Tracking of curvilinear structures is a task of fundamental importance in the quantitative analysis of biological structures such as neurons, blood vessels, retinal interconnects, microtubules, etc. The state of the art HMM-based contour tracking scheme for tracking microtubules, while performing well in most scenarios, can miss the track if, during its growth, it intersects another microtubule in its neighbourhood. In this paper we present a graphical model-based tracking algorithm which propagates across frames information about the dynamics of all the microtubules. This allows the algorithm to faithfully differentiate the contour of interest from others that contribute to the clutter, and maintain tracking accuracy. We present results of experiments on real microtubule images captured using fluorescence microscopy, and show that our proposed scheme outperforms the existing HMM-based scheme.