Interstitial fluid flow is a feature of many solid tumors. In vitro experiments have shown that such fluid flow can direct tumor cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis (cell migration up stress gradients) and autologous chemotaxis (downstream cell movement in response to flow-induced gradients of self-secreted chemoattractants). In this work we develop a probabilistic-continuum, two-phase model for cell migration in response to interstitial flow. We use a kinetic description for the cell velocity probability density function, and model the flow-dependent mechanical and chemical stimuli as forcing terms that bias cell migration upstream and downstream. Using velocity-space averaging, we reformulate the model as a system of continuum equations for the spatiotemporal evolution of the cell volume fraction and flux in response to forcing terms that depend on the local direction and magnitude of the mechanochemical cues. We specialize our model to describe a one-dimensional cell layer subject to fluid flow. Using a combination of numerical simulations and asymptotic analysis, we delineate the parameter regime where transitions from downstream to upstream cell migration occur. As has been observed experimentally, the model predicts downstream-oriented chemotactic migration at low cell volume fractions, and upstream-oriented tensotactic migration at larger volume fractions. We show that the locus of the critical volume fraction, at which the system transitions from downstream to upstream migration, is dominated by the ratio of the rate of chemokine secretion and advection. Our model also predicts that, because the tensotactic stimulus depends strongly on the cell volume fraction, upstream, tensotaxis-dominated migration occurs only transiently when the cells are initially seeded, and transitions to downstream, chemotaxis-dominated migration occur at later times due to the dispersive effect of cell diffusion.

中文翻译：

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使用概率方法推导流诱导细胞迁移的两相模型

间质液流动是许多实体瘤的特征。体外实验表明，这种流体流动可以引导肿瘤细胞向上游或下游移动，具体取决于张趋性（细胞沿应力梯度迁移）和自体趋化性（细胞响应流动诱导的自身梯度而向下游移动）之间的竞争机制之间的平衡。 -分泌的化学引诱剂）。在这项工作中，我们开发了一个概率连续体、两相模型，用于响应间隙流的细胞迁移。我们使用细胞速度概率密度函数的动力学描述，并将依赖于流动的机械和化学刺激建模为使细胞向上游和下游迁移偏向的强迫项。使用速度空间平均，我们将模型重新表述为连续介质方程系统，用于响应取决于机械化学线索的局部方向和大小的强迫项，细胞体积分数和通量的时空演化。我们专门使用我们的模型来描述受流体流动影响的一维细胞层。使用数值模拟和渐近分析的组合，我们描绘了从下游到上游细胞迁移发生转变的参数范围。正如实验所观察到的，该模型预测低细胞体积分数下的下游导向趋化迁移，以及较大体积分数下的上游导向的张趋迁移。我们表明，系统从下游迁移到上游迁移的临界体积分数的轨迹由趋化因子分泌速率与平流速率的比率决定。我们的模型还预测，由于张趋性刺激强烈依赖于细胞体积分数，上游、趋化性主导的迁移仅在细胞最初接种时短暂发生，而过渡到下游、趋化性主导的迁移则在稍后时间发生，因为细胞扩散的分散效应。