Physiological Relevance of Uniform Elastic Tube-Models to Infer Descending Aortic Wave Reflection: A Problem of Identifiability

Abstract

A uniform, frictional elastic tube terminating in a pure resistor (model A), was compared with a uniform, frictionless elastic tube, terminating in a first-order low-pass filter load (model B). The aim was to address an identifiability problem in uniqueness of parameter estimates and to evaluate the physiological meaning of tube-length estimates obtained from these models applied to the descending aortic circulation. Measurements of high descending aortic pressure and flow were taken from three anaesthetized, open-chest dogs and used to estimate the model parameters. A simultaneous measurement of terminal aortic pressure was used to estimate the foot-to-foot pulse wave velocity. A flow-fitting procedure yielded a multiplicity of equivalent solutions for the wave transit time across the transmission tubes (${\tau }_{ai}$ for model A and ${\tau }_{bi}$ for model B, $i = 0,1,2,...,N,...$ and the related tube-lengths $d_{ai}$ and $d_{bi}$ respectively. The tube length represents the distance to an effective reflection site (effective length) of the descending aortic circulation. Assuming that this length should be no longer than the dimensions of the body, the lowest estimates (i=0) of wave transit time and tube length (average ±SE: ${\tau }_{ao} = 85.7 \pm 10.8{ms}$ and $d_{ao} = 53.4 \pm 3.7 {cm}$ for model A; ${\tau }_{bo} = 46.6 \pm 6.7 {ms}$ and $d_{bo} = 29.1 \pm 3.5{cm}$ for model B) were identifiable as unique and acceptable solutions. Model A located the effective reflection site a few centimeters below the terminal aortic region. This location is inconsistent with the use of a pure resistor as a tube's terminal load. Further, relatively high estimates of longitudinal frictional losses violated the assumption of small losses across the transmission path and yielded an unphysiological mean-pressure drop of 7.1$\pm$2.3mm Hg. The estimates of $d_{bo}$ provided by model B located the effective reflection site near the origin of the renal arteries. The model-predicted pressure wave at this location approximated the measured pressure. Thus, model B represents a significant improvement over model A as a tool to infer wave travel and reflection in the descending aortic circulation. © 2000 Biomedical Engineering Society.

PAC00: 8719Uv, 4760+i