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]
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2008 (1)

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]

2007 (8)

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]

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).

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]

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]

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]

2006 (3)

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]

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]

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]

2005 (5)

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]

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

2004 (2)

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, 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]

2003 (2)

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

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]

2002 (1)

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 (1)

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

1998 (2)

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]

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 (1)

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 (1)

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

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] [PubMed]

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] [PubMed]

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]

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] [PubMed]

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] [PubMed]

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).
[CrossRef]

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] [PubMed]

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] [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]

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]

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] [PubMed]

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] [PubMed]

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).
[CrossRef]

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] [PubMed]

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).
[CrossRef]

Greenstein, J. L.

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

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] [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]

Henyey, L. G.

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

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] [PubMed]

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]

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]

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]

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] [PubMed]

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. 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] [PubMed]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[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] [PubMed]

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).
[CrossRef]

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] [PubMed]

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] [PubMed]

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] [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]

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]

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).
[PubMed]

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).
[CrossRef]

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).
[CrossRef]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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]

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).
[PubMed]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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] [PubMed]

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. (1)

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 (1)

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. (1)

Astrophys. (1)

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

Current Opinion in Biotechnology (1)

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

Current Opinion in Drug Discovery & Development (1)

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]

Cytometry Part A (1)

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 (4)

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]

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

J. Compt. Phys. (1)

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. (1)

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. (1)

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. (1)

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 (1)

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 (2)

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]

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. (2)

Optics Express (1)

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]

Phys. Med. Biol. (3)

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]

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]

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]

Proc. SPIE (1)

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]

Rev. Sci. Instrum. (1)

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]

SIAM J. Sci. Comp. (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]

SIAM J. Sci. Stat. Comput. (1)

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 (5)

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).

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

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

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).

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Figures (23)

Fig. 1.
Fig. 1.

Schematic of the numerical phantom used in this section. The source location is indicated by the read arrow, and the detector positions are given by the black arrows.

Fig. 2.
Fig. 2.

Normalized SNR values for the AC signal as a function of source-modulation frequency for six different source-detector pairs (see Fig. 1 for reference). The 4 graphs show 4 sets of optical properties. The absorption coefficient µ a increases with a column, while the reduced scattering coefficient µ s increases with a row.

Fig. 3.
Fig. 3.

Normalized SNR of phase shifts at various frequencies. The absorption coefficient µ a goes higher in the column direction, while the reduced scattering coefficient µ s goes higher in the row direction.

Fig. 4.
Fig. 4.

Problem set up and normalized SNR values; (a) schematic of a square phantom; (b) amplitude SNR values; (c) phase SNR values.

Fig. 5.
Fig. 5.

Reconstructed images of µ a and µ s for 5 different source-modulation frequencies using a numerical phantom. Noise was added to the synthetic data in accordance with Eq. (10).

Fig. 6.
Fig. 6.

Frequency dependence of correlation (ρ) and deviation (δ) factors for the reconstructed images shown in Fig. 5.

Fig. 7.
Fig. 7.

Experimental setup of the frequency-domain system; (a) photograph; (b) schematic: 1. Laser diode, 2. Laser diode drive, 3. & 7. Signal generator, 4. Sample, 5. Lens, 6. ICCD camera, 8. High rate imager, 9. Computer.

Fig. 8.
Fig. 8.

Schematic of an experimental square phantom; (a) dimensions; (b) & (c) camera orientation for measurments. The CCD camera is fixed to the left side from the phantom. The turning arrow indicates that measurements are taken counterclockwise over the three sides.

Fig. 9.
Fig. 9.

Reconstruction images of µ a and µ s for a tissue phantom, with well-known optical properties. The source modulation frequency was varied from 0 to 800 MHz.

Fig. 10.
Fig. 10.

Correlation (r) and deviation (d) factors for the reconstructed images shown in Fig. 9.

Fig. 11.
Fig. 11.

Structure of a finger phantom; (a) layout of major parts; (b) schematic of source-detector configuration.

Fig. 12.
Fig. 12.

Profiles of amplitude and phase shift obtained along the line-of-measurement at 600MHz. The laser source is located at the joint center, on the opposite side of the phantom (see Fib. 11b).

Fig. 13.
Fig. 13.

SNR values of amplitude and phase shift obtained for the real finger phantom; (a) no RA; (b) RA

Fig. 14.
Fig. 14.

The schematic of the finger phantom: cylinder height H=3.2 cm, diameter D=2 cm; (a) source-detector configuration; (b) computation domain with 11023 tetrahedrons and simplified cross-section view of the orientation of the finger joint phantom (red: bone, blue: synovial fluid, green: skin tissue).

Fig. 15.
Fig. 15.

Example of reconstructed distributions of µ a values for the healthy (left) and RA (right) finger phantom. In this case the source-modulation frequency was 600 MHz.

Fig. 16.
Fig. 16.

Interactive images using VolView software, obtained for Fig. 15. (a) Healthy (View 1). (b) Affected (View 2).

Fig. 17.
Fig. 17.

Reconstruction images of µ s obtained for the healthy finger-joint phantom at different frequencies. Note that the cross-talk in the bone is greatly diminished with increasing frequency. Note that the cross-talk in the bone is greatly diminished with increasing frequency.

Fig. 18.
Fig. 18.

Interactive images using VolView software, obtained for Fig. 17. The images are shown here for (a) 0 MHz (View 3) and (b) 600 MHz (View 4) only.

Fig. 19.
Fig. 19.

Numerical model of a mouse anatomy. Black arrows indicate cross-section for which reconstructions results were produced.

Fig. 20.
Fig. 20.

Cross-sectional images of µ a and µ s in the brain of the virtual mouse, obtained with source-modulation frequencies of f=0 MHz (steady state) and f=600 MHz.

Fig. 21.
Fig. 21.

Correlation (ρ)(left) and deviation (δ)(right) factors for the reconstructed µ a and µ s images in a cross-section that includes the brain of the virtual mouse (see Figs. 19 and 20), obtained with the noise-added synthetic data at 0 (steady-state), 200, 400, 600, and 800 MHz.

Fig. 22.
Fig. 22.

Same as Fig. 21, however for images of a cross-section that includes the lungs of the virtual mouse in Fig. 19.

Fig. 23.
Fig. 23.

Same as Fig. 22, however for images of a cross-section that includes the liver of the virtual mouse in Fig. 19.

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Tables (3)

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Table 1. Optical properties of the homogeneous numerical phantom for the SNR study.

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Table 2. Optical properties of the finger phantom shown in Fig. 11. The two sets of properties mimic the fingers of a normal healthy person and a patient affected by rheumatoid arthritis.

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Table 3. Min. and max. values of reconstructed µ a and µ s for the ROI that covers the joint center and the bone area while excluding 2mm from the boundary. The values in parentheses represent the ratios (max./min.).

Equations (13)

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( · Ω ) ψ ( r , Ω , ϖ ) + ( μ a + μ s + i ϖ c ) ψ ( r , Ω , ϖ ) = μ s 4 π 4 π ψ ( r , Ω + , ϖ ) Φ ( Ω + , Ω ) d Ω + + S m ( r , Ω , ϖ ) ,
Φ = 1 g 2 ( 1 + g 2 2 g cos θ ) 3 2 .
ψ b ( r b , Ω , ϖ ) n b · Ω < 0 = ψ 0 ( r b , Ω , ϖ ) + R ( Ω , Ω ) · ψ ( r b , Ω , ϖ ) n b · Ω > 0 ,
j = 1 N surf ( n j · Ω m ) ψ j m d A j + ( μ a + μ s + i ϖ c ) ψ N m = μ s 4 π Δ V N m = 1 N Ω ψ N m Φ m m ω m ,
A u = b ,
min f ( x ; u ) = 1 2 s = 1 N s d = 1 N d ( Q d u s z s , d σ s , d ) ( Q d u s z s , d σ s , d ) * ,
A T λ s = d = 1 N d Q d T ( Q d u s z s , d σ s , d ) * ,
μ a i f = s = 1 N s ( λ s T δ V i u s ) Re ,
μ s i f = s = 1 N s ( λ s T δ V i ( u s 1 4 π m u s Φ ω ) ) Re ,
SNR AC = AC σ AC AC DC ; SNR Φ = Φ σ Φ Φ SNR AC ,
ψ ( s , Ω , ϖ ) = ψ ( 0 , Ω , ϖ ) e 0 s ( μ a + μ s + i ϖ c ) ds + 0 s Q s ( s ) d s · e s s ( μ a + μ s + i ϖ c ) ds .
Q s ( s , Ω , ϖ ) = S m ( s , Ω , ϖ ) + μ s 4 π 4 π ψ ( s , Ω + , ϖ ) Φ ( Ω + , Ω ) d Ω + ,
ρ ( μ e , μ r ) = i = 1 N t ( μ i e μ ¯ i e ) ( μ i r μ ¯ i r ) ( N t 1 ) σ ( μ e ) σ ( μ r ) , δ ( μ e , μ r ) = i = 1 N t ( μ i e μ i r ) 2 N t σ ( μ e ) .

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