Multiscale Parareal Algorithm for Long-Time Mesoscopic Simulations of Microvascular Blood Flow in Zebrafish

TL;DR

This paper introduces a multiscale parareal algorithm that accelerates long-time mesoscopic blood flow simulations in zebrafish by combining continuum and mesoscopic models with iterative correction, achieving high accuracy and efficiency.

Contribution

The paper presents a novel multiscale parareal algorithm that enables fast, accurate long-time mesoscopic simulations of blood flow by supervising mesoscopic models with continuum models.

Findings

Less than 1% error in flowrate for Newtonian flow

Less than 3% error in non-Newtonian blood flow

Converges in only two iterations for zebrafish blood flow simulation

Abstract

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.