Abstract

We introduce a transport-theory-based PDE-constrained multispectral model for direct imaging of the spatial distributions of chromophores concentrations in biological tissue. The method solves the forward problem (boundary radiance at each wavelength) and the inverse problem (spatial distribution of chromophores concentrations), in an all-at-once manner in the framework of a reduced Hessian sequential quadratic programming method. To illustrate the code’s performance, we present numerical and experimental studies involving tumor bearing mice. It is shown that the PDE-constrained multispectral method accelerates the reconstruction process by up to 15 times compared to unconstrained reconstruction algorithms and provides more accurate results as compared to the so-called two-step approach to multi-wavelength imaging.

© 2010 OSA

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2009 (1)

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 Probl. 25(1), 015010 (2009).
[CrossRef]

2007 (2)

J. M. Lasker, J. M. Masciotti, M. Schoenecker, C. H. Schmitz, and A. H. Hielscher, “Digital-signal-processor-based dynamic imaging system for optical tomography,” Rev. Sci. Instrum. 78(8), 083706 (2007).
[CrossRef] [PubMed]

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

2006 (1)

K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28(4), 1463–1489 (2006).
[CrossRef]

2005 (2)

2004 (3)

J. Glade Bender, E. M. Cooney, J. J. Kandel, and D. J. Yamashiro, “Vascular remodeling and clinical resistance to antiangiogenic cancer therapy,” Drug Resist. Updat. 7(4-5), 289–300 (2004).
[CrossRef] [PubMed]

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29(3), 256–258 (2004).
[CrossRef] [PubMed]

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9(5), 1046–1062 (2004).
[CrossRef] [PubMed]

2003 (3)

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

A. Corlu, T. Durduran, R. Choe, M. Schweiger, E. M. C. Hillman, S. R. Arridge, and A. G. Yodh, “Uniqueness and wavelength optimization in continuous-wave multispectral diffuse optical tomography,” Opt. Lett. 28(23), 2339–2341 (2003).
[CrossRef] [PubMed]

A. D. Klose and A. H. Hielscher, “Quasi-newton methods in optical tomographic image reconstruction,” Inverse Probl. 19(2), 387 (2003).
[CrossRef]

2002 (1)

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[PubMed]

2001 (1)

1998 (1)

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(5), 1285–1302 (1998).
[CrossRef] [PubMed]

1986 (1)

Y. Saad and M. H. Schultz, “GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. Comput. 7(3), 856–869 (1986).
[CrossRef]

Abdoulaev, G. S.

G. S. Abdoulaev, K. Ren, and A. H. Hielscher, “Optical tomography as a PDE-constrained optimization problem,” Inverse Probl. 21(5), 1507–1530 (2005).
[CrossRef]

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9(5), 1046–1062 (2004).
[CrossRef] [PubMed]

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9(5), 1046–1062 (2004).
[CrossRef] [PubMed]

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[PubMed]

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(5), 1285–1302 (1998).
[CrossRef] [PubMed]

Arridge, S. R.

Bal, G.

K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28(4), 1463–1489 (2006).
[CrossRef]

Barbour, R. L.

Y. Pei, H. L. Graber, and R. L. Barbour, “Influence of systematic errors in reference states on image quality and on stability of derived information for DC optical imaging,” Appl. Opt. 40(31), 5755–5769 (2001).
[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(5), 1285–1302 (1998).
[CrossRef] [PubMed]

Beuthan, J.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[PubMed]

Bluestone, A. Y.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9(5), 1046–1062 (2004).
[CrossRef] [PubMed]

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[PubMed]

Boas, D. A.

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29(3), 256–258 (2004).
[CrossRef] [PubMed]

Boverman, G.

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

Brooks, D. H.

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

Carp, S. A.

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

Choe, R.

Cooney, E. M.

J. Glade Bender, E. M. Cooney, J. J. Kandel, and D. J. Yamashiro, “Vascular remodeling and clinical resistance to antiangiogenic cancer therapy,” Drug Resist. Updat. 7(4-5), 289–300 (2004).
[CrossRef] [PubMed]

Corlu, A.

Culver, J. P.

Durduran, T.

Fang, Q.

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

Frischer, J. S.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Glade Bender, J.

J. Glade Bender, E. M. Cooney, J. J. Kandel, and D. J. Yamashiro, “Vascular remodeling and clinical resistance to antiangiogenic cancer therapy,” Drug Resist. Updat. 7(4-5), 289–300 (2004).
[CrossRef] [PubMed]

Graber, H. L.

Hielscher, A. H.

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 Probl. 25(1), 015010 (2009).
[CrossRef]

J. M. Lasker, J. M. Masciotti, M. Schoenecker, C. H. Schmitz, and A. H. Hielscher, “Digital-signal-processor-based dynamic imaging system for optical tomography,” Rev. Sci. Instrum. 78(8), 083706 (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. Comput. 28(4), 1463–1489 (2006).
[CrossRef]

G. S. Abdoulaev, K. Ren, and A. H. Hielscher, “Optical tomography as a PDE-constrained optimization problem,” Inverse Probl. 21(5), 1507–1530 (2005).
[CrossRef]

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9(5), 1046–1062 (2004).
[CrossRef] [PubMed]

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9(5), 1046–1062 (2004).
[CrossRef] [PubMed]

A. D. Klose and A. H. Hielscher, “Quasi-newton methods in optical tomographic image reconstruction,” Inverse Probl. 19(2), 387 (2003).
[CrossRef]

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[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(5), 1285–1302 (1998).
[CrossRef] [PubMed]

Hillman, E. M. C.

Huang, J.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Kandel, J. J.

J. Glade Bender, E. M. Cooney, J. J. Kandel, and D. J. Yamashiro, “Vascular remodeling and clinical resistance to antiangiogenic cancer therapy,” Drug Resist. Updat. 7(4-5), 289–300 (2004).
[CrossRef] [PubMed]

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Kim, E. S.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Kim, H. K.

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 Probl. 25(1), 015010 (2009).
[CrossRef]

Klose, A. D.

A. D. Klose and A. H. Hielscher, “Quasi-newton methods in optical tomographic image reconstruction,” Inverse Probl. 19(2), 387 (2003).
[CrossRef]

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[PubMed]

Kopans, D. B.

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

Lasker, J.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9(5), 1046–1062 (2004).
[CrossRef] [PubMed]

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[PubMed]

Lasker, J. M.

J. M. Lasker, J. M. Masciotti, M. Schoenecker, C. H. Schmitz, and A. H. Hielscher, “Digital-signal-processor-based dynamic imaging system for optical tomography,” Rev. Sci. Instrum. 78(8), 083706 (2007).
[CrossRef] [PubMed]

Lee, K.

Li, A.

Mansukhani, M.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Masciotti, J. M.

J. M. Lasker, J. M. Masciotti, M. Schoenecker, C. H. Schmitz, and A. H. Hielscher, “Digital-signal-processor-based dynamic imaging system for optical tomography,” Rev. Sci. Instrum. 78(8), 083706 (2007).
[CrossRef] [PubMed]

McCrudden, K. W.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Miller, E. L.

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29(3), 256–258 (2004).
[CrossRef] [PubMed]

Moore, R. H.

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

Netz, U.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[PubMed]

New, T.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

O’toole, K.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Pei, Y.

Ren, K.

K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28(4), 1463–1489 (2006).
[CrossRef]

G. S. Abdoulaev, K. Ren, and A. H. Hielscher, “Optical tomography as a PDE-constrained optimization problem,” Inverse Probl. 21(5), 1507–1530 (2005).
[CrossRef]

Saad, Y.

Y. Saad and M. H. Schultz, “GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. Comput. 7(3), 856–869 (1986).
[CrossRef]

Schmitz, C. H.

J. M. Lasker, J. M. Masciotti, M. Schoenecker, C. H. Schmitz, and A. H. Hielscher, “Digital-signal-processor-based dynamic imaging system for optical tomography,” Rev. Sci. Instrum. 78(8), 083706 (2007).
[CrossRef] [PubMed]

Schoenecker, M.

J. M. Lasker, J. M. Masciotti, M. Schoenecker, C. H. Schmitz, and A. H. Hielscher, “Digital-signal-processor-based dynamic imaging system for optical tomography,” Rev. Sci. Instrum. 78(8), 083706 (2007).
[CrossRef] [PubMed]

Schultz, M. H.

Y. Saad and M. H. Schultz, “GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. Comput. 7(3), 856–869 (1986).
[CrossRef]

Schweiger, M.

Selb, J.

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[CrossRef] [PubMed]

Serur, A.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Soffer, S. Z.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Stewart, M.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9(5), 1046–1062 (2004).
[CrossRef] [PubMed]

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[PubMed]

Yamashiro, D. J.

J. Glade Bender, E. M. Cooney, J. J. Kandel, and D. J. Yamashiro, “Vascular remodeling and clinical resistance to antiangiogenic cancer therapy,” Drug Resist. Updat. 7(4-5), 289–300 (2004).
[CrossRef] [PubMed]

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Yodh, A. G.

Yokoi, A.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Yuan, J.

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Zhang, Q.

Appl. Opt. (2)

Dis. Markers (1)

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).
[PubMed]

Drug Resist. Updat. (1)

J. Glade Bender, E. M. Cooney, J. J. Kandel, and D. J. Yamashiro, “Vascular remodeling and clinical resistance to antiangiogenic cancer therapy,” Drug Resist. Updat. 7(4-5), 289–300 (2004).
[CrossRef] [PubMed]

Inverse Probl. (3)

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 Probl. 25(1), 015010 (2009).
[CrossRef]

G. S. Abdoulaev, K. Ren, and A. H. Hielscher, “Optical tomography as a PDE-constrained optimization problem,” Inverse Probl. 21(5), 1507–1530 (2005).
[CrossRef]

A. D. Klose and A. H. Hielscher, “Quasi-newton methods in optical tomographic image reconstruction,” Inverse Probl. 19(2), 387 (2003).
[CrossRef]

J. Biomed. Opt. (1)

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, G. S. Abdoulaev, and A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9(5), 1046–1062 (2004).
[CrossRef] [PubMed]

J. Pediatr. Surg. (1)

A. Yokoi, K. W. McCrudden, J. Huang, E. S. Kim, S. Z. Soffer, J. S. Frischer, A. Serur, T. New, J. Yuan, M. Mansukhani, K. O’toole, D. J. Yamashiro, and J. J. Kandel, “Human epidermal growth factor receptor signaling contributes to tumor growth via angiogenesis in her2/neu-expressing experimental Wilms’ tumor,” J. Pediatr. Surg. 38(11), 1569–1573 (2003).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Med. Biol. (2)

G. Boverman, Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore, D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobin in the compressed breast with diffuse optical tomography,” Phys. Med. Biol. 52(12), 3619–3641 (2007).
[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(5), 1285–1302 (1998).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

J. M. Lasker, J. M. Masciotti, M. Schoenecker, C. H. Schmitz, and A. H. Hielscher, “Digital-signal-processor-based dynamic imaging system for optical tomography,” Rev. Sci. Instrum. 78(8), 083706 (2007).
[CrossRef] [PubMed]

SIAM J. Sci. Comput. (2)

K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28(4), 1463–1489 (2006).
[CrossRef]

Y. Saad and M. H. Schultz, “GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. Comput. 7(3), 856–869 (1986).
[CrossRef]

Other (5)

S. Prahl, “Optical properties spectra,” retrieved 16 March 2003, http://omlc.ogi.edu/spectra/index.html , 2001.

J. Nocedal and S. J. Wright, Numerical optimization, (Spinger-Verlag, New York, 1999).

M. Modest, Riative heat transfer, MacGraw-Hill Inc., New York, 1993.

L. C. Enfield, A. P. Gibson, J. C. Hebden, and M. Douek, “Optical tomography of breast cancer—monitoring response to primary medical therapy,” Targ. Oncol. 4(3) 219-233 (2009).
[CrossRef]

J. Masciotti, F. Provenzano, J. Papa, A. 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,” in Multimodal Biomedical Imaging; Fred S. Azar, Dimitris N. Metaxas, eds., SPIE International Symposium on Biomedical Optics, Proc. SPIE 6081, #608105 (2006).

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Figures (6)

Fig. 1
Fig. 1

Circular enclosure (left) and absorption spectra of HbO2 (right): the test medium has two objects of perturbation: one in [HbO2] and one in [Hb].

Fig. 2
Fig. 2

Convergence history of the PDE-constrained multispectral method with iteration: (a) forward error; (b) inverse error.

Fig. 3
Fig. 3

Images of reconstructed [HbO2] (top row) and [Hb] (bottom row), obtained with the PDE-constrained multispectral and unconstrained two-step methods for two different wavelength sets.

Fig. 4
Fig. 4

Optical imaging probe with mouse positioned in the cylinder (a) and signal changes observed over a 5 day period for the sum of all measurements (b).

Fig. 5
Fig. 5

Reconstructed distributions of [THb] (1st row), [HbO2](2nd row) and [Hb] (3rd row) as observed over the 5 day period, using the proposed PDE-constrained multispectral method, with a wavelength set of 760nm and 830 nm. Shown is the 2cmx3cmx3cm volume that includes a growing tumor in vivo.

Fig. 6
Fig. 6

Reconstructed distributions of [THb](1st row), [HbO2](2nd row) and [Hb](3rd row) over a 5-day period, using the conventional two-step method, with a wavelength set of 760nm and 830 nm. Shown is the 2cmx3cmx3cm volume that includes a growing tumor in vivo.

Tables (2)

Tables Icon

Table 1 Chromophore concentrations and optical properties of the background medium and the objects

Tables Icon

Table 2 Image quality of reconstructed [HbO2] and [Hb] obtained with the PDE-constrained multispectral and unconstrained two-step methods

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

[ Ω + μ a ( λ ) + μ s ( λ ) + i ω c ] u λ ( r , Ω , ω ) = μ s λ 4 π 4 π u λ ( r , Ω + , ω ) Φ ( Ω + , Ω ) d Ω + + Q λ ( r , Ω , ω )
μ a ( λ ) = i = 1 N c ε i ( λ ) C i
ϕ [ μ a ( λ n ) , μ s ( λ n ) ] = 1 2 d = 1 N D | Q u d λ z d λ | 2 .
[ HbO 2 Hb Water Lipid ] = [ ε HbO 2 λ 1 ε Hb λ 1 ε Water λ 1 ε Lipid λ 1 ε HbO 2 λ 2 ε Hb λ 2 ε Water λ 2 ε Lipid λ 2 ε HbO 2 λ 3 ε Hb λ 3 ε Water λ 3 ε Lipid λ 3 ε HbO 2 λ 4 ε Hb λ 4 ε Water λ 4 ε Lipid λ 4 ] 1 [ μ a ( λ 1 ) μ a ( λ 2 ) μ a ( λ 3 ) μ a ( λ 4 ) ]
f ( C i ) = n = 1 N λ ϕ [ μ a ( λ n ) , μ s ( λ n ) ] = 1 2 n = 1 N λ d = 1 N D | Q u d λ n z d λ n | 2
min   f ( μ λ ; u λ ) = 1 2 | Q u λ z λ o b s | 2 + β R   subject to  c ( μ λ ; u λ ) = A u λ b = 0
minimize     f ( μ λ ) = 1 2 | Q A 1 b z λ o b s | 2 + β R
L ( μ λ , u λ ; η λ ) 1 2 | Q u λ z λ o b s | 2 + η λ T ( A u λ b )
min   f ( x ; u λ ) = 1 2 λ | Q u λ z o b s | 2 + β R ( x )   subject to  c ( x ; u λ ) = A u λ b = 0
L ( x , u λ ; η λ ) 1 2 λ | Q u λ z λ o b s | 2 + λ η λ T ( A u λ b )
min     Δ x k T g r k + 1 2 Δ x k T H r k Δ x k    subject to    C k Δ p k + ( A u λ b ) k = 0
Δ x k = ( H r k ) 1 g r k Δ u λ k = A 1 [ ( A u λ ) k b ( A u λ ) x k T Δ x k ]
g r , j k = λ ε j λ ( u λ k T A x j T η λ k ) + x j f k
A k T η λ k = Q T ( Q u λ k z λ o b s ) *
φ η k ( u λ , x ) = f ( u λ , x ) + λ η λ A u λ b 1
x k + 1 = x k + α k Δ x u λ k + 1 = u λ k + α k Δ u λ k .
ϕ [ HbO 2 ,Hb ] = 1 2 λ s d | M tar , s , d λ M ref, s , d λ P ref , s , d λ P tar , s , d λ | 2

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