Abstract: According to the cerebrovascular volume data after segmentation, the author proposes a cerebrovascular expression model based on ball B-spline curves and tree structure, which can be described as the following three steps.Firstly, we can get the centerline and radius of cerebral vessels according to a hessian matrix combined with elastic ball model, this improves the accuracy of center extraction and get radius simultaneously during the extraction process.Secondly, we deal with the centerline and radius got in the first step by tree reconstruction, because it accords with the topology of vascular and is easy to traverse.Finally, we describe every branch vessel by ball B-spline curves after reconstruction.This method of depiction can detect the lesion areas precisely and can draw the graph in multi-scale way to adapt to the display windows in different sizes.The experimental results show that this model has a great advantage in vessel display and cerebrovascular lesions detection.