Distensibility characteristics of caval veins and empirical exponential formulae

Abstract

The stress-strain curves of the vena cava have been measured of vena cava superior, and the intrathoracic and abdominal portions of vena cava inferior excised from dogs. The stress σ is expressed by the exponential function of the strain γ as follows: $$\mathit{\sigma }={\mathit{\sigma }}_0[exp\mathrm{(}\mathit{\gamma }\mathrm{/}{\mathit{\gamma }}_0\mathrm{)}-1]$$ in the longitudinal direction, and $$\mathit{\sigma }={\mathit{\sigma }}_1[exp\mathrm{(}\mathit{\gamma }\mathrm{/}{\mathit{\gamma }}_1\mathrm{)}-1]+{\mathit{\sigma }}_2[exp\mathrm{(}\mathit{\gamma }\mathrm{/}{\mathit{\gamma }}_2\mathrm{)}-1]$$ in the circumferential one for all the three kinds of veins. The constants ${\mathit{\sigma }}_0$ , ${\mathit{\gamma }}_0$ , ${\mathit{\sigma }}_1$ , ${\mathit{\gamma }}_1$ , ${\mathit{\sigma }}_2$ and ${\mathit{\gamma }}_2$ are determined by a nonlinear least squares method.