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In current clinical practice, radiotherapy treatments are often fractionated, i.e. the total radiation dose is equally divided into small fractions to be delivered daily over a period of few days or weeks. It has recently been shown in silico that spatiotemporal fractionation schemes, i.e. delivering distinct dose distributions in different fractions, can potentially improve the treatment. This is possible if these dose distributions are designed such that different fractions deliver similar doses to normal tissues (i.e. exploit the fractionation effect), but each fraction delivers high single-fraction doses to alternating parts of the tumor (i.e. achieve partial hypofractionation in the tumor). Thereby, the ratio of biological dose in the tumor versus the normal tissue can be improved. In this project, we further developed this innovative and novel concept. In particular, we focused on: 1. Developing new treatment planning algorithms for spatiotemporal fractionation 2. Identifying potential clinical applications of spatiotemporal fractionation with the aim of bringing spatiotemporal fractionation towards the design and implementation of a phase I clinical trial. Spatiotemporal fractionation is associated with higher complexity in treatment planning and delivery. Different plans with distinct dose distributions for different fractions must be designed such that all fractions together deliver the prescribed biological dose to the tumor. To that end, novel mathematical optimization methods for treatment planning have been developed, which are based on the cumulative biological dose rather than the physical dose. In particular, we developed robust treatment planning methods to account for geometric uncertainty in the patient setup and biological uncertainty in the fractionation sensitivity, which may lead to a degradation of the resulting treatment if not accounted for. It was shown that spatiotemporally fractionated treatments can be obtained which are robust against

BACKGROUND Stereotactic radiosurgery (SRS) is an established treatment for patients with brain metastases (BMs). However, damage to the healthy brain may limit the tumor dose for patients with multiple lesions. PURPOSE In this study, we investigate the potential of spatiotemporal fractionation schemes to reduce the biological dose received by the healthy brain in SRS of multiple BMs, and also demonstrate a novel concept of spatiotemporal fractionation for polymetastatic cancer patients that faces less hurdles for clinical implementation. METHODS Spatiotemporal fractionation (STF) schemes aim at partial hypofractionation in the metastases along with more uniform fractionation in the healthy brain. This is achieved by delivering distinct dose distributions in different fractions, which are designed based on their cumulative biologically effective dose ( ) such that each fraction contributes with high doses to complementary parts of the target volume, while similar dose baths are delivered to the normal tissue. For patients with multiple brain metastases, a novel constrained approach to spatiotemporal fractionation (cSTF) is proposed, which is more robust against setup and biological uncertainties. The approach aims at irradiating entire metastases with possibly different doses, but spatially similar dose distributions in every fraction, where the optimal dose contribution of every fraction to each metastasis is determined using a new planning objective to be added to the BED-based treatment plan optimization problem. The benefits of spatiotemporal fractionation schemes are evaluated for three patients, each with >25 BMs. RESULTS For the same tumor BED$_{10}$ and the same brain volume exposed to high doses in all plans, the mean brain BED$_{2}$ can be reduced compared to uniformly fractionated plans by 9%-12% with the cSTF plans and by 13%-19% with the STF plans. In contrast to the STF plans, the cSTF plans avoid partial irradiation of the individual metastases and are