Qureshi M Umar, Vaughan Gareth D A, Sainsbury Christopher, Johnson Martin, Peskin Charles S, Olufsen Mette S, Hill N A
Department of Mathematics, International Islamic University, Sector H10, Islamabad, 44000, Pakistan,
Biomech Model Mechanobiol. 2014 Oct;13(5):1137-54. doi: 10.1007/s10237-014-0563-y. Epub 2014 Mar 9.
A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281-1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of 'large' arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the 'smaller' arteries and veins of radii ≥ 50 μm. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung.
本文提出了一种新型的肺循环多尺度数学和计算模型，并用于分析动脉和静脉压力及血流。这项工作相对于Olufsen等人（《生物医学工程年鉴》28:1281 - 1299, 2012）之前的研究有了重大进展，他们仅考虑了动脉循环。对于肺循环中的前三代血管，其几何形状是根据使用磁共振成像（MRI）获得的患者特定测量数据确定的。使用弹性管中牛顿流体的非线性、横截面积平均方程组预测较大动脉和静脉中的血流和压力。主肺动脉的流入量来自MRI测量，而从主肺静脉进入左心房的压力保持恒定在2 mmHg的正常平均值。“大”动脉网络中的每个末梢血管通过代表较小动脉和静脉血管床的血管网络与其相应的末梢静脉相连。我们开发并实现了一种算法，使用分叉结构树和递归计算每个血管床的导纳。结构树模型考虑了半径≥50μm的“较小”动脉和静脉的几何形状和材料特性。我们研究了通过较大和较小血管硬化以及血管稀疏所表现出的三类肺动脉高压对血流和压力的影响。模拟这些病理状况的结果与临床观察结果一致，表明该模型具有辅助诊断和治疗肺部循环疾病的潜力。
