The treatment and management of gliomas, particularly glioblastomas, are significantly challenged by their infiltrative growth patterns. Despite the visibility of tumor margins in imaging scans, glioma cells often invade surrounding brain tissue far beyond these apparent boundaries. This characteristic poses a substantial obstacle in tailoring radiotherapy to the unique spread of an individual patient's tumor, a crucial aspect in improving therapeutic outcomes. The current clinical practice of applying uniform safety margins around visible tumors is a rudimentary approach that fails to encapsulate the complexity of individual tumor dynamics. Addressing this critical gap, our study introduces an innovative method to enhance the accuracy of radiotherapy planning. By integrating mass effects through dynamic tissue models within a Lagrangian frame of reference, our approach transcends the limitations of static models. A pivotal element of our methodology is the extension of the GliODIL framework, which employs PDE-constrained optimization to infer the spatial distribution of tumor cells. This framework is unique in its use of PDEs to regularize data as a soft constraint, enabling a more refined approximation of patient-specific tumor dynamics. Our novel approach allows for simultaneous brain registration and tumor modeling, a significant departure from the conventional reliance on predefined templates. Through a harmonious blend of physics-based constraints and data-driven approaches, the framework improves the accuracy of estimating tumor cell distribution and, clinically highly relevant, also predicting tumor recurrences.