## 1 Introduction  
Stereotactic body radiotherapy (SBRT) represents a non-invasive, ablative local treatment applied to several anatomical sites for both oligorecurrent and oligoprogressive cancer diseases, and it has become a particularly valuable treatment option for managingoligometastatic prostate cancer (PCa) patients. In fact, although chemo-hormonal therapy represents the standard treatment for high-volume metastatic castration-sensitive PCa patients [1], no additional chemo-therapy treatment has demonstrated survival benefits for low-volume metastatic PCa [2]. Indeed, SBRT represents an emerging low-toxicity technique for oligometastasis [3]. In an oligometastatic PCa setting, considered as an intermediate phase of tumor spreading with a limited metastatic capacity (no more than five sites of the disease) [4; 5], treating all the metastatic lesions with small-volume, high-dose SBRT can potentially eliminate all the macroscopic cancer foci, thereby achieving local control, extending progression-free survival (PFS), and improving the overall survival (OS) [6], with no relevant side effects [7; 8]. Hence, SBRT treatment represents a valid instrument for achieving local control, delaying progression, and postponing the need for further treatment. Despite these excellent results, SBRT is more affected by single daily uncertainty, since the total treatment error is not averaged over several daily sessions, as in conventional radiotherapy. In this scenario, the estimation of uncertainties during the entire treatment is mandatory so as to permit the evaluation of the delivery accuracy, the definition of the narrower margins, the comprehension of the surrounding organ displacement, and, consequently, the possibility of increasing the dose to the target volume without compromising the normal tissue function [9; 10; 11]. Advances in radiation therapy (RT) planning have led to the safe delivery of doses to tumors, improving local control and sparing healthy tissues, consequently improving patients' quality of life. A goal of all RT treatments is to deliver radiation to the target organs at volumes as close to the planned dose distribution as possible. However, delivery conditions, patient set-up, and internal anatomy represent uncertainties that can affect the treatment delivery accuracy. In particular, discrepancies can be due to inaccuracies in the patient positioning, intra- or inter-fraction organ motion, and volume variation (i.e., bowel displacement for abdominal pelvic lesions or bladder/ rectum filling). As these modifications can impact the actual dose distribution and, consequently, the compliance with OAR constraints, the quantification of these variations and a high degree of accuracy are desirable. In all RT treatments, it is possible to distinguish between two classes of errors that might affect the treatment quality: (i) the set-up errors, linked to the immobilization of the patient and accuracy of the imaging system, and (ii) inter- and intra-fraction errors, related to organ motion and the volume variability, which are independent of the set-up errors. Set-up errors are corrected using image-guided RT (IGRT) systems, which enable us to acquire patient's image in the treatment room immediately prior to irradiation and correct the tumor displacement and observe the simulation frame through couch rotation and translation. However, since the human body is not rigid, the inter- or intra-fraction errors, due to organ motion, deformation, shrinkage, and the filling status, cannot be corrected by the rationale of IGRT alone. Therefore, the expansion of the target structures (i.e., planning target volume, PTV) or OARs (i.e., planning risk volume, PRV) by the use of clinical margins has to be applied so as to consider such modifications. Thus, the second type of error is more critical, creating a different picture from the one used during the planning, and this work will focus on the inter-fraction variations in the abdominal and pelvic organs.