Abstract

Optical measurements of tissue can be performed in discrete, time-averaged, and time-varying data collection modes. This information can be evaluated to yield estimates of either absolute optical coefficient values or some relative change in these values compared with a defined state. In the case of time-varying data, additional analysis can be applied to define various dynamic features. Here we have explored the accuracy with which such information can be recovered from dense scattering media using linear perturbation theory, as a function of the accuracy of the reference medium that serves as the initial guess. Within the framework of diffusion theory and a first-order solution, we have observed the following inequality regarding the sensitivity of computed measures to inaccuracy in the reference medium: Absolute measures ≫ relative measures > dynamic measures. In fact, the fidelity of derived dynamic measures was striking; we observed that accurate measures of dynamic behavior could be defined even if the quality of the image data from which these measures were derived was comparatively modest. In other studies we identified inaccuracy in the estimates of the reference detector values, and not to corresponding errors in the image operators, as the primary factor responsible for instability of absolute measures. The significance of these findings for practical imaging studies of tissue is discussed.

© 2001 Optical Society of America

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2000

1999

1996

T. M. Griffith, “Temporal chaos in the microcirculation,” Cardiovasc. Res. 31, 342–358 (1996).
[PubMed]

J. Theiler, P. E. Rapp, “Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram,” Electroencephalogr. Clin. Neurophysiol. 98, 213–222 (1996).
[CrossRef] [PubMed]

1995

R. L. Barbour, H. L. Graber, J. Chang, S.-L. S. Barbour, P. C. Koo, R. Aronson, “MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).

1994

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

1993

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65, 1331–1392 (1993).
[CrossRef]

1990

K. Briggs, “An improved method for estimating Liapunov exponents of chaotic time series,” Phys. Lett. A 151, 27–32 (1990).
[CrossRef]

1989

S. Sunberg, M. Castrén, “Drug- and temperature-induced changes in peripheral circulation measured by laser-Doppler flowmetry and digital-pulse plethysmography,” Scand. J. Clin. Lab. Invest. 46, 359–365 (1989).
[CrossRef]

1983

P. Grassberger, I. Procaccia, “Characterization of strange attractors,” Phys. Rev. Lett. 50, 346–349 (1983).
[CrossRef]

Abarbanel, H. D. I.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65, 1331–1392 (1993).
[CrossRef]

Andronica, R.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Arif, I.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A (to be published).

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 409–410.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

H. L. Graber, S. Zheng, Y. Pei, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 407–408.

R. L. Barbour, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, “Optical imaging of the response of vascular dynamics to a cold shock,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

Aronson, R.

R. L. Barbour, H. L. Graber, J. Chang, S.-L. S. Barbour, P. C. Koo, R. Aronson, “MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 87–120.

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 121–143.

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, 41–93 (1999).
[CrossRef]

S. R. Arridge, “The forward and inverse problems in time resolved infra-red imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 35–64.

Axelsson, O.

O. Axelsson, V. A. Barker, Finite Element Solution of Boundary Value Problems: Theory and Computation (Academic, New York, 1984).

Balachandran, B.

A. H. Nayfeh, B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (Wiley, New York, 1995), Chap. 7, Subsec. 7.4.

Barbour, R. L.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, J. Chang, S.-L. S. Barbour, P. C. Koo, R. Aronson, “MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” in Proceedings of Inter-Institute Workshop on in vivo Optical Imaging at the NIH, 1999 (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A (to be published).

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 121–143.

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 87–120.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

H. L. Graber, S. Zheng, Y. Pei, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 407–408.

R. L. Barbour, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, “Optical imaging of the response of vascular dynamics to a cold shock,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by dynamic optical tomography,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 153–163 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 409–410.

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

C. H. Schmitz, H. L. Graber, R. L. Barbour, “A fast versatile instrument for dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 94–96.

Barbour, S.-L. S.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, J. Chang, S.-L. S. Barbour, P. C. Koo, R. Aronson, “MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” in Proceedings of Inter-Institute Workshop on in vivo Optical Imaging at the NIH, 1999 (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

Barker, V. A.

O. Axelsson, V. A. Barker, Finite Element Solution of Boundary Value Problems: Theory and Computation (Academic, New York, 1984).

Bendat, J. S.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures, 2nd ed. (Wiley, New York, 1986), Chap. 12, Subsec. 12.1.

Blattman, S.

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” in Proceedings of Inter-Institute Workshop on in vivo Optical Imaging at the NIH, 1999 (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 409–410.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

Bluestone, A.

Boas, D. A.

X. Cheng, D. A. Boas, “Systematic diffuse optical image errors resulting from uncertainty in the background optical properties,” Opt. Express 4, 299–307 (1999), http://www.opticsexpress.org .
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2839, 320–327 (1995).
[CrossRef]

Bohrer, R. E.

S. W. Porges, R. E. Bohrer, “The analysis of periodic processes in psychophysiological research,” in Principles of Psychophysiology: Physical, Social, and Inferential Elements (Cambridge University, New York, 1991), pp. 708–753.

Briggs, K.

K. Briggs, “An improved method for estimating Liapunov exponents of chaotic time series,” Phys. Lett. A 151, 27–32 (1990).
[CrossRef]

Brown, R.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65, 1331–1392 (1993).
[CrossRef]

Castrén, M.

S. Sunberg, M. Castrén, “Drug- and temperature-induced changes in peripheral circulation measured by laser-Doppler flowmetry and digital-pulse plethysmography,” Scand. J. Clin. Lab. Invest. 46, 359–365 (1989).
[CrossRef]

Chance, B.

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).
[CrossRef] [PubMed]

V. Ntziachristos, B. Chance, A. G. Yodh, “Differential diffuse optical tomography,” Opt. Express 5, 230–242 (1999), http://www.opticsexpress.org .

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2839, 320–327 (1995).
[CrossRef]

Chang, J.

R. L. Barbour, H. L. Graber, J. Chang, S.-L. S. Barbour, P. C. Koo, R. Aronson, “MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 121–143.

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

Chang, J.-H.

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 87–120.

Cheng, X.

Graber, H. L.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, J. Chang, S.-L. S. Barbour, P. C. Koo, R. Aronson, “MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 121–143.

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” in Proceedings of Inter-Institute Workshop on in vivo Optical Imaging at the NIH, 1999 (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A (to be published).

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 87–120.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by dynamic optical tomography,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 153–163 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, “Optical imaging of the response of vascular dynamics to a cold shock,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 409–410.

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

C. H. Schmitz, H. L. Graber, R. L. Barbour, “A fast versatile instrument for dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 94–96.

H. L. Graber, S. Zheng, Y. Pei, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 407–408.

Grassberger, P.

P. Grassberger, I. Procaccia, “Characterization of strange attractors,” Phys. Rev. Lett. 50, 346–349 (1983).
[CrossRef]

Griffith, T. M.

T. M. Griffith, “Temporal chaos in the microcirculation,” Cardiovasc. Res. 31, 342–358 (1996).
[PubMed]

Hansen, P. C.

P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1998).
[CrossRef]

Hira, J.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A (to be published).

R. L. Barbour, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, “Optical imaging of the response of vascular dynamics to a cold shock,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

H. L. Graber, S. Zheng, Y. Pei, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 407–408.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 409–410.

Jenkins, G. M.

G. M. Jenkins, D. G. Watts, Spectral Analysis and its Applications (Holden-Day, Oakland, Calif., 1968).

Kak, A. C.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 214–218.

Koo, P. C.

R. L. Barbour, H. L. Graber, J. Chang, S.-L. S. Barbour, P. C. Koo, R. Aronson, “MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).

Lubowsky, J.

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

Luo, H.

Nayfeh, A. H.

A. H. Nayfeh, B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (Wiley, New York, 1995), Chap. 7, Subsec. 7.4.

Ntziachristos, V.

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).
[CrossRef] [PubMed]

V. Ntziachristos, B. Chance, A. G. Yodh, “Differential diffuse optical tomography,” Opt. Express 5, 230–242 (1999), http://www.opticsexpress.org .

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2839, 320–327 (1995).
[CrossRef]

Panetta, T.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” in Proceedings of Inter-Institute Workshop on in vivo Optical Imaging at the NIH, 1999 (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

Pei, Y.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” in Proceedings of Inter-Institute Workshop on in vivo Optical Imaging at the NIH, 1999 (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A (to be published).

R. L. Barbour, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, “Optical imaging of the response of vascular dynamics to a cold shock,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

Y. Pei, “Optical tomographic imaging using finite element method,” Ph.D. dissertation (Polytechnic University, Brooklyn, N.Y., 1999).

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by dynamic optical tomography,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 153–163 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 409–410.

H. L. Graber, S. Zheng, Y. Pei, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 407–408.

Piersol, A. G.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures, 2nd ed. (Wiley, New York, 1986), Chap. 12, Subsec. 12.1.

Porges, S. W.

S. W. Porges, R. E. Bohrer, “The analysis of periodic processes in psychophysiological research,” in Principles of Psychophysiology: Physical, Social, and Inferential Elements (Cambridge University, New York, 1991), pp. 708–753.

Procaccia, I.

P. Grassberger, I. Procaccia, “Characterization of strange attractors,” Phys. Rev. Lett. 50, 346–349 (1983).
[CrossRef]

Ramirez, N.

Rapp, P. E.

J. Theiler, P. E. Rapp, “Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram,” Electroencephalogr. Clin. Neurophysiol. 98, 213–222 (1996).
[CrossRef] [PubMed]

Schmitz, C. H.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A (to be published).

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” in Proceedings of Inter-Institute Workshop on in vivo Optical Imaging at the NIH, 1999 (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

C. H. Schmitz, H. L. Graber, R. L. Barbour, “A fast versatile instrument for dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 94–96.

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

Schnall, M.

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).
[CrossRef] [PubMed]

Sha, Q.

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Sidorowich, J. J.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65, 1331–1392 (1993).
[CrossRef]

Slaney, M.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 214–218.

Soller, I.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Sunberg, S.

S. Sunberg, M. Castrén, “Drug- and temperature-induced changes in peripheral circulation measured by laser-Doppler flowmetry and digital-pulse plethysmography,” Scand. J. Clin. Lab. Invest. 46, 359–365 (1989).
[CrossRef]

Theiler, J.

J. Theiler, P. E. Rapp, “Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram,” Electroencephalogr. Clin. Neurophysiol. 98, 213–222 (1996).
[CrossRef] [PubMed]

Tsimring, L. S.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65, 1331–1392 (1993).
[CrossRef]

Wang, Y.

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 87–120.

Watts, D. G.

G. M. Jenkins, D. G. Watts, Spectral Analysis and its Applications (Holden-Day, Oakland, Calif., 1968).

Yodh, A. G.

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).
[CrossRef] [PubMed]

V. Ntziachristos, B. Chance, A. G. Yodh, “Differential diffuse optical tomography,” Opt. Express 5, 230–242 (1999), http://www.opticsexpress.org .

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2839, 320–327 (1995).
[CrossRef]

Zheng, S.

R. L. Barbour, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, “Optical imaging of the response of vascular dynamics to a cold shock,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 409–410.

H. L. Graber, S. Zheng, Y. Pei, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 407–408.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

Zhong, S.

C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
[CrossRef]

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” in Proceedings of Inter-Institute Workshop on in vivo Optical Imaging at the NIH, 1999 (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A (to be published).

Appl. Opt.

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IEEE Comput. Sci. Eng.

R. L. Barbour, H. L. Graber, J. Chang, S.-L. S. Barbour, P. C. Koo, R. Aronson, “MRI-guided optical tomography: prospects and computation for a new imaging method,” IEEE Comput. Sci. Eng. 2(4), 63–77 (1995).

Inverse Probl.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, 41–93 (1999).
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Opt. Express

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V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Rev. Mod. Phys.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65, 1331–1392 (1993).
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G. M. Jenkins, D. G. Watts, Spectral Analysis and its Applications (Holden-Day, Oakland, Calif., 1968).

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures, 2nd ed. (Wiley, New York, 1986), Chap. 12, Subsec. 12.1.

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, J. Hira, I. Arif, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A (to be published).

More precisely, while certainly there are dynamic-feature measures (e.g., Fourier transform amplitude at a given frequency, magnitude of the cross correlation at a given time lag) whose values would be affected by a change in the properties assigned to the reference medium, there also are others [e.g., the frequency at which a peak occurs (or fails to occur) in a Fourier transform map] for which there should be essentially no effect.

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 121–143.

R. L. Barbour, H. L. Graber, Y. Wang, J.-H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 87–120.

S. R. Arridge, “The forward and inverse problems in time resolved infra-red imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute for Advanced Optical Technologies Series (SPIE Optical Engineering Press, Bellingham, Wash., 1993), pp. 35–64.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 214–218.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2839, 320–327 (1995).
[CrossRef]

R. L. Barbour, H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, “Spatiotemporal imaging of vascular reactivity by optical tomography,” in Proceedings of Inter-Institute Workshop on in vivo Optical Imaging at the NIH, 1999 (Optical Society of America, Washington, D.C., 2000), pp. 161–166.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatio-temporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by dynamic optical tomography,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 153–163 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, C. H. Schmitz, “Imaging of vascular chaos,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 577–590 (2001).
[CrossRef]

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

O. Axelsson, V. A. Barker, Finite Element Solution of Boundary Value Problems: Theory and Computation (Academic, New York, 1984).

A. H. Nayfeh, B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (Wiley, New York, 1995), Chap. 7, Subsec. 7.4.

R. L. Barbour, R. Andronica, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPTIscanner, a general purpose optical tomographic imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

C. H. Schmitz, H. L. Graber, R. L. Barbour, “A fast versatile instrument for dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 94–96.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 409–410.

S. Blattman, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, R. L. Barbour, “Imaging of differential reactivity of the vascular tree in the human forearm by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

H. L. Graber, S. Zheng, Y. Pei, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 407–408.

R. L. Barbour, H. L. Graber, S. Zheng, Y. Pei, J. Hira, I. Arif, “Optical imaging of the response of vascular dynamics to a cold shock,” in Biomedical Topical Meetings, Postconference Digest, Vol. 38 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 458–460.

P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1998).
[CrossRef]

Y. Pei, “Optical tomographic imaging using finite element method,” Ph.D. dissertation (Polytechnic University, Brooklyn, N.Y., 1999).

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Figures (10)

Fig. 1
Fig. 1

Geometry and composition of the tissuelike target media and source–detector configuration used for measurement simulations and imaging reconstructions. Target diameter, 8 cm; inclusion diameter, 1 cm; distance between inclusions’ centers, 3 cm.

Fig. 2
Fig. 2

Reconstructed images of absorption coefficient obtained at time points (a) 1, (b) 5, and (c) 13, based on the simulated dynamic measurement data associated with the time-varying absorption [see Figs. 3(a) and 3(b) for functional form of fluctuations]. Accurate prior knowledge of the optical properties of the background, i.e., μ a = 0.06 cm-1 and μs = 10 cm-1, was assumed.

Fig. 3
Fig. 3

Panels (a) and (b) are plots of the temporally fluctuating μ a assigned to the left- and the right-hand inclusions, respectively, and the corresponding PSS trajectories for m = 3, τ = 1 (see Subsection 3.E for explanation of symbols). Panels (c) and (d) are the corresponding plots of reconstructed time series for selected pixels lying within the two inclusions (examples of individual reconstructed images in the time series are shown in Fig. 2).

Fig. 4
Fig. 4

Demonstration of weak dependence on reference medium properties of image time series obtained by use of Eq. (3) to perform the reconstructions. Conditions modeled are the same as for Fig. 3, except that optical coefficients of reference medium are μ a = 0.02 cm-1 and μs = 25 cm-1. Panels (a) and (b) are time courses and corresponding PSS trajectories for selected pixels in the left- and the right-hand inclusions, respectively.

Fig. 5
Fig. 5

Results obtained from test case 1 listed in Table 1 {i.e., NDM formulation [Eq. (3)], “experimental” data fixed, reference medium properties are varied}: (a) absorption profiles, (b) diffusion profiles.

Fig. 6
Fig. 6

Results obtained from test case 2 listed in Table 1 {i.e., conventional first-order Born formulation [Eq. (1)], “experimental” data fixed, reference medium properties are varied}: (a) absorption profiles, (b) diffusion profiles. Note that in every instance, the set of reference properties used in the calculation of the computed detector readings is the same as that used in the calculation of the imaging operator.

Fig. 7
Fig. 7

Results obtained from test case 3 listed in Table 1 (i.e., conventional first-order Rytov formulation, “experimental” data fixed, reference medium properties are varied): (a) absorption profiles, (b) diffusion profiles. Note that in every instance, the set of reference properties used in the calculation of the computed detector readings is the same as that used in the calculation of the imaging operator.

Fig. 8
Fig. 8

Results obtained from test case 4 listed in Table 1 {i.e., conventional first-order Born formulation [Eq. (1)], “experimental” data and computed detector readings fixed, reference medium properties used for computation of imaging operator are varied}: (a) absorption profiles; (b) diffusion profiles.

Fig. 9
Fig. 9

Results obtained from test case 5 listed in Table 1 {i.e., conventional first-order Born formulation [Eq. (1)], “experimental” data and imaging operator fixed, reference medium properties used for computation of computed detector readings are varied}: (a) absorption profiles; (b) diffusion profiles.

Fig. 10
Fig. 10

(a) Dependence of δu r , i.e., (δu r ) i = (u r ) i {[u i - (u 0) i ]/(u 0) i }, on angular separation between source and detector, for reference-medium properties corresponding to row 3 of Fig. 5 (test case 1, NDM formulation). (b) Dependence of δu, i.e., (δu) i = u i - (u r ) i , on angular separation between source and detector, for reference-medium properties corresponding to row 3 of Fig. 6 (test case 2, standard Born formulation). The source located at the “12 o’clock” position indicated in Fig. 1 was used for both panels. Because the quantities plotted on the ordinate scales take on positive and negative values, logarithmic scaling is not appropriate. Instead, we make use of the transformation y = x 1/n , with n = 7 in the examples plotted here, to permit the display of data ranging over several orders of magnitude on a single set of axes.

Tables (2)

Tables Icon

Table 1 Summary of the Test Cases Exploreda

Tables Icon

Table 2 Ratio of Average Contrasts of Reconstructed Absorption and Diffusion Coefficients Shown in Figs. 5(a) and 5(b), Respectivelya,b

Equations (5)

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

u-ur=δu=Wrδx,
u1i-u2iu2iuri=jWrijδxj,
Du1Du2-1-Iur=Wrδx,
δx=Wr-1u1-ur+Wr-1DurDu2-1-Iu1,
·Drϕr-μarϕr=-δr-rs,  rΛ,

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