Parameter Estimation Theory for Respiratory Physiology

Abstract

The Belgian painter, René Magritte, painted “The Betrayal of Images” in 1929, in which a realistic painting of a pipe is over the statement “This is not a pipe”. His very graphic point is that the image of a pipe is not reality. In direct analogy, it must be remembered that the mathematical equations describing a physiological process are not reality, either. An equation such as PV = RT is only an approximation to nature, and does not hold for shock waves, very high pressures, very low pressures, etc. If we were to measure the pressure-volume relationship of a gas at a constant temperature, the measurements could be made only to a certain accuracy. The point is that PV = RT is a useful approximation for many purposes for adequately describing the behavior of a gas, and as such is robust. However, choice of this model PV = RT depends on the purpose for which the model is to be used.