Fluid pressure actuated blood pumping systems and methods with continuous inflow and pulsatile outflow conditions

A blood processing method comprising

• placing first and second fluid pressure actuated pump stations in in-line communication between a source and a destination,
• applying fluid pressure pump strokes to the first and second pump stations to convey fluid from the source to the destination,
• establishing a first flow mode comprising a first draw pump stroke having a first duration to draw fluid into the first pump station from the source and a first expel pump stroke having a first expel duration less than the first draw duration to expel fluid from the second pump station to the destination,
• establishing a second flow mode comprising a second draw pump stroke having a second draw duration to draw fluid into the second pump station from the source and a second expel pump stroke having a second expel duration less than the second draw duration to expel fluid from the first pump station to the destination,
• switching in succession between the first flow mode and the second flow mode so that fluid flow from the source is essentially continuous while fluid flow to the destination is pulsatile.