A three-dimensional simulation of the formation of metachronal waves in rows of pulmonary cilia is presented. The cilia move in a two-layer fluid model. The fluid layer adjacent to the cilia bases is purely viscous while the tips of the cilia move through a viscoelastic fluid. An overlapping fixed-moving grid formulation is employed to capture the effect of the cilia on the surrounding fluid. In contrast with immersed boundary methods, this technique allows a natural enforcement of boundary conditions without the need for smoothing of singular force distributions. The fluid domains are discretized using a finite volume method. The 9 + 2 internal microtubule structure of an individual cilium is modeled using large-deflection, curved, finite-element beams. The microtubule skeleton is cross-linked to itself and to the cilium membrane through spring elements which model nexin links. The cilium membrane itself is considered to be elastic and subject to fluid stresses computed from the moving grid formulation as well as internal forces transmitted from the microtubule skeleton. A cilium is set into motion by the action of dynein molecules exerting forces between adjacent microtubules. Realistic models of the forces exerted by dynein molecules are extracted from measurements of observed cilia shapes.

中文翻译：

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肺纤毛模型中的异时波形成

提出了肺纤毛行中异时波形成的三维模拟。纤毛在两层流体模型中移动。纤毛基部附近的流体层是纯粘性的，而纤毛的尖端则通过粘弹性流体移动。采用重叠的固定移动网格公式来捕捉纤毛对周围流体的影响。与浸入边界方法相比，该技术允许自然执行边界条件，而无需平滑奇异力分布。流体域使用有限体积方法离散化。单个纤毛的 9 + 2 内部微管结构使用大偏转、弯曲、有限元梁建模。微管骨架通过模拟连接蛋白链接的弹簧元件与自身和纤毛膜交联。纤毛膜本身被认为是有弹性的，并受到由移动网格公式计算出的流体应力以及从微管骨架传递的内力的影响。通过动力蛋白分子在相邻微管之间施加力的作用，纤毛开始运动。动力蛋白分子施加的力的真实模型是从观察到的纤毛形状的测量中提取的。通过动力蛋白分子在相邻微管之间施加力的作用，纤毛开始运动。动力蛋白分子施加的力的真实模型是从观察到的纤毛形状的测量中提取的。通过动力蛋白分子在相邻微管之间施加力的作用，纤毛开始运动。动力蛋白分子施加的力的真实模型是从观察到的纤毛形状的测量中提取的。