A new treatment planning formalism for catheter-based beta sources used in intravascular brachytherapy

Intravascular brachytherapy (IVBT) is an emerging modality for the treatment of atherosclerotic lesions in the artery. As part of the refinement in this rapidly evolving modality of treatment, the current simplistic dosimetry approach based on a fixed-point prescription must be challenged by future rigorous dosimetry method employing image-based three-dimensional (3D) treatment planning. The goals of 3D IVBT treatment planning calculations include (1) achieving high accuracy in a slim cylindrical region of interest, (2) accounting for the edge effect around the source ends, and (3) supporting multiple dwell positions. The formalism recommended by Task Group 60 (TG-60) of the American Association of Physicists in Medicine (AAPM) is applicable for gamma sources, as well as short beta sources with lengths less than twice the beta particle range. However, for the elongated beta sources and/or seed trains with lengths greater than twice the beta range, a new formalism is required to handle their distinctly different dose characteristics. Specifically, these characteristics consist of (a) flat isodose curves in the central region, (b) steep dose gradient at the source ends, and (c) exponential dose fall-off in the radial direction. In this paper, we present a novel formalism that evolved from TG-60 in maintaining the dose rate as a product of four key quantities. We propose to employ cylindrical coordinates (R, Z, phi), which are more natural and suitable to the slim cylindrical shape of the volume of interest, as opposed to the spherical coordinate system (r, theta, phi) used in the TG-60 formalism. The four quantities used in this formalism include (1) the distribution factor, H(R, Z), (2) the modulation function, M(R, Z), (3) the transverse dose function, h(R), and (4) the reference dose rate at 2 mm along the perpendicular bisector, D(R0=2 mm, Z0=0). The first three are counterparts of the geometry factor, the anisotropy function and the radial dose function in the TG-60 formalism, respectively. The reference dose rate is identical to that recommended by TG-60. The distribution factor is intended to resemble the dose profile due to the spatial distribution of activity in the elongated beta source, and it is a modified Fermi-Dirac function in mathematical form. The utility of this formalism also includes the slow-varying nature of the modulation function, allowing for more accurate treatment planning calculations based on interpolation. The transverse dose function describes the exponential fall-off of the dose in the radial direction, and an exponential or a polynomial can fit it. Simultaneously, the decoupling nature of these dose-related quantities facilitates image-based 3D treatment planning calculations for long beta sources used in IVBT. The new formalism also supports the dosimetry involving multiple dwell positions required for lesions longer than the source length. An example of the utilization of this formalism is illustrated for a 90Y coil source in a carbon dioxide-filled balloon. The pertinent dosimetric parameters were generated and tabulated for future use.