Multiscale parareal algorithm for long-time mesoscopic simulations of microvascular blood flow in zebrafish
Multiscale parareal algorithm for long-time mesoscopic simulations of microvascular blood flow in zebrafish
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DOI：
10.1007/s00466-021-02062-w
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发表时间：
2021-08-17
影响因子：
4.1
通讯作者：
Karniadakis, George Em
中科院分区：
文献类型：
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作者：
Blumers, Ansel L.;Yin, Minglang;Karniadakis, George Em
各种生物过程，如氧气和营养物质的运输，血栓形成，血管生成和重塑与细胞/亚细胞水平的生物过程有关，其中解决详细的细胞动力学的介观模拟提供了理解和识别疾病的细胞基础的关键。然而，内在随机效应可以在介观过程中发挥重要作用，而介观模拟中允许的时间步长受到快速细胞/亚细胞动力学过程的限制。这些挑战极大地限制了介观模拟即使在高性能计算的情况下也可以达到的时间尺度。为了打破这一瓶颈，实现生物意义的时间尺度，我们提出了一个多尺度parareal算法，其中一个基于连续求解器监督在时域中观模拟。使用迭代预测-校正策略，由其基于连续介质的对应物监督的时间上并行的介观模拟可以快速收敛。首先，在一个时间相关的流与正弦流量通过Y形分叉通道验证所提出的方法的有效性。结果表明，牛顿流体和非牛顿流体的有监督介观模拟经过几次迭代后收敛到参考解。感兴趣的物理量，包括速度，壁面剪切应力和流量的计算与参考解决方案进行比较，显示在牛顿流的流量小于1%的相对误差和小于3%的相对误差在非牛顿血流。该方法被应用到一个大规模的介观模拟微血管血流在斑马鱼后脑的时间加速。血管的三维几何结构是直接从共聚焦显微镜下的活斑马鱼的图像构建的，从而导致具有95个分支和57个分叉的复杂血管网络。本文采用耗散粒子动力学作为介观模型，在多个时域子域内用一维血流模型（基于连续介质的模型）来模拟斑马鱼脑血管网络中心脏搏动时变的血流.计算分析表明，所得到的微血管血流收敛到参考解决方案后，只有两个迭代。该方法适用于复杂流体和几何形状的长时间介观模拟。它可以很容易地与经典的空间分解相结合，以进一步加速。
Various biological processes such as transport of oxygen and nutrients, thrombus formation, vascular angiogenesis and remodeling are related to cellular/subcellular level biological processes, where mesoscopic simulations resolving detailed cell dynamics provide a key to understanding and identifying the cellular basis of disease. However, the intrinsic stochastic effects can play an important role in mesoscopic processes, while the time step allowed in a mesoscopic simulation is restricted by rapid cellular/subcellular dynamic processes. These challenges significantly limit the timescale that can be reached by mesoscopic simulations even with high-performance computing. To break this bottleneck and achieve a biologically meaningful timescale, we propose a multiscale parareal algorithm in which a continuum-based solver supervises a mesoscopic simulation in the time-domain. Using an iterative prediction-correction strategy, the parallel-in-time mesoscopic simulation supervised by its continuum-based counterpart can converge fast. The effectiveness of the proposed method is first verified in a time-dependent flow with a sinusoidal flowrate through a Y-shaped bifurcation channel. The results show that the supervised mesoscopic simulations of both Newtonian fluids and non-Newtonian bloods converge to reference solutions after a few iterations. Physical quantities of interest including velocity, wall shear stress and flowrate are computed to compare against those of reference solutions, showing a less than 1% relative error on flowrate in the Newtonian flow and a less than 3% relative error in the non-Newtonian blood flow. The proposed method is then applied to a large-scale mesoscopic simulation of microvessel blood flow in a zebrafish hindbrain for temporal acceleration. The three-dimensional geometry of the vasculature is constructed directly from the images of live zebrafish under a confocal microscope, resulting in a complex vascular network with 95 branches and 57 bifurcations. The time-dependent blood flow from heartbeats in this realistic vascular network of zebrafish hindbrain is simulated using dissipative particle dynamics as the mesoscopic model, which is supervised by a one-dimensional blood flow model (continuum-based model) in multiple temporal sub-domains. The computational analysis shows that the resulting microvessel blood flow converges to the reference solution after only two iterations. The proposed method is suitable for long-time mesoscopic simulations with complex fluids and geometries. It can be readily combined with classical spatial decomposition for further acceleration.