Abstract

Laser-induced fluorescence spectroscopy can be used to discriminate between normal and atherosclerotic tissue and guide the delivery of high-power laser energy for laser angioplasty. The depth of tissue from which fluorescence is measured should closely match the depth of laser ablation and, from a practical standpoint, should be neither too small nor too large. This paper investigates the depth of the fluorescence signal. A simple mathematical model is presented. An experimental procedure for determining this depth is described. The results agree well with the model. The implications of the findings to the development of a practical fluorescence-guided laser angioplasty system are discussed.

© 1988 Optical Society of America

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References

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  1. T. R. Sanborn, D. P. Faxon, C. G. Haudenschild, S. B. Gottsman, T. J. Ryan, “Angiographic and Histopathologic Consequences of in-vivo Laser Radiation of Atherosclerotic Lesions,” Circulation Suppl. III 68, 145 (1983).
  2. G. Lee, R. M. Ikeda, R. M. Dwyer, H. Hussein, P. Dietrich, D. T. Mason, “Feasibility of Intravascular Laser Irradiation for in-vivo Visualization and Therapy of Cardiocirculatory Diseases,” Am. Heart J. 103, 1076 (1982).
    [CrossRef] [PubMed]
  3. J. M. Isner et al., “Factors Contributing to Perforations Resulting from Laser Coronary Angioplasty: Observations in an Intact Human Postmortum Preparation of Interoperative Laser Angioplasty,” Circulation Suppl. II 72, 191 (1985).
  4. R. R. Alfano, D. Tata, J. Corder, P. Tomashefsky, F. Longo, M. A. Alfano, “Laser Induced Fluorescence Spectroscopy from Native Cancerous and Normal Tissues,” IEEE J. Quantum Electron. QE-20, 1507 (1984).
    [CrossRef]
  5. R. R. Alfano et al., “Human Teeth With and Without Caries Studied by Laser Scattering Fluorescence and Absorption Spectroscopy,” IEEE J. Quantum Electron. QE-20, 1512 (1984).
    [CrossRef]
  6. D. H. Blackenhorn, H. Braunstein, “Carotenoids in Man. III. The Microscopic Pattern of Fluorescence in Atheromas, and Its Relation to Their Growth,” J. Clin. Invest. 37, 160 (1958).
    [CrossRef]
  7. M. R. Prince, R. Gargolis, T. Deutsch, J. A. Parrish, A. R. Oseroff, “Selective Light Absorption in Atheromas,” Clin. Res. 33, 218A (1985).
  8. I. Banga, M. Bihari-Varga, “Investigations of Free and Elastin-Bound Fluorescent Substances Present in the Atherosclerotic Lipid and Calcium Plaques,” Connect. Tissue Res. 2, 237 (1974).
    [CrossRef] [PubMed]
  9. M. Sartori, P. D. Henry, R. Roberts, R. P. Chin, M. J. Berry, “Estimation of Arterial Wall Thickness and Detection of Atherosclerosis by Laser Induced Argon Fluorescence,” J. Am. Coll. Cardiol. 7, 207A (1986).
  10. C. Kittrell et al., “Diagnosis of Fibrous Arterial Atherosclerosis Using Fluorescence,” Appl. Opt. 24, 2280 (1985).
    [CrossRef] [PubMed]
  11. L. I. Deckelbaum, J. K. Lam, H. S. Cabin, K. S. Clubb, M. B. Long, “Discrimination of Normal and Aterosclerotic Aorta by Laser-Induced Fluorescence,” Lasers in Medicine and Surgery 7, 330 (1987).
    [CrossRef]
  12. L. Esterowitz, C. A. Hoffman, D. C. Tran, “Angioplasty with a Laser and Fiber Optics at 2.94 μm,” Proc. Soc. Photo-Opt. Instrum. Eng. 605, 32 (1986).
  13. L. I. Deckelbaum et al., “Reduction of Laser-Induced Pathologic Tissue Injury Using Pulsed Energy Delivery,” Am. J. Cardiol. 56, 662 (1985).
    [CrossRef] [PubMed]
  14. L. I. Deckelbaum et al., “Fiberoptic Laser-Induced Fluorescence Detection of Atherosclerosis and Plaque Ablation: Potential for Laser Angioplasty Guidance,” Circulation Suppl. II 74, 7 (1986).

1987 (1)

L. I. Deckelbaum, J. K. Lam, H. S. Cabin, K. S. Clubb, M. B. Long, “Discrimination of Normal and Aterosclerotic Aorta by Laser-Induced Fluorescence,” Lasers in Medicine and Surgery 7, 330 (1987).
[CrossRef]

1986 (3)

L. Esterowitz, C. A. Hoffman, D. C. Tran, “Angioplasty with a Laser and Fiber Optics at 2.94 μm,” Proc. Soc. Photo-Opt. Instrum. Eng. 605, 32 (1986).

M. Sartori, P. D. Henry, R. Roberts, R. P. Chin, M. J. Berry, “Estimation of Arterial Wall Thickness and Detection of Atherosclerosis by Laser Induced Argon Fluorescence,” J. Am. Coll. Cardiol. 7, 207A (1986).

L. I. Deckelbaum et al., “Fiberoptic Laser-Induced Fluorescence Detection of Atherosclerosis and Plaque Ablation: Potential for Laser Angioplasty Guidance,” Circulation Suppl. II 74, 7 (1986).

1985 (4)

C. Kittrell et al., “Diagnosis of Fibrous Arterial Atherosclerosis Using Fluorescence,” Appl. Opt. 24, 2280 (1985).
[CrossRef] [PubMed]

L. I. Deckelbaum et al., “Reduction of Laser-Induced Pathologic Tissue Injury Using Pulsed Energy Delivery,” Am. J. Cardiol. 56, 662 (1985).
[CrossRef] [PubMed]

J. M. Isner et al., “Factors Contributing to Perforations Resulting from Laser Coronary Angioplasty: Observations in an Intact Human Postmortum Preparation of Interoperative Laser Angioplasty,” Circulation Suppl. II 72, 191 (1985).

M. R. Prince, R. Gargolis, T. Deutsch, J. A. Parrish, A. R. Oseroff, “Selective Light Absorption in Atheromas,” Clin. Res. 33, 218A (1985).

1984 (2)

R. R. Alfano, D. Tata, J. Corder, P. Tomashefsky, F. Longo, M. A. Alfano, “Laser Induced Fluorescence Spectroscopy from Native Cancerous and Normal Tissues,” IEEE J. Quantum Electron. QE-20, 1507 (1984).
[CrossRef]

R. R. Alfano et al., “Human Teeth With and Without Caries Studied by Laser Scattering Fluorescence and Absorption Spectroscopy,” IEEE J. Quantum Electron. QE-20, 1512 (1984).
[CrossRef]

1983 (1)

T. R. Sanborn, D. P. Faxon, C. G. Haudenschild, S. B. Gottsman, T. J. Ryan, “Angiographic and Histopathologic Consequences of in-vivo Laser Radiation of Atherosclerotic Lesions,” Circulation Suppl. III 68, 145 (1983).

1982 (1)

G. Lee, R. M. Ikeda, R. M. Dwyer, H. Hussein, P. Dietrich, D. T. Mason, “Feasibility of Intravascular Laser Irradiation for in-vivo Visualization and Therapy of Cardiocirculatory Diseases,” Am. Heart J. 103, 1076 (1982).
[CrossRef] [PubMed]

1974 (1)

I. Banga, M. Bihari-Varga, “Investigations of Free and Elastin-Bound Fluorescent Substances Present in the Atherosclerotic Lipid and Calcium Plaques,” Connect. Tissue Res. 2, 237 (1974).
[CrossRef] [PubMed]

1958 (1)

D. H. Blackenhorn, H. Braunstein, “Carotenoids in Man. III. The Microscopic Pattern of Fluorescence in Atheromas, and Its Relation to Their Growth,” J. Clin. Invest. 37, 160 (1958).
[CrossRef]

Alfano, M. A.

R. R. Alfano, D. Tata, J. Corder, P. Tomashefsky, F. Longo, M. A. Alfano, “Laser Induced Fluorescence Spectroscopy from Native Cancerous and Normal Tissues,” IEEE J. Quantum Electron. QE-20, 1507 (1984).
[CrossRef]

Alfano, R. R.

R. R. Alfano et al., “Human Teeth With and Without Caries Studied by Laser Scattering Fluorescence and Absorption Spectroscopy,” IEEE J. Quantum Electron. QE-20, 1512 (1984).
[CrossRef]

R. R. Alfano, D. Tata, J. Corder, P. Tomashefsky, F. Longo, M. A. Alfano, “Laser Induced Fluorescence Spectroscopy from Native Cancerous and Normal Tissues,” IEEE J. Quantum Electron. QE-20, 1507 (1984).
[CrossRef]

Banga, I.

I. Banga, M. Bihari-Varga, “Investigations of Free and Elastin-Bound Fluorescent Substances Present in the Atherosclerotic Lipid and Calcium Plaques,” Connect. Tissue Res. 2, 237 (1974).
[CrossRef] [PubMed]

Berry, M. J.

M. Sartori, P. D. Henry, R. Roberts, R. P. Chin, M. J. Berry, “Estimation of Arterial Wall Thickness and Detection of Atherosclerosis by Laser Induced Argon Fluorescence,” J. Am. Coll. Cardiol. 7, 207A (1986).

Bihari-Varga, M.

I. Banga, M. Bihari-Varga, “Investigations of Free and Elastin-Bound Fluorescent Substances Present in the Atherosclerotic Lipid and Calcium Plaques,” Connect. Tissue Res. 2, 237 (1974).
[CrossRef] [PubMed]

Blackenhorn, D. H.

D. H. Blackenhorn, H. Braunstein, “Carotenoids in Man. III. The Microscopic Pattern of Fluorescence in Atheromas, and Its Relation to Their Growth,” J. Clin. Invest. 37, 160 (1958).
[CrossRef]

Braunstein, H.

D. H. Blackenhorn, H. Braunstein, “Carotenoids in Man. III. The Microscopic Pattern of Fluorescence in Atheromas, and Its Relation to Their Growth,” J. Clin. Invest. 37, 160 (1958).
[CrossRef]

Cabin, H. S.

L. I. Deckelbaum, J. K. Lam, H. S. Cabin, K. S. Clubb, M. B. Long, “Discrimination of Normal and Aterosclerotic Aorta by Laser-Induced Fluorescence,” Lasers in Medicine and Surgery 7, 330 (1987).
[CrossRef]

Chin, R. P.

M. Sartori, P. D. Henry, R. Roberts, R. P. Chin, M. J. Berry, “Estimation of Arterial Wall Thickness and Detection of Atherosclerosis by Laser Induced Argon Fluorescence,” J. Am. Coll. Cardiol. 7, 207A (1986).

Clubb, K. S.

L. I. Deckelbaum, J. K. Lam, H. S. Cabin, K. S. Clubb, M. B. Long, “Discrimination of Normal and Aterosclerotic Aorta by Laser-Induced Fluorescence,” Lasers in Medicine and Surgery 7, 330 (1987).
[CrossRef]

Corder, J.

R. R. Alfano, D. Tata, J. Corder, P. Tomashefsky, F. Longo, M. A. Alfano, “Laser Induced Fluorescence Spectroscopy from Native Cancerous and Normal Tissues,” IEEE J. Quantum Electron. QE-20, 1507 (1984).
[CrossRef]

Deckelbaum, L. I.

L. I. Deckelbaum, J. K. Lam, H. S. Cabin, K. S. Clubb, M. B. Long, “Discrimination of Normal and Aterosclerotic Aorta by Laser-Induced Fluorescence,” Lasers in Medicine and Surgery 7, 330 (1987).
[CrossRef]

L. I. Deckelbaum et al., “Fiberoptic Laser-Induced Fluorescence Detection of Atherosclerosis and Plaque Ablation: Potential for Laser Angioplasty Guidance,” Circulation Suppl. II 74, 7 (1986).

L. I. Deckelbaum et al., “Reduction of Laser-Induced Pathologic Tissue Injury Using Pulsed Energy Delivery,” Am. J. Cardiol. 56, 662 (1985).
[CrossRef] [PubMed]

Deutsch, T.

M. R. Prince, R. Gargolis, T. Deutsch, J. A. Parrish, A. R. Oseroff, “Selective Light Absorption in Atheromas,” Clin. Res. 33, 218A (1985).

Dietrich, P.

G. Lee, R. M. Ikeda, R. M. Dwyer, H. Hussein, P. Dietrich, D. T. Mason, “Feasibility of Intravascular Laser Irradiation for in-vivo Visualization and Therapy of Cardiocirculatory Diseases,” Am. Heart J. 103, 1076 (1982).
[CrossRef] [PubMed]

Dwyer, R. M.

G. Lee, R. M. Ikeda, R. M. Dwyer, H. Hussein, P. Dietrich, D. T. Mason, “Feasibility of Intravascular Laser Irradiation for in-vivo Visualization and Therapy of Cardiocirculatory Diseases,” Am. Heart J. 103, 1076 (1982).
[CrossRef] [PubMed]

Esterowitz, L.

L. Esterowitz, C. A. Hoffman, D. C. Tran, “Angioplasty with a Laser and Fiber Optics at 2.94 μm,” Proc. Soc. Photo-Opt. Instrum. Eng. 605, 32 (1986).

Faxon, D. P.

T. R. Sanborn, D. P. Faxon, C. G. Haudenschild, S. B. Gottsman, T. J. Ryan, “Angiographic and Histopathologic Consequences of in-vivo Laser Radiation of Atherosclerotic Lesions,” Circulation Suppl. III 68, 145 (1983).

Gargolis, R.

M. R. Prince, R. Gargolis, T. Deutsch, J. A. Parrish, A. R. Oseroff, “Selective Light Absorption in Atheromas,” Clin. Res. 33, 218A (1985).

Gottsman, S. B.

T. R. Sanborn, D. P. Faxon, C. G. Haudenschild, S. B. Gottsman, T. J. Ryan, “Angiographic and Histopathologic Consequences of in-vivo Laser Radiation of Atherosclerotic Lesions,” Circulation Suppl. III 68, 145 (1983).

Haudenschild, C. G.

T. R. Sanborn, D. P. Faxon, C. G. Haudenschild, S. B. Gottsman, T. J. Ryan, “Angiographic and Histopathologic Consequences of in-vivo Laser Radiation of Atherosclerotic Lesions,” Circulation Suppl. III 68, 145 (1983).

Henry, P. D.

M. Sartori, P. D. Henry, R. Roberts, R. P. Chin, M. J. Berry, “Estimation of Arterial Wall Thickness and Detection of Atherosclerosis by Laser Induced Argon Fluorescence,” J. Am. Coll. Cardiol. 7, 207A (1986).

Hoffman, C. A.

L. Esterowitz, C. A. Hoffman, D. C. Tran, “Angioplasty with a Laser and Fiber Optics at 2.94 μm,” Proc. Soc. Photo-Opt. Instrum. Eng. 605, 32 (1986).

Hussein, H.

G. Lee, R. M. Ikeda, R. M. Dwyer, H. Hussein, P. Dietrich, D. T. Mason, “Feasibility of Intravascular Laser Irradiation for in-vivo Visualization and Therapy of Cardiocirculatory Diseases,” Am. Heart J. 103, 1076 (1982).
[CrossRef] [PubMed]

Ikeda, R. M.

G. Lee, R. M. Ikeda, R. M. Dwyer, H. Hussein, P. Dietrich, D. T. Mason, “Feasibility of Intravascular Laser Irradiation for in-vivo Visualization and Therapy of Cardiocirculatory Diseases,” Am. Heart J. 103, 1076 (1982).
[CrossRef] [PubMed]

Isner, J. M.

J. M. Isner et al., “Factors Contributing to Perforations Resulting from Laser Coronary Angioplasty: Observations in an Intact Human Postmortum Preparation of Interoperative Laser Angioplasty,” Circulation Suppl. II 72, 191 (1985).

Kittrell, C.

Lam, J. K.

L. I. Deckelbaum, J. K. Lam, H. S. Cabin, K. S. Clubb, M. B. Long, “Discrimination of Normal and Aterosclerotic Aorta by Laser-Induced Fluorescence,” Lasers in Medicine and Surgery 7, 330 (1987).
[CrossRef]

Lee, G.

G. Lee, R. M. Ikeda, R. M. Dwyer, H. Hussein, P. Dietrich, D. T. Mason, “Feasibility of Intravascular Laser Irradiation for in-vivo Visualization and Therapy of Cardiocirculatory Diseases,” Am. Heart J. 103, 1076 (1982).
[CrossRef] [PubMed]

Long, M. B.

L. I. Deckelbaum, J. K. Lam, H. S. Cabin, K. S. Clubb, M. B. Long, “Discrimination of Normal and Aterosclerotic Aorta by Laser-Induced Fluorescence,” Lasers in Medicine and Surgery 7, 330 (1987).
[CrossRef]

Longo, F.

R. R. Alfano, D. Tata, J. Corder, P. Tomashefsky, F. Longo, M. A. Alfano, “Laser Induced Fluorescence Spectroscopy from Native Cancerous and Normal Tissues,” IEEE J. Quantum Electron. QE-20, 1507 (1984).
[CrossRef]

Mason, D. T.

G. Lee, R. M. Ikeda, R. M. Dwyer, H. Hussein, P. Dietrich, D. T. Mason, “Feasibility of Intravascular Laser Irradiation for in-vivo Visualization and Therapy of Cardiocirculatory Diseases,” Am. Heart J. 103, 1076 (1982).
[CrossRef] [PubMed]

Oseroff, A. R.

M. R. Prince, R. Gargolis, T. Deutsch, J. A. Parrish, A. R. Oseroff, “Selective Light Absorption in Atheromas,” Clin. Res. 33, 218A (1985).

Parrish, J. A.

M. R. Prince, R. Gargolis, T. Deutsch, J. A. Parrish, A. R. Oseroff, “Selective Light Absorption in Atheromas,” Clin. Res. 33, 218A (1985).

Prince, M. R.

M. R. Prince, R. Gargolis, T. Deutsch, J. A. Parrish, A. R. Oseroff, “Selective Light Absorption in Atheromas,” Clin. Res. 33, 218A (1985).

Roberts, R.

M. Sartori, P. D. Henry, R. Roberts, R. P. Chin, M. J. Berry, “Estimation of Arterial Wall Thickness and Detection of Atherosclerosis by Laser Induced Argon Fluorescence,” J. Am. Coll. Cardiol. 7, 207A (1986).

Ryan, T. J.

T. R. Sanborn, D. P. Faxon, C. G. Haudenschild, S. B. Gottsman, T. J. Ryan, “Angiographic and Histopathologic Consequences of in-vivo Laser Radiation of Atherosclerotic Lesions,” Circulation Suppl. III 68, 145 (1983).

Sanborn, T. R.

T. R. Sanborn, D. P. Faxon, C. G. Haudenschild, S. B. Gottsman, T. J. Ryan, “Angiographic and Histopathologic Consequences of in-vivo Laser Radiation of Atherosclerotic Lesions,” Circulation Suppl. III 68, 145 (1983).

Sartori, M.

M. Sartori, P. D. Henry, R. Roberts, R. P. Chin, M. J. Berry, “Estimation of Arterial Wall Thickness and Detection of Atherosclerosis by Laser Induced Argon Fluorescence,” J. Am. Coll. Cardiol. 7, 207A (1986).

Tata, D.

R. R. Alfano, D. Tata, J. Corder, P. Tomashefsky, F. Longo, M. A. Alfano, “Laser Induced Fluorescence Spectroscopy from Native Cancerous and Normal Tissues,” IEEE J. Quantum Electron. QE-20, 1507 (1984).
[CrossRef]

Tomashefsky, P.

R. R. Alfano, D. Tata, J. Corder, P. Tomashefsky, F. Longo, M. A. Alfano, “Laser Induced Fluorescence Spectroscopy from Native Cancerous and Normal Tissues,” IEEE J. Quantum Electron. QE-20, 1507 (1984).
[CrossRef]

Tran, D. C.

L. Esterowitz, C. A. Hoffman, D. C. Tran, “Angioplasty with a Laser and Fiber Optics at 2.94 μm,” Proc. Soc. Photo-Opt. Instrum. Eng. 605, 32 (1986).

Am. Heart J. (1)

G. Lee, R. M. Ikeda, R. M. Dwyer, H. Hussein, P. Dietrich, D. T. Mason, “Feasibility of Intravascular Laser Irradiation for in-vivo Visualization and Therapy of Cardiocirculatory Diseases,” Am. Heart J. 103, 1076 (1982).
[CrossRef] [PubMed]

Am. J. Cardiol. (1)

L. I. Deckelbaum et al., “Reduction of Laser-Induced Pathologic Tissue Injury Using Pulsed Energy Delivery,” Am. J. Cardiol. 56, 662 (1985).
[CrossRef] [PubMed]

Appl. Opt. (1)

Circulation Suppl. II (2)

J. M. Isner et al., “Factors Contributing to Perforations Resulting from Laser Coronary Angioplasty: Observations in an Intact Human Postmortum Preparation of Interoperative Laser Angioplasty,” Circulation Suppl. II 72, 191 (1985).

L. I. Deckelbaum et al., “Fiberoptic Laser-Induced Fluorescence Detection of Atherosclerosis and Plaque Ablation: Potential for Laser Angioplasty Guidance,” Circulation Suppl. II 74, 7 (1986).

Circulation Suppl. III (1)

T. R. Sanborn, D. P. Faxon, C. G. Haudenschild, S. B. Gottsman, T. J. Ryan, “Angiographic and Histopathologic Consequences of in-vivo Laser Radiation of Atherosclerotic Lesions,” Circulation Suppl. III 68, 145 (1983).

Clin. Res. (1)

M. R. Prince, R. Gargolis, T. Deutsch, J. A. Parrish, A. R. Oseroff, “Selective Light Absorption in Atheromas,” Clin. Res. 33, 218A (1985).

Connect. Tissue Res. (1)

I. Banga, M. Bihari-Varga, “Investigations of Free and Elastin-Bound Fluorescent Substances Present in the Atherosclerotic Lipid and Calcium Plaques,” Connect. Tissue Res. 2, 237 (1974).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

R. R. Alfano, D. Tata, J. Corder, P. Tomashefsky, F. Longo, M. A. Alfano, “Laser Induced Fluorescence Spectroscopy from Native Cancerous and Normal Tissues,” IEEE J. Quantum Electron. QE-20, 1507 (1984).
[CrossRef]

R. R. Alfano et al., “Human Teeth With and Without Caries Studied by Laser Scattering Fluorescence and Absorption Spectroscopy,” IEEE J. Quantum Electron. QE-20, 1512 (1984).
[CrossRef]

J. Am. Coll. Cardiol. (1)

M. Sartori, P. D. Henry, R. Roberts, R. P. Chin, M. J. Berry, “Estimation of Arterial Wall Thickness and Detection of Atherosclerosis by Laser Induced Argon Fluorescence,” J. Am. Coll. Cardiol. 7, 207A (1986).

J. Clin. Invest. (1)

D. H. Blackenhorn, H. Braunstein, “Carotenoids in Man. III. The Microscopic Pattern of Fluorescence in Atheromas, and Its Relation to Their Growth,” J. Clin. Invest. 37, 160 (1958).
[CrossRef]

Lasers in Medicine and Surgery (1)

L. I. Deckelbaum, J. K. Lam, H. S. Cabin, K. S. Clubb, M. B. Long, “Discrimination of Normal and Aterosclerotic Aorta by Laser-Induced Fluorescence,” Lasers in Medicine and Surgery 7, 330 (1987).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

L. Esterowitz, C. A. Hoffman, D. C. Tran, “Angioplasty with a Laser and Fiber Optics at 2.94 μm,” Proc. Soc. Photo-Opt. Instrum. Eng. 605, 32 (1986).

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Figures (6)

Fig. 1
Fig. 1

Concept of a smart laser angioplasty system. A low-power laser excites tissue fluorescence. The spectral signature is used to discriminate the tissue type and control the firing of a high-power laser for ablation.

Fig. 2
Fig. 2

Geometry of fiber–tissue interface. The shaded region indicates the region of tissue that contributes to the fluorescence signal. The heavily shaded region indicates the region of uniform collection efficiency.

Fig. 3
Fig. 3

Experimental setup for excitation and measurement of the tissue fluorescence.

Fig. 4
Fig. 4

Typical laser-induced fluorescence spectra. This example was from a section of normal human aorta.

Fig. 5
Fig. 5

Example of experimental data. The parameters of the theoretical curve were obtained using a nonlinear regression analysis.

Fig. 6
Fig. 6

Linearity of β with intensity I0. The curves for four different wavelengths are shown. All are normalized to the intensity at 0-dB attenuation.

Tables (1)

Tables Icon

Table I Attenuation Coefficient and Fluorescence Depth for Tissue Samples

Equations (6)

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

I ( z ) = I 0 exp ( α 0 z ) .
I ( z , λ ) = β λ I 0 exp ( α 0 z ) .
I ( z , λ ) = Ω β λ I 0 exp ( α 0 z ) exp ( α λ z ) ,
I ( z , λ ) = 0 z Ω β λ I 0 exp ( α 0 z ) exp ( α λ z ) d z
= Ω β λ I 0 α 0 + α λ { 1 exp [ ( α 0 + α λ ) z ] } .
I ( z ) = A [ 1 exp ( α z ) ] .

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