Branching exponent heterogeneity and wall shear stress distribution in vascular trees.
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.
Karau
K L
KL
Department of Biomedical Engineering, Marquette University, Milwaukee, WI 53201-1881, USA.
Krenz
G S
GS
Dawson
C A
CA
D005246:Feedback / Q000502:physiology; D006801:Humans; D008833:Microcirculation / Q000502:physiology; D008955:Models, Cardiovascular; D011651:Pulmonary Artery / Q000502:physiology*; D011652:Pulmonary Circulation / Q000502:physiology; D013314:Stress, Mechanical