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

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    [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]
  7. A. D. Klose and A. H. Hielscher, "Quasi-newton methods in optical tomographic image reconstruction," Inverse Problems 19, 309-87 (2003).
    [CrossRef]
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    [CrossRef]
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  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).
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    [CrossRef]

2008

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]

2007

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]

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]

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).

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]

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]

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).

2006

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).

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]

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]

2005

A. H, Hielscher, "Optical tomographic imaging of small animals," Current Opinion in Biotechnology 16, 79-88 (2005).
[CrossRef]

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]

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]

G. S. Abddoulaev, K. Ren and A.H. Hielscher, " Optical tomography as a PDE-constrained optimization problem," Inverse Problems 21, 1507-1530 (2005).
[CrossRef]

2004

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]

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]

2003

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).

A. D. Klose and A. H. Hielscher, "Quasi-newton methods in optical tomographic image reconstruction," Inverse Problems 19, 309-87 (2003).
[CrossRef]

2002

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]

1999

S. R. Arridge, "Optical tomography in medical imaging," Inverse Problems 15, R41-93 (1999).
[CrossRef]

1998

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]

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]

1989

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).

1941

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. 90, 70 (1941).

Abddoulaev, G. S.

G. S. Abddoulaev, K. Ren and A.H. Hielscher, " Optical tomography as a PDE-constrained optimization problem," Inverse Problems 21, 1507-1530 (2005).
[CrossRef]

Abdoulaev, G. S.

Alcouffe, R. E.

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]

Arridge, S. R.

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]

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]

S. R. Arridge, "Optical tomography in medical imaging," Inverse Problems 15, R41-93 (1999).
[CrossRef]

Askri, F.

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).

Backhaus, M.

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]

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]

Bal, G.

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]

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]

Bangerth, W.

Barbieri, B.

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).

Barbour, R. L.

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]

Baum, J. D.

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]

Ben Nasrallah, S.

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).

Ben Salah, M.

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).

Beuthan, J.

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]

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]

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]

Burmester, G. R.

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]

Carpenter, C. M.

Charette, A.

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]

Chatziioannou, A. F.

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).

Choe, R.

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]

Chow, P. L.

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).

Corlu, A.

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]

D'Amico, E.

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).

De, A.

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).

Dehghani, H.

Deroose, C. M.

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).

Durduran, T.

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]

Forero, J.

Gambhir, S. S.

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).

Gratton, E.

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).

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. 90, 70 (1941).

Grissa, H.

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).

Gu, X.

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]

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).

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. 90, 70 (1941).

Hermann, K.-G. A.

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]

Hielscher, A. H.

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]

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]

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]

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).

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]

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]

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]

A. D. Klose and A. H. Hielscher, "Quasi-newton methods in optical tomographic image reconstruction," Inverse Problems 19, 309-87 (2003).
[CrossRef]

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]

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).

Hielscher, A.H.

G. S. Abddoulaev, K. Ren and A.H. Hielscher, " Optical tomography as a PDE-constrained optimization problem," Inverse Problems 21, 1507-1530 (2005).
[CrossRef]

Holloway, J. P.

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]

Hueber, D.

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).

Hur, J.

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).

Jiang, H.

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]

Jiang, S.

Joshi, A.

Kandel, J.

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).

Kaufman, P. A.

Kim, H. K.

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]

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).

Klose, A. D.

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).

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]

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]

A. D. Klose and A. H. Hielscher, "Quasi-newton methods in optical tomographic image reconstruction," Inverse Problems 19, 309-87 (2003).
[CrossRef]

Kogel, C.

Loening, A. M.

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).

Löhner, R.

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]

Luo, H.

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]

Masciotti, J.

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).

Moa-Anderson, B.

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]

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]

Muller, G. A.

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]

Nassilä, I.

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]

Netz, U. J.

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]

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]

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]

Nilsson, F.Y.

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).

Papa, J.

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).

Patton, B. W.

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]

Paulsen, K. D.

Pogue, B. W.

Poplack, S. P.

Provenzano, F.

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).

Ray, P.

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).

Ren, K.

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]

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]

G. S. Abddoulaev, K. Ren and A.H. Hielscher, " Optical tomography as a PDE-constrained optimization problem," Inverse Problems 21, 1507-1530 (2005).
[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]

Rosen, M. A.

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]

Saad, Y.

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).

Scheel, A. K.

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]

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]

Schnall, M. D.

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]

Schultz, M. H.

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).

Schweiger, M.

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]

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]

Sevick-Muraca, E. M.

Tolmachev, V.

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).

Toronov, V.

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).

Wang, X.

Weaver, J. B.

Webb, A.

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).

Wells, W. A.

Wessels, J. T.

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]

Yamashiro, D.

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).

Yodh, A. G.

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]

Zhang, Q.

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]

Ann. Rheum. Dis.

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]

Annals of Nuclear Energy

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]

Appl. Opt.

Astrophys.

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. 90, 70 (1941).

Current Opinion in Biotechnology

A. H, Hielscher, "Optical tomographic imaging of small animals," Current Opinion in Biotechnology 16, 79-88 (2005).
[CrossRef]

Current Opinion in Drug Discovery & Development

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).

Cytometry Part A

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]

Inverse Problems

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).

S. R. Arridge, "Optical tomography in medical imaging," Inverse Problems 15, R41-93 (1999).
[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]

J. Compt. Phys.

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]

J. Nuclear Med.

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).

J. Opt. A: Pure Appl. Opt.

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]

J. Quant. Spec. Rad. Trans.

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]

JQSRT

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).

Opt. Express

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).

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]

Opt. Lett.

Optics Express

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]

Phys. Med. Biol.

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]

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]

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]

Proc. SPIE

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).

Rev. Sci. Instrum.

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]

SIAM J. Sci. Comp.

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]

SIAM J. Sci. Stat. Comput.

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).

Other

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).

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).

OlegM.  Alifanov, Inverse Heat Transfer Problems (Spring-Verlag, New York, 1994).

J. Nocedal and S. J. Wright, Numerical Optimization (Springer, New York, 2006).

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