We propose a surface model that can be used as part of an internet based educational medical simulator to train physicians in cardiovascular interventions. This is the first step towards building a real device which can be placed in a remote laboratory and operated upon by physicians from the comfort of their homes. The model assembles arteries and has planar segmentation to increase efficiency of the collision-detection algorithm. It is based on Sweep Surfaces and can be extended to T- and Y-like bifurcations with small mesh deformations. We also describe a continuous force vector field, representing the interaction between the catheter and the surface. The computation time is almost unaffected when the resolution of the artery is increased, and the algorithm allows real-time executions which are very important for remote learning.