PURPOSE: The objectives of this study were to model and calculate the absorbed fraction ϕ of energy emitted from yttrium-90 ((90)Y) microsphere treatment of necrotic liver tumors. METHODS AND MATERIALS: The tumor necrosis model was proposed for the calculation of ϕ over the spherical shell region. Two approaches, the semianalytic method and the probabilistic method, were adopted. In the former method, the range--energy relationship and the sampling of electron paths were applied to calculate the energy deposition within the target region, using the straight-ahead and continuous-slowing-down approximation (CSDA) method. In the latter method, the Monte Carlo PENELOPE code was used to verify results from the first method. RESULTS: The fraction of energy, ϕ, absorbed from (90)Y by 1-cm thickness of tumor shell from microsphere distribution by CSDA with complete beta spectrum was 0.832 ± 0.001 and 0.833 ± 0.001 for smaller (r(T) = 5 cm) and larger (r(T) = 10 cm) tumors (where r is the radii of the tumor [T] and necrosis [N]). The fraction absorbed depended mainly on the thickness of the tumor necrosis configuration, rather than on tumor necrosis size. The maximal absorbed fraction φ that occurred in tumors without central necrosis for each size of tumor was different: 0.950 ± 0.000, and 0.975 ± 0.000 for smaller (r(T) = 5 cm) and larger (r(T) = 10 cm) tumors, respectively (p < 0.0001). CONCLUSIONS: The tumor necrosis model was developed for dose calculation of (90)Y microsphere treatment of hepatic tumors with central necrosis. With this model, important information is provided regarding the absorbed fraction applicable to clinical (90)Y microsphere treatment.
PURPOSE: The objectives of this study were to model and calculate the absorbed fraction ϕ of energy emitted from yttrium-90 ((90)Y) microsphere treatment of necrotic liver tumors. METHODS AND MATERIALS: The tumor necrosis model was proposed for the calculation of ϕ over the spherical shell region. Two approaches, the semianalytic method and the probabilistic method, were adopted. In the former method, the range--energy relationship and the sampling of electron paths were applied to calculate the energy deposition within the target region, using the straight-ahead and continuous-slowing-down approximation (CSDA) method. In the latter method, the Monte Carlo PENELOPE code was used to verify results from the first method. RESULTS: The fraction of energy, ϕ, absorbed from (90)Y by 1-cm thickness of tumor shell from microsphere distribution by CSDA with complete beta spectrum was 0.832 ± 0.001 and 0.833 ± 0.001 for smaller (r(T) = 5 cm) and larger (r(T) = 10 cm) tumors (where r is the radii of the tumor [T] and necrosis [N]). The fraction absorbed depended mainly on the thickness of the tumor necrosis configuration, rather than on tumor necrosis size. The maximal absorbed fraction φ that occurred in tumors without central necrosis for each size of tumor was different: 0.950 ± 0.000, and 0.975 ± 0.000 for smaller (r(T) = 5 cm) and larger (r(T) = 10 cm) tumors, respectively (p < 0.0001). CONCLUSIONS: The tumor necrosis model was developed for dose calculation of (90)Y microsphere treatment of hepatic tumors with central necrosis. With this model, important information is provided regarding the absorbed fraction applicable to clinical (90)Y microsphere treatment.