Variability of arterial wall shear stress, its dependence on vessel diameter and implications for Murray's Law

Arteries, the vasculature responsible for transporting blood from the heart, possess robust walls capable of enduring the elevated pressures exerted by the heartbeat. Arteries near the heart are especially thick-walled and enriched with elastic fibers across their three tunics, classifying them as elastic or conducting arteries. These arteries, usually with a diameter exceeding 10 mm, are characterized by their ability to dilate in response to the blood pumped from the heart's ventricles and...

Vascular resistance is a critical concept in understanding blood flow dynamics in the circulatory system. It refers to the resistance that blood encounters as it flows through the blood vessels. This resistance is a key factor in determining blood pressure and cardiac workload.
The primary determinants of vascular resistance are vessel diameter, blood viscosity, and vessel length. Among these, vessel diameter plays the most significant role due to the fourth power relationship described by...

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.

The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...

Blood flow through a cylindrical blood vessel can be mathematically described using the principles of laminar flow, a regime in which fluid moves smoothly in parallel layers. In this model, the velocity of the blood is not uniform across the cross-section of the vessel; rather, it varies with the radial distance from the center. The maximum velocity occurs along the central axis, decreasing progressively toward the vessel walls, where it reaches zero due to viscous drag.Approximating Blood...

Blood is circulated throughout the human body through a network of blood vessels called the circulatory system. This system includes arteries that transport blood from the heart to various body parts. These arterial pathways divide into smaller vessels until they reach the arterioles, which further split into capillaries. It is within these minuscule capillaries that the exchange of nutrients and waste products takes place. After this exchange, the blood is collected by venules, which fuse to...