The ability to constrain the geometry of deformable models for image segmentation can be useful when information about the expected shape or positioning of the objects in a scene is known a priori. An example of this occurs when segmenting neural cross sections in electron microscopy. Such images often contain multiple nested boundaries separating regions of homogeneous intensities. For these applications, multiphase level sets provide a partitioning framework that allows for the segmentation of multiple deformable objects by combining several level set functions. Although there has been much effort in the study of statistical shape priors that can be used to constrain the geometry of each partition, none of these methods allow for the direct modeling of geometric arrangements of partitions. In this paper, we show how to define elastic couplings between multiple level set functions to model ribbon-like partitions. We build such couplings using dynamic force fields that can depend on the image content and relative location and shape of the level set functions. To the best of our knowledge, this is the first work that shows a direct way of geometrically constraining multiphase level sets for image segmentation. We demonstrate the robustness of our method by comparing it with previous level set segmentation methods.