Comparison of mathematical models for cat lung and viscoelastic balloon derived by laplace transform methods from pressurevolume data

Abstract

The mechanical properties of some hollow organs are most conveniently described by a pressure-volume relationship. If the material exhibits hysteresis, thep-v relation must include provision for time-dependent or path-dependent properties. Provided the amplitude of deformation is fairly small and the hysteresis is primarily of the viscoelastic type, a linear description is possible. That this may take the form of a simple transfer function in which material properties are implicit is illustrated for the case of a rubber balloon. The transfer function was derived from the pressure transients which follow step changes in volume produced in a fluid-filled plethysmograph. The applicability of the transfer function in predicting responses to other forcing functions was tested by varying the balloon volume sinusoidally over a frequency range of 1000, at 4 different amplitudes. The good agreement between the linear model and all types of data justifies the use of Laplace transform methods and the assumption that superposition holds. When isolated cat lung is tested in the same manner, the transfer function quantitatively predicts the magnitude ratio of sinusoidal responses but only about two-thirds of the phase angle. The additional energy loss per cycle is interpreted as arising from static hysteresis. The analysis thus provides a simple means of estimating the relative contributions of viscoelastic (dynamic) and static hysteretic processes to the total damping in a material.