Olufsen Mette S, Hill N A, Vaughan Gareth D A, Sainsbury Christopher, Johnson Martin
Department of Mathematics, North Carolina State University, Raleigh, NC 27502, USA.
J Fluid Mech. 2012 Aug 1;705:280-305. doi: 10.1017/jfm.2012.220. Epub 2012 Jul 2.
The effects of vascular rarefaction (the loss of small arteries) on the circulation of blood are studied using a multiscale mathematical model that can predict blood flow and pressure in the systemic and pulmonary arteries. We augmented a model originally developed for the systemic arteries (Olufsen et al. 1998, 1999, 2000, 2004) to (a) predict flow and pressure in the pulmonary arteries, and (b) predict pressure propagation along the small arteries in the vascular beds. The systemic and pulmonary arteries are modelled as separate, bifurcating trees of compliant and tapering vessels. Each tree is divided into two parts representing the large' and small' arteries. Blood flow and pressure in the large arteries are predicted using a nonlinear cross-sectional area-averaged model for a Newtonian fluid in an elastic tube with inflow obtained from magnetic resonance measurements. Each terminal vessel within the network of the large arteries is coupled to a vascular bed of small `resistance' arteries, which are modelled as asymmetric structured trees with specified area and asymmetry ratios between the parent and daughter arteries. For the systemic circulation, each structured tree represents a specific vascular bed corresponding to major organs and limbs. For the pulmonary circulation, there are four vascular beds supplied by the interlobar arteries. This manuscript presents the first theoretical calculations of the propagation of the pressure and flow waves along systemic and pulmonary large and small arteries. Results for all networks were in agreement with published observations. Two studies were done with this model. First, we showed how rarefaction can be modelled by pruning the tree of arteries in the microvascular system. This was done by modulating parameters used for designing the structured trees. Results showed that rarefaction leads to increased mean and decreased pulse pressure in the large arteries. Second, we investigated the impact of decreasing vessel compliance in both large and small arteries. Results showed, that the effects of decreased compliance in the large arteries far outweigh the effects observed when decreasing the compliance of the small arteries. We further showed that a decrease of compliance in the large arteries results in pressure increases consistent with observations of isolated systolic hypertension, as occurs in ageing.
利用一个多尺度数学模型研究了血管稀疏（小动脉丧失）对血液循环的影响，该模型能够预测体循环和肺动脉中的血流和压力。我们对最初为体动脉开发的模型（Olufsen等人，1998年、1999年、2000年、2004年）进行了扩充，以（a）预测肺动脉中的血流和压力，以及（b）预测压力沿血管床中小动脉的传播。体动脉和肺动脉被建模为相互独立的、由顺应性且逐渐变细的血管组成的分支树。每棵树分为两部分，分别代表“大”动脉和“小”动脉。使用非线性横截面积平均模型预测弹性管中牛顿流体的大动脉中的血流和压力，其流入量通过磁共振测量获得。大动脉网络中的每个末梢血管都与一个由小“阻力”动脉组成的血管床相连，这些小动脉被建模为具有特定面积以及母动脉和子动脉之间不对称比率的不对称结构树。对于体循环，每个结构树代表对应于主要器官和肢体的特定血管床。对于肺循环，有四个由叶间动脉供血的血管床。本手稿展示了压力和流动波沿体循环和肺循环的大、小动脉传播的首次理论计算。所有网络的结果与已发表的观察结果一致。使用该模型进行了两项研究。首先，我们展示了如何通过修剪微血管系统中的动脉树来模拟血管稀疏。这是通过调节用于设计结构树的参数来实现的。结果表明，血管稀疏会导致大动脉中的平均压升高和脉压降低。其次，我们研究了大小动脉中血管顺应性降低的影响。结果表明，大动脉中顺应性降低的影响远远超过小动脉顺应性降低时观察到的影响。我们还进一步表明，大动脉中顺应性的降低会导致压力升高，这与衰老时出现的孤立性收缩期高血压的观察结果一致。
