Fig. 2.

Physiological forces acting on blood vessels. A) Physiological parameters involved in the forces and stresses acting on the vascular wall. In red, blood flow parameters: pressure (P) and volumetric flow (Q). In gray, the longitudinal tissue tethering (T); B) Physiological forces acting on blood vessels resulted from the blood pressure and flow, and surrounding tissues: radial force resulted from the blood pressure ($F_{r-P}$, tensile and cyclic), longitudinal force resulted from the blood pressure ($F_{l-P}$, tensile and cyclic), tangential force resulted from the blood flow ($F_{t-P}$, shear and constant), longitudinal force resulted from the tethering ($F_{l-T}$, tensile, constant); C) Stresses generated in the vascular wall from the physiological forces: circumferential stress $\left({\sigma }_C\right)$, longitudinal stress $\left({\sigma }_L\right)$ and shear stress $\left({\tau }_w\right)$. Longitudinal stress is composed by a stress due to pressure $\left({\sigma }_{l-P}\right)$ and a stress due to tethering $\left({\sigma }_{l-T}\right)$; D) Stresses relationships assuming incompressibility and uniform strain across the vascular wall [15,17,70]. Blood viscosity (μ) is required for the shear stress calculation. The vascular wall dimensions are inner radius $\left(r_i\right)$, external radius $\left(r_e\right)$, length (l), and wall thickness (t).