TABLE II.

Notations.

Symbol	Definition of symbol
r	Radial direction in cylindrical coordinate system (m)
z	Axial direction in cylindrical coordinate system (m)
$c\left(t\right)$	Creep function (Pa−1)
$\epsilon \left(t\right)$	Vascular strain
${\tau }_{\sigma }$	Relaxation time for constant stress (s)
${\tau }_{\epsilon }$	Relaxation time for constant strain (s)
σ	Applied stress on the vessel (Pa)
μ0	Spring constant on first branch (Pa)
μ1	Spring constant on second branch (Pa)
η1	Viscosity of dashpot (Pa s)
$D_{\mathrm{Max}}$	Maximum vessel displacement (m)
$D\left(t\right)$	Vessel displacement (m)
${\mathit{v}}_f$	Fluid velocity (m/s)
ρ	Fluid density (kg/m3)
μ	Dynamic viscosity of the fluid (Pa s)
P	Pressure in the fluid (Pa)
$P_b$	Bubble pressure at the wall (Pa)
$P_g$	Gas pressure (Pa)
$P_{\mathrm{g}0}$	Gas pressure at resting state (Pa)
$P_0$	Ambient pressure in microvessels (Pa)
$R_0$	Initial bubble radius (m)
R	Bubble radius (m)
κ	Total curvature (m−1)
γ	Surface tension as a function of bubble area (N/m)
$P_{\gamma }$	Laplace pressure (Pa)
k	Polytropic index
$P_i$	Intravascular pressure (Pa)
$P_{\text{out}}$	Pressure on the outer diameter of vessel wall (Pa)
$r_i$	Inner vessel diameter (m)
$r_o$	Outer vessel diameter (m)
χ	Shell elastic modulus (N/m)
${\kappa }_{\mathrm{s}}$	Shell viscosity (kg/s)
${\gamma }_{\text{water}}$	Surface tension of water (N/m)
A	Bubble area (m2)
$A_{\text{buckling}}$	Bubble area at shell buckling regime (m2)
$R_{\text{break}-\text{up}}$	Bubble radius at break-up regime (m)
$A_{\text{break}-\text{up}}$	Bubble area at break-up regime (m2)
$R_{\text{eq}}$	Spherical bubble's equivalent radius (m)
$R_{\max }$	Maximum bubble radius (m)
$r_{v\max }$	Maximum vessel radius (m)
${\sigma }_{\theta \theta }$	Circumferential (hoop) stress (Pa)