<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

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[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.

We developed a numerical method for large-scale simulations of cellular flow in microvessels. We employed a particle method, where all blood components were modeled using a finite number of particles. Red blood cell deformation was modeled by a spring network of membrane particles. A domain decomposition method was used for parallel implementation on distributed memory systems. In a strong scaling test up to 64 CPU cores, we obtained a linear speedup with the number of CPU cores, and demonstrated that our model can simulate <i>O</i>(10³) red blood cells in vessels a few tens of micrometers in diameter. For quantitative validation, we analyzed the Fåhræus effect and the formation of a cell-depleted peripheral layer. Simulations were performed for tube hematocrit ranging from 20 to 45%, and microvessel diameters from 9 to 50 µm. Our numerical results were in good agreement with previous experimental results both for the discharge hematocrit and cell-depleted peripheral layer thickness.

Keywords

Large-Scale Simulation, Red Blood Cell, Microcirculation, Cell-Depleted Peripheral Layer, Fåhræus Effect

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Davod ALIZADEHRAD, Yohsuke IMAI, Keita NAKAAKI, Takuji ISHIKAWA and Takami YAMAGUCHI, “Parallel Simulation of Cellular Flow in Microvessels Using a Particle Method”, Journal of Biomechanical Science and Engineering, Vol. 7, No. 1 (2012), pp.57-71 . doi:10.1299/jbse.7.57

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Paper information

Shinsuk PARK, Kyehan RHEE and Takuji ISHIKAWA, “Preface”, Journal of Biomechanical Science and Engineering, Vol. 6, No. 3 (2011), pp.134 . doi:10.1299/jbse.6.134

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Takuji ISHIKAWA, “Preface”, Journal of Biomechanical Science and Engineering, Vol. 6, No. 2 (2011), pp.63-63 . doi:10.1299/jbse.6.63

Pneumothorax is characterized by lung collapse. Its effect on hemodynamics, especially on pulmonary arterial blood flow, remains unclear. This patient-specific study investigated the effects of lung deformation on pulmonary blood flow during acute phase and after recovery. Arterial geometry was extracted up to the fifth generation from computed tomography images in three patients and reconstructed. Different geometrical parameters (artery bores, area ratios, and between-branch angles) were computed. The shapes of the pulmonary trunk and its branches were affected strongly by pneumothorax. To clarify the effect of geometrical perturbations on blood flow, the Navier--Stokes equations for a steady laminar flow of Newtonian incompressible fluid were solved in a reconstructed domain. The change in flow structure between acute phase and recovery was associated with variations in flow rate ratio between the right and left lungs. This study shows, possibly for the first time, that from a patient-specific numerical test, pneumothorax has a considerable impact on pulmonary arterial morphology and hemodynamics.

Keywords

Pneumothorax, Computational Fluid Dynamics, Morphological Analysis, Pulmonary Arteries, Patient-specific Model

Paper information

Jean-Joseph CHRISTOPHE, Takuji ISHIKAWA, Noriaki MATSUKI, Yohsuke IMAI, Kei TAKASE, Marc THIRIET and Takami YAMAGUCHI, “Patient-specific Morphological and Blood Flow Analysis of Pulmonary Artery in the Case of Severe Deformations of the Lung due to Pneumothorax”, Journal of Biomechanical Science and Engineering, Vol. 5, No. 5 (2010), pp.485-498 . doi:10.1299/jbse.5.485

We have performed numerical simulations to examine saccular cerebral aneurysm formation at the outer curve of a bent artery. A U-shaped arterial geometry with torsion, which was modeled on part of the human internal carotid artery, has been employed. A new numerical model was proposed to take into account proliferation as well as degradation of the arterial wall. Proliferation of the arterial wall was modeled by surface area expansion in high wall shear stress region. Based on wall shear stress distribution on the artery, we have investigated aneurysm formation for the following three conditions: (a) strength degradation of the wall, (b) proliferation of the wall, and (c) both strength degradation and proliferation of the wall. A saccular aneurysm shape was not observed when considering only arterial wall degradation up to 90%. However, the saccular shape formed when proliferation of the arterial wall was also taken into consideration. The resultant shape was consistent with clinical observations. Our findings have suggested that a saccular aneurysm may not be formed by degradation of the arterial wall alone, but also require its proliferation.

Keywords

Cerebral Aneurysm, Growth, Modeling, Wall Shear Stress, Numerical Analysis

Paper information

Yuji SHIMOGONYA, Takuji ISHIKAWA, Yohsuke IMAI, Daisuke MORI, Noriaki MATSUKI and Takami YAMAGUCHI, “Formation of Saccular Cerebral Aneurysms May Require Proliferation of the Arterial Wall: Computational Investigation”, Journal of Biomechanical Science and Engineering, Vol. 3, No. 3 (2008), pp.431-442 . doi:10.1299/jbse.3.431

Study of the development of aneurysm is a difficult task due to lack of experimental and clinical data. The current study takes advantage of fluid-structure interaction (FSI) to simulate the formation and growth of aneurysms by focusing on the interplay between the wall shear stress, degeneration of the vessel wall, and the wall deformation. We construct numerical aneurysm models arisen from both straight and curved arteries, under the hypothesis that high local wall shear stress larger than a certain threshold value will lead to a linear decrease in the wall mechanical properties. In the straight model, the growth of aneurysm is small and only at the distal neck region, and the aneurysm stops growing after several steps. In contrast, in the curved model, the aneurysm continues to grow in height and width. Our computer simulation study shows that even if the wall shear stress inside an aneurysm is low, aneurysm development can occur due to degeneration of the wall distal and proximal to the aneurysm. Our study demonstrates the potential utility of rule-based numerical methods in the investigation of developmental biology of cardiovascular diseases.

Keywords

Intracranial Aneurysm, Development, Computer Aided Analysis, Fluid-Structure Interaction, Rule-Based, Wall Shear Stress

Paper information

Yixiang FENG, Shigeo WADA, Takuji ISHIKAWA, Ken-ichi TSUBOTA and Takami YAMAGUCHI, “A Rule-Based Computational Study on the Early Progression of Intracranial Aneurysms Using Fluid-Structure Interaction: Comparison between Straight Model and Curved Model”, Journal of Biomechanical Science and Engineering, Vol. 3, No. 2 (2008), pp.124-137 . doi:10.1299/jbse.3.124

The distribution of wall shear stress (WSS) in arteries is affected by both blood and wall motion. Most studies have ignored wall motion by assuming that the artery wall is rigid. To investigate the influence of wall motion we have solved the coupled fluid-solid problem in a straight homogeneous tube. The inlet boundary condition of the tube was given as a pulse of velocity imposed at the inlet of the tube upon a steady flow of Reynolds number 1000. A commercial code (Radioss, Altair Engineering) was used to solve the fluid-solid interactions. Two kinds of waves are generated on the wall by the pulse imposed in the inlet flow; a wave of longitudinal motion of the wall (the longitudinal wave) and a wave of radial motion of the wall (the elastic wave). The ends of the vessel are assumed to be fixed which results in the reflection of both waves. The longitudinal wall motion reduces the relative speed of the blood, reducing WSS by up to 0.5 Pa. The largest effect of wall motion occurs when the longitudinal and elastic waves coincide, where the peak WSS is reduced by 1.0 Pa, which is a significant fraction of the observed WSS. Thus we can say that the effect of wall motion is important in considering physiological response of arterial wall to the blood flow.

Keywords

Fluid-Solid Interactions, Wall Shear Stress, Wall Motion, Longitudinal Wave, Elastic Wave, Atherosclerosis, Large Artery

Paper information

Tomohiro FUKUI, Kim H. PARKER, Yohsuke IMAI, Ken-ichi TSUBOTA, Takuji ISHIKAWA, Shigeo WADA and Takami YAMAGUCHI, “Effect of Wall Motion on Arterial Wall Shear Stress”, Journal of Biomechanical Science and Engineering, Vol. 2, No. 2 (2007), pp.58-68 . doi:10.1299/jbse.2.58

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Paper information

Takami YAMAGUCHI and Takuji ISHIKAWA, “Preface”, Journal of Biomechanical Science and Engineering, Vol. 2, No. 2 (2007), pp.45-45 . doi:10.1299/jbse.2.45