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.

各种生物过程，如氧气和营养物质的运输、血栓形成、血管血管生成和重塑，都与细胞/亚细胞水平的生物过程有关，其中解析详细细胞动力学的细观模拟为理解和识别疾病的细胞基础提供了关键。然而，内在随机效应可以在细观过程中发挥重要作用，而细观模拟中允许的时间步长受到快速细胞/亚细胞动态过程的限制。即使使用高性能计算，这些挑战也极大地限制了细观模拟可以达到的时间尺度。为了打破这个瓶颈并实现一个具有生物学意义的时间尺度，我们提出了一种多尺度拟实算法，其中基于连续体的求解器在时域中监督细观模拟。使用迭代预测校正策略，由其基于连续体的对应物监督的时间并行细观模拟可以快速收敛。该方法的有效性首先在通过 Y 形分叉通道的正弦流量的时间相关流中得到验证。结果表明，经过几次迭代后，牛顿流体和非牛顿血液的监督细观模拟收敛到参考解。计算感兴趣的物理量，包括速度、壁面剪切应力和流速，以与参考溶液的物理量进行比较，显示牛顿血流中流速的相对误差小于 1%，非牛顿血流的相对误差小于 3%。然后将所提出的方法应用于斑马鱼后脑微血管血流的大规模细观模拟，以实现时间加速。脉管系统的三维几何结构是直接从共聚焦显微镜下活斑马鱼的图像构建的，从而形成具有 95 个分支和 57 个分叉的复杂血管网络。在这个真实的斑马鱼后脑血管网络中，来自心跳的时间依赖性血流使用耗散粒子动力学作为细观模型进行模拟，该模型由多个时间子域中的一维血流模型（基于连续体的模型）监督. 计算分析表明，所得微血管血流仅经过两次迭代就收敛到参考解决方案。所提出的方法适用于具有复杂流体和几何形状的长时间细观模拟。它可以很容易地与经典空间分解相结合以进一步加速。