Document Type
Article
Language
eng
Format of Original
8 p.
Publication Date
3-2001
Publisher
American Physiological Society
Source Publication
American Journal of Physiology: Heart and Circulatory Physiology
Source ISSN
1522-1539
Original Item ID
DOI: 10.1152/ajpheart.2001.280.3.H1256
Abstract
A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent (z) = 3 [where z is defined by (D 1)z = (D 2)z + (D 3)z; D 1 is the parent vessel diameter and D 2 and D 3 are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in z values, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.
Recommended Citation
Karau, Kelly Lynn; Krenz, Gary S.; and Dawson, Christopher A., "Branching Exponent Heterogeneity and Wall Shear Stress Distribution in Vascular Trees" (2001). Mathematics, Statistics and Computer Science Faculty Research and Publications. 33.
https://epublications.marquette.edu/mscs_fac/33
ADA Accessible Version
Comments
Accepted version. American Journal of Physiology, Vol. 280, No. 3 (March 2001): H1256-H1263. DOI. © 2001 American Physiological Society. Used with permission.