger joints,” Phys. Med. Biol. 49, 1147 (2004). [CrossRef] [PubMed]
18. A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. J. Netz, K.-G. A. Hermann, J. Beuthan, G. A. Muller, G. R. Burmester, and A. H. Hielscher, “First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints,” Ann. Rheum. Dis. 64, 239–245 (2005). [CrossRef]
33. U. J. Netz, J. Beuthan, and A. H. Hielscher, “Multipixel system for gigahertz frequency-domain optical imaging of finger joints,” Rev. Sci. Instrum. 79, 034301 (2008). [CrossRef] [PubMed]
33. U. J. Netz, J. Beuthan, and A. H. Hielscher, “Multipixel system for gigahertz frequency-domain optical imaging of finger joints,” Rev. Sci. Instrum. 79, 034301 (2008). [CrossRef] [PubMed]
17. A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. J. Netz, and J. Beuthan, “ Sagittal laser optical tomography for imaging of rheumatoid finger joints,” Phys. Med. Biol. 49, 1147 (2004). [CrossRef] [PubMed]
18. A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. J. Netz, K.-G. A. Hermann, J. Beuthan, G. A. Muller, G. R. Burmester, and A. H. Hielscher, “First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints,” Ann. Rheum. Dis. 64, 239–245 (2005). [CrossRef]
3.4 Small animal studies
33. U. J. Netz, J. Beuthan, and A. H. Hielscher, “Multipixel system for gigahertz frequency-domain optical imaging of finger joints,” Rev. Sci. Instrum. 79, 034301 (2008). [CrossRef] [PubMed]
4. Conclusion
Acknowledgements
References and links
1. | K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comp. 28, 1463–89 (2006). [CrossRef] |
2. | C. M. Carpenter, B. W. Pogue, S. Jiang, H. Dehghani, X. Wang, K. D. Paulsen, W. A. Wells, J. Forero, C. Kogel, J. B. Weaver, S. P. Poplack, and P. A. Kaufman, “Image-guided optical spectroscopy provides molecular-specific information in vivo: MRI-guided spectroscopy of breast cancer hemoglobin, water, and scatter size,” Opt. Lett. 32, 933–935 (2007). [CrossRef] [PubMed] |
3. | A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2006) [CrossRef] |
4. | A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Optics Express 15, 6696–6716 (2007). [CrossRef] [PubMed] |
5. | H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spec. Rad. Trans. 104, 24–39 (2007). [CrossRef] |
6. | G. S. Abddoulaev, K. Ren, and A.H. Hielscher, “Optical tomography as a PDE-constrained optimization problem,” Inverse Problems 21, 1507–1530 (2005). [CrossRef] |
7. | A. D. Klose and A. H. Hielscher, “Quasi-newton methods in optical tomographic image reconstruction,” Inverse Problems 19, 309–87 (2003). [CrossRef] |
8. | M. Schweiger, S. R. Arridge, and I. Nassilä, “Gauss-Newton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005). [CrossRef] [PubMed] |
9. | S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, R41–93 (1999). [CrossRef] |
10. | K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain,” Opt. Lett. 29, 578–580 (2004). [CrossRef] [PubMed] |
11. | A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998). [CrossRef] [PubMed] |
12. | A. H Hielscher, “Optical tomographic imaging of small animals,” Current Opinion in Biotechnology 16, 79–88 (2005). [CrossRef] [PubMed] |
13. | J. T. Wessels, A. C. Busse AC, J. Mahrt, C. Dullin, E. Grabbe, and G. A. Mueller, “In vivo imaging in experimental preclinical tumor research - A review,” Cytometry Part A 71A, 542–549 (2007). [CrossRef] |
14. | C. M. Deroose, A. De, A. M. Loening, P. L. Chow, P. Ray, A. F. Chatziioannou, and S. S. Gambhir, “Multimodality imaging of tumor xenografts and metastases in mice with combined small-animal PET, small-animal CT, and bioluminescence imaging,” J. Nuclear Med. 48, 295–303 (2007). |
15. | F.Y. Nilsson and V. Tolmachev, “Affibody (R) molecules: New protein domains for molecular imaging and targeted tumor therapy,” Current Opinion in Drug Discovery & Development 10, 167–175 (2007). [PubMed] |
16. | J. Masciotti, F. Provenzano, J. Papa, A. D. Klose, J. Hur, X. Gu, D. Yamashiro, J. Kandel, and A. H. Hielscher, “Monitoring tumor growth and treatment in small animals with magnetic resonance optical tomographic imaging,” Proc. SPIE 6081, 608105 (2006). [CrossRef] |
17. | A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. J. Netz, and J. Beuthan, “ Sagittal laser optical tomography for imaging of rheumatoid finger joints,” Phys. Med. Biol. 49, 1147 (2004). [CrossRef] [PubMed] |
18. | A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. J. Netz, K.-G. A. Hermann, J. Beuthan, G. A. Muller, G. R. Burmester, and A. H. Hielscher, “First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints,” Ann. Rheum. Dis. 64, 239–245 (2005). [CrossRef] |
19. | Q. Zhang and H. Jiang, “Three-dimensional diffuse optical tomography of simulated hand joints with a 64×64-channel photodiodes-based optical system,” J. Opt. A: Pure Appl. Opt. 7, 224–231 (2005). [CrossRef] |
20. | Michael F. Modest, Radiative Heat Transfer (McGraw-Hill, New York, 2003). |
21. | W. J. Minkowycz, E. M. Sparrow, and J. Y. Murthy, Handbook of numerical heat transfer (J. Wiley Hoboken NJ, 2006). |
22. | V. Toronov, E. D’Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, “Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain,” Opt. Express 11, 2117–729 (2003). [CrossRef] |
23. | X. Gu, K. Ren, and A. H. Hielscher, “Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer,” Appl. Opt. 46, 1624–32 (2007). [CrossRef] [PubMed] |
24. | L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. 90, 70 (1941). [CrossRef] |
25. | E. Meese, Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids, Ph.D. thesis, Norwegian University of Science and Technology, Trondheim, Norway (1998). |
26. | H. Grissa, F. Askri, M. Ben Salah, and S. Ben Nasrallah, “Three-dimensional radiative transfer modeling using the control volume finite element method,” JQSRT 105, 388–404 (2007). |
27. | H. K. Kim and A. H. Hielscher, “A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer,” Inverse Problems (in press). |
28. | Y. Saad and M. H. Schultz, “GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 3, 856–869 (1989). |
29. | H. Luo, J. D. Baum, and R. Löhner, “A fast matrix-free implicit method for compressible flows on unstructured grids,” J. Compt. Phys. 146, 664–690 (1998). [CrossRef] |
30. | B. W. Patton and J. P. Holloway, “Application of preconditioned GMRES to the numerical solution of the neutron transport equation,” Annals of Nuclear Energy 29, 109–136 (2002). [CrossRef] |
31. | Oleg M. Alifanov, Inverse Heat Transfer Problems (Spring-Verlag, New York, 1994). |
32. | J. Nocedal and S. J. Wright, Numerical Optimization (Springer, New York, 2006). |
33. | U. J. Netz, J. Beuthan, and A. H. Hielscher, “Multipixel system for gigahertz frequency-domain optical imaging of finger joints,” Rev. Sci. Instrum. 79, 034301 (2008). [CrossRef] [PubMed] |
OCIS Codes
(060.2630) Fiber optics and optical communications : Frequency modulation
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.4090) Medical optics and biotechnology : Modulation techniques
(170.4500) Medical optics and biotechnology : Optical coherence tomography
(110.6955) Imaging systems : Tomographic imaging
ToC Category:
Medical Optics and Biotechnology
History
Original Manuscript: July 9, 2008
Revised Manuscript: October 15, 2008
Manuscript Accepted: October 18, 2008
Published: October 21, 2008
Virtual Issues
Vol. 3, Iss. 12 Virtual Journal for Biomedical Optics
Interactive Science Publishing (2008) Optics Express
Citation
Hyun Keol Kim, Uwe J. Netz, Jürgen Beuthan, and Andreas H. Hielscher, "Optimal source-modulation frequencies for transport-theory-based optical tomography of small-tissue volumes," Opt. Express 16, 18082-18101 (2008)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-16-22-18082
Sort: Year | Journal | Reset
References
- K. Ren, G. Bal and A. H. Hielscher, "Frequency domain optical tomography based on the equation of radiative transfer," SIAM J. Sci. Comp. 28, 1463-89 (2006). [CrossRef]
- C. M. Carpenter, B. W. Pogue, S. Jiang, H. Dehghani, X. Wang, K. D. Paulsen, W. A. Wells, J. Forero, C. Kogel, J. B. Weaver, S. P. Poplack and P. A. Kaufman, "Image-guided optical spectroscopy provides molecular-specific information in vivo: MRI-guided spectroscopy of breast cancer hemoglobin, water, and scatter size," Opt. Lett. 32, 933-935 (2007). [CrossRef] [PubMed]
- A. Joshi, W. Bangerth and E. M. Sevick-Muraca, "Adaptive finite element based tomography for fluorescence optical imaging in tissue," Opt. Express 12, 5402-5417 (2006) [CrossRef]
- A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall and A. G. Yodh "Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans," Optics Express 15, 6696-6716 (2007). [CrossRef] [PubMed]
- H. K. Kim and A. Charette, "A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer," J. Quant. Spec. Rad. Trans. 104, 24-39 (2007). [CrossRef]
- G. S. Abddoulaev, K. Ren and A.H. Hielscher, " Optical tomography as a PDE-constrained optimization problem," Inverse Problems 21, 1507-1530 (2005). [CrossRef]
- A. D. Klose and A. H. Hielscher, "Quasi-newton methods in optical tomographic image reconstruction," Inverse Problems 19, 309-87 (2003). [CrossRef]
- M. Schweiger, S. R. Arridge and I. Nassilä, "Gauss-Newton method for image reconstruction in diffuse optical tomography," Phys. Med. Biol. 50, 2365-2386 (2005). [CrossRef] [PubMed]
- S. R. Arridge, "Optical tomography in medical imaging," Inverse Problems 15, R41-93 (1999). [CrossRef]
- K. Ren, G. S. Abdoulaev, G. Bal and A. H. Hielscher, "Algorithm for solving the equation of radiative transfer in the frequency domain," Opt. Lett. 29, 578-580 (2004). [CrossRef] [PubMed]
- A. H. Hielscher, R. E. Alcouffe and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998). [CrossRef] [PubMed]
- A. H, Hielscher, "Optical tomographic imaging of small animals," Current Opinion in Biotechnology 16, 79-88 (2005). [CrossRef] [PubMed]
- J. T. Wessels, A. C. Busse AC, J. Mahrt, C. Dullin, E. Grabbe and G. A. Mueller, "In vivo imaging in experimental preclinical tumor research - A review," Cytometry Part A 71A, 542-549 (2007). [CrossRef]
- C. M. Deroose, A. De, A. M. Loening, P. L. Chow, P. Ray, A. F. Chatziioannou and S. S. Gambhir, "Multimodality imaging of tumor xenografts and metastases in mice with combined small-animal PET, small-animal CT, and bioluminescence imaging," J. Nuclear Med. 48, 295-303 (2007).
- F.Y. Nilsson and V. Tolmachev, "Affibody (R) molecules: New protein domains for molecular imaging and targeted tumor therapy," Current Opinion in Drug Discovery & Development 10, 167-175 (2007). [PubMed]
- J. Masciotti, F. Provenzano, J. Papa, A. D. Klose, J. Hur, X. Gu, D. Yamashiro, J. Kandel and A. H. Hielscher, "Monitoring tumor growth and treatment in small animals with magnetic resonance optical tomographic imaging," Proc. SPIE 6081,608105 (2006). [CrossRef]
- A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. J. Netz and J. Beuthan, " Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147 (2004). [CrossRef] [PubMed]
- A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. J. Netz, K.-G. A. Hermann, J. Beuthan, G. A. Muller, G. R. Burmester and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005). [CrossRef]
- Q. Zhang and H. Jiang, "Three-dimensional diffuse optical tomography of simulated hand joints with a 64 × 64-channel photodiodes-based optical system," J. Opt. A: Pure Appl. Opt. 7, 224-231 (2005). [CrossRef]
- MichaelF. Modest, Radiative Heat Transfer (McGraw-Hill, New York, 2003).
- W. J. Minkowycz, E. M. Sparrow and J. Y. Murthy, Handbook of numerical heat transfer (J. Wiley Hoboken NJ, 2006).
- V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-729 (2003). [CrossRef]
- X. Gu, K. Ren and A. H. Hielscher, "Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer," Appl. Opt. 46, 1624-32 (2007). [CrossRef] [PubMed]
- L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. 90, 70 (1941). [CrossRef]
- E. Meese, Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids, Ph.D. thesis, Norwegian University of Science and Technology, Trondheim, Norway (1998).
- H. Grissa, F. Askri, M. Ben Salah and S. Ben Nasrallah, "Three-dimensional radiative transfer modeling using the control volume finite element method," JQSRT 105, 388-404 (2007).
- H. K. Kim and A. H. Hielscher, "A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer," Inverse Problems (in press).
- Y. Saad and M. H. Schultz, "GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM J. Sci. Stat. Comput. 3, 856-869 (1989).
- H. Luo, J. D. Baum and R. Löhner, "A fast matrix-free implicit method for compressible flows on unstructured grids," J. Compt. Phys. 146, 664-690 (1998). [CrossRef]
- B. W. Patton, J. P. Holloway, "Application of preconditioned GMRES to the numerical solution of the neutron transport equation," Annals of Nuclear Energy 29, 109-136 (2002). [CrossRef]
- OlegM. Alifanov, Inverse Heat Transfer Problems (Spring-Verlag, New York, 1994).
- J. Nocedal and S. J. Wright, Numerical Optimization (Springer, New York, 2006).
- U. J. Netz, J. Beuthan and A. H. Hielscher, "Multipixel system for gigahertz frequency-domain optical imaging of finger joints," Rev. Sci. Instrum. 79034301 (2008). [CrossRef] [PubMed]
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
Figures
Fig. 1. | Fig. 2. | Fig. 3. |
Fig. 4. | Fig. 5. | Fig. 6. |
Fig. 7. | Fig. 8. | Fig. 9. |
Fig. 10. | Fig. 11. | Fig. 12. |
Fig. 13. | Fig. 14. | Fig. 15. |
Fig. 16. | Fig. 17. | Fig. 18. |
Fig. 19. | Fig. 20. | Fig. 21. |
Fig. 22. | Fig. 23. | |
« Previous Article | Next Article »
OSA is a member of CrossRef.