Abstract: One problem of traditional fast marching method (FM) for DTI is to trace the wrong pathways, thereby reflect the incorrect fiber tendency in particular regions.To solve this problem, topology persevered model is proposed in this paper to help the pathways revolve in a reasonable way.This optimized algorithm refines the evolution process by introducing curvature into the speed function.The reconstruction results using our method show that topology structures are well kept and fiber directions are clearer.Additionally, it is robust to noise.The possible application is medical diagnosis and brain tumor treatment.By combining magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI) information of the same patient in a single image, the oppression and pathological changes of tumors is revealed with abnormal position of the fiber.This application will benefit the clinic and medical research.