Purpose: To investigate the impact of using spatiotemporal optimization, i.e., intensity modulated spatial optimization followed by fractionation schedule optimization, to select the patient-specific fractionation schedule that maximizes the tumor biologically equivalent dose (BED) under dose constraints for multiple organs-at-risk (OAR). Methods: The optimal fractionation schedule for a patient using the linear-quadratic (LQ) cell survival model depends on the tumor and OAR sensitivity to fraction size, the effective tumor doubling time (Td), and the size and location of tumor target relative to one or more OAR (dose distribution). We used a spatiotemporal optimization method to identify the optimal number of fractions N that maximizes the 3D tumor BED distribution for sixteen lung phantom cases. The 15 selection of the optimal fractionation schedule used equivalent (30-fraction) OAR constraints for the heart (Dmean 45 Gy), lungs (Dmean 20 Gy), cord (Dmax 45 Gy), esophagus (Dmax 63 Gy), and unspecifed tissues (D05 60 Gy). To assess plan quality, we compared the minimum, mean, maximum, and D95 of tumor BED, as well as the equivalent uniform dose (EUD) for optimized plans to conventional IMRT plans prescribing 60 Gy in 30 fractions. A sensitivity analysis was 20 performed to assess the effects of Td (3 to 100 days), tumor lag-time (Tk = 0 to 10 days), and the size of tumors on optimal fractionation schedule. Results: Using an alpha/beta ratio of 10 Gy, the average values of tumor max, min, mean BED, and D95 were up to 19%, 21%, 20%, and 19% larger than those from conventional prescription, depending on Td and Tk used. Tumor EUD was up to 17% larger than the conventional prescription. For fast 25 proliferating tumors with Td less than 10 days, there was no significant increase in tumor BED but the treatment course could be shortened without a loss in tumor BED. The improvement in the tumor mean BED was more pronounced with smaller tumors (p-value = 0.08). Conclusions: Spatiotemporal optimization of patient plans has the potential to significantly improve local tumor control (larger BED/EUD) of patients with a favorable geometry, such as 30 smaller tumors with larger distances between the tumor target and nearby OARs. In patients with a less favorable geometry and for fast growing tumors, plans optimized using spatiotemporal optimization and conventional (spatial-only) optimization are equivalent (negligible differences in tumor BED/EUD). However, spatiotemporal optimization yields shorter treatment courses than conventional spatial-only optimization. Personalized, spatiotemporal optimization of treatment 35 schedules can increase patient convenience and help with the efficient allocation of clinical resources. Spatiotemporal optimization can also help identify a subset of patients that might benefit from non-conventional (large dose per fraction) treatments that are ineligible for the current practice of stereotactic body radiation therapy
