Abstract: A breathing simulator for simulating the dynamic breathing patterns is disclosed. The breathing simulator may include: a gas holding chamber capable of expanding and contracting having a movable portion for expanding and contracting the gas holding chamber; a motion imparting mechanism operatively connected to movable portion of the gas holding chamber; a motion control device for controlling the expansion and contraction of the gas holding chamber; and a motion controller in communication with the motion control device. The motion controller includes software thereon, wherein the software contains an algorithm that express the motion of the movable portion of the gas holding chamber in terms of the equations for a circle in a Cartesian coordinate system, wherein the algorithm provides a mathematically-based breathing profile that is executed by the motion control device.