Haemodynamics of atherosclerosis: a matter of higher hydrostatic pressure or lower shear stress?

Atherosclerosis is prone to large and medium arteries which must bear much higher mechanical force, mainly hydrostatic pressure, shear stress, and tensile stretch. In general, with gradual increase of branches and total sectional area, velocity and pressure of blood will gradually decrease from aorta to capillaries. However, local velocity and pressure of blood might also be different even in the same transection of artery for variations of vessel structure and location. Blood belongs to viscous fluid with certain viscosity in the body. In the large and medium arteries, blood velocity is so fast that viscoelasticity could be negligible. Therefore, the Bernoulli’s equation could be applied to these arteries: P + 12ρv2 + ρgh = constant or P = constant − 12ρv2 − ρgh (P: hydrostatic pressure, ρ: fluid density, v: blood velocity, g: gravitational acceleration, h: height). ρ and g are constants in an individual. The essence of Bernoulli’s equation is energy conservation. At any point of per unit mass of fluid micro cluster, the sum of P, 12ρv2 and ρgh is a constant. Even if the viscosity of blood is considered, the energy loss of blood flow should be very small over a very short distance (few centimetres, Figure 1). In addition, the energy loss of blood flow in the same transection is also very small due to the small diameter of blood vessel. At the same timepoint in a cardiac cycle, the constants (sums of P, 12ρv2 and ρgh) of unit mass of fluid micro cluster are basically equal in a very short distance or in the same transection of artery, and Bernoulli’s equation is still applicable here. At any point of per unit mass of fluid micro cluster here, the reduction of 12ρv2 would be converted into P (ΔP = 12ρ (Δv)2). Therefore, P is negatively related to v2 in a very short distance or in the same transection of the artery (Figure 1). Since the direction of 12ρv2 is parallel to the tangent direction of the vessel and the perpendicular force to the wall from 12ρv2 at the tangent point is zero, 12ρv2 has little effect on the vessel wall unless it is converted into P when the blood flow meets a curved or bifurcated vessel.