Heart disease is the leading cause of death in the developed world. Cardiac pathologies include abnormal closure of the mitral valve, which can be treated by surgical operations, but the repair outcome varies greatly based on the experience of the surgeon. Simulating the procedure with a computer-based tool can greatly improve valve repair. Various teams are working on biomechanical models to compute the valve behaviour during peak systole. Although they use an accurate finite element method, they also use a tedious manual segmentation of the valve. Providing means to automatically segment the chordae and the leaflets would allow significant progress in the perspective of simulating the surgical gesture for the mitral valve repair. Valve chordae are generalized cylinders: Instead of being limited to a line, the central axis is a continuous curve. Instead of a constant radius, the radius varies along the axis. In most of the cases chordae sections are flattened ellipses and classical model-based methods commonly used for vessel enhancement or vessel segmentation fail. In this paper, we exploit the fact that there are no other generalized cylinders than the chordae in the micro CT scan and we propose a topology-based method for the chordae extraction. This approach is flexible and only requires the knowledge of an upper bound of the maximum chordae radius. Examples of segmentation are provided on three porcine datasets. The reliability of the segmentation is proved with a dataset where the ground truth is available.