Fluid Shear Stress Sensing by the Endothelial Layer

Abstract

Blood flow produces mechanical frictional forces, parallel to the blood flow exerted on the endothelial wall of the vessel, the so-called wall shear stress (WSS). WSS sensing is associated with several vascular pathologies, but it is first a physiological phenomenon. Endothelial cell sensitivity to WSS is involved in several developmental and physiological vascular processes such as angiogenesis and vascular morphogenesis, vascular remodeling, and vascular tone. Local conditions of blood flow determine the characteristics of WSS, i.e., intensity, direction, pulsatility, sensed by the endothelial cells that, through their effect of the vascular network, impact WSS. All these processes generate a local-global retroactive loop that determines the ability of the vascular system to ensure the perfusion of the tissues. In order to account for the physiological role of WSS, the so-called shear stress set point theory has been proposed, according to which WSS sensing acts locally on vessel remodeling so that WSS is maintained close to a set point value, with local and distant effects of vascular blood flow. The aim of this article is (1) to review the existing literature on WSS sensing involvement on the behavior of endothelial cells and its short-term (vasoreactivity) and long-term (vascular morphogenesis and remodeling) effects on vascular functioning in physiological condition; (2) to present the various hypotheses about WSS sensors and analyze the conceptual background of these representations, in particular the concept of tensional prestress or biotensegrity; and (3) to analyze the relevance, explanatory value, and limitations of the WSS set point theory, that should be viewed as dynamical, and not algorithmic, processes, acting in a self-organized way. We conclude that this dynamic set point theory and the biotensegrity concept provide a relevant explanatory framework to analyze the physiological mechanisms of WSS sensing and their possible shift toward pathological situations.

Keywords: angiogenesis; endothelial cell; regulation – physiological; shear stress; tensegrity; vascular remodeling; vasoreactivity.

FIGURE 1

Fluid shear stress. (A) Schematic representation of the shear stress. The fluid exerts a tangential force F on the surface A of a solid (blue cube), which tends to deform the solid. (B) Shear stress, shear rate, and viscosity. A plate (blue block) of area A submitted to a tangential force F moves on the surface of a liquid of depth Y. The displacement at the surface of the liquid (U) generates, at the y distance to the surface, a movement of the fluid u. The shear rate is the ratio du/dy. For a Newtonian fluid, du/dy is constant. (C) Schematic representation of the shear stress exerted by the blood flow on the wall of a cylindrical vessel. Red arrows represent the velocity (V) of laminar blood flow. The shear stress (τ, black arrows) exerted by the blood on the wall of the tube depends on the blood flow mean velocity, the blood viscosity, and the diameter (D) of the tube (Eqs. 3 and 4).

FIGURE 2

Schematic representation classical set point theory according to the concepts of control theory. The WSS value is sensed by mechanosensors and compared with a reference value. If the two values are similar, the system remains in a steady state. If not, positive or negative variations from the set point activate feedback mechanisms that, respectively, lower or increase WSS value. The diamond represents the decisional step of the regulatory loop.

FIGURE 3

WSS-induced vasoreactivity. Graphical representation of WSS and vessel radius from Table 3 data. r, vessel radius; WSS, wall shear stress. The curves are the graphical representation of the function r = f(WSS) calculated according to Eq. 11. Values for blood viscosity (η), blood flow (Q), r, and WSS are the experimental ones given in Table 3, and the curve is built by varying WSS value and calculating r from the equation. Panels (A), (B), and (C) are the curves built from the data obtained in human common coronary artery (A), human brachial artery (B), and rat cremaster muscle arterioles (C). Full black lines represent WSS sensitivity, the slope of the line being the sensitivity coefficient S_WSS. Intercepts of the line with the curves are the observed radius and WSS values. Horizontal and vertical dot lines correspond, respectively, to the absence of WSS sensitivity, and uniform WSS.

FIGURE 4

Scheme of the set point model for vascular remodeling. (A,B) Scheme of the dynamic model proposed by Baeyens and Schwartz (2016), redrawn from the original publication. A, B, and C are three WSS-dependent intercellular pathways determining vessel remodeling and quiescence. (A) Independent activation profile of A, B, and C. (B) Activation profile of A, B, and C outputs (A′, B′, and C′, respectively), when C inhibits B, and B inhibits C. If A′ determines inward remodeling, B′ quiescence, and A′C′ outward remodeling, the model predicts a “set point” zone of WSS for which B′ is greater than A′ and C′, corresponding to the quiescent state. (C) Graphical representation of the mathematical formulation of the model (Eqs 12–17) with A_m = 10, C_m = 10, α = 3, β = 0.5, γ = 19, ha = 0.4, and hc = 0.2. (D) Model prediction for A′, B′, and C′ for I_c = 100% and I_b = 80%. (E) Model prediction for A′, B′, and C′ for γ = 15 instead of 19. Values are expressed in arbitrary units (A.U.). (F) Model prediction for A′, B′, and C′ for I_b = 40% instead of 80%. Vertical arrows indicate the set point value, defined as maximal B′ value above A′ and C′ values. Values are expressed in arbitrary units (A.U.).

FIGURE 5

Scheme of the set point model for vessel stabilization. The model is based on two pathways, D and E, defined by Eqs 18–21, E inhibiting D. (A) Independent activation profiles of D and E with D_m = 10, E_m = 10, δ= 5, ϵ= 10, hd = 0.5, and hc = 0.3. (B) Predicted activation profiles of D and E outputs (D′ and E′, respectively), for I_e = 100%. Values are expressed in arbitrary units (A.U.). The model predicts a minimal WSS threshold for WSS sensitivity. If D determines cell migration and E cell polarization, and if vessel stabilization is defined by maximal EC polarization and the end of EC migration, the model predicts a set point value for vessel stabilization, cell migration being maximal before the set point value is obtained.

FIGURE 6

Scheme of WSS-induced vasoreactivity regulation. (A) WSS-induced vasorelaxant agents (VA) production by ECs. An increase in WSS induces an increase in VA production, which leads to an increase in VA concentration (VA) in the smooth muscle cells (SMC) of the vessel wall. (B) VA-induced vasorelaxation of SMCs induces an increase in vessel radius. (C) Because of the physical relationship between vessel radius and WSS, increase in radius induces a decrease in WSS. Taken together, these processes constitute a causal loop that limits WSS variations: the consequence of an initial increase in WSS is WSS decrease, and reciprocally.