Light delivery device modelling for homogenous irradiation distribution in photodynamic therapy of non-spherical hollow organs

Significance: Photodynamic therapy (PDT) is a useful treatment for select cancers. Homogeneous illumination is a key factor in the successful application of PDT treatment of tumours in hollow organs. Over illumination may damage normal tissue while under illumination may not ablate the target. Background: There have been many approaches to provide homogeneous irradiation for PDT treatment of hollow organs, including light-scattering medium and isotropic emitter to diffuse light, a balloon filled with solution to expand the organ wall, and shaped fibres. In most studies, the organ is assumed to be spherical. However, many hollow organs treated by PDT are non-spherical, and the uniformity of azimuthal irradiation remains an unsolved problem for cylindrical light sources. Objective: Find a design principle for homogeneous irradiation in a non-spherical cavity for PDT treatment. Method: A PDT light delivery device is modeled by a series of sub light sources placed along the longitudinal axis of an ellipsoid. In order to achieve a homogeneous azimuthal irradiation distribution on the elliptical arc, a cost function is solved by adding modulation coefficient to the emission profile. The coefficient of variation of uniformity (U_cov) describes the statistical dispersion of the variation in irradiation over the ellipsoid to the average value. U_cov is used to evaluate the homogeneity of the azimuthal irradiation distribution. Result: By minimizing the cost function, we found that the truncated Gaussian function can be chosen as the emission profile to generate homogeneous irradiation profile within an ellipsoid cavity model. The emission profile can be tailored to generate U_cov of 96.7 %. Further discussion shows that the light distribution could be generated practically by a side-emitting optical fibre, a LED array, or moving an isotropic emitter successively. The impact of emission angle of light sub-source is analysed and the irradiation profile from discrete longitudinal emissions is calculated. Conclusion: Theory analysis and simulation indicate that a cylindrical emitter with a non-uniform longitudinal emission profile (truncated Gaussian functions) results in an approximate homogeneous irradiance profile within an ellipsoidal cavity.