To perform an epidural, a needle is inserted through the patient's skin and guided between the patient's vertebrae to the yellow ligament, which is resistant. Once the yellow ligament has passed, the needle must stop so that the anesthetic fluid in the epidural space can be injected. What makes this operation complicated is that the resistance of the yellow ligament varies greatly depending on the patient's physiognomy. To enhance the sensations of the anesthetist, we proposed to use a bilateral teleoperation system. The anesthetist manipulates a master arm while a needle is fixed on the slave arm to perform the epidural operation. In this paper, we discuss the tuning of the gains to reach ideal transparency at steady and transient states. Transparency depending on the number of control channels is calculated with the Hannaford matrix. Building on previous works, a new modeling, which allows extremely simple equations, is presented and a new experimental test-bed is proposed.