The AFE System is a medical device intended to dilate the cephalic vein by increasing the blood flow and wall shear stress (WSS) in the vein over a period of 10-14 days prior to creation of an arteriovenous fistula (AVF) for haemodialysis; the system functions as a means of increasing eligibility for AVF surgery and reducing rates of AVF failure. During treatment, maintaining WSS around 4 Pa in the treated vein is desirable to provide optimal vein wall stimulation while avoiding wall injury that could lead to venous stenosis. Developing a model of the AFE System and the related venous circulation could help design a control system for maintaining WSS in the treated vein during the period of treatment when the vein is increasing in diameter. Using a broad application of the Hagen-Poiseuille law, WSS calculation could be based on differential pressure and the flow rate. The AFE System pump was characterised in a test rig utilising sensors and a data acquisition system for measuring mechanical parameters. A data-based model of the AFE pump which includes pump head estimation based on flow rate or electrical current, and motor speed measurements has been developed, and is presented in this paper. All data fitted the developed relationships well, with a correlation coefficient of 93% or above.