Medical imaging is currently employed in the diagnosis, planning, delivery and response monitoring of cancer treatments. Due to physiological motion and/or treatment response, the shape and location of the pathology and organs-at-risk may change over time. Establishing their location within the acquired images is therefore paramount for an accurate treatment delivery and monitoring. A feasible solution for tracking anatomical changes during an image-guided cancer treatment is provided by image registration algorithms. Such methods are, however, often built upon elements originating from the computer vision/graphics domain. Since the original design of such elements did not take into consideration the material properties of particular biological tissues, the anatomical plausibility of the estimated deformations may not be guaranteed. In the current work we adapt two existing variational registration algorithms, namely Horn-Schunck and EVolution, to online soft tissue tracking. This is achieved by enforcing an incompressibility constraint on the estimated deformations during the registration process. The existing and the modified registration methods were comparatively tested against several quality assurance criteria on abdominal in vivo MR and CT data. These criteria included: the Dice similarity coefficient (DSC), the Jaccard index, the target registration error (TRE) and three additional criteria evaluating the anatomical plausibility of the estimated deformations. Results demonstrated that both the original and the modified registration methods have similar registration capabilities in high-contrast areas, with DSC and Jaccard index values predominantly in the 0.8-0.9 range and an average TRE of 1.6-2.0 mm. In contrast-devoid regions of the liver and kidneys, however, the three additional quality assurance criteria have indicated a considerable improvement of the anatomical plausibility of the deformations estimated by the incompressibility-constrained methods. Moreover, the proposed registration models maintain the potential of the original methods for online image-based guidance of cancer treatments.