A dynamic blood flow model to compute absorbed dose to circulating blood and lymphocytes in liver external beam radiotherapy

We have developed a novel 4D dynamic liver blood flow model, capable of accurate dose estimation to circulating blood cells during liver-directed external beam radiotherapy, accounting for blood recirculation and radiation delivery time structure. Adult male and adult female liver computational phantoms with detailed vascular trees were developed to include the hepatic arterial, hepatic portal venous, and hepatic venous trees. A discrete time Markov Chain approach was applied to determine the spatiotemporal distribution of 10(5) blood particles (BP) in the human body based on reference values for cardiac output and organ blood volumes. For BPs entering the liver, an explicit Monte Carlo simulation was implemented to track their propagation along similar to 2000 distinct vascular pathways through the liver. The model tracks accumulated absorbed dose from time-dependent radiation fields with a 0.1 s time resolution. The computational model was then evaluated for 3 male and 3 female patients receiving photon (VMAT and IMRT) and proton (passive SOBP and active PBS) treatments. The dosimetric impact of treatment modality, delivery time, and fractionation on circulating blood cells was investigated and quantified using the mean dose (mu(dose,b)), V (>0Gy), V (>0.125Gy,) and D-2%. Average reductions in mu(dose,b), V (>0Gy), V (>0.125Gy) and D-2% of 45%, 6%, 53%, 19% respectively, were observed for proton treatments as compared to photon treatments. Our simulation also showed that V->0Gy, V (>0.125Gy), and D-2% were highly sensitive to the beam-on time. Both V (>0Gy) and V (>0.125Gy) increased with beam-on time, whereas D (2%) decreased with increasing beam-on time, demonstrating the tradeoff between low dose to a large fraction of blood cells and high dose to a small fraction of blood cells. Consequently, proton treatments are not necessarily advantageous in terms of dose to the blood simply based on integral dose considerations. Instead, both integral dose and beam-on time can substantially impact relevant dosimetric indices.