Estimating tissue conductivity parameters from electrograms (EGMs) could be an important tool for diagnosing and treating heart rhythm disorders such as atrial fibrillation (AF). One of these parameters is the fibre direction, often assumed to be known in conductivity estimation methods. In this paper, a novel method to estimate the fibre direction from EGMs is presented. This method is based on local conduction slowness vectors of a propagating activation wave. These conduction slowness vectors follow an elliptical pattern that depends on the underlying conductivity parameters. The fibre direction and conductivity anisotropy ratio can therefore be estimated by fitting an ellipse to the conduction slowness vectors. Applying the presented method on simulated data shows that it can estimate the fibre direction more accurately than existing methods, and that its performance depends mostly on the range of wavefront directions present in the measurement area. The main advantage of the presented method is that it still functions relatively well in the presence of conduction blocks, as long as the surrounding tissue is approximately homogeneous.@en