Shear Stress at the Vessel Wall

Shear Stress at the Vessel Wall is the frictional force per unit area exerted by flowing blood tangentially against the inner surface of the vessel wall, arising from the velocity gradient present between the rapidly moving blood near the center of the lumen and the essentially stationary layer of blood immediately adjacent to the wall itself. Wall shear stress represents the mechanical signal through which the endothelium senses the physical characteristics of blood flow, converting a purely physical, hemodynamic quantity into a biological stimulus capable of regulating vascular tone, structure, and function.

Physical Origin of Wall Shear Stress

The Velocity Gradient at the Wall

Under laminar flow conditions, blood velocity varies continuously from a maximum at the central axis of the vessel to essentially zero immediately at the wall, a consequence of the no slip boundary condition, and the rate at which velocity changes with radial distance from the wall, referred to as the velocity gradient or shear rate, is greatest precisely at the wall itself, since this is where the transition from moving fluid to the stationary boundary is most abrupt.

Relationship Between Viscosity, Shear Rate, and Shear Stress

Wall shear stress is calculated as the product of blood viscosity and the shear rate present at the wall, reflecting the fact that shear stress arises from the internal friction of a viscous fluid being sheared at a given rate.

Quantitative Expression for a Cylindrical Vessel

Derivation From the Poiseuille Velocity Profile

For fully developed laminar flow through a cylindrical vessel, wall shear stress can be expressed directly in terms of flow rate, viscosity, and vessel radius by combining the parabolic velocity profile with the definition of shear stress, yielding an expression showing that wall shear stress increases with flow rate and viscosity, and decreases sharply as vessel radius increases.

In this expression, tau sub w represents wall shear stress, eta represents blood viscosity, Q represents volumetric flow rate, and r represents vessel radius, with the inverse cube dependence on radius indicating that wall shear stress is highly sensitive to vessel diameter, though somewhat less steeply so than the fourth power dependence governing resistance itself.

Biological Detection of Wall Shear Stress

The Endothelium as a Mechanosensor

The endothelial cells lining the vessel wall are directly exposed to wall shear stress and possess a range of mechanosensitive structures, including the glycocalyx, ion channels, cell surface receptors, and cytoskeletal elements, that collectively detect the magnitude and direction of the shear force acting on the luminal surface and transduce this mechanical signal into intracellular biochemical responses.

Flow Mediated Release of Nitric Oxide

A principal biological consequence of increased wall shear stress is the stimulation of endothelial nitric oxide synthase activity, leading to increased production and release of nitric oxide, which diffuses to the adjacent smooth muscle layer and produces vasodilation, a response referred to as flow mediated dilation, which serves to adjust vessel diameter in a manner that tends to normalize wall shear stress toward a physiologically preferred set point.

Visual Representation of Wall Shear Stress

Physiological and Pathological Significance

Set Point Regulation of Vessel Diameter

Over longer time scales, sustained deviation of wall shear stress from its normal physiological range triggers structural remodeling of the vessel, with chronically elevated shear stress promoting outward remodeling and an increase in luminal diameter that tends to restore shear stress toward its normal value, and chronically reduced shear stress promoting inward remodeling that similarly acts to restore the normal shear stress set point, illustrating that wall shear stress functions as a regulated physiological variable in its own right, subject to homeostatic control through structural as well as functional vascular adjustment.

Association Between Low Shear Stress and Atherosclerosis

Regions of the arterial tree that experience chronically low or disturbed wall shear stress, such as the outer walls of arterial bifurcations and the inner curvature of arterial bends, are preferentially susceptible to the development of atherosclerotic plaque, an association attributed to the reduced protective signaling, including diminished nitric oxide production, that occurs under low shear conditions compared to the atheroprotective signaling associated with sustained, unidirectional, physiologically normal levels of wall shear stress.