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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 1, Iss. 3 — Oct. 1, 2010
  • pp: 812–824

PDE-constrained multispectral imaging of tissue chromophores with the equation of radiative transfer

Hyun Keol Kim, Molly Flexman, Darrell J. Yamashiro, Jessica J. Kandel, and Andreas H. Hielscher  »View Author Affiliations

Biomedical Optics Express, Vol. 1, Issue 3, pp. 812-824 (2010)

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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

OCIS Codes
(170.5280) Medical optics and biotechnology : Photon migration
(110.4234) Imaging systems : Multispectral and hyperspectral imaging
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
Image Reconstruction and Inverse Problems

Original Manuscript: June 14, 2010
Revised Manuscript: August 25, 2010
Manuscript Accepted: September 7, 2010
Published: September 8, 2010

Virtual Issues
Optical Imaging and Spectroscopy (2010) Biomedical Optics Express

Hyun Keol Kim, Molly Flexman, Darrell J. Yamashiro, Jessica J. Kandel, and Andreas H. Hielscher, "PDE-constrained multispectral imaging of tissue chromophores with the equation of radiative transfer," Biomed. Opt. Express 1, 812-824 (2010)

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  1. 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]
  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]
  3. 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).
  4. A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005). [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. M. Modest, Riative heat transfer, MacGraw-Hill Inc., New York, 1993.
  13. 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]
  14. S. Prahl, “Optical properties spectra,” retrieved 16 March 2003, http://omlc.ogi.edu/spectra/index.html , 2001.
  15. 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]
  16. J. Nocedal and S. J. Wright, Numerical optimization, (Spinger-Verlag, New York, 1999).
  17. A. D. Klose and A. H. Hielscher, “Quasi-newton methods in optical tomographic image reconstruction,” Inverse Probl. 19(2), 387 (2003). [CrossRef]
  18. 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]
  19. 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]
  20. 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]
  21. 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]

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