Effects of chamber shape and fiber orientation on relations between fiber dynamics and chamber dynamics

The function of a chamber depends on its hydrodynamic properties: isometric pressures it can exert in the operating range of distensions, compliances in the operating range of distensions, and wall-displacement resistances in the operating range of distensions. Wall-displacement resistance is the departure of pressure from isometric pressure relative to rate of cavity-volume change. The dependence of pressure on average stress and wall/cavity volume ratio is indifferent to chamber shape, which suggests that the volume-based compliance-elastance and resistance-viscosity equations would be only moderately shape dependent. The present study shows that this supposition is correct. If the wall is thin, these relations are shape indifferent. At higher wall/cavity volume ratio, cylindricity increases slightly the P-V-curve slope relative to elastance and either increases slightly or does not affect resistance relative to viscosity. The compliance-elastance and resistance-viscosity relations also depend only slightly on fiber orientation. Therefore, with the sphere equations, one can account accurately for normal and abnormal function of a prolate spheroid in terms of volume dimensions of the wall and apparent average fiber properties.