  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. 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. 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 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.
