Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA.
School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, UK.
Biomech Model Mechanobiol. 2019 Feb;18(1):219-243. doi: 10.1007/s10237-018-1078-8. Epub 2018 Oct 3.
This study uses a one-dimensional fluid dynamics arterial network model to infer changes in hemodynamic quantities associated with pulmonary hypertension in mice. Data for this study include blood flow and pressure measurements from the main pulmonary artery for 7 control mice with normal pulmonary function and 5 mice with hypoxia-induced pulmonary hypertension. Arterial dimensions for a 21-vessel network are extracted from micro-CT images of lungs from a representative control and hypertensive mouse. Each vessel is represented by its length and radius. Fluid dynamic computations are done assuming that the flow is Newtonian, viscous, laminar, and has no swirl. The system of equations is closed by a constitutive equation relating pressure and area, using a linear model derived from stress-strain deformation in the circumferential direction assuming that the arterial walls are thin, and also an empirical nonlinear model. For each dataset, an inflow waveform is extracted from the data, and nominal parameters specifying the outflow boundary conditions are computed from mean values and characteristic timescales extracted from the data. The model is calibrated for each mouse by estimating parameters that minimize the least squares error between measured and computed waveforms. Optimized parameters are compared across the control and the hypertensive groups to characterize vascular remodeling with disease. Results show that pulmonary hypertension is associated with stiffer and less compliant proximal and distal vasculature with augmented wave reflections, and that elastic nonlinearities are insignificant in the hypertensive animal.
本研究使用一维流体动力学动脉网络模型来推断与肺动脉高压相关的血液动力学量的变化。本研究的数据包括来自 7 只具有正常肺功能的对照小鼠和 5 只缺氧诱导的肺动脉高压小鼠的主肺动脉的血流和压力测量。从代表性对照和高血压小鼠的肺部微 CT 图像中提取了 21 个血管网络的动脉尺寸。每个血管都用其长度和半径表示。流体动力学计算假设流动是牛顿的、粘性的、层流的，没有旋转。通过一个压力与面积相关的本构方程来封闭方程组，该方程使用从圆周方向的应力-应变变形推导的线性模型，假设动脉壁很薄，以及一个经验非线性模型。对于每个数据集，从数据中提取出一个入口波形，并且根据从数据中提取的平均值和特征时间尺度来计算指定流出边界条件的标称参数。通过估计最小化测量和计算波形之间的最小二乘误差的参数，对每个小鼠进行模型校准。优化后的参数在对照和高血压组之间进行比较，以描述与疾病相关的血管重塑。结果表明，肺动脉高压与近端和远端血管的刚性增加和顺应性降低以及波反射增强有关，并且高血压动物中的弹性非线性是不重要的。
