Bernhard Stefan, Möhlenkamp Stefan, Tilgner Andreas
Department of Physics, Georg-August-Universität Göttingen, Friedrich-Hundt-Platz 1, 37077 Göttingen, Germany.
Biomed Eng Online. 2006 Jun 21;5:42. doi: 10.1186/1475-925X-5-42.
The pressure drop-flow relations in myocardial bridges and the assessment of vascular heart disease via fractional flow reserve (FFR) have motivated many researchers the last decades. The aim of this study is to simulate several clinical conditions present in myocardial bridges to determine the flow reserve and consequently the clinical relevance of the disease. From a fluid mechanical point of view the pathophysiological situation in myocardial bridges involves fluid flow in a time dependent flow geometry, caused by contracting cardiac muscles overlying an intramural segment of the coronary artery. These flows mostly involve flow separation and secondary motions, which are difficult to calculate and analyse.
Because a three dimensional simulation of the haemodynamic conditions in myocardial bridges in a network of coronary arteries is time-consuming, we present a boundary layer model for the calculation of the pressure drop and flow separation. The approach is based on the assumption that the flow can be sufficiently well described by the interaction of an inviscid core and a viscous boundary layer. Under the assumption that the idealised flow through a constriction is given by near-equilibrium velocity profiles of the Falkner-Skan-Cooke (FSC) family, the evolution of the boundary layer is obtained by the simultaneous solution of the Falkner-Skan equation and the transient von-Kármán integral momentum equation.
The model was used to investigate the relative importance of several physical parameters present in myocardial bridges. Results have been obtained for steady and unsteady flow through vessels with 0 - 85% diameter stenosis. We compare two clinical relevant cases of a myocardial bridge in the middle segment of the left anterior descending coronary artery (LAD). The pressure derived FFR of fixed and dynamic lesions has shown that the flow is less affected in the dynamic case, because the distal pressure partially recovers during re-opening of the vessel in diastole. We have further calculated the wall shear stress (WSS) distributions in addition to the location and length of the flow reversal zones in dependence on the severity of the disease.
The described boundary layer method can be used to simulate frictional forces and wall shear stresses in the entrance region of vessels. Earlier models are supplemented by the viscous effects in a quasi three-dimensional vessel geometry with a prescribed wall motion. The results indicate that the translesional pressure drop and the mean FFR compares favourably to clinical findings in the literature. We have further shown that the mean FFR under the assumption of Hagen-Poiseuille flow is overestimated in developing flow conditions.
在过去几十年中，心肌桥中的压降 - 流量关系以及通过血流储备分数（FFR）评估血管性心脏病激发了众多研究人员的兴趣。本研究的目的是模拟心肌桥中存在的几种临床情况，以确定血流储备，进而确定该疾病的临床相关性。从流体力学角度来看，心肌桥中的病理生理情况涉及由于覆盖冠状动脉壁内段的心肌收缩而导致的随时间变化的流动几何形状中的流体流动。这些流动大多涉及流动分离和二次流动，难以进行计算和分析。
由于对冠状动脉网络中心肌桥的血流动力学状况进行三维模拟耗时较长，我们提出了一种用于计算压降和流动分离的边界层模型。该方法基于这样的假设，即流动可以通过无粘核心和粘性边界层的相互作用得到充分描述。在理想化通过狭窄处的流动由Falkner - Skan - Cooke（FSC）族的近平衡速度剖面给出的假设下，通过同时求解Falkner - Skan方程和瞬态冯·卡门积分动量方程来获得边界层的演变。
该模型用于研究心肌桥中存在的几个物理参数的相对重要性。已获得了直径狭窄0 - 85%的血管中稳定和不稳定流动的结果。我们比较了左前降支冠状动脉（LAD）中段心肌桥的两个临床相关病例。固定和动态病变的压力衍生FFR表明，在动态情况下血流受影响较小，因为在舒张期血管重新开放时远端压力会部分恢复。除了根据疾病严重程度计算流动逆转区域的位置和长度外，我们还进一步计算了壁面剪切应力（WSS）分布。
所描述的边界层方法可用于模拟血管入口区域的摩擦力和壁面剪切应力。早期模型通过在具有规定壁运动的准三维血管几何形状中的粘性效应得到补充。结果表明，跨病变压降和平均FFR与文献中的临床发现相比具有优势。我们还表明，在发展中的流动条件下，假设为哈根 - 泊肃叶流动时平均FFR被高估。
