Purpose: The objectives of this study were to model and calculate the absorbed fraction {phi} of energy emitted from yttrium-90 ({sup 90}Y) microsphere treatment of necrotic liver tumors. Methods and Materials: The tumor necrosis model was proposed for the calculation of {phi} 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, {phi}, absorbed from {sup 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{sub T} = 5 cm) and larger (r{sub 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 {phi} that occurred in tumors without central necrosis formore » each size of tumor was different: 0.950 {+-} 0.000, and 0.975 {+-} 0.000 for smaller (r{sub T} = 5 cm) and larger (r{sub T} = 10 cm) tumors, respectively (p < 0.0001). Conclusions: The tumor necrosis model was developed for dose calculation of {sup 90}Y microsphere treatment of hepatic tumors with central necrosis. With this model, important information is provided regarding the absorbed fraction applicable to clinical {sup 90}Y microsphere treatment.« less
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