Developing patient specific model for the simulation of chemotherapy drug injection is important in medical application. This paper proposed a two-phase fluidic method to simulate chemotherapy drug injection and an improved lumped element method to simulate deformation of vessel at real-time by using GPU for general computing. Firstly, a three-dimensional (3-D) model of hepatic vessels is reconstructed from clinical CT-images using multi-layer method. A 3-D thinning algorithm based on Valence Driven Spatial Median (VDSM) is applied to generate unit-width skeleton of the vessel tree. The two-phase flow simulation of drug injection is based on Hagen-Poiseuille model by introducing a friction factor using bubbly flow Reynolds number. The improved lumped element method achieves good simulation realism at high computational speed to simulate deformable object. Real-time rendering and interaction of vessel deformation, self collision, and surface tearing has been realized and demonstrated in a virtual experiment.