Determining how uncertainties in optical properties affect light dose calculations

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1 Determining how uncertainties in optical properties affect light dose calculations Julia Sandell 1, Jarod Finlay, Timothy Zhu 1 Department of Physics, University of Pennsylvania Radiation Oncology, Hospital of the University of Pennsylvania

2 Introduction Optical Properties and PDT Light Dose Calculations Uncertainties in a, s, and Φ Phantom Studies Conclusion Light wand At Diaphragmatic Sulcus January 3, 011 SPIE Photonics West 011

wave reflectance spectroscopy data can be fitted to determine optical properties Multi-fiber probe

3 Optical Properties: Overview Inherent absorption a ) and scattering s ) of tissues determine how light propagates through Need well defined properties for accurate light dosimetry in PDT Continuous wave reflectance spectroscopy data can be fitted to determine optical properties Multi-fiber probe Source Source distances in mm January 3, 011 SPIE Photonics West 011 3

Optical Properties: Algorithms Used Reflectance is a function, Rρ,μ a,μ s ) where μ a,μ s are λ dependent Light propagation model: Hybrid Diffusion/P3 model of light transport, extrapolated

4 Optical Properties: Algorithms Used Reflectance is a function, Rρ,μ a,μ s ) where μ a,μ s are λ dependent Light propagation model: Hybrid Diffusion/P3 model of light transport, extrapolated boundary conditions 1 Assume isotropic, continuous wave point source in a semi-infinite slab geometry January 3, 011 SPIE Photonics West Hull & Foster, J. Opt. Soc. Am. 18, )

Optical Properties: Cuvette Studies a was calculated from measuring 9 concentrations of black india ink in a cuvette study CCD Measurements made using Ocean Optics cuvette holder and LN-cooled CCD

5 Optical Properties: Cuvette Studies a was calculated from measuring 9 concentrations of black india ink in a cuvette study CCD Measurements made using Ocean Optics cuvette holder and LN-cooled CCD Spectrograph Phantom spectroscopic data analyzed using wavelength fitting for each source detector separation Controller 403-nm Laser Spectrograph White light Phantom January 3, 011 SPIE Photonics West 011 5

6 Optical Properties: Phantom Studies 4 different phantoms were made using black India ink, intralipid, and water Each phantom was measured 4 different times Spectroscopic data was processed and fitted for a and for s 3 of 4 phantoms display a negative slope for the spread in optical properties January 3, 011 SPIE Photonics West 011 6

7 Optical Properties: Phantom Studies: Wavelength fitting January 3, 011 SPIE Photonics West 011 7

8 Optical Properties: Phantom Studies: Wavelength fitting January 3, 011 SPIE Photonics West 011 8

9 Optical Properties: Phantom Studies: Wavelength fitting January 3, 011 SPIE Photonics West 011 9

10 Light Dose Calculations: Intracavity PDT Light fluence calculations must account for the integrating sphere effect Based on Willem Star s derivation 4, the fluence in a spherical cavity with homogeneous optical properties: S S & # total, cavity = where eff # = t 4" r 4" r ' 3 c % a " with t = " c 0 t fresnel cos" sin" d" S = source W) r = radius of cavity cm) eff =3 a s ) 1/ θ c = critical angle t fresnel = 1-R fresnel, a function of the indices of refraction and incidence angle January 3, 011 SPIE Photonics West [] W. M. Star,Phys. Med. Biol. 40, ).

11 Uncertainty Analysis: 10% and 0% uncertainty in a and s January 3, 011 SPIE Photonics West

12 Uncertainty Analysis: uncertainty in eff Same uncertainties in eff result in a more accurate light dose Optimum trend in eff is circular in nature rather than linear A greater range in in eff is permissible for same dose accuracy January 3, 011 SPIE Photonics West 011 1

13 Results Spread in measured optical properties runs in opposite direction of optimum trend in accurate light dose Wavelength fitting tends to overestimate in reduced scattering coefficient and underestimate in absorption coefficient January 3, 011 SPIE Photonics West

14 Results Up to a 0% difference in light dose 30% of optical properties give result in dose within 10% of ideal dose Average a = ); Average s = ); January 3, 011 SPIE Photonics West

15 Conclusion Optimum region of dose accuracy and optical properties is relatively small Algorithm fits with in 1% for best fit wavelength dependent fitting Algorithm breaks down at ±50% for s and ±100% for a for phantom data For dose model accuracy discussion, please see Poster January 3, 011 SPIE Photonics West

16 Acknowledgements NIH R01-CA T. Busch) ACS IRG J. Finlay) Fontaine Foundation for travel and graduate studies funding Dr. Xing Liang for his advice and assistance Thank you January 3, 011 SPIE Photonics West

Future Work Evaluate algorithms for any constraints or alterations Conduct phantom experiment to confirm calculated change in dosage Apply fluence

17 Future Work Evaluate algorithms for any constraints or alterations Conduct phantom experiment to confirm calculated change in dosage Apply fluence solution to clinical scenarios Use knowledge of optical properties and fluence model in real time PDT dosimetry system January 3, 011 SPIE Photonics West

18 Uncertainty Analysis: uncertainty in a and s in arbitrary geometry January 3, 011 SPIE Photonics West

19 January 3, 011 SPIE Photonics West Light Dose Calculations: Sources of Uncertainty a, s, indices of refraction, radius of cavity, source strength Standard propagation of error gives: ) " # % & " # % & " # % & ± = ' r S r S S total ) ) 1 " # % & ' ), - ' ' ), =.. /. / 0 a eff eff a eff ) " # % & ' ), - ' ± = 4 1 r S S r S r S s. / " # % & ' ), -. ), - / / ), ), -. 5 = a a s s a a s a eff 6

ESTIMATION OF 90 SCATTERING COEFFICIENT IN THE SHIELDING CALCULATION OF DIAGNOSTIC X-RAY EQUIPMENT

Proceedings of the Eleventh EGS4 Users' Meeting in Japan, KEK Proceedings 2003-15, p.107-113 ESTIMATION OF 90 SCATTERING COEFFICIENT IN THE SHIELDING CALCULATION OF DIAGNOSTIC X-RAY EQUIPMENT K. Noto and