An apparatus and method of assessing off-line a narrowing in a fluid filled tube being a blood vessel of a cyclic fluid flow system, in particular a cardiac environment, comprising: receiving from a storage device previously taken measurements of blood pressure on either side of the narrowing； identifying from the pressure-only measurements a time window when the differential of flow velocity (dU) is minimal or absent； deriving the backward- and forward-originating pressure components for pressure measurements for the time window, and deriving an instantaneous flow ratio as pressure ratio of pressures on either side of the narrowing by using the backward-originating and/or the forward-originating pressure components so as to provide an assessment of the severity of the narrowing.
