#### 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.