A volume-equivalent spherical necrosis-tumor-normal liver model for estimating absorbed dose in yttrium-90 microsphere therapy

Purpose: Primary hepatocellular carcinoma and metastatic liver tumors are highly malignant tumors in Asia. The incidence of fatal liver cancer is also increasing in the United States. The aim of this study was to establish a spherical tumor model and determine its accuracy in predicting the absorbed dose in yttrium-90 (Y-90) microsphere therapy for liver cancer.Methods: Liver morphology can be approximated by a spherical model comprising three concentric regions representing necrotic, tumor, and normal liver tissues. The volumes of these three regions represent those in the actual liver. A spherical tumor model was proposed to calculate the absorbed fractions in the spherical tumor, necrotic, and normal tissue regions. The THORplan treatment planning system and Monte Carlo N-particle extended codes were used for this spherical tumor model. Using the volume-equivalent method, a spherical tumor model was created to calculate the total absorbed fraction [under different tumor-to-healthy-liver ratios (TLRs)]. The patient-specific model (THORplan) results were used to verify the spherical tumor model results. Results: The results for both the Y-90 spectrum and the Y-90 mean energy indicated that the absorbed fraction was a function of the tumor radius and mass. The absorbed fraction increased with tumor radius. The total absorbed fractions calculated using the spherical tumor model for necrotic, liver tumor, and normal liver tissues were in good agreement with the THORplan results, with differences of less than 3% for TLRs of 2-5. The results for the effect of TLR indicate that for the same tumor configuration, the total absorbed fraction decreased with increasing TLR; for the same shell tumor thickness and TLR, the total absorbed fraction was approximately constant; and for tumors with the same radius, the total fraction absorbed by the tumor increased with the shell thickness. Conclusions: The results from spherical tumor models with different tumor-to-healthy-liver ratios were highly consistent with the reference results (THORplan). These findings indicate that a spherical tumor model can provide good estimates of Y-90 doses in microsphere therapy and can be considered a first approximation for dose estimation in Y-90 microsphere therapy.