Effective length of the arterial circulation determined in the dog by aid of a model of the systemic input impedance

Downstream from the Heart Left Ventricle

“…When an elastic and frictionless tube is loaded with a resistor, the ϑ i (f oi ) equals zero and Eq. (21.23) reduces to the one-quarter wavelength formula [2,3,10,19,20]. Because the ratio of Eq.…”

“…So-called tube-load models have been set-up in the attempt to meet a suitable compromise between reduced model complexity for mathematical tractability and ability to capture essential features of aortic pressureÀflow relationships [1À3, 10,13,19À28,30]. One of these models, constituted by a uniform, lossless elastic tube terminating in complex and frequency-dependent load, has been shown to be able to describe some experimental aortic pressureÀflow relationships well [10,13,19,20]. However, a shortcoming was found in that it cannot describe a condition in which there is a prominent diastolic oscillation in the aortic pressure waveform [10,21].…”

“…(21.19)). As a consequence, the effective lengths, d h and d b , can be estimated according to the following equation [19,20]:…”

“…At the level of each effective reflection site, arterial reflections from peripheral sites are supposed to compose one wave traveling backward, toward the LV [1À3,10,21À28]. The denomination of effective length of the related arterial circulation is then used for both d h and d b [19,20].…”

Input impedance of distributed arterial structures as used in investigations of underlying concepts in arterial haemodynamics

“…Womersley [50] showed that minimal reflection coefficient is a function of the non-dimensional parameter a, and so the optimal area ratio also becomes a function of a, such that as a decreases a larger area ratio of parent to daughter branches is required for minimal reflection [23,50]. When simplified to single tube models [23,28], the concept of effective length to determine the distance to the functional reflecting site is determined from the frequency of the minimum of impedance modulus [7,13,21,23]. This arises from the resonance concept in tubes [21,23] where impedance minimum corresponds with a frequency of phase zero crossing, or approaching close to zero.…”