Abstract

Photodynamic therapy (PDT) dosimetric tools are crucial for treatment planning and noninvasive monitoring by means of fluorescence. Present approaches consider usually a 1D problem, a simple photochemical process, or a spatially homogeneous photosensitizer. In this work, a radially resolved superficial photosensitizer fluorescence and 3D photochemical time-dependent PDT model are presented. The model provides a time-dependent estimation of tissue fluorescence and the photosensitizer and singlet oxygen 3D concentrations. The model is applied to a basal cell carcinoma treated by Metvix topical photosensitizer protocol. The analysis shows the potentiality in treatment planning and monitoring. The fluorescence results are in agreement with previous measurements.

© 2014 Optical Society of America

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References

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  1. B. C. Wilson and M. S. Patterson, Phys. Med. Biol. 53, R61 (2008).
    [CrossRef]
  2. B. C. Wilson, M. S. Patterson, and L. Lilge, Lasers Med. Sci. 12, 182 (1997).
    [CrossRef]
  3. B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 55, 5913 (2010).
    [CrossRef]
  4. B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 57, 825 (2012).
    [CrossRef]
  5. M. A. Weston and M. S. Patterson, Phys. Med. Biol. 58, 7039 (2013).
    [CrossRef]
  6. R. M. Valentine, C. T. A. Brown, H. Moseley, S. Ibbotson, and K. Wood, J. Biomed. Opt. 16, 048002 (2011).
    [CrossRef]
  7. I. Salas-García, F. Fanjul-Vélez, N. Ortega-Quijano, M. López-Escobar, and J. L. Arce-Diego, Proc. SPIE 7715, 77152R1 (2010).
    [CrossRef]
  8. L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
    [CrossRef]
  9. E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, J. Biomed. Opt. 11, 064026 (2006).
    [CrossRef]
  10. L. O. Svaasand, P. Wyss, M. T. Wyss, Y. Tadir, B. J. Tromberg, and M. W. Berns, Laser Med. Surg. News 18, 139 (1996).
    [CrossRef]
  11. I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Intern. J. Photoenergy 2012, 1 (2012).
    [CrossRef]
  12. T. H. Foster, R. S. Murant, R. G. Bryant, R. S. Knox, S. L. Gibson, and R. Hilf, Radiat. Res. 126, 296 (1991).
    [CrossRef]
  13. X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
    [CrossRef]
  14. I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, J. Photochem. Photobiology B 114, 79 (2012).
    [CrossRef]
  15. I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Opt. Commun. 285, 1581 (2012).
    [CrossRef]
  16. S. L. Jacques, Handbook of Biomedical Fluorescence, B. W. Rogue and M.-A. Mycek, eds. (CRC, 2003), pp. 61.
  17. W. J. Cottrell, A. D. Paquette, K. R. Keymel, T. H. Foster, and A. R. Oseroff, Clin. Cancer Res. 14, 4475 (2008).
    [CrossRef]

2013 (1)

M. A. Weston and M. S. Patterson, Phys. Med. Biol. 58, 7039 (2013).
[CrossRef]

2012 (4)

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 57, 825 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Intern. J. Photoenergy 2012, 1 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, J. Photochem. Photobiology B 114, 79 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Opt. Commun. 285, 1581 (2012).
[CrossRef]

2011 (1)

R. M. Valentine, C. T. A. Brown, H. Moseley, S. Ibbotson, and K. Wood, J. Biomed. Opt. 16, 048002 (2011).
[CrossRef]

2010 (2)

I. Salas-García, F. Fanjul-Vélez, N. Ortega-Quijano, M. López-Escobar, and J. L. Arce-Diego, Proc. SPIE 7715, 77152R1 (2010).
[CrossRef]

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 55, 5913 (2010).
[CrossRef]

2008 (2)

B. C. Wilson and M. S. Patterson, Phys. Med. Biol. 53, R61 (2008).
[CrossRef]

W. J. Cottrell, A. D. Paquette, K. R. Keymel, T. H. Foster, and A. R. Oseroff, Clin. Cancer Res. 14, 4475 (2008).
[CrossRef]

2006 (1)

E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, J. Biomed. Opt. 11, 064026 (2006).
[CrossRef]

2005 (1)

X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
[CrossRef]

1997 (1)

B. C. Wilson, M. S. Patterson, and L. Lilge, Lasers Med. Sci. 12, 182 (1997).
[CrossRef]

1996 (1)

L. O. Svaasand, P. Wyss, M. T. Wyss, Y. Tadir, B. J. Tromberg, and M. W. Berns, Laser Med. Surg. News 18, 139 (1996).
[CrossRef]

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef]

1991 (1)

T. H. Foster, R. S. Murant, R. G. Bryant, R. S. Knox, S. L. Gibson, and R. Hilf, Radiat. Res. 126, 296 (1991).
[CrossRef]

Allison, R. R.

X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
[CrossRef]

Arce-Diego, J. L.

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Intern. J. Photoenergy 2012, 1 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, J. Photochem. Photobiology B 114, 79 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Opt. Commun. 285, 1581 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, N. Ortega-Quijano, M. López-Escobar, and J. L. Arce-Diego, Proc. SPIE 7715, 77152R1 (2010).
[CrossRef]

Berns, M. W.

L. O. Svaasand, P. Wyss, M. T. Wyss, Y. Tadir, B. J. Tromberg, and M. W. Berns, Laser Med. Surg. News 18, 139 (1996).
[CrossRef]

Brown, C. T. A.

R. M. Valentine, C. T. A. Brown, H. Moseley, S. Ibbotson, and K. Wood, J. Biomed. Opt. 16, 048002 (2011).
[CrossRef]

Bryant, R. G.

T. H. Foster, R. S. Murant, R. G. Bryant, R. S. Knox, S. L. Gibson, and R. Hilf, Radiat. Res. 126, 296 (1991).
[CrossRef]

Cottrell, W. J.

W. J. Cottrell, A. D. Paquette, K. R. Keymel, T. H. Foster, and A. R. Oseroff, Clin. Cancer Res. 14, 4475 (2008).
[CrossRef]

Cuenca, R. E.

X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
[CrossRef]

Downie, G. H.

X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
[CrossRef]

Fanjul-Vélez, F.

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Intern. J. Photoenergy 2012, 1 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, J. Photochem. Photobiology B 114, 79 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Opt. Commun. 285, 1581 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, N. Ortega-Quijano, M. López-Escobar, and J. L. Arce-Diego, Proc. SPIE 7715, 77152R1 (2010).
[CrossRef]

Farrell, T. J.

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 57, 825 (2012).
[CrossRef]

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 55, 5913 (2010).
[CrossRef]

Feng, Y.

X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
[CrossRef]

Foster, T. H.

W. J. Cottrell, A. D. Paquette, K. R. Keymel, T. H. Foster, and A. R. Oseroff, Clin. Cancer Res. 14, 4475 (2008).
[CrossRef]

T. H. Foster, R. S. Murant, R. G. Bryant, R. S. Knox, S. L. Gibson, and R. Hilf, Radiat. Res. 126, 296 (1991).
[CrossRef]

Gibson, S. L.

T. H. Foster, R. S. Murant, R. G. Bryant, R. S. Knox, S. L. Gibson, and R. Hilf, Radiat. Res. 126, 296 (1991).
[CrossRef]

Hilf, R.

T. H. Foster, R. S. Murant, R. G. Bryant, R. S. Knox, S. L. Gibson, and R. Hilf, Radiat. Res. 126, 296 (1991).
[CrossRef]

Hu, X. H.

X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
[CrossRef]

Ibbotson, S.

R. M. Valentine, C. T. A. Brown, H. Moseley, S. Ibbotson, and K. Wood, J. Biomed. Opt. 16, 048002 (2011).
[CrossRef]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef]

S. L. Jacques, Handbook of Biomedical Fluorescence, B. W. Rogue and M.-A. Mycek, eds. (CRC, 2003), pp. 61.

Jiang, B.

E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, J. Biomed. Opt. 11, 064026 (2006).
[CrossRef]

Keymel, K. R.

W. J. Cottrell, A. D. Paquette, K. R. Keymel, T. H. Foster, and A. R. Oseroff, Clin. Cancer Res. 14, 4475 (2008).
[CrossRef]

Knox, R. S.

T. H. Foster, R. S. Murant, R. G. Bryant, R. S. Knox, S. L. Gibson, and R. Hilf, Radiat. Res. 126, 296 (1991).
[CrossRef]

Lilge, L.

B. C. Wilson, M. S. Patterson, and L. Lilge, Lasers Med. Sci. 12, 182 (1997).
[CrossRef]

Liu, B.

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 57, 825 (2012).
[CrossRef]

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 55, 5913 (2010).
[CrossRef]

López-Escobar, M.

I. Salas-García, F. Fanjul-Vélez, N. Ortega-Quijano, M. López-Escobar, and J. L. Arce-Diego, Proc. SPIE 7715, 77152R1 (2010).
[CrossRef]

Lu, J. Q.

X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
[CrossRef]

Moseley, H.

R. M. Valentine, C. T. A. Brown, H. Moseley, S. Ibbotson, and K. Wood, J. Biomed. Opt. 16, 048002 (2011).
[CrossRef]

Murant, R. S.

T. H. Foster, R. S. Murant, R. G. Bryant, R. S. Knox, S. L. Gibson, and R. Hilf, Radiat. Res. 126, 296 (1991).
[CrossRef]

Novak, J.

E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, J. Biomed. Opt. 11, 064026 (2006).
[CrossRef]

Ortega-Quijano, N.

I. Salas-García, F. Fanjul-Vélez, N. Ortega-Quijano, M. López-Escobar, and J. L. Arce-Diego, Proc. SPIE 7715, 77152R1 (2010).
[CrossRef]

Oseroff, A. R.

W. J. Cottrell, A. D. Paquette, K. R. Keymel, T. H. Foster, and A. R. Oseroff, Clin. Cancer Res. 14, 4475 (2008).
[CrossRef]

Paquette, A. D.

W. J. Cottrell, A. D. Paquette, K. R. Keymel, T. H. Foster, and A. R. Oseroff, Clin. Cancer Res. 14, 4475 (2008).
[CrossRef]

Patterson, M. S.

M. A. Weston and M. S. Patterson, Phys. Med. Biol. 58, 7039 (2013).
[CrossRef]

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 57, 825 (2012).
[CrossRef]

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 55, 5913 (2010).
[CrossRef]

B. C. Wilson and M. S. Patterson, Phys. Med. Biol. 53, R61 (2008).
[CrossRef]

B. C. Wilson, M. S. Patterson, and L. Lilge, Lasers Med. Sci. 12, 182 (1997).
[CrossRef]

Salas-García, I.

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, J. Photochem. Photobiology B 114, 79 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Opt. Commun. 285, 1581 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Intern. J. Photoenergy 2012, 1 (2012).
[CrossRef]

I. Salas-García, F. Fanjul-Vélez, N. Ortega-Quijano, M. López-Escobar, and J. L. Arce-Diego, Proc. SPIE 7715, 77152R1 (2010).
[CrossRef]

Salomatina, E.

E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, J. Biomed. Opt. 11, 064026 (2006).
[CrossRef]

Sibata, C. H.

X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
[CrossRef]

Svaasand, L. O.

L. O. Svaasand, P. Wyss, M. T. Wyss, Y. Tadir, B. J. Tromberg, and M. W. Berns, Laser Med. Surg. News 18, 139 (1996).
[CrossRef]

Tadir, Y.

L. O. Svaasand, P. Wyss, M. T. Wyss, Y. Tadir, B. J. Tromberg, and M. W. Berns, Laser Med. Surg. News 18, 139 (1996).
[CrossRef]

Tromberg, B. J.

L. O. Svaasand, P. Wyss, M. T. Wyss, Y. Tadir, B. J. Tromberg, and M. W. Berns, Laser Med. Surg. News 18, 139 (1996).
[CrossRef]

Valentine, R. M.

R. M. Valentine, C. T. A. Brown, H. Moseley, S. Ibbotson, and K. Wood, J. Biomed. Opt. 16, 048002 (2011).
[CrossRef]

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef]

Weston, M. A.

M. A. Weston and M. S. Patterson, Phys. Med. Biol. 58, 7039 (2013).
[CrossRef]

Wilson, B. C.

B. C. Wilson and M. S. Patterson, Phys. Med. Biol. 53, R61 (2008).
[CrossRef]

B. C. Wilson, M. S. Patterson, and L. Lilge, Lasers Med. Sci. 12, 182 (1997).
[CrossRef]

Wood, K.

R. M. Valentine, C. T. A. Brown, H. Moseley, S. Ibbotson, and K. Wood, J. Biomed. Opt. 16, 048002 (2011).
[CrossRef]

Wyss, M. T.

L. O. Svaasand, P. Wyss, M. T. Wyss, Y. Tadir, B. J. Tromberg, and M. W. Berns, Laser Med. Surg. News 18, 139 (1996).
[CrossRef]

Wyss, P.

L. O. Svaasand, P. Wyss, M. T. Wyss, Y. Tadir, B. J. Tromberg, and M. W. Berns, Laser Med. Surg. News 18, 139 (1996).
[CrossRef]

Yaroslavsky, A. N.

E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, J. Biomed. Opt. 11, 064026 (2006).
[CrossRef]

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef]

Clin. Cancer Res. (1)

W. J. Cottrell, A. D. Paquette, K. R. Keymel, T. H. Foster, and A. R. Oseroff, Clin. Cancer Res. 14, 4475 (2008).
[CrossRef]

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef]

Intern. J. Photoenergy (1)

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Intern. J. Photoenergy 2012, 1 (2012).
[CrossRef]

J. Biomed. Opt. (2)

E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, J. Biomed. Opt. 11, 064026 (2006).
[CrossRef]

R. M. Valentine, C. T. A. Brown, H. Moseley, S. Ibbotson, and K. Wood, J. Biomed. Opt. 16, 048002 (2011).
[CrossRef]

J. Photochem. Photobiology B (1)

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, J. Photochem. Photobiology B 114, 79 (2012).
[CrossRef]

Laser Med. Surg. News (1)

L. O. Svaasand, P. Wyss, M. T. Wyss, Y. Tadir, B. J. Tromberg, and M. W. Berns, Laser Med. Surg. News 18, 139 (1996).
[CrossRef]

Lasers Med. Sci. (1)

B. C. Wilson, M. S. Patterson, and L. Lilge, Lasers Med. Sci. 12, 182 (1997).
[CrossRef]

Opt. Commun. (1)

I. Salas-García, F. Fanjul-Vélez, and J. L. Arce-Diego, Opt. Commun. 285, 1581 (2012).
[CrossRef]

Photochem. Photobiol. (1)

X. H. Hu, Y. Feng, J. Q. Lu, R. R. Allison, R. E. Cuenca, G. H. Downie, and C. H. Sibata, Photochem. Photobiol. 81, 1460 (2005).
[CrossRef]

Phys. Med. Biol. (4)

B. C. Wilson and M. S. Patterson, Phys. Med. Biol. 53, R61 (2008).
[CrossRef]

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 55, 5913 (2010).
[CrossRef]

B. Liu, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 57, 825 (2012).
[CrossRef]

M. A. Weston and M. S. Patterson, Phys. Med. Biol. 58, 7039 (2013).
[CrossRef]

Proc. SPIE (1)

I. Salas-García, F. Fanjul-Vélez, N. Ortega-Quijano, M. López-Escobar, and J. L. Arce-Diego, Proc. SPIE 7715, 77152R1 (2010).
[CrossRef]

Radiat. Res. (1)

T. H. Foster, R. S. Murant, R. G. Bryant, R. S. Knox, S. L. Gibson, and R. Hilf, Radiat. Res. 126, 296 (1991).
[CrossRef]

Other (1)

S. L. Jacques, Handbook of Biomedical Fluorescence, B. W. Rogue and M.-A. Mycek, eds. (CRC, 2003), pp. 61.

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Figures (6)

Fig. 1.
Fig. 1.

Total superficial fluorescence irradiance [W/cm2] from BCC as a function of radial position, for different irradiation times.

Fig. 2.
Fig. 2.

Photosensitizer concentration [cm3] as a function of depth within the tumor, at different treatment times for r=1.125mm.

Fig. 3.
Fig. 3.

Singlet oxygen concentration [cm3] as a function of depth within the tumor at different treatment times for r=1.125mm.

Fig. 4.
Fig. 4.

Photosensitizer concentration [cm3] as a function of the radial component at different treatment times for z=1.55mm.

Fig. 5.
Fig. 5.

Singlet oxygen concentration [cm3] as a function of the radial component at different treatment times for z=1.55mm.

Fig. 6.
Fig. 6.

Average normalized total PpIX fluorescence obtained with the MAL-PDT model proposed at 100mW/cm2 (red line), and with clinical results at 150mW/cm2 [17] (blue line), as a function of treatment time.

Equations (11)

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

s^·¯I(r,s^)=(μa+μs)I(r,s^)+μs4π4πp(s^·s^)I(r,s^)dΩ.
M(t)=Mo0t(KDπtez24DtK2DeKDzeK2Dterfc(KDt+z2Dt))etτdt.
S0(t)=εpτpτapM(t).
d[S0]dt=νρσpsa[S0]kpb[O12][S0]+η10τ1[S1]+η30τ3[T]+αsτ3[T][O32],
d[S1]dt=1τ1[S1]+νρσpsa[S0],
d[T]dt=η30τ3[T]αsτ3[T][O32]+η13τ1[S1],
d[O32]dt=αsτ3[T][O32]+η0τ0[O12]+P,
d[O12]dt=kpb[S0][O12]kcx[R][O12]ksc[C]i[O12]η0τ0[O12]+αsτ3[T][O32],
d[R]dt=kcx[O12][R]+U.
Pf(r,z,t)=v·ρ·σpsa·[S0].η10·Ephotonλem,
Jf(r,t)=rszsPf(rs,zx,t)ΔV(rs,zs)T(rs,zs,r).

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