A method of making a blood pump comprises selecting a desired flow pattern in a pumping chamber defined by an extensible bladder wherein the flow pattern is based generally on blood flow in a natural heart, using an initial computer model of the desired flow pattern to determine the material composition and dynamic operation conditions of each portion of the bladder, designing a bladder and pump operating system, computer modeling the actual design, testing and refining the design, and constructing a prototype based thereon. The desired flow pattern includes guiding and directing the flow of blood through the pumping chamber by reason of the action of an expansile bladder on the blood flow. A continuous circular or spiral fluid path is obtained that more effectively washes all areas of the bladder including the inlet and discharge ports with blood to reduce thrombosis.