The deformability of blood vessels in one-dimensional blood flow models is typically described through a pressure-area relation, known as the tube law. The most used tube laws take into account the elastic and viscous components of the tension of the vessel wall. Accurately parametrizing the tube laws is vital for replicating pressure and flow wave propagation phenomena. Here, we present a novel mathematical-property-preserving approach for the estimation of the parameters of the elastic and viscoelastic tube laws. Our goal was to estimate the parameters by using ovine and human in vitro data, while constraining them to meet prescribed mathematical properties. Results show that both elastic and viscoelastic tube laws accurately describe experimental pressure-area data concerning both quantitative and qualitative aspects. Additionally, the viscoelastic tube law can provide a qualitative explanation for the observed hysteresis cycles. The two models were evaluated using two approaches: (i) allowing all parameters to freely vary within their respective ranges and (ii) fixing some of the parameters. The former approach was found to be the most suitable for reproducing pressure-area curves.

中文翻译：

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使用体外数据对动脉和静脉中的一维血流进行管定律参数化

一维血流模型中血管的变形性通常通过压力面积关系（称为管定律）来描述。最常用的管定律考虑了血管壁张力的弹性和粘性分量。准确地参数化管定律对于复制压力和流动波传播现象至关重要。在这里，我们提出了一种新颖的数学性质保持方法，用于估计弹性和粘弹性管定律的参数。我们的目标是通过使用绵羊和人类体外数据来估计参数，同时限制它们满足规定的数学特性。结果表明，弹性管定律和粘弹性管定律都准确地描述了定量和定性方面的实验压力面积数据。此外，粘弹性管定律可以为观察到的滞后循环提供定性解释。使用两种方法评估这两个模型：（i）允许所有参数在各自的范围内自由变化；（ii）固定一些参数。发现前一种方法最适合再现压力面积曲线。