Kresch (1977)
presented the results of calculations which determined the cross-sectional shapes assumed by flexible, elastic tubes for varying transmural pressures. Extensions of these results are presented here in the form of graphs of the cross-sectional area as a function of the transmural pressure. Since the circumferential arc length, the X-axis intercept and the Y-axis intercept were necessarily computed, and are of interest, graphs of these are also presented.
Each graph is a composite of several curves. Each curve in the graph shows the behavior of the parameter as a function of the relative pressure (P) for a specific value of R, a parameter related to the wall thickness. The curves are shown for both positive and negative values of P. The most negative value of P shown is the point where the walls touch and the most positive value shown is the point where the equations fail to converge.
The cross sections were assumed to be elliptical when the transmural pressure was zero. Graphs for three of these initial shapes are shown: nearly circular, major-to-minor axis ratio equal to 2, and an intermediate case.
For the nearly circular case, the curves divide into two regimes: one where stretching clearly predominates and another where bending clearly predominates. For the more eccentric initial cross-sections, the distinction between the two regimes cannot be made in this simple manner.