一维收集淋巴管数学模型结合电-流体-机械收缩模型和阀门动力学
A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics
AI总结：
本文提出了一种结合新型电-流体-机械收缩（EFMC）模型的一维淋巴管模型，用于模拟收缩动力学，并分析了阀门在不同压力条件下的影响。
摘要：
我们提出了一种用于收集淋巴管的一维模型，结合了基于修改的FitzHugh-Nagumo模型的新型电-流体-机械收缩（EFMC）模型，用于动态收缩。一维淋巴管模型是一个超几何偏微分方程组。EFMC模型结合了淋巴管的电活动（动作电位）与流体-机械反馈（淋巴管壁的拉伸和壁剪应力）以及淋巴管壁性质的机械变化（收缩）。EFMC模型由四个常微分方程（ODEs）控制，并依赖于：（1）环境钙离子内流，（2）拉伸激活钙离子内流，以及（3）由壁剪应力引起的收缩抑制。我们对EFMC模型的稳态稳定性进行了完整的数学分析。总体而言，EFMC模型允许模拟压力和壁剪应力对实验中观察到的收缩频率的影响。淋巴管阀门使用一个已建立的集中参数模型来模拟狭窄和反流阀门。我们分析了单个淋巴管在广泛上游和下游压力组合下的多个淋巴动力学指标。狭窄和反流阀门被建模，并对其影响进行了量化。狭窄阀门的结果显示，在下游淋巴管中，对于低频收缩，计算泵流量（CPF）指数几乎不变，而对于高频收缩，CPF随着狭窄程度的增加而大幅下降（严重狭窄可达93%）。对于不完全阀门的结果显示，随着不完全程度的增加，淋巴循环中的净流量趋于零。
英文摘要：
We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh-Nagumo model for action potentials. The one-dimensional model for a compliant lymphatic vessel is a set of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (stretch of the lymphatic wall and wall shear stress) and the mechanical variation of the lymphatic wall properties (contractions). The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a complete mathematical analysis of the stability of the stationary state of the EFMC model. Overall, the EFMC model allows imitating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled using a well-established lumped-parameter model which allows simulating stenotic and regurgitant valves. We analysed several lymphodynamical indexes of a single lymphangion for a wide range of upstream and downstream pressure combinations. Stenotic and regurgitant valves were modelled, and their effects are here quantified. Results for stenotic valves showed in the downstream lymphangion that for low frequencies of contractions the Calculated Pump Flow (CPF) index remained almost unaltered, while for high frequencies the CPF dramatically decreased depending on the severity of the stenosis (up to 93% for a severe stenosis). Results for incompetent valves showed that the net flow during a lymphatic cycle tends to zero as the degree of incompetence increases.
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