Abstract

Certain polymer gels become turbid on exposure to ionizing radiation, a property exploited in medical dosimetry to produce three-dimensional dose maps for radiotherapy. These maps can be read using optical computed tomography (CT). A test phantom of complex shape (“layered tube”) was developed to investigate the optical properties of polymer gel dosimeters when read using optical CT. Extinction coefficient profiles from tomographically reconstructed slices of the phantom exhibited several artifacts. A simple model invoking scattered light in the gel was able to account for all artifacts, which in a real dosimeter may have been mistaken for other phenomena, resulting in incorrect readings of dose.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2009 (1)

S. G. Bosi, S. Brown, S. Sarabipour, Y. De Deene, and C. Baldock, “Modelling optical scattering artefacts for varying pathlength in a gel dosimeter phantom,” Phys. Med. Biol. 54, 275-283 (2009).
[CrossRef]

2008 (4)

H. S. Sakhalkar and M. Oldham, “Area detector based optical-CT scanner for 3D dosimetry,” Med. Phys. 35, 101-111(2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

H. S. Sakhalkar and M. Oldham, “Area detector based optical-CT scanner for 3D dosimetry,” Med. Phys. 35, 101-111 (2008).
[CrossRef] [PubMed]

2007 (2)

N. Krstajić and S. J. Doran, “Fast laser scanning optical-CT apparatus for 3D radiation dosimetry,” Phys. Med. Biol. 52, N257-N263 (2007).
[CrossRef] [PubMed]

S. Bosi, P. Naseri, A. Puran, J. Davies, and C. Baldock, “Initial investigation of a novel light-scattering gel phantom for evaluation of optical CT scanners for radiotherapy gel dosimetry,” Phys. Med. Biol. 52, 2893-2903 (2007).
[CrossRef] [PubMed]

2006 (5)

M. Bertram, J. Wiegert, and G. Rose, “Scatter correction for cone-beam computed tomography using simulated object models,” Proc. SPIE 6142, doi:10.1117/12.651027 (2006).
[CrossRef]

K. McAuley, “Fundamentals of polymer gel dosimeters,” J. Phys. Conf. Ser. 56, 35-44 (2006).
[CrossRef]

S. J. Doran and N. Krstajić, “The history and principles of optical computed tomography for scanning 3-D radiation dosimeters,” J. Phys. Conf. Ser. 56, 45-57 (2006).
[CrossRef]

L. J. Schreiner, “Dosimetry in modern radiation therapy: limitations and needs,” J. Phys. Conf. Ser. 56, 1-13 (2006).
[CrossRef]

C. Baldock, “Historical overview of the development of gel dosimetry: a personal perspective,” J. Phys. Conf. Ser. 56, 14-22 (2006).
[CrossRef]

2005 (4)

A. J. Venning, K. N. Nitschke, P. J. Keall, and C. Baldock, “Radiological properties of normoxic polymer gel dosimeters,” Med. Phys. 32, 1047-1053 (2005).
[CrossRef] [PubMed]

A. J. Venning, B. Hill, S. Brindha, B. J. Healy, and C. Baldock, “Investigation of the PAGAT polymer gel dosimeter using magnetic resonance imaging,” Phys. Med. Biol. 50, 3875-3888(2005).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

J. Miller, J. Adamovics, and J. Dietrich, “Cone beam optical CT scanner for 3D dosimetry,” Med. Phys. 32, 2138 (2005).
[CrossRef]

2003 (1)

M. L. Mather and C. Baldock, “Ultrasound tomography imaging of radiation dose distributions in polymer gel dosimeters: preliminary study,” Med. Phys. 30, 2140-2148 (2003).
[CrossRef] [PubMed]

2002 (1)

L. Wind and W. W. Szymanski, “Quantification of scattering corrections to the Beer-Lambert law for transmittance measurements in turbid media,” Meas. Sci. Technol. 13, 270-275(2002).
[CrossRef]

2001 (4)

M. Lepage, A. K. Whittaker, L. Rintoul, S. Å. J. Bäck, and C. Baldock, “Modelling of post-irradiation events in polymer gel dosimeters,” Phys. Med. Biol. 46, 2827-2839 (2001).
[CrossRef] [PubMed]

C. Baldock, P. J. Harris, A. R. Piercy, and B. Healy, “Experimental determination of the diffusion coefficient in two-dimensions in ferrous sulphate gels using the finite element method,” Australas. Phys. Eng. Sci. Med. 24, 19-30(2001).
[CrossRef] [PubMed]

M. Oldham, J. H. Siewerdsen, A. Shetty, and D. A. Jaffray, “High resolution gel-dosimetry by optical-CT and MR scanning,” Med. Phys. 28, 1436-1445 (2001).
[CrossRef] [PubMed]

J. Trapp, S. Å. J. Bäck, M. Lepage, G. Michael, and C. Baldock, “An experimental study of the dose response of polymer gel dosimeters imaged with x-ray computed tomography,” Phys. Med. Biol. 46, 2939-2951 (2001).
[CrossRef] [PubMed]

2000 (1)

Y. De Deene, P. Hanselaer, C. De Wagter, E. Achten, and W. De Neve, “An investigation of the chemical stability of a monomer/polymer gel dosimeter,” Phys. Med. Biol. 45, 859-878 (2000).
[CrossRef] [PubMed]

1999 (1)

J. G. Wolodzko, C. Marsden, and A. Appleby, “CCD imaging for optical tomography of gel radiation dosimeters,” Med. Phys. 26, 2508-2513 (1999).
[CrossRef] [PubMed]

1998 (1)

C. Baldock, R. P. Burford, N. Billingham, G. S. Wagner, S. Patval, R. D. Badawi, and S. F. Keevil, “Experimental procedure for the manufacture and calibration of polyacrylamide gel (PAG) for magnetic resonance imaging (MRI) radiation dosimetry,” Phys. Med. Biol. 43, 695-702(1998).
[CrossRef] [PubMed]

1997 (1)

S. R. Arridge and J. C. Hebdenz, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841-853 (1997).
[CrossRef] [PubMed]

1996 (2)

P. J. Harris, A. R. Piercy, and C. Baldock, “A method for determining the diffusion coefficient in Fe(II/III) radiation dosimetry gels using finite elements,” Phys. Med. Biol. 41, 1745-1753 (1996).
[CrossRef] [PubMed]

J. C. Gore, M. Ranade, M. J. Maryanski, and R. J. Schulz, “Radiation dose distributions in three dimensions from tomographic optical density scanning of polymer gels. I. Development of an optical scanner,” Phys. Med. Biol. 41, 2695-2704 (1996).
[CrossRef] [PubMed]

1993 (1)

M. J. Maryanski, J. C. Gore, R. P. Kennan, and R. J. Schulz, “NMR relaxation enhancement in gels polymerized and cross-linked by ionizing radiations: a new approach to 3-D dosimetry by MRI,” Magn. Reson. Imaging 11, 253-258 (1993).
[CrossRef] [PubMed]

1991 (1)

A. Appleby and A. Leghrouz, “Imaging of radiation dose by visible color development in ferrous-agarose-xylenol orange gels,” Med. Phys. 18, 309-312 (1991).
[CrossRef] [PubMed]

1984 (1)

1974 (1)

B. L. Gupta and K. R. Gomathy, “Consistency of ferrous sulphate-benzoic acid-xylenol orange dosimeter,” Int. J. Appl. Radiat. Isot. 25, 509-513 (1974).
[CrossRef] [PubMed]

1927 (1)

H. Fricke and S. Morse, “The chemical action of roentgen rays on dilute ferrosulphate as a measure of dose,” Am J Roentgenol Radium Ther 18, 430-432 (1927).

Achten, E.

Y. De Deene, P. Hanselaer, C. De Wagter, E. Achten, and W. De Neve, “An investigation of the chemical stability of a monomer/polymer gel dosimeter,” Phys. Med. Biol. 45, 859-878 (2000).
[CrossRef] [PubMed]

Adamovics, J.

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

J. Miller, J. Adamovics, and J. Dietrich, “Cone beam optical CT scanner for 3D dosimetry,” Med. Phys. 32, 2138 (2005).
[CrossRef]

Appleby, A.

J. G. Wolodzko, C. Marsden, and A. Appleby, “CCD imaging for optical tomography of gel radiation dosimeters,” Med. Phys. 26, 2508-2513 (1999).
[CrossRef] [PubMed]

A. Appleby and A. Leghrouz, “Imaging of radiation dose by visible color development in ferrous-agarose-xylenol orange gels,” Med. Phys. 18, 309-312 (1991).
[CrossRef] [PubMed]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

S. R. Arridge and J. C. Hebdenz, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841-853 (1997).
[CrossRef] [PubMed]

Bäck, S. Å. J.

M. Lepage, A. K. Whittaker, L. Rintoul, S. Å. J. Bäck, and C. Baldock, “Modelling of post-irradiation events in polymer gel dosimeters,” Phys. Med. Biol. 46, 2827-2839 (2001).
[CrossRef] [PubMed]

J. Trapp, S. Å. J. Bäck, M. Lepage, G. Michael, and C. Baldock, “An experimental study of the dose response of polymer gel dosimeters imaged with x-ray computed tomography,” Phys. Med. Biol. 46, 2939-2951 (2001).
[CrossRef] [PubMed]

Badawi, R. D.

C. Baldock, R. P. Burford, N. Billingham, G. S. Wagner, S. Patval, R. D. Badawi, and S. F. Keevil, “Experimental procedure for the manufacture and calibration of polyacrylamide gel (PAG) for magnetic resonance imaging (MRI) radiation dosimetry,” Phys. Med. Biol. 43, 695-702(1998).
[CrossRef] [PubMed]

Baldock, C.

S. G. Bosi, S. Brown, S. Sarabipour, Y. De Deene, and C. Baldock, “Modelling optical scattering artefacts for varying pathlength in a gel dosimeter phantom,” Phys. Med. Biol. 54, 275-283 (2009).
[CrossRef]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Bosi, P. Naseri, A. Puran, J. Davies, and C. Baldock, “Initial investigation of a novel light-scattering gel phantom for evaluation of optical CT scanners for radiotherapy gel dosimetry,” Phys. Med. Biol. 52, 2893-2903 (2007).
[CrossRef] [PubMed]

C. Baldock, “Historical overview of the development of gel dosimetry: a personal perspective,” J. Phys. Conf. Ser. 56, 14-22 (2006).
[CrossRef]

A. J. Venning, K. N. Nitschke, P. J. Keall, and C. Baldock, “Radiological properties of normoxic polymer gel dosimeters,” Med. Phys. 32, 1047-1053 (2005).
[CrossRef] [PubMed]

A. J. Venning, B. Hill, S. Brindha, B. J. Healy, and C. Baldock, “Investigation of the PAGAT polymer gel dosimeter using magnetic resonance imaging,” Phys. Med. Biol. 50, 3875-3888(2005).
[CrossRef] [PubMed]

M. L. Mather and C. Baldock, “Ultrasound tomography imaging of radiation dose distributions in polymer gel dosimeters: preliminary study,” Med. Phys. 30, 2140-2148 (2003).
[CrossRef] [PubMed]

J. Trapp, S. Å. J. Bäck, M. Lepage, G. Michael, and C. Baldock, “An experimental study of the dose response of polymer gel dosimeters imaged with x-ray computed tomography,” Phys. Med. Biol. 46, 2939-2951 (2001).
[CrossRef] [PubMed]

M. Lepage, A. K. Whittaker, L. Rintoul, S. Å. J. Bäck, and C. Baldock, “Modelling of post-irradiation events in polymer gel dosimeters,” Phys. Med. Biol. 46, 2827-2839 (2001).
[CrossRef] [PubMed]

C. Baldock, P. J. Harris, A. R. Piercy, and B. Healy, “Experimental determination of the diffusion coefficient in two-dimensions in ferrous sulphate gels using the finite element method,” Australas. Phys. Eng. Sci. Med. 24, 19-30(2001).
[CrossRef] [PubMed]

C. Baldock, R. P. Burford, N. Billingham, G. S. Wagner, S. Patval, R. D. Badawi, and S. F. Keevil, “Experimental procedure for the manufacture and calibration of polyacrylamide gel (PAG) for magnetic resonance imaging (MRI) radiation dosimetry,” Phys. Med. Biol. 43, 695-702(1998).
[CrossRef] [PubMed]

P. J. Harris, A. R. Piercy, and C. Baldock, “A method for determining the diffusion coefficient in Fe(II/III) radiation dosimetry gels using finite elements,” Phys. Med. Biol. 41, 1745-1753 (1996).
[CrossRef] [PubMed]

Bertram, M.

M. Bertram, J. Wiegert, and G. Rose, “Scatter correction for cone-beam computed tomography using simulated object models,” Proc. SPIE 6142, doi:10.1117/12.651027 (2006).
[CrossRef]

Billingham, N.

C. Baldock, R. P. Burford, N. Billingham, G. S. Wagner, S. Patval, R. D. Badawi, and S. F. Keevil, “Experimental procedure for the manufacture and calibration of polyacrylamide gel (PAG) for magnetic resonance imaging (MRI) radiation dosimetry,” Phys. Med. Biol. 43, 695-702(1998).
[CrossRef] [PubMed]

Bosi, S.

S. Bosi, P. Naseri, A. Puran, J. Davies, and C. Baldock, “Initial investigation of a novel light-scattering gel phantom for evaluation of optical CT scanners for radiotherapy gel dosimetry,” Phys. Med. Biol. 52, 2893-2903 (2007).
[CrossRef] [PubMed]

Bosi, S. G.

S. G. Bosi, S. Brown, S. Sarabipour, Y. De Deene, and C. Baldock, “Modelling optical scattering artefacts for varying pathlength in a gel dosimeter phantom,” Phys. Med. Biol. 54, 275-283 (2009).
[CrossRef]

Brindha, S.

A. J. Venning, B. Hill, S. Brindha, B. J. Healy, and C. Baldock, “Investigation of the PAGAT polymer gel dosimeter using magnetic resonance imaging,” Phys. Med. Biol. 50, 3875-3888(2005).
[CrossRef] [PubMed]

Brown, S.

S. G. Bosi, S. Brown, S. Sarabipour, Y. De Deene, and C. Baldock, “Modelling optical scattering artefacts for varying pathlength in a gel dosimeter phantom,” Phys. Med. Biol. 54, 275-283 (2009).
[CrossRef]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

Burford, R. P.

C. Baldock, R. P. Burford, N. Billingham, G. S. Wagner, S. Patval, R. D. Badawi, and S. F. Keevil, “Experimental procedure for the manufacture and calibration of polyacrylamide gel (PAG) for magnetic resonance imaging (MRI) radiation dosimetry,” Phys. Med. Biol. 43, 695-702(1998).
[CrossRef] [PubMed]

Davies, J.

S. Bosi, P. Naseri, A. Puran, J. Davies, and C. Baldock, “Initial investigation of a novel light-scattering gel phantom for evaluation of optical CT scanners for radiotherapy gel dosimetry,” Phys. Med. Biol. 52, 2893-2903 (2007).
[CrossRef] [PubMed]

Davis, L. C.

De Deene, Y.

S. G. Bosi, S. Brown, S. Sarabipour, Y. De Deene, and C. Baldock, “Modelling optical scattering artefacts for varying pathlength in a gel dosimeter phantom,” Phys. Med. Biol. 54, 275-283 (2009).
[CrossRef]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

Y. De Deene, P. Hanselaer, C. De Wagter, E. Achten, and W. De Neve, “An investigation of the chemical stability of a monomer/polymer gel dosimeter,” Phys. Med. Biol. 45, 859-878 (2000).
[CrossRef] [PubMed]

De Neve, W.

Y. De Deene, P. Hanselaer, C. De Wagter, E. Achten, and W. De Neve, “An investigation of the chemical stability of a monomer/polymer gel dosimeter,” Phys. Med. Biol. 45, 859-878 (2000).
[CrossRef] [PubMed]

De Wagter, C.

Y. De Deene, P. Hanselaer, C. De Wagter, E. Achten, and W. De Neve, “An investigation of the chemical stability of a monomer/polymer gel dosimeter,” Phys. Med. Biol. 45, 859-878 (2000).
[CrossRef] [PubMed]

Dietrich, J.

J. Miller, J. Adamovics, and J. Dietrich, “Cone beam optical CT scanner for 3D dosimetry,” Med. Phys. 32, 2138 (2005).
[CrossRef]

Doran, S. J.

N. Krstajić and S. J. Doran, “Fast laser scanning optical-CT apparatus for 3D radiation dosimetry,” Phys. Med. Biol. 52, N257-N263 (2007).
[CrossRef] [PubMed]

S. J. Doran and N. Krstajić, “The history and principles of optical computed tomography for scanning 3-D radiation dosimeters,” J. Phys. Conf. Ser. 56, 45-57 (2006).
[CrossRef]

Feldkamp, L. A.

Fricke, H.

H. Fricke and S. Morse, “The chemical action of roentgen rays on dilute ferrosulphate as a measure of dose,” Am J Roentgenol Radium Ther 18, 430-432 (1927).

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

Gomathy, K. R.

B. L. Gupta and K. R. Gomathy, “Consistency of ferrous sulphate-benzoic acid-xylenol orange dosimeter,” Int. J. Appl. Radiat. Isot. 25, 509-513 (1974).
[CrossRef] [PubMed]

Gore, J. C.

J. C. Gore, M. Ranade, M. J. Maryanski, and R. J. Schulz, “Radiation dose distributions in three dimensions from tomographic optical density scanning of polymer gels. I. Development of an optical scanner,” Phys. Med. Biol. 41, 2695-2704 (1996).
[CrossRef] [PubMed]

M. J. Maryanski, J. C. Gore, R. P. Kennan, and R. J. Schulz, “NMR relaxation enhancement in gels polymerized and cross-linked by ionizing radiations: a new approach to 3-D dosimetry by MRI,” Magn. Reson. Imaging 11, 253-258 (1993).
[CrossRef] [PubMed]

Gupta, B. L.

B. L. Gupta and K. R. Gomathy, “Consistency of ferrous sulphate-benzoic acid-xylenol orange dosimeter,” Int. J. Appl. Radiat. Isot. 25, 509-513 (1974).
[CrossRef] [PubMed]

Hanselaer, P.

Y. De Deene, P. Hanselaer, C. De Wagter, E. Achten, and W. De Neve, “An investigation of the chemical stability of a monomer/polymer gel dosimeter,” Phys. Med. Biol. 45, 859-878 (2000).
[CrossRef] [PubMed]

Harris, P. J.

C. Baldock, P. J. Harris, A. R. Piercy, and B. Healy, “Experimental determination of the diffusion coefficient in two-dimensions in ferrous sulphate gels using the finite element method,” Australas. Phys. Eng. Sci. Med. 24, 19-30(2001).
[CrossRef] [PubMed]

P. J. Harris, A. R. Piercy, and C. Baldock, “A method for determining the diffusion coefficient in Fe(II/III) radiation dosimetry gels using finite elements,” Phys. Med. Biol. 41, 1745-1753 (1996).
[CrossRef] [PubMed]

Healy, B.

C. Baldock, P. J. Harris, A. R. Piercy, and B. Healy, “Experimental determination of the diffusion coefficient in two-dimensions in ferrous sulphate gels using the finite element method,” Australas. Phys. Eng. Sci. Med. 24, 19-30(2001).
[CrossRef] [PubMed]

Healy, B. J.

A. J. Venning, B. Hill, S. Brindha, B. J. Healy, and C. Baldock, “Investigation of the PAGAT polymer gel dosimeter using magnetic resonance imaging,” Phys. Med. Biol. 50, 3875-3888(2005).
[CrossRef] [PubMed]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

Hebdenz, J. C.

S. R. Arridge and J. C. Hebdenz, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841-853 (1997).
[CrossRef] [PubMed]

Hill, B.

A. J. Venning, B. Hill, S. Brindha, B. J. Healy, and C. Baldock, “Investigation of the PAGAT polymer gel dosimeter using magnetic resonance imaging,” Phys. Med. Biol. 50, 3875-3888(2005).
[CrossRef] [PubMed]

Jaffray, D. A.

M. Oldham, J. H. Siewerdsen, A. Shetty, and D. A. Jaffray, “High resolution gel-dosimetry by optical-CT and MR scanning,” Med. Phys. 28, 1436-1445 (2001).
[CrossRef] [PubMed]

Keall, P. J.

A. J. Venning, K. N. Nitschke, P. J. Keall, and C. Baldock, “Radiological properties of normoxic polymer gel dosimeters,” Med. Phys. 32, 1047-1053 (2005).
[CrossRef] [PubMed]

Keevil, S. F.

C. Baldock, R. P. Burford, N. Billingham, G. S. Wagner, S. Patval, R. D. Badawi, and S. F. Keevil, “Experimental procedure for the manufacture and calibration of polyacrylamide gel (PAG) for magnetic resonance imaging (MRI) radiation dosimetry,” Phys. Med. Biol. 43, 695-702(1998).
[CrossRef] [PubMed]

Kennan, R. P.

M. J. Maryanski, J. C. Gore, R. P. Kennan, and R. J. Schulz, “NMR relaxation enhancement in gels polymerized and cross-linked by ionizing radiations: a new approach to 3-D dosimetry by MRI,” Magn. Reson. Imaging 11, 253-258 (1993).
[CrossRef] [PubMed]

Kress, J. W.

Krstajic, N.

N. Krstajić and S. J. Doran, “Fast laser scanning optical-CT apparatus for 3D radiation dosimetry,” Phys. Med. Biol. 52, N257-N263 (2007).
[CrossRef] [PubMed]

S. J. Doran and N. Krstajić, “The history and principles of optical computed tomography for scanning 3-D radiation dosimeters,” J. Phys. Conf. Ser. 56, 45-57 (2006).
[CrossRef]

Leghrouz, A.

A. Appleby and A. Leghrouz, “Imaging of radiation dose by visible color development in ferrous-agarose-xylenol orange gels,” Med. Phys. 18, 309-312 (1991).
[CrossRef] [PubMed]

Lepage, M.

M. Lepage, A. K. Whittaker, L. Rintoul, S. Å. J. Bäck, and C. Baldock, “Modelling of post-irradiation events in polymer gel dosimeters,” Phys. Med. Biol. 46, 2827-2839 (2001).
[CrossRef] [PubMed]

J. Trapp, S. Å. J. Bäck, M. Lepage, G. Michael, and C. Baldock, “An experimental study of the dose response of polymer gel dosimeters imaged with x-ray computed tomography,” Phys. Med. Biol. 46, 2939-2951 (2001).
[CrossRef] [PubMed]

Marsden, C.

J. G. Wolodzko, C. Marsden, and A. Appleby, “CCD imaging for optical tomography of gel radiation dosimeters,” Med. Phys. 26, 2508-2513 (1999).
[CrossRef] [PubMed]

Maryanski, M. J.

J. C. Gore, M. Ranade, M. J. Maryanski, and R. J. Schulz, “Radiation dose distributions in three dimensions from tomographic optical density scanning of polymer gels. I. Development of an optical scanner,” Phys. Med. Biol. 41, 2695-2704 (1996).
[CrossRef] [PubMed]

M. J. Maryanski, J. C. Gore, R. P. Kennan, and R. J. Schulz, “NMR relaxation enhancement in gels polymerized and cross-linked by ionizing radiations: a new approach to 3-D dosimetry by MRI,” Magn. Reson. Imaging 11, 253-258 (1993).
[CrossRef] [PubMed]

Mather, M. L.

M. L. Mather and C. Baldock, “Ultrasound tomography imaging of radiation dose distributions in polymer gel dosimeters: preliminary study,” Med. Phys. 30, 2140-2148 (2003).
[CrossRef] [PubMed]

McAuley, K.

K. McAuley, “Fundamentals of polymer gel dosimeters,” J. Phys. Conf. Ser. 56, 35-44 (2006).
[CrossRef]

Michael, G.

J. Trapp, S. Å. J. Bäck, M. Lepage, G. Michael, and C. Baldock, “An experimental study of the dose response of polymer gel dosimeters imaged with x-ray computed tomography,” Phys. Med. Biol. 46, 2939-2951 (2001).
[CrossRef] [PubMed]

Miller, J.

J. Miller, J. Adamovics, and J. Dietrich, “Cone beam optical CT scanner for 3D dosimetry,” Med. Phys. 32, 2138 (2005).
[CrossRef]

Morse, S.

H. Fricke and S. Morse, “The chemical action of roentgen rays on dilute ferrosulphate as a measure of dose,” Am J Roentgenol Radium Ther 18, 430-432 (1927).

Naseri, P.

S. Bosi, P. Naseri, A. Puran, J. Davies, and C. Baldock, “Initial investigation of a novel light-scattering gel phantom for evaluation of optical CT scanners for radiotherapy gel dosimetry,” Phys. Med. Biol. 52, 2893-2903 (2007).
[CrossRef] [PubMed]

Nitschke, K. N.

A. J. Venning, K. N. Nitschke, P. J. Keall, and C. Baldock, “Radiological properties of normoxic polymer gel dosimeters,” Med. Phys. 32, 1047-1053 (2005).
[CrossRef] [PubMed]

Oldham, M.

H. S. Sakhalkar and M. Oldham, “Area detector based optical-CT scanner for 3D dosimetry,” Med. Phys. 35, 101-111 (2008).
[CrossRef] [PubMed]

H. S. Sakhalkar and M. Oldham, “Area detector based optical-CT scanner for 3D dosimetry,” Med. Phys. 35, 101-111(2008).
[CrossRef] [PubMed]

M. Oldham, J. H. Siewerdsen, A. Shetty, and D. A. Jaffray, “High resolution gel-dosimetry by optical-CT and MR scanning,” Med. Phys. 28, 1436-1445 (2001).
[CrossRef] [PubMed]

Oliver, L.

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

Patval, S.

C. Baldock, R. P. Burford, N. Billingham, G. S. Wagner, S. Patval, R. D. Badawi, and S. F. Keevil, “Experimental procedure for the manufacture and calibration of polyacrylamide gel (PAG) for magnetic resonance imaging (MRI) radiation dosimetry,” Phys. Med. Biol. 43, 695-702(1998).
[CrossRef] [PubMed]

Piercy, A. R.

C. Baldock, P. J. Harris, A. R. Piercy, and B. Healy, “Experimental determination of the diffusion coefficient in two-dimensions in ferrous sulphate gels using the finite element method,” Australas. Phys. Eng. Sci. Med. 24, 19-30(2001).
[CrossRef] [PubMed]

P. J. Harris, A. R. Piercy, and C. Baldock, “A method for determining the diffusion coefficient in Fe(II/III) radiation dosimetry gels using finite elements,” Phys. Med. Biol. 41, 1745-1753 (1996).
[CrossRef] [PubMed]

Puran, A.

S. Bosi, P. Naseri, A. Puran, J. Davies, and C. Baldock, “Initial investigation of a novel light-scattering gel phantom for evaluation of optical CT scanners for radiotherapy gel dosimetry,” Phys. Med. Biol. 52, 2893-2903 (2007).
[CrossRef] [PubMed]

Ranade, M.

J. C. Gore, M. Ranade, M. J. Maryanski, and R. J. Schulz, “Radiation dose distributions in three dimensions from tomographic optical density scanning of polymer gels. I. Development of an optical scanner,” Phys. Med. Biol. 41, 2695-2704 (1996).
[CrossRef] [PubMed]

Rintoul, L.

M. Lepage, A. K. Whittaker, L. Rintoul, S. Å. J. Bäck, and C. Baldock, “Modelling of post-irradiation events in polymer gel dosimeters,” Phys. Med. Biol. 46, 2827-2839 (2001).
[CrossRef] [PubMed]

Rose, G.

M. Bertram, J. Wiegert, and G. Rose, “Scatter correction for cone-beam computed tomography using simulated object models,” Proc. SPIE 6142, doi:10.1117/12.651027 (2006).
[CrossRef]

Sakhalkar, H. S.

H. S. Sakhalkar and M. Oldham, “Area detector based optical-CT scanner for 3D dosimetry,” Med. Phys. 35, 101-111(2008).
[CrossRef] [PubMed]

H. S. Sakhalkar and M. Oldham, “Area detector based optical-CT scanner for 3D dosimetry,” Med. Phys. 35, 101-111 (2008).
[CrossRef] [PubMed]

Sarabipour, S.

S. G. Bosi, S. Brown, S. Sarabipour, Y. De Deene, and C. Baldock, “Modelling optical scattering artefacts for varying pathlength in a gel dosimeter phantom,” Phys. Med. Biol. 54, 275-283 (2009).
[CrossRef]

Schreiner, L. J.

L. J. Schreiner, “Dosimetry in modern radiation therapy: limitations and needs,” J. Phys. Conf. Ser. 56, 1-13 (2006).
[CrossRef]

Schulz, R. J.

J. C. Gore, M. Ranade, M. J. Maryanski, and R. J. Schulz, “Radiation dose distributions in three dimensions from tomographic optical density scanning of polymer gels. I. Development of an optical scanner,” Phys. Med. Biol. 41, 2695-2704 (1996).
[CrossRef] [PubMed]

M. J. Maryanski, J. C. Gore, R. P. Kennan, and R. J. Schulz, “NMR relaxation enhancement in gels polymerized and cross-linked by ionizing radiations: a new approach to 3-D dosimetry by MRI,” Magn. Reson. Imaging 11, 253-258 (1993).
[CrossRef] [PubMed]

Shetty, A.

M. Oldham, J. H. Siewerdsen, A. Shetty, and D. A. Jaffray, “High resolution gel-dosimetry by optical-CT and MR scanning,” Med. Phys. 28, 1436-1445 (2001).
[CrossRef] [PubMed]

Siewerdsen, J. H.

M. Oldham, J. H. Siewerdsen, A. Shetty, and D. A. Jaffray, “High resolution gel-dosimetry by optical-CT and MR scanning,” Med. Phys. 28, 1436-1445 (2001).
[CrossRef] [PubMed]

Szymanski, W. W.

L. Wind and W. W. Szymanski, “Quantification of scattering corrections to the Beer-Lambert law for transmittance measurements in turbid media,” Meas. Sci. Technol. 13, 270-275(2002).
[CrossRef]

Trapp, J.

J. Trapp, S. Å. J. Bäck, M. Lepage, G. Michael, and C. Baldock, “An experimental study of the dose response of polymer gel dosimeters imaged with x-ray computed tomography,” Phys. Med. Biol. 46, 2939-2951 (2001).
[CrossRef] [PubMed]

Venning, A.

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

Venning, A. J.

A. J. Venning, K. N. Nitschke, P. J. Keall, and C. Baldock, “Radiological properties of normoxic polymer gel dosimeters,” Med. Phys. 32, 1047-1053 (2005).
[CrossRef] [PubMed]

A. J. Venning, B. Hill, S. Brindha, B. J. Healy, and C. Baldock, “Investigation of the PAGAT polymer gel dosimeter using magnetic resonance imaging,” Phys. Med. Biol. 50, 3875-3888(2005).
[CrossRef] [PubMed]

Vial, P.

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

Wagner, G. S.

C. Baldock, R. P. Burford, N. Billingham, G. S. Wagner, S. Patval, R. D. Badawi, and S. F. Keevil, “Experimental procedure for the manufacture and calibration of polyacrylamide gel (PAG) for magnetic resonance imaging (MRI) radiation dosimetry,” Phys. Med. Biol. 43, 695-702(1998).
[CrossRef] [PubMed]

Whittaker, A. K.

M. Lepage, A. K. Whittaker, L. Rintoul, S. Å. J. Bäck, and C. Baldock, “Modelling of post-irradiation events in polymer gel dosimeters,” Phys. Med. Biol. 46, 2827-2839 (2001).
[CrossRef] [PubMed]

Wiegert, J.

M. Bertram, J. Wiegert, and G. Rose, “Scatter correction for cone-beam computed tomography using simulated object models,” Proc. SPIE 6142, doi:10.1117/12.651027 (2006).
[CrossRef]

Wind, L.

L. Wind and W. W. Szymanski, “Quantification of scattering corrections to the Beer-Lambert law for transmittance measurements in turbid media,” Meas. Sci. Technol. 13, 270-275(2002).
[CrossRef]

Wolodzko, J. G.

J. G. Wolodzko, C. Marsden, and A. Appleby, “CCD imaging for optical tomography of gel radiation dosimeters,” Med. Phys. 26, 2508-2513 (1999).
[CrossRef] [PubMed]

Am J Roentgenol Radium Ther (1)

H. Fricke and S. Morse, “The chemical action of roentgen rays on dilute ferrosulphate as a measure of dose,” Am J Roentgenol Radium Ther 18, 430-432 (1927).

Appl. Radiat. Isot. (2)

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

S. Brown, A. Venning, Y. De Deene, P. Vial, L. Oliver, J. Adamovics, and C. Baldock, “Radiological properties of the PRESAGE and PAGAT polymer dosimeters,” Appl. Radiat. Isot. 66, 1970-1974 (2008).
[CrossRef] [PubMed]

Australas. Phys. Eng. Sci. Med. (1)

C. Baldock, P. J. Harris, A. R. Piercy, and B. Healy, “Experimental determination of the diffusion coefficient in two-dimensions in ferrous sulphate gels using the finite element method,” Australas. Phys. Eng. Sci. Med. 24, 19-30(2001).
[CrossRef] [PubMed]

Int. J. Appl. Radiat. Isot. (1)

B. L. Gupta and K. R. Gomathy, “Consistency of ferrous sulphate-benzoic acid-xylenol orange dosimeter,” Int. J. Appl. Radiat. Isot. 25, 509-513 (1974).
[CrossRef] [PubMed]

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

J. Phys. Conf. Ser. (4)

S. J. Doran and N. Krstajić, “The history and principles of optical computed tomography for scanning 3-D radiation dosimeters,” J. Phys. Conf. Ser. 56, 45-57 (2006).
[CrossRef]

K. McAuley, “Fundamentals of polymer gel dosimeters,” J. Phys. Conf. Ser. 56, 35-44 (2006).
[CrossRef]

L. J. Schreiner, “Dosimetry in modern radiation therapy: limitations and needs,” J. Phys. Conf. Ser. 56, 1-13 (2006).
[CrossRef]

C. Baldock, “Historical overview of the development of gel dosimetry: a personal perspective,” J. Phys. Conf. Ser. 56, 14-22 (2006).
[CrossRef]

Magn. Reson. Imaging (1)

M. J. Maryanski, J. C. Gore, R. P. Kennan, and R. J. Schulz, “NMR relaxation enhancement in gels polymerized and cross-linked by ionizing radiations: a new approach to 3-D dosimetry by MRI,” Magn. Reson. Imaging 11, 253-258 (1993).
[CrossRef] [PubMed]

Meas. Sci. Technol. (1)

L. Wind and W. W. Szymanski, “Quantification of scattering corrections to the Beer-Lambert law for transmittance measurements in turbid media,” Meas. Sci. Technol. 13, 270-275(2002).
[CrossRef]

Med. Phys. (8)

J. Miller, J. Adamovics, and J. Dietrich, “Cone beam optical CT scanner for 3D dosimetry,” Med. Phys. 32, 2138 (2005).
[CrossRef]

H. S. Sakhalkar and M. Oldham, “Area detector based optical-CT scanner for 3D dosimetry,” Med. Phys. 35, 101-111 (2008).
[CrossRef] [PubMed]

H. S. Sakhalkar and M. Oldham, “Area detector based optical-CT scanner for 3D dosimetry,” Med. Phys. 35, 101-111(2008).
[CrossRef] [PubMed]

M. L. Mather and C. Baldock, “Ultrasound tomography imaging of radiation dose distributions in polymer gel dosimeters: preliminary study,” Med. Phys. 30, 2140-2148 (2003).
[CrossRef] [PubMed]

A. J. Venning, K. N. Nitschke, P. J. Keall, and C. Baldock, “Radiological properties of normoxic polymer gel dosimeters,” Med. Phys. 32, 1047-1053 (2005).
[CrossRef] [PubMed]

J. G. Wolodzko, C. Marsden, and A. Appleby, “CCD imaging for optical tomography of gel radiation dosimeters,” Med. Phys. 26, 2508-2513 (1999).
[CrossRef] [PubMed]

M. Oldham, J. H. Siewerdsen, A. Shetty, and D. A. Jaffray, “High resolution gel-dosimetry by optical-CT and MR scanning,” Med. Phys. 28, 1436-1445 (2001).
[CrossRef] [PubMed]

A. Appleby and A. Leghrouz, “Imaging of radiation dose by visible color development in ferrous-agarose-xylenol orange gels,” Med. Phys. 18, 309-312 (1991).
[CrossRef] [PubMed]

Phys. Med. Biol. (12)

P. J. Harris, A. R. Piercy, and C. Baldock, “A method for determining the diffusion coefficient in Fe(II/III) radiation dosimetry gels using finite elements,” Phys. Med. Biol. 41, 1745-1753 (1996).
[CrossRef] [PubMed]

C. Baldock, R. P. Burford, N. Billingham, G. S. Wagner, S. Patval, R. D. Badawi, and S. F. Keevil, “Experimental procedure for the manufacture and calibration of polyacrylamide gel (PAG) for magnetic resonance imaging (MRI) radiation dosimetry,” Phys. Med. Biol. 43, 695-702(1998).
[CrossRef] [PubMed]

A. J. Venning, B. Hill, S. Brindha, B. J. Healy, and C. Baldock, “Investigation of the PAGAT polymer gel dosimeter using magnetic resonance imaging,” Phys. Med. Biol. 50, 3875-3888(2005).
[CrossRef] [PubMed]

M. Lepage, A. K. Whittaker, L. Rintoul, S. Å. J. Bäck, and C. Baldock, “Modelling of post-irradiation events in polymer gel dosimeters,” Phys. Med. Biol. 46, 2827-2839 (2001).
[CrossRef] [PubMed]

J. Trapp, S. Å. J. Bäck, M. Lepage, G. Michael, and C. Baldock, “An experimental study of the dose response of polymer gel dosimeters imaged with x-ray computed tomography,” Phys. Med. Biol. 46, 2939-2951 (2001).
[CrossRef] [PubMed]

J. C. Gore, M. Ranade, M. J. Maryanski, and R. J. Schulz, “Radiation dose distributions in three dimensions from tomographic optical density scanning of polymer gels. I. Development of an optical scanner,” Phys. Med. Biol. 41, 2695-2704 (1996).
[CrossRef] [PubMed]

N. Krstajić and S. J. Doran, “Fast laser scanning optical-CT apparatus for 3D radiation dosimetry,” Phys. Med. Biol. 52, N257-N263 (2007).
[CrossRef] [PubMed]

S. R. Arridge and J. C. Hebdenz, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841-853 (1997).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

Y. De Deene, P. Hanselaer, C. De Wagter, E. Achten, and W. De Neve, “An investigation of the chemical stability of a monomer/polymer gel dosimeter,” Phys. Med. Biol. 45, 859-878 (2000).
[CrossRef] [PubMed]

S. Bosi, P. Naseri, A. Puran, J. Davies, and C. Baldock, “Initial investigation of a novel light-scattering gel phantom for evaluation of optical CT scanners for radiotherapy gel dosimetry,” Phys. Med. Biol. 52, 2893-2903 (2007).
[CrossRef] [PubMed]

S. G. Bosi, S. Brown, S. Sarabipour, Y. De Deene, and C. Baldock, “Modelling optical scattering artefacts for varying pathlength in a gel dosimeter phantom,” Phys. Med. Biol. 54, 275-283 (2009).
[CrossRef]

Proc. SPIE (1)

M. Bertram, J. Wiegert, and G. Rose, “Scatter correction for cone-beam computed tomography using simulated object models,” Proc. SPIE 6142, doi:10.1117/12.651027 (2006).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Scanning electron microscope images of PAG gel (a) unexposed and (b) exposed to 25 Gy of photons from a clinical linear accelerator operating at 6 MV . Compare the smooth consistency of (a) with the granular texture in (b) due to polymerization and cross linking after exposure. The size of both scale bars is 300 nm . Specimen preparation: fixed in Os O 4 , dehydrated, critical-point-dried, then cut.

Fig. 2
Fig. 2

Vista cone beam optical CT scanner (Modus Medical Devices Inc.). (a) Spatially extended light source with diffusing panel, (b) dosimeter mounted in a rotating clamp, (c) aquarium containing index matching liquid, (d) optical filter wheel, and (e) CCD camera.

Fig. 3
Fig. 3

Layered tube phantom. (a) Raw transmission projection image of the phantom. (b) Horizontal profiles of apparent transmittance through successive layers of a projection image (reference baseline corrected), both experimental and modeled. The lowermost plot represents the top layer of the phantom. For clarity, only one-third of the experimental points are plotted. The boundaries between the inner, outer, and mantle fields within the horizontal profiles of the 2D projection image are identified.

Fig. 4
Fig. 4

(a) Rendered image of the layered tube phantom reconstruction. Darker pixels denote lower extinction coefficient Δ. (b) Extinction coefficient profiles along radial horizontal lines through several layers within the reconstruction. Ideally, all profiles should resemble the shape of the overlaid twin rectangular plateaus (apart from height).

Fig. 5
Fig. 5

Top views of 3D regions within the volume of the layered tube phantom marked with the region labels used in Eqs. (2, 3, 4, 5). Also shown are example optical paths used to calculate model transmittances through the three distinct 2D fields (inner, outer, and mantle) within each layer of a reference baseline corrected projection image.

Fig. 6
Fig. 6

Baseline subtracted extinction coefficients within successive layers of the tube region Δ tube versus concentration of antiseptic ( w / w ) derived from the reconstruction and from fits to transmittance profiles taken from reference baseline corrected projection images using the Bouguer–Lambert plus stray light model. The straight line is fitted to the Δ tube values derived from the model.

Fig. 7
Fig. 7

Example of a fit with smoothing (seven-point moving average) and spike truncation disabled to reveal an example of severe boundary spikes. Note that away from the spikes, the model still fits well. Only one-third of the points are plotted.

Fig. 8
Fig. 8

Spurious elevation δ Δ of extinction coefficient (derived from the reconstruction) within the pith region versus concentration of antiseptic ( w / w ) in the nearest layer of the surrounding tube region.

Equations (5)

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

T = exp ( d Δ ) ,
T ref ( x , y ) = exp ( d ref ( x ) Δ B ) + S ref ( y ) ,
T mantle ( x , y ) = [ exp ( d 7 ( x ) Δ B ) + S 7 ( y ) ] / T ref ( x , y ) ,
T outer ( x , y ) = [ exp ( d 6 ( x ) Δ B ) + S 6 ( y ) ] [ exp ( d 4 ( x ) Δ tube ( y ) ) + S 4 ( y ) ] [ exp ( d 5 ( x ) Δ B ) + S 5 ( y ) ] / T ref ( x , y ) ,
T inner ( x , y ) = [ exp ( d 6 ( x ) Δ B ) + S 6 ( y ) ] [ exp ( d 3 ( x ) Δ tube ( y ) ) + S 3 ( y ) ] [ exp ( d 1 ( x ) Δ B ) + S 1 ( y ) ] [ exp ( d 2 ( x ) Δ tube ( y ) ) + S 2 ( y ) ] [ exp ( d 5 ( x ) Δ B ) + S 5 ( y ) ] / T ref ( x , y ) ,

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