Image-guided radiotherapy (IGRT) allows observation of the location and shape of the tumor and organs-at-risk (OAR) over the course of a radiation cancer treatment. Such information may in turn be used for reducing geometric uncertainties during therapeutic planning, dose delivery and response assessment. However, given the multiple imaging modalities and/or contrasts potentially included within the imaging protocol over the course of the treatment, the current manual approach to determining tissue displacement may become time-consuming and error prone. In this context, variational multi-modal deformable image registration (DIR) algorithms allow automatic estimation of tumor and OAR deformations across the acquired images. In addition, they require short computational times and a low number of input parameters, which is particularly beneficial for online adaptive applications, which require on-the-fly adaptions with the patient on the treatment table. However, the majority of such DIR algorithms assume that all structures across the entire field-of-view (FOV) undergo a similar deformation pattern. Given that various anatomical structures may behave considerably different, this may lead to the estimation of anatomically implausible deformations at some locations, thus limiting their validity. Therefore, in this paper we propose an anatomically-adaptive variational multi-modal DIR algorithm, which employs a regionalized registration model in accordance with the local underlying anatomy. The algorithm was compared against two existing methods which employ global assumptions on the estimated deformations patterns. Compared to the existing approaches, the proposed method has demonstrated an improved anatomical plausibility of the estimated deformations over the entire FOV as well as displaying overall higher accuracy. Moreover, despite the more complex registration model, the proposed approach is very fast and thus suitable for online scenarios. Therefore, future adaptive IGRT workflows may benefit from an anatomically-adaptive registration model for precise contour propagation and dose accumulation, in areas showcasing considerable variations in anatomical properties.