Abstract

A novel approach is presented for computing optode placements that are adapted to specific geometries and tissue characteristics, e.g., in optical tomography and photodynamic cancer therapy. The method is based on optimal control techniques together with a sparsity-promoting penalty that favors pointwise solutions, yielding both locations and magnitudes of light sources. In contrast to current discrete approaches, the need for specifying an initial set of candidate configurations as well as the exponential increase in complexity with the number of optodes are avoided. This is demonstrated with computational examples from photodynamic therapy.

© 2012 OSA

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  1. J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: A singular-value analysis,” Opt. Lett.26, 701–703 (2001).
    [CrossRef]
  2. H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt.8, 102–110 (2003).
    [CrossRef] [PubMed]
  3. E. E. Graves, J. P. Culver, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography,” J. Opt. Soc. Am. A21, 231–241 (2004).
    [CrossRef]
  4. T. Lasser and V. Ntziachristos, “Optimization of 360° projection fluorescence molecular tomography,” Med. Image Anal.11, 389–399 (2007).
    [CrossRef] [PubMed]
  5. D. Dolmans, D. Fukumura, and R. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3, 380–387 (2003).
    [CrossRef] [PubMed]
  6. H. Schouwink and P. Baas, “Foscan-mediated photodynamic therapy and operation for malignant pleural mesothelioma,” Ann. Thorac. Surg.78, 388; author reply 388–388; author reply 389 (2004).
    [CrossRef] [PubMed]
  7. P. J. Dwyer, W. M. White, R. L. Fabian, and R. R. Anderson, “Optical integrating balloon device for photodynamic therapy,” Lasers Surg. Med.26, 58–66 (2000).
    [CrossRef] [PubMed]
  8. J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
    [CrossRef] [PubMed]
  9. T. Krueger, H. J. Altermatt, D. Mettler, B. Scholl, L. Magnusson, and H.-B. Ris, “Experimental photodynamic therapy for malignant pleural mesothelioma with pegylated mTHPC,” Lasers Surg. Med.32, 61–68 (2003).
    [CrossRef] [PubMed]
  10. P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
    [CrossRef] [PubMed]
  11. P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
    [CrossRef] [PubMed]
  12. B. Selm, M. Rothmaier, M. Camenzind, T. Khan, and H. Walt, “Novel flexible light diffuser and irradiation properties for photodynamic therapy,” J. Biomed. Opt.12, 034024 (2007).
    [CrossRef] [PubMed]
  13. M. Rothmaier, B. Selm, S. Spichtig, D. Haensse, and M. Wolf, “Photonic textiles for pulse oximetry,” Opt. Express16, 12973–12986 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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  18. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl.15, R41–R93 (1999).
    [CrossRef]
  19. M. Freiberger, C. Clason, and H. Scharfetter, “Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach,” Appl. Opt.49, 3741–3747 (2010).
    [CrossRef] [PubMed]
  20. C. Clason and K. Kunisch, “A duality-based approach to elliptic control problems in non-reflexive Banach spaces,” ESAIM Control Optim. Calc. Var.17, 243–266 (2011).
    [CrossRef]
  21. C. Clason and K. Kunisch, “A measure space approach to optimal source placement,” Comput. Optim. Appl. (online first, Nov. 9, 2011).
  22. E. Casas, C. Clason, and K. Kunisch, “Approximation of elliptic control problems in measure spaces with sparse solutions,” SIAM J. Control Optim. (to be published).
  23. A. Logg, K.-A. Mardal, G. N. Wells, and , Automated Solution of Differential Equations by the Finite Element Method (Springer, 2012); software available from http://fenicsproject.org .
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2011 (1)

C. Clason and K. Kunisch, “A duality-based approach to elliptic control problems in non-reflexive Banach spaces,” ESAIM Control Optim. Calc. Var.17, 243–266 (2011).
[CrossRef]

2010 (2)

M. Freiberger, C. Clason, and H. Scharfetter, “Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach,” Appl. Opt.49, 3741–3747 (2010).
[CrossRef] [PubMed]

Y. Hu, K. Wang, and T. C. Zhu, “Pre-clinic study of uniformity of light blanket for intraoperative photodynamic therapy,” Proc. SPIE7551, 755112 (2010).
[CrossRef]

2009 (2)

G. Stadler, “Elliptic optimal control problems with L1-control cost and applications for the placement of control devices,” Comput. Optim. Appl.44, 159–181 (2009).
[CrossRef]

Y. Hu, K. Wang, and T. C. Zhu, “A light blanket for intraoperative photodynamic therapy,” Proc. SPIE7380, 73801W (2009).
[CrossRef]

2008 (1)

2007 (2)

B. Selm, M. Rothmaier, M. Camenzind, T. Khan, and H. Walt, “Novel flexible light diffuser and irradiation properties for photodynamic therapy,” J. Biomed. Opt.12, 034024 (2007).
[CrossRef] [PubMed]

T. Lasser and V. Ntziachristos, “Optimization of 360° projection fluorescence molecular tomography,” Med. Image Anal.11, 389–399 (2007).
[CrossRef] [PubMed]

2004 (2)

H. Schouwink and P. Baas, “Foscan-mediated photodynamic therapy and operation for malignant pleural mesothelioma,” Ann. Thorac. Surg.78, 388; author reply 388–388; author reply 389 (2004).
[CrossRef] [PubMed]

E. E. Graves, J. P. Culver, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography,” J. Opt. Soc. Am. A21, 231–241 (2004).
[CrossRef]

2003 (4)

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

T. Krueger, H. J. Altermatt, D. Mettler, B. Scholl, L. Magnusson, and H.-B. Ris, “Experimental photodynamic therapy for malignant pleural mesothelioma with pegylated mTHPC,” Lasers Surg. Med.32, 61–68 (2003).
[CrossRef] [PubMed]

D. Dolmans, D. Fukumura, and R. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3, 380–387 (2003).
[CrossRef] [PubMed]

H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt.8, 102–110 (2003).
[CrossRef] [PubMed]

2001 (2)

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: A singular-value analysis,” Opt. Lett.26, 701–703 (2001).
[CrossRef]

P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
[CrossRef] [PubMed]

2000 (2)

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

P. J. Dwyer, W. M. White, R. L. Fabian, and R. R. Anderson, “Optical integrating balloon device for photodynamic therapy,” Lasers Surg. Med.26, 58–66 (2000).
[CrossRef] [PubMed]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl.15, R41–R93 (1999).
[CrossRef]

1997 (1)

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

Altermatt, H. J.

T. Krueger, H. J. Altermatt, D. Mettler, B. Scholl, L. Magnusson, and H.-B. Ris, “Experimental photodynamic therapy for malignant pleural mesothelioma with pegylated mTHPC,” Lasers Surg. Med.32, 61–68 (2003).
[CrossRef] [PubMed]

Anderson, R. R.

P. J. Dwyer, W. M. White, R. L. Fabian, and R. R. Anderson, “Optical integrating balloon device for photodynamic therapy,” Lasers Surg. Med.26, 58–66 (2000).
[CrossRef] [PubMed]

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl.15, R41–R93 (1999).
[CrossRef]

Baas, P.

H. Schouwink and P. Baas, “Foscan-mediated photodynamic therapy and operation for malignant pleural mesothelioma,” Ann. Thorac. Surg.78, 388; author reply 388–388; author reply 389 (2004).
[CrossRef] [PubMed]

P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
[CrossRef] [PubMed]

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

Babich, D.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Bellnier, D. A.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Busch, T. M.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Buyske, J.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Camenzind, M.

B. Selm, M. Rothmaier, M. Camenzind, T. Khan, and H. Walt, “Novel flexible light diffuser and irradiation properties for photodynamic therapy,” J. Biomed. Opt.12, 034024 (2007).
[CrossRef] [PubMed]

Casas, E.

E. Casas, C. Clason, and K. Kunisch, “Approximation of elliptic control problems in measure spaces with sparse solutions,” SIAM J. Control Optim. (to be published).

Clason, C.

C. Clason and K. Kunisch, “A duality-based approach to elliptic control problems in non-reflexive Banach spaces,” ESAIM Control Optim. Calc. Var.17, 243–266 (2011).
[CrossRef]

M. Freiberger, C. Clason, and H. Scharfetter, “Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach,” Appl. Opt.49, 3741–3747 (2010).
[CrossRef] [PubMed]

C. Clason and K. Kunisch, “A measure space approach to optimal source placement,” Comput. Optim. Appl. (online first, Nov. 9, 2011).

E. Casas, C. Clason, and K. Kunisch, “Approximation of elliptic control problems in measure spaces with sparse solutions,” SIAM J. Control Optim. (to be published).

Cooper, M. T.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Culver, J. P.

Dee, A. S.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Dehghani, H.

H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt.8, 102–110 (2003).
[CrossRef] [PubMed]

Dolmans, D.

D. Dolmans, D. Fukumura, and R. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3, 380–387 (2003).
[CrossRef] [PubMed]

Dunn, J. F.

H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt.8, 102–110 (2003).
[CrossRef] [PubMed]

Dwyer, P. J.

P. J. Dwyer, W. M. White, R. L. Fabian, and R. R. Anderson, “Optical integrating balloon device for photodynamic therapy,” Lasers Surg. Med.26, 58–66 (2000).
[CrossRef] [PubMed]

Fabian, R. L.

P. J. Dwyer, W. M. White, R. L. Fabian, and R. R. Anderson, “Optical integrating balloon device for photodynamic therapy,” Lasers Surg. Med.26, 58–66 (2000).
[CrossRef] [PubMed]

Frawley, N. P.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Freiberger, M.

Friedberg, J. S.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Fukumura, D.

D. Dolmans, D. Fukumura, and R. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3, 380–387 (2003).
[CrossRef] [PubMed]

Glatstein, E.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Graves, E. E.

Greco, W. R.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Haensse, D.

Hahn, S. M.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Henderson, B. W.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Holboke, M. J.

Hu, Y.

Y. Hu, K. Wang, and T. C. Zhu, “Pre-clinic study of uniformity of light blanket for intraoperative photodynamic therapy,” Proc. SPIE7551, 755112 (2010).
[CrossRef]

Y. Hu, K. Wang, and T. C. Zhu, “A light blanket for intraoperative photodynamic therapy,” Proc. SPIE7380, 73801W (2009).
[CrossRef]

Jain, R.

D. Dolmans, D. Fukumura, and R. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3, 380–387 (2003).
[CrossRef] [PubMed]

Khan, T.

B. Selm, M. Rothmaier, M. Camenzind, T. Khan, and H. Walt, “Novel flexible light diffuser and irradiation properties for photodynamic therapy,” J. Biomed. Opt.12, 034024 (2007).
[CrossRef] [PubMed]

Krueger, T.

T. Krueger, H. J. Altermatt, D. Mettler, B. Scholl, L. Magnusson, and H.-B. Ris, “Experimental photodynamic therapy for malignant pleural mesothelioma with pegylated mTHPC,” Lasers Surg. Med.32, 61–68 (2003).
[CrossRef] [PubMed]

Kunisch, K.

C. Clason and K. Kunisch, “A duality-based approach to elliptic control problems in non-reflexive Banach spaces,” ESAIM Control Optim. Calc. Var.17, 243–266 (2011).
[CrossRef]

C. Clason and K. Kunisch, “A measure space approach to optimal source placement,” Comput. Optim. Appl. (online first, Nov. 9, 2011).

E. Casas, C. Clason, and K. Kunisch, “Approximation of elliptic control problems in measure spaces with sparse solutions,” SIAM J. Control Optim. (to be published).

Lasser, T.

T. Lasser and V. Ntziachristos, “Optimization of 360° projection fluorescence molecular tomography,” Med. Image Anal.11, 389–399 (2007).
[CrossRef] [PubMed]

Magnusson, L.

T. Krueger, H. J. Altermatt, D. Mettler, B. Scholl, L. Magnusson, and H.-B. Ris, “Experimental photodynamic therapy for malignant pleural mesothelioma with pegylated mTHPC,” Lasers Surg. Med.32, 61–68 (2003).
[CrossRef] [PubMed]

Mettler, D.

T. Krueger, H. J. Altermatt, D. Mettler, B. Scholl, L. Magnusson, and H.-B. Ris, “Experimental photodynamic therapy for malignant pleural mesothelioma with pegylated mTHPC,” Lasers Surg. Med.32, 61–68 (2003).
[CrossRef] [PubMed]

Metz, J.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Mick, R.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Murrer, L.

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

Ntziachristos, V.

Oseroff, A. R.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Pass, H. I.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Paulsen, K. D.

H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt.8, 102–110 (2003).
[CrossRef] [PubMed]

Peterse, J. L.

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

Pogue, B. W.

H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt.8, 102–110 (2003).
[CrossRef] [PubMed]

Ripoll, J.

Ris, H. B.

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

Ris, H.-B.

T. Krueger, H. J. Altermatt, D. Mettler, B. Scholl, L. Magnusson, and H.-B. Ris, “Experimental photodynamic therapy for malignant pleural mesothelioma with pegylated mTHPC,” Lasers Surg. Med.32, 61–68 (2003).
[CrossRef] [PubMed]

Rothmaier, M.

M. Rothmaier, B. Selm, S. Spichtig, D. Haensse, and M. Wolf, “Photonic textiles for pulse oximetry,” Opt. Express16, 12973–12986 (2008).
[CrossRef] [PubMed]

B. Selm, M. Rothmaier, M. Camenzind, T. Khan, and H. Walt, “Novel flexible light diffuser and irradiation properties for photodynamic therapy,” J. Biomed. Opt.12, 034024 (2007).
[CrossRef] [PubMed]

Rutgers, E. J.

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

Scharfetter, H.

Scholl, B.

T. Krueger, H. J. Altermatt, D. Mettler, B. Scholl, L. Magnusson, and H.-B. Ris, “Experimental photodynamic therapy for malignant pleural mesothelioma with pegylated mTHPC,” Lasers Surg. Med.32, 61–68 (2003).
[CrossRef] [PubMed]

Schouwink, H.

H. Schouwink and P. Baas, “Foscan-mediated photodynamic therapy and operation for malignant pleural mesothelioma,” Ann. Thorac. Surg.78, 388; author reply 388–388; author reply 389 (2004).
[CrossRef] [PubMed]

Schouwink, J. H.

P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
[CrossRef] [PubMed]

Selm, B.

M. Rothmaier, B. Selm, S. Spichtig, D. Haensse, and M. Wolf, “Photonic textiles for pulse oximetry,” Opt. Express16, 12973–12986 (2008).
[CrossRef] [PubMed]

B. Selm, M. Rothmaier, M. Camenzind, T. Khan, and H. Walt, “Novel flexible light diffuser and irradiation properties for photodynamic therapy,” J. Biomed. Opt.12, 034024 (2007).
[CrossRef] [PubMed]

Sosa, T. A.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Spichtig, S.

Springett, R.

H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt.8, 102–110 (2003).
[CrossRef] [PubMed]

Stadler, G.

G. Stadler, “Elliptic optimal control problems with L1-control cost and applications for the placement of control devices,” Comput. Optim. Appl.44, 159–181 (2009).
[CrossRef]

Star, W. M.

P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
[CrossRef] [PubMed]

Sterenborg, H. J.

P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
[CrossRef] [PubMed]

Sterman, D. H.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Stevenson, J.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Stewart, F. A.

P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
[CrossRef] [PubMed]

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

van der Sijp, J. R.

P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
[CrossRef] [PubMed]

van Veen, P.

P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
[CrossRef] [PubMed]

van Zandwijk, N.

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

Vaughan, L. A.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Walt, H.

B. Selm, M. Rothmaier, M. Camenzind, T. Khan, and H. Walt, “Novel flexible light diffuser and irradiation properties for photodynamic therapy,” J. Biomed. Opt.12, 034024 (2007).
[CrossRef] [PubMed]

Wang, K.

Y. Hu, K. Wang, and T. C. Zhu, “Pre-clinic study of uniformity of light blanket for intraoperative photodynamic therapy,” Proc. SPIE7551, 755112 (2010).
[CrossRef]

Y. Hu, K. Wang, and T. C. Zhu, “A light blanket for intraoperative photodynamic therapy,” Proc. SPIE7380, 73801W (2009).
[CrossRef]

Weissleder, R.

White, W. M.

P. J. Dwyer, W. M. White, R. L. Fabian, and R. R. Anderson, “Optical integrating balloon device for photodynamic therapy,” Lasers Surg. Med.26, 58–66 (2000).
[CrossRef] [PubMed]

Wolf, M.

Xu, H.

H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt.8, 102–110 (2003).
[CrossRef] [PubMed]

Yodh, A. G.

Zhu, T.

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Zhu, T. C.

Y. Hu, K. Wang, and T. C. Zhu, “Pre-clinic study of uniformity of light blanket for intraoperative photodynamic therapy,” Proc. SPIE7551, 755112 (2010).
[CrossRef]

Y. Hu, K. Wang, and T. C. Zhu, “A light blanket for intraoperative photodynamic therapy,” Proc. SPIE7380, 73801W (2009).
[CrossRef]

Zoetmulder, F. A.

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

Zollo, J. D.

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Ann. Thorac. Surg. (2)

H. Schouwink and P. Baas, “Foscan-mediated photodynamic therapy and operation for malignant pleural mesothelioma,” Ann. Thorac. Surg.78, 388; author reply 388–388; author reply 389 (2004).
[CrossRef] [PubMed]

J. S. Friedberg, R. Mick, J. Stevenson, J. Metz, T. Zhu, J. Buyske, D. H. Sterman, H. I. Pass, E. Glatstein, and S. M. Hahn, “A phase I study of Foscan-mediated photodynamic therapy and surgery in patients with mesothelioma,” Ann. Thorac. Surg.75, 952–959 (2003).
[CrossRef] [PubMed]

Appl. Opt. (1)

Br. J. Cancer (1)

P. Baas, L. Murrer, F. A. Zoetmulder, F. A. Stewart, H. B. Ris, N. van Zandwijk, J. L. Peterse, and E. J. Rutgers, “Photodynamic therapy as adjuvant therapy in surgically treated pleural malignancies,” Br. J. Cancer76, 819–826 (1997).
[CrossRef] [PubMed]

Canc. Treat. (1)

B. W. Henderson, T. M. Busch, L. A. Vaughan, N. P. Frawley, D. Babich, T. A. Sosa, J. D. Zollo, A. S. Dee, M. T. Cooper, D. A. Bellnier, W. R. Greco, and A. R. Oseroff, “Photofrin photodynamic therapy can significantly deplete or preserve oxygenation in human basal cell carcinomas during treatment, depending on fluence rate,” Canc. Treat.60, 525–529 (2000).

Comput. Optim. Appl. (1)

G. Stadler, “Elliptic optimal control problems with L1-control cost and applications for the placement of control devices,” Comput. Optim. Appl.44, 159–181 (2009).
[CrossRef]

ESAIM Control Optim. Calc. Var. (1)

C. Clason and K. Kunisch, “A duality-based approach to elliptic control problems in non-reflexive Banach spaces,” ESAIM Control Optim. Calc. Var.17, 243–266 (2011).
[CrossRef]

Inverse Probl. (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl.15, R41–R93 (1999).
[CrossRef]

J. Biomed. Opt. (2)

B. Selm, M. Rothmaier, M. Camenzind, T. Khan, and H. Walt, “Novel flexible light diffuser and irradiation properties for photodynamic therapy,” J. Biomed. Opt.12, 034024 (2007).
[CrossRef] [PubMed]

H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt.8, 102–110 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Lasers Surg. Med. (2)

T. Krueger, H. J. Altermatt, D. Mettler, B. Scholl, L. Magnusson, and H.-B. Ris, “Experimental photodynamic therapy for malignant pleural mesothelioma with pegylated mTHPC,” Lasers Surg. Med.32, 61–68 (2003).
[CrossRef] [PubMed]

P. J. Dwyer, W. M. White, R. L. Fabian, and R. R. Anderson, “Optical integrating balloon device for photodynamic therapy,” Lasers Surg. Med.26, 58–66 (2000).
[CrossRef] [PubMed]

Med. Image Anal. (1)

T. Lasser and V. Ntziachristos, “Optimization of 360° projection fluorescence molecular tomography,” Med. Image Anal.11, 389–399 (2007).
[CrossRef] [PubMed]

Nat. Rev. Cancer (1)

D. Dolmans, D. Fukumura, and R. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3, 380–387 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Med. Biol. (1)

P. van Veen, J. H. Schouwink, W. M. Star, H. J. Sterenborg, J. R. van der Sijp, F. A. Stewart, and P. Baas, “Wedge-shaped applicator for additional light delivery and dosimetry in the diaphragmal sinus during photodynamic therapy for malignant pleural mesothelioma,” Phys. Med. Biol.46, 1873–1883 (2001).
[CrossRef] [PubMed]

Proc. SPIE (2)

Y. Hu, K. Wang, and T. C. Zhu, “A light blanket for intraoperative photodynamic therapy,” Proc. SPIE7380, 73801W (2009).
[CrossRef]

Y. Hu, K. Wang, and T. C. Zhu, “Pre-clinic study of uniformity of light blanket for intraoperative photodynamic therapy,” Proc. SPIE7551, 755112 (2010).
[CrossRef]

Other (3)

C. Clason and K. Kunisch, “A measure space approach to optimal source placement,” Comput. Optim. Appl. (online first, Nov. 9, 2011).

E. Casas, C. Clason, and K. Kunisch, “Approximation of elliptic control problems in measure spaces with sparse solutions,” SIAM J. Control Optim. (to be published).

A. Logg, K.-A. Mardal, G. N. Wells, and , Automated Solution of Differential Equations by the Finite Element Method (Springer, 2012); software available from http://fenicsproject.org .
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Two-dimensional model geometries (numbers denote curvature κ).

Fig. 2
Fig. 2

Three-dimensional model. The admissible manifold ωq for optodes is indicated in purple.

Fig. 3
Fig. 3

Optode positions and relative magnitudes (height-coded) for representative single-curved and double-curved models for three different values of alpha (from top to bottom: α = 0.1, α = 0.01, α = 0.001).

Fig. 4
Fig. 4

Photon densities φγ (in Wm−2, normalized to unit mean) plotted along part of the observation region (left line in Fig. 1) for representative single-curved and double-curved models for three different values of alpha (from top to bottom: α = 0.1, α = 0.01, α = 0.001).

Fig. 5
Fig. 5

Optode positions and magnitudes (left) and photon densities (right; in Wm−2, normalized to unit mean) for the three-dimensional model and three different values of α.

Tables (4)

Tables Icon

Table 1 Algorithm 1 Semismooth Newton method with continuation

Tables Icon

Table 1 Results for single-curved models. Shown are the number N of active nodes and the coefficient of variation cv of the photon density in the observation domain for different curvatures κ and values of α.

Tables Icon

Table 2 Results for double-curved models. Shown are the number N of active nodes and the coefficient of variation cv of the photon density in the observation domain for different curvatures κ and values of α.

Tables Icon

Table 3 Results for three-dimensional model. Shown are the number N of active nodes and the coefficient of variation cv of the photon density in the observation domain for different values of α.

Equations (12)

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{ ( κ ( x ) φ ( x ) ) + μ a ( x ) φ ( x ) = q ( x ) in Ω , κ ( x ) n ( x ) φ ( x ) + ρ φ ( x ) = 0 on Γ .
{ ( κ ( x ) p ( x ) ) + μ a ( x ) p ( x ) = f ( x ) in Ω , κ ( x ) n ( x ) p ( x ) + ρ p ( x ) = 0 on Γ
min q ( Ω ) J ( q ) + α q ,
q = sup f C 0 ( Ω ) f C 1 Ω f d q ,
q = Ω | q ( x ) | d x = q L 1
min φ H 1 ( Ω ) , q ( ω q ) 1 2 φ | ω o z L 2 ( ω o ) 2 + α q ( ω q ) subject to ( 2.1 ) and q 0 .
q γ + γ min ( 0 , p γ + α ) = 0 ,
q γ = i = 1 N ( T ) q i δ ( x x i ) .
q γ , e j = i = 1 N ( T ) q i δ ( x x i ) , e j = q j ,
{ A φ γ q γ = 0 , M o φ γ + A T p γ = M o z , q γ + γ min ( 0 , p γ | ω q + α ) = 0 ,
( A D k M o A ) ( φ k + 1 p k + 1 ) = ( α d k M o z ) ,
d j k = { γ if ( p k | ω q ) j < α , 0 else ,

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