<div>etermination of left-right asymmetry of the body plan is achieved in the early embryo. At the 4-6 somite stage, a cavity structure, called a node, is observed in the ventral midline surface, in which hundreds of cilia rotate. Nodal cilia are typically tilted toward the posterior and rotate in the clockwise direction, resulting in the generation of leftward flow in the node. Such leftward flow acts as a trigger of left-specific gene expression, and fluid mechanics plays a role in left-right symmetry breaking. To understand the cilia-driven nodal flow, it is necessary to determine the hydrodynamic interactions among rotating cilia, as ciliary motions interact with each other through fluid motion. In this study, we numerically investigated the elastohydrodynamic synchronization of two rotating cilia, as well as the flow field. The ciliary motion was determined by the balance of cytoskeletal elastic force, motor protein-induced active force, and fluid viscous force. According to the geometric clutch hypothesis, the frequency of rotating cilia is controlled by the bending curvature. Owing to hydrodynamic interactions, bending deformations of two cilia become time-dependent, and the rotation is finally locked in anti-phase regardless of the relative position and initial phase difference. By locking in the reverse phase, the average propulsion flow rate becomes 2-3 times larger than in-phase beating. The results of this study form a basis for understanding cilium-driven nodal flow.</div>

Keywords

Nodal cilia, Left-right asymmetry, Hydrodynamic synchronization, Stokes flow, Computational biomechanics

Paper information

[Advance Publication] (Proper information for citation will be announced after formal publication)

Although boundary element (BE) based methods are highly accurate for simulating capsule suspensions in Stokes flows, computational time has been a major issue, even when only a few capsules are simulated. We propose a full graphics processing unit (GPU) implementation of a numerical method coupling the BE method of fluid mechanics with the finite element method of membrane mechanics. In single GPU computing, the performance achieves 0.12 TFlop/s when computing one capsule (2562 nodes and 5120 elements) and 0.29 TFlop/s for two capsules. The performance increases with the number of capsules, achieving a maximum of 0.59 TFlop/s. We also implement a multi-GPU method with the data communication overlapping the computation. A weak scaling test shows perfect scalability for any number of computational nodes per GPU, indicating that the communication time is completely hidden. For a practical use of the present results, we estimate the computational time required for 10000 time steps. When we simulate one capsule and two capsules on one GPU, only 2.0 and 9.1 minutes are required to complete the simulation, respectively, and a simulation with 256 capsules on 16 GPUs takes 3.8 days. <span class="caption gzu"></span>

Keywords

Suspension, Boundary integral formulation, Multi GPUs, Parallel computing, Stokes flow

Paper information

Daiki MATSUNAGA, Yohsuke IMAI, Toshihiro OMORI, Takuji ISHIKAWA and Takami YAMAGUCHI, “A full GPU implementation of a numerical method for simulating capsule suspensions”, Journal of Biomechanical Science and Engineering, Vol.9, No.3 (2014), p.14-00039. doi:10.1299/jbse.14-00039. Final Version Released on December 26, 2014, Advance Publication Released on July 31, 2014.