Abstract

Methods used in optical tomography have thus far proven to produce images of complex target media (e.g., tissue) having, at best, relatively modest spatial resolution. This presents a challenge in differentiating artifact from true features. Further complicating such efforts is the expectation that the optical properties of tissue for any individual are largely unknown and are likely to be quite variable due to the occurrence of natural vascular rhythms whose amplitudes are sensitive to a host of autonomic stimuli that are easily induced. We recognize, however, that rather than frustrating efforts to validate the accuracy of image features, the time-varying properties of the vasculature can be exploited to aid in such efforts, owing to the known structure-dependent frequency response of the vasculature and to the fact that hemoglobin is a principal contrast feature of the vasculature at near-infrared wavelengths. To accomplish this, it is necessary to generate a time series of image data. In this report we have tested the hypothesis that through analysis of time-series data, independent contrast features can be derived that serve to validate, at least qualitatively, the accuracy of imaging data, in effect establishing a self-referencing scheme. A significant finding is the observation that analysis of such data can produce high-contrast images that reveal features that are mainly obscured in individual image frames or in time-averaged image data. Given the central role of hemoglobin in tissue function, this finding suggests that a wealth of new features associated with vascular dynamics can be identified from the analysis of time-series image data.

© 2001 Optical Society of America

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2001

2000

1999

1998

S. R. Arridge, W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).
[CrossRef]

J. Mayhew, D. Hu, Y. Zheng, S. Askew, Y. Hou, J. Berwick, P. J. Coffey, N. Brown, “An evaluation of linear model analysis techniques for processing images of microcirculation activity,” Neuroimage 7, 49–71 (1998).
[CrossRef] [PubMed]

A. H. Hielscher, R. E. Alcouffe, 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]

1997

C. Sohn, F. Beldermann, H. Frey, S. Reinhart, J. Sohn, G. Bastert, “Durchblutungsdiagnostik von Mammatumoren unter Blutdruckerhöhung: neue Möglichkeiten in der Dignitätsdiagnostik,” Radiologe 37, 643–650 (1997).
[CrossRef] [PubMed]

A. Villringer, B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435–442 (1997).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Österberg, M. S. Patterson, “Frequency-domain optical image reconstruction in turbid media: an experimental study of single-target detectability,” Appl. Opt. 36, 52–63 (1997).
[CrossRef] [PubMed]

L. McMackin, R. J. Hugo, R. E. Pierson, C. R. Truman, “High speed optical tomography system for imaging dynamic transparent media,” Opt. Express 1, 302–311 (1997). http://www.opticsexpress.org .
[CrossRef] [PubMed]

1996

J. K. Kantors, M. V. Højgaard, E. Agner, N.-H. Holstein-Rathlou, “Short- and long-term variations in non-linear dynamics of heart rate variability,” Cardiovasc. Res. 31, 400–409 (1996).
[CrossRef]

P. Mansier, J. Clairambault, N. Charlotte, C. Médigue, C. Vermeiren, G. LePape, F. Carré, A. Gounaropoulou, B. Swynghedauw, “Linear and non-linear analyses of heart rate variability: a minireview,” Cardiovasc. Res. 31, 371–379 (1996).
[CrossRef] [PubMed]

J. E. W. Mayhew, S. Askew, Y. Zheng, J. Porrill, G. W. M. Westby, P. Redgrave, D. M. Rector, R. M. Harper, “Cerebral vasomotion: a 0.1-Hz oscillation in reflected light imaging of neural activity,” Neuroimage 4, 183–193 (1996).
[CrossRef] [PubMed]

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 1, 343–355 (1996).
[CrossRef]

1995

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

H. Liu, B. Chance, A. H. Hielscher, S. L. Jacques, F. K. Tittel, “Influence of blood vessels on the measurement of hemoglobin oxygenation as determined by time-resolved reflectance spectroscopy,” Med. Phys. 22, 1209–1217 (1995).
[CrossRef] [PubMed]

C. Holvombe, N. Pugh, K. Lyons, A. Douglas-Jones, R. E. Mansel, K. Horgan, “Blood flow in breast cancer and fibroadenoma estimated by colour Doppler ultrasonography,” Br. J. Surg. 82, 787–788 (1995).
[CrossRef]

J. Theiler, “On the evidence for low-dimensional chaos in an epileptic electroencephalogram,” Phys. Lett. A 196, 334–341 (1995).
[CrossRef]

J. Bélair, L. Glass, U. an der Heiden, J. Milton, “Dynamical disease: identification, temporal aspects and treatment strategies of human illness,” Chaos 5, 1–7 (1995).
[CrossRef] [PubMed]

1994

J. N. Weiss, A. Garfinkel, M. L. Spano, W. L. Ditto, “Chaos and chaos control in biology,” J. Clin. Invest. 93, 1355–1360 (1994).
[CrossRef] [PubMed]

C. G. Ellis, S. M. Wrigley, A. C. Groom, “Heterogeneity of red blood cell perfusion in capillary networks supplied by a single arteriole in resting skeletal muscle,” Circ. Res. 75, 357–368 (1994).
[CrossRef] [PubMed]

T. M. Griffith, “Chaos and fractals in vascular biology,” Vasc. Med. Rev. 5, 161–182 (1994).

J. Folkman, “Angiogenesis and breast cancer,” J. Clin. Oncol. 12, 441–443 (1994).
[PubMed]

1993

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite-element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vision 3, 263–283 (1993).
[CrossRef]

1992

I. T. Joliffe, B. J. T. Morgan, “Principal component analysis and exploratory factor analysis,” Stat. Meth. Med. Res. 1, 69–95 (1992).
[CrossRef]

C. Franssen, H. Wollershein, A. de Haan, T. Thien, “The influence of different beta-blocking drugs on the peripheral circulation in Raynaud’s phenomenon and in hypertension,” J. Clin. Pharm. 32, 652–659 (1992).
[CrossRef]

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intraplipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef]

1991

1990

M. H. Sherebrin, R. Z. Sherebrin, “Frequency analysis of the peripheral pulse wave detected in the finger with a photoplethysmograph,” IEEE Trans. Biomed. Eng. 37, 313–317 (1990).
[CrossRef] [PubMed]

1989

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

1986

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 (1986).
[CrossRef]

1984

C. W. Song, A. Lokshina, J. G. Rhee, M. Patten, S. H. Levitt, “Implication of blood flow in hyperthermic treatment of tumors,” IEEE Trans. Biomed. Eng. 31, 9–16 (1984).
[CrossRef] [PubMed]

1973

Agner, E.

J. K. Kantors, M. V. Højgaard, E. Agner, N.-H. Holstein-Rathlou, “Short- and long-term variations in non-linear dynamics of heart rate variability,” Cardiovasc. Res. 31, 400–409 (1996).
[CrossRef]

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, 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]

Alfano, R. R.

R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear optical imaging for medical applications,” in Advances in Optical Biopsy and Optical Mammography, Vol. 838 of the Annals of the New York Academy of Sciences (New York Academy of Sciences, New York, 1998), pp. 14–27.

an der Heiden, U.

J. Bélair, L. Glass, U. an der Heiden, J. Milton, “Dynamical disease: identification, temporal aspects and treatment strategies of human illness,” Chaos 5, 1–7 (1995).
[CrossRef] [PubMed]

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 MigrationJ. 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.

Ariagno, R. L.

S. F. Glotzbach, R. L. Ariagno, R. M. Harper, “Sleep and the sudden infant death syndrome,” in Principles and Practice of Sleep Medicine in the Child, R. Ferber, M. H. Kryger, eds. (Saunders, Philadelphia, Pa., 1995), pp. 231–244.

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]

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, OSA Technical (Optical Society of America, Washington D.C., 2000), pp. 458–460.

H. L. Graber, S. Zheng, Y. Pei, C. H. Schmitz, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, OSA Technical Digest (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 tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, OSA Technical Digest (Optical Society of America, Washington D.C., 2000), pp. 409–410.

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, OSA Technical Digest (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

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S. R. Arridge, W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).
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[CrossRef]

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. E. Fry, M. Schweiger, D. T. Delpy, “Initial clinical testing of the UCL 32 channel time-resolved instrument for optical tomography,” in Biomedical Topical Meetings, OSA Technical Digest (Optical Society of America, Washington D.C., 2000), pp. 100–102.

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J. Mayhew, D. Hu, Y. Zheng, S. Askew, Y. Hou, J. Berwick, P. J. Coffey, N. Brown, “An evaluation of linear model analysis techniques for processing images of microcirculation activity,” Neuroimage 7, 49–71 (1998).
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Y. Pei, H. L. Graber, 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, 5755–5769 (2001).
[CrossRef]

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]

A. H. Hielscher, R. E. Alcouffe, 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]

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H. L. Graber, S. Zheng, Y. Pei, C. H. Schmitz, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, OSA Technical Digest (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, OSA Technical (Optical Society of America, Washington D.C., 2000), pp. 458–460.

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, OSA Technical Digest (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatiotemporal 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, 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 MigrationJ. 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.

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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, “Spatiotemporal imaging of vascular reactivity,” in Physiology and Function from Multidimensional Imaging, A. V. Clough, C.-T. Chen, eds., Proc. SPIE3978, 32–43 (2000).

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C. Sohn, F. Beldermann, H. Frey, S. Reinhart, J. Sohn, G. Bastert, “Durchblutungsdiagnostik von Mammatumoren unter Blutdruckerhöhung: neue Möglichkeiten in der Dignitätsdiagnostik,” Radiologe 37, 643–650 (1997).
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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, OSA Technical (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, OSA Technical Digest (Optical Society of America, Washington D.C., 2000), pp. 409–410.

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E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. E. Fry, M. Schweiger, D. T. Delpy, “Initial clinical testing of the UCL 32 channel time-resolved instrument for optical tomography,” in Biomedical Topical Meetings, OSA Technical Digest (Optical Society of America, Washington D.C., 2000), pp. 100–102.

K. Wells, J. C. Hebden, F. E. W. Schmidt, D. T. Delpy, “The UCL multichannel time-resolved system for optical tomography,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 599–607 (1997).
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Frey, H.

C. Sohn, F. Beldermann, H. Frey, S. Reinhart, J. Sohn, G. Bastert, “Durchblutungsdiagnostik von Mammatumoren unter Blutdruckerhöhung: neue Möglichkeiten in der Dignitätsdiagnostik,” Radiologe 37, 643–650 (1997).
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Fry, M. E.

E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. E. Fry, M. Schweiger, D. T. Delpy, “Initial clinical testing of the UCL 32 channel time-resolved instrument for optical tomography,” in Biomedical Topical Meetings, OSA Technical Digest (Optical Society of America, Washington D.C., 2000), pp. 100–102.

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R. R. Alfano, S. G. Demos, P. Galland, S. K. Gayen, Y. Guo, P. P. Ho, X. Liang, F. Liu, L. Wang, Q. Z. Wang, W. B. Wang, “Time-resolved and nonlinear optical imaging for medical applications,” in Advances in Optical Biopsy and Optical Mammography, Vol. 838 of the Annals of the New York Academy of Sciences (New York Academy of Sciences, New York, 1998), pp. 14–27.

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J. N. Weiss, A. Garfinkel, M. L. Spano, W. L. Ditto, “Chaos and chaos control in biology,” J. Clin. Invest. 93, 1355–1360 (1994).
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Y. Pei, H. L. Graber, 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, 5755–5769 (2001).
[CrossRef]

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]

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, OSA Technical (Optical Society of America, Washington D.C., 2000), pp. 458–460.

H. L. Graber, S. Zheng, Y. Pei, C. H. Schmitz, I. Arif, J. Hira, R. L. Barbour, “Dynamic imaging of muscle activity by optical tomography,” in Biomedical Topical Meetings, OSA Technical Digest (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 tissue reperfusion by dynamic optical tomography,” in Biomedical Topical Meetings, OSA Technical Digest (Optical Society of America, Washington D.C., 2000), pp. 409–410.

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, OSA Technical Digest (Optical Society of America, Washington, D.C., 2000), pp. 430–432.

H. L. Graber, C. H. Schmitz, Y. Pei, S. Zhong, S.-L. S. Barbour, S. Blattman, T. Panetta, R. L. Barbour, “Spatiotemporal 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, 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 MigrationJ. 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.

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Harper, R. M.

J. E. W. Mayhew, S. Askew, Y. Zheng, J. Porrill, G. W. M. Westby, P. Redgrave, D. M. Rector, R. M. Harper, “Cerebral vasomotion: a 0.1-Hz oscillation in reflected light imaging of neural activity,” Neuroimage 4, 183–193 (1996).
[CrossRef] [PubMed]

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E. M. C. Hillman, J. C. Hebden, F. E. W. Schmidt, S. R. Arridge, M. E. Fry, M. Schweiger, D. T. Delpy, “Initial clinical testing of the UCL 32 channel time-resolved instrument for optical tomography,” in Biomedical Topical Meetings, OSA Technical Digest (Optical Society of America, Washington D.C., 2000), pp. 100–102.

K. Wells, J. C. Hebden, F. E. W. Schmidt, D. T. Delpy, “The UCL multichannel time-resolved system for optical tomography,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 599–607 (1997).
[CrossRef]

Hielscher, A. H.

A. H. Hielscher, R. E. Alcouffe, 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. Liu, B. Chance, A. H. Hielscher, S. L. Jacques, F. K. Tittel, “Influence of blood vessels on the measurement of hemoglobin oxygenation as determined by time-resolved reflectance spectroscopy,” Med. Phys. 22, 1209–1217 (1995).
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As the temporal variations of the target media used in the studies considered here were perfectly periodic, the length and number of records can be set to any desired value. The effects of record number and length (and also other considerations such as filtering and windowing) lie outside the scope of the present report.

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The last interpretation given is particularly intriguing for us, as it immediately brings to mind an analogy between this general concept of signal coherence and the particular physical meaning of “coherence” that applies to light. It suggests that the “coherence radius” and “coherence time” that could be defined for each pixel in an image time series may be parameters worth considering.

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Figures (12)

Fig. 1
Fig. 1

Medium used in simulation experiments. This finite element mesh was derived from a coronal section of a MR mammogram, following segmentation into three tissue types.

Fig. 2
Fig. 2

Sketch of the essential components of the apparatus used for the laboratory phantom experiments, showing (a) the mechanism used to rhythmically inflate two balloons, (b) the position of the latex balloons in the cylinder, and (c) the geometric arrangement of optical fibers about the cylinder.

Fig. 3
Fig. 3

Sketch showing the details of the arrangement of latex balloons in the two laboratory phantom experiments, and the frequencies and (where applicable) relative phases of the pulsating balloons.

Fig. 4
Fig. 4

(a) mean value, in each pixel, of Vb in the tumor-bearing target medium averaged over all 100 time points during which the absorption coefficients of the tissues were modulated. (b) and (c) Vb images of the tumor-bearing and tumor-free target, respectively.

Fig. 5
Fig. 5

Mean value of the differences between images of the tumor-bearing and tumor-free media, ΔVb.

Fig. 6
Fig. 6

Cross correlations, for zero time lag, between Vb time series of the target media and of the reconstructed images. (a) map of ccuv(0) for the tumor-free medium, where u is the target Vb and v is the image Vb; (b) analogous map, for the tumor-bearing medium; (c) bar graphs of the cumulative percentage of pixels for which ccuv(0) is between -1 and (0.1n-1), n=1,2 ,, 20, for both media.

Fig. 7
Fig. 7

DFT amplitude map of the Vb images of the tumor-bearing target medium. The frequency selected for display purposes is 0.06 Hz, which is the tumor modulation frequency.

Fig. 8
Fig. 8

DFTs of the Vb images of the tumor-bearing target medium. In both panels the frequency selected for display purposes is 0.52 Hz, which is the sum of the modulation frequencies of the adipose and parenchyma tissues. (a) DFT amplitude; (b) DFT phase.

Fig. 9
Fig. 9

Maps of cross-spectral density between the temporal trend in a particular “index pixel” and those of all pixels in the target medium, for the Vb images. For all results shown here, index pixel is at coordinates (20,20) (i.e., center of image), and the frequency component displayed is f=0.52 Hz (i.e., sum of adipose and parenchyma modulation frequencies). (a) amplitude, target with tumor; (b) phase, target with tumor; (c) amplitude, target without tumor; (d) phase, target without tumor.

Fig. 10
Fig. 10

Selected frequency component of the coherence functions computed by comparison of the temporal trend in a particular “index pixel” and those of all pixels in the target medium, for the Vb images. All results shown here are for frequency of 0.54 Hz. (a) target medium contains tumor, index pixel is row 11, column 13 (i.e., outside tumor); (b) target medium without tumor, index pixel is row 11, column 13.

Fig. 11
Fig. 11

Results from laboratory phantom experiment (see Figs. 2 and 3). Prior to reconstruction, each individual detector reading was normalized to the reading obtained for that detector when the balloons and frame were removed from the phantom. (a) image reconstructed from the 6×18 detector readings acquired at one specific time point. (b) 0.12-Hz component of the amplitude of the image sequence’s DFT, 180° phase difference between oscillating balloons; (c) 0.12-Hz component of the phase of the image sequence’s DFT, no phase difference between oscillating balloons; (d) 0.12-Hz component of the phase of the image sequence’s DFT, 180° phase difference between oscillating balloons.

Fig. 12
Fig. 12

Amplitude of the discrete DFTs of a representative detector readings time series, for the model medium with (solid curve, solid circles) and without (dashed curve, open circles) the tumor. Strong peaks are present at the adipose frequency (0.12 Hz) and the parenchyma frequency (0.4 Hz) for both target media, while a peak at the tumor frequency (0.06 Hz) occurs only in the tumor-bearing medium. Peaks also are seen at overtone and mixing frequencies.

Tables (2)

Tables Icon

Table 1 Mean Values of the Tissue Blood Volume and Hemoglobin Oxygen Saturation, and Modulation Frequencies Assigned to Each Tissue Type in the Dynamic Simulations

Tables Icon

Table 2 Mean Values of the Absorption and Scattering Coefficients Assigned to Each Tissue Type in the Dynamic Simulations

Equations (10)

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

μatisλ=Vb[SO2μaoxλ+(1-SO2)μaredλ].
Vb=(μared840-μaox840)μatis760-(μared760-μaox760)μatis840μared840μaox760-μared760μaox840,
SO2=μared840μatis760-μared760μatis840(μared840-μaox840)μatis760-(μared760-μaox760)μatis840.
unu(tn),n=1 ,, N0,n<1orn>N,
vnv(tn),n=1 ,, N0,n<1orn>N,
UkR+jUkI=n=1Nun exp[-j(2knπ/N)],
VkR+jVkl=n=1Nvn exp[-j(2knπ/N)],
ccuv(m)1(N-1)susvn=1N(un-u¯)(vn+m-v¯),
Guv(k)=2Nn=1nd[UkR(n)-jUkI(n)][VkR(n)+jVkI(n)],
γuv2(k)=Guv(k)·Guv*(k)Guu(k)·Gvv(k).

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