A medical injection system (100) including a valve apparatus (23) including a pinching member (233) and two spring-loaded anvils (271, 272). Two tubing lines (27-F, 27-1) of the injection system are positioned between the pinching member and the anvils, such that when the pinching member is moved into a pinching position adjacent to an anvil by rotation of a shaft (232) to which the member is coupled, the pinching member compresses the corresponding tubing line against the spring-loaded anvil. The pinching member is rotatable about an auxiliary axis, which is eccentric, or offset from a central axis of the shaft. A spring member of each spring-loaded anvil is pre-loaded. In certain applications, the pinching member, when moved into the pinching position, applies a pinching force of greater than approximately 45 pounds, for example, to prevent flow through the tubing line at an injection pressure of up to approximately 1200 psi.