Hudetz A G, Monos E
Acta Physiol Hung. 1986;67(2):173-91.
A mathematical model was developed for the characterization of quasistatic nonlinear viscoelastic behaviour of large arteries with activated smooth muscle. Arteries were considered to belong to the class of viscoelastic materials with fading memory and the first order term of the integral polynomial constitutive equations of Pipkin and Rogers satisfying the nonlinear superposition principle was modified to handle responses to increasing and decreasing loads independently. The two creep functions contained by the obtained one dimensional constitutive equation were determined experimentally from the series of creep and recovery tests of increasing amplitude performed on isolated canine iliac arteries following the activation of the vascular smooth muscle by normal dose of norepinephrine in vitro. Utilizing the constitutive equation of the arterial wall and the tabulated values of creep functions successive stress-strain hysteresis loops of various constant stress rates were simulated by digital computer. The computed hysteresis loops demonstrated the main characteristics, such as the weak and asymmetric rate-sensitivity of the experimentally observed hysteresis of arteries qualitatively well, thus allowing certain conclusions on the mechanism of quasistatic viscoelastic behaviour of vascular smooth muscle.
建立了一个数学模型，用于表征具有激活平滑肌的大动脉的准静态非线性粘弹性行为。动脉被认为属于具有衰退记忆的粘弹性材料类别，并且对满足非线性叠加原理的Pipkin和Rogers积分多项式本构方程的一阶项进行了修改，以便独立处理对递增和递减载荷的响应。通过对体外正常剂量去甲肾上腺素激活血管平滑肌后的离体犬髂动脉进行一系列振幅递增的蠕变和恢复试验，从实验上确定了所得到的一维本构方程所包含的两个蠕变函数。利用动脉壁的本构方程和蠕变函数的列表值，通过数字计算机模拟了各种恒定应力率下连续的应力-应变滞后环。计算得到的滞后环定性地很好地展示了实验观察到的动脉滞后的主要特征，如较弱和不对称的速率敏感性，从而可以对血管平滑肌准静态粘弹性行为的机制得出某些结论。
