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Microbial flora in the intestine has been thoroughly investigated, as it plays an important role in the health of the host. Jemielita et al. (2014) showed experimentally that Aeromonas bacteria in the intestine of zebrafish larvae have a heterogeneous spatial distribution. Although bacterial aggregation is important biologically and clinically, there is no mathematical model describing the phenomenon and its mechanism remains largely unknown. In this study, we developed a computational model to describe the heterogeneous distribution of bacteria in the intestine of zebrafish larvae. The results showed that biological taxis could cause the bacterial aggregation. Intestinal peristalsis had the effect of reducing bacterial aggregation through mixing function. Using a scaling argument, we showed that the taxis velocity of bacteria must be larger than the sum of the diffusive velocity and background bulk flow velocity to induce bacterial aggregation. Our model and findings will be useful to further the scientific understanding of intestinal microbial flora., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

An important habit of ciliates, namely, their behavioral preference for walls, is revealed through experiments and hydrodynamic simulations. A simple mechanical response of individual ciliary beating (i.e., the beating is stalled by the cilium contacting a wall) can solely determine the sliding motion of the ciliate along the wall and result in a wall-preferring behavior. Considering ciliate ethology, this mechanosensing system is likely an advantage in the single cell's ability to locate nutrition. In other words, ciliates can skillfully use both the sliding motion to feed on a surface and the traveling motion in bulk water to locate new surfaces according to the single "swimming" mission., Competing Interests: The authors declare no conflict of interest., (Copyright © 2018 the Author(s). Published by PNAS.)

To gain insight into the nature of biological synchronization at the microscopic scale, we here investigate the hydrodynamic synchronization between conically rotating objects termed nodal cilia. A mechanical model of three rotating cilia is proposed with consideration of variation in their shapes and geometrical arrangement. We conduct numerical estimations of both near-field and far-field hydrodynamic interactions, and we apply a conventional averaging method for weakly coupled oscillators. In the nonidentical case, the three cilia showed stable locked-phase differences around ±π/2. However, such phase locking also occurred with three identical cilia when allocated in a triangle except for the equilateral triangle. The effects of inhomogeneity in cilia shapes and geometrical arrangement on such asymmetric interaction is discussed to understand the role of biological variation in synchronization via hydrodynamic interactions.

Due to its transparency, the intestine of zebrafish larvae has been widely used in studies of gastrointestinal diseases and the microbial flora of the gut. However, transport phenomena in the intestine of zebrafish larvae have not been fully clarified. In this study, therefore, transport caused by peristaltic motion in the intestine of zebrafish larvae was investigated by numerical simulation. An anatomically realistic three-dimensional geometric model of the intestine at various times after feeding was constructed based on the experimental data of Field et al. (2009). The flow of digested chyme was analyzed using the governing equations of fluid mechanics, together with peristaltic motion and long-term contraction of the intestinal wall. The results showed that retrograde peristaltic motion was the main contributor to the mixing function. The dispersion caused by peristalsis over 30min was in the order of 10 -12 m 2 /s, which is greater than the Brownian diffusion of a sphere of 0.4µm diameter. In contrast, anterograde peristaltic motion contributed mainly to the pumping function. The pressure decrease due to peristalsis was in the order of millipascals, which may reduce the activation and maintenance heat of intestinal muscle. These findings enhance our understanding of the mixing and pumping functions of the intestine of zebrafish larvae., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

Mucous flow in a tracheal lumen is generated by the beat motion of ciliated cells to provide a clearance function by discharging harmful dust particles and viruses. Due to its physiological importance, the cilia-generated flow and the rheological properties of mucus have been investigated intensively. The effects of viscosity on the cilia-generated flow, however, have not been fully clarified. In this study, we measured bulk background velocity of ciliary flow using a micro particle tracking velocimetry method under various viscosity conditions in mice. The results showed that the flow velocity decreased as the increase with viscosity of ambient fluid. Moreover, no previous study has clarified the pump power generated by cilia, which provides important information with regard to understanding the molecular motor properties of cilia. Measurements of both the ciliary flow and the ciliary motion were conducted to determine the cilia pump power. Our results indicated that the cilia pump during the effective stroke did not drive the ciliary flow efficiently under high viscosity conditions; these findings are necessary to resolve the clearance function.

In the past decade, numerical methods for the computational biomechanics of blood flow have progressed to overcome difficulties in diverse applications from cellular to organ scales. Such numerical methods may be classified by the type of computational mesh used for the fluid domain, into fixed mesh methods, moving mesh (boundary-fitted mesh) methods, and mesh-free methods. The type of computational mesh used is closely related to the characteristics of each method. We herein provide an overview of numerical methods recently used to simulate blood flow at macro and micro scales, with a focus on computational meshes. We also discuss recent progress in the multi-scale modeling of blood flow., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

Mammalian sperm cells are required to swim over long distances, typically around 1000-fold their own length. They must orient themselves and maintain a swimming motion to reach the ovum, or egg cell. Although the mechanism of long-distance navigation is still unclear, one possible mechanism, rheotaxis, was reported recently. This work investigates the mechanism of the rheotaxis in detail by simulating the motions of a sperm cell in shear flow adjacent to a flat surface. A phase diagram was developed to show the sperm's swimming motion under different shear rates, and for varying flagellum waveform conditions. The results showed that, under shear flow, the sperm is able to hydrodynamically change its swimming direction, allowing it to swim upwards against the flow, which suggests that the upward swimming of sperm cells can be explained using fluid mechanics, and this can then be used to further understand physiology of sperm cell navigation.

Quantifying the behavior of circulating tumor cells (CTCs) in the blood stream is of fundamental importance for understanding metastasis. Here, we investigate the flow mode and velocity of CTCs interacting with red blood cells (RBCs) in various sized microvessels. The flow of leukocytes in microvessels has been described previously; a leukocyte forms a train with RBCs in small microvessels and exhibits margination in large microvessels. Important differences in the physical properties of leukocytes and CTCs result from size. The dimensions of leukocytes are similar to those of RBCs, but CTCs are significantly larger. We investigate numerically the size effects on the flow mode and the cell velocity, and we identify similarities and differences between leukocytes and CTCs. We find that a transition from train formation to margination occurs when (R-a)/t(R)≈1, where R is the vessel radius, a is the cell radius, and t(R) is the thickness of RBCs, but that the motion of RBCs differs from the case of leukocytes. Our results also show that the velocities of CTCs and leukocytes are larger than the average blood velocity, but only CTCs move faster than RBCs for microvessels of R/a≈1.5-2.0. These findings are expected to be useful not only for understanding metastasis, but also for developing microfluidic devices.

Although diffusion properties of a suspension of swimming microorganisms in equilibrium have been studied intensively, those under nonequilibrium conditions remain unclear. In this study, we investigate the spreading of model microorganisms from high concentration to low by the Stokesian dynamics method. The results reveal that the spreading is neither purely diffusive nor ballistic. When the dipole component of the swimming velocity is small, the cells actively direct themselves towards lower concentrations. The concentration distribution shows stronger oscillations than would be expected for ballistic swimmers with constant orientations. The mechanism can be explained by the near-field hydrodynamic interactions between cells and the spatial gradient of the collision rate. Comparison of the numerical results with a simple continuum model and a Monte Carlo simulation shows that those conventional models can capture the basic features of the present results. These new findings pave the way towards a mathematical description of the dispersion of microorganisms in various environments.

It is known that some kinds of bacteria swim by forming a bundle of their multiple flagella. However, the details of flagella synchronization as well as the swimming efficiency of such bacteria have not been fully understood. In this study, swimming of multiflagellated bacteria is investigated numerically by the boundary element method. We assume that the cell body is a rigid ellipsoid and the flagella are rigid helices suspended on flexible hooks. Motors apply constant torque to the hooks, rotating the flagella either clockwise or counterclockwise. Rotating all flagella clockwise, bundling of all flagella is observed in every simulated case. It is demonstrated that the counter rotation of the body speeds up the bundling process. During this procedure the flagella synchronize due to hydrodynamic interactions. Moreover, the results illustrated that during running the multiflagellated bacterium shows higher propulsive efficiency (distance traveled per one flagellar rotation) over a bacterium with a single thick helix. With an increasing number of flagella the propulsive efficiency increases, whereas the energetic efficiency decreases, which indicates that efficiency is something multiflagellated bacteria are assigning less priority to than to motility. These findings form a fundamental basis in understanding bacterial physiology and metabolism.

Although we inhale air that contains many harmful substances, including, for example, dust and viruses, these small particles are trapped on the surface of the tracheal lumen and transported towards the larynx by cilia-generated flow. The transport phenomena are affected not only by the time- and space-average flow field but also by the fluctuation of the flow. Because flow fluctuation has received little attention, we investigated it experimentally in mice. To understand the origin of flow fluctuation, we first measured the distribution of ciliated cells in the trachea and individual ciliary motions. We then measured the detailed flow field using a confocal micro-PTV system. Strong flow fluctuations were observed, caused by the unsteadiness of the ciliary beat and the spatial inhomogeneity of ciliated cells. The spreading of particles relative to the bulk motion became diffusive if the time scale was sufficiently larger than the beat period. Finally, we quantified the effects of flow fluctuation on bulk flow by evaluating the Peclet number of the system, which indicated that the directional transport was an order of magnitude larger than the isotropic diffusion. These results are important in understanding transport phenomena in the airways on a cellular scale.

Rotational movement of mouse node cilia generates leftward fluid flow in the node cavity, playing an important role in left-right determination in the embryo. Although rotation of numerous cilia was believed necessary to trigger the determination, recent reports indicate the action of two cilia to be sufficient. We examine cooperative cilia movement via hydrodynamic interaction. Results show cilia to be cooperative, having phases locked in a certain relation; a system with a pair of nonidentical cilia can achieve phase-locked states more easily than one with a pair of identical cilia.

Rotational movement of isolated single cilia in mice embryo was investigated, which generates leftward fluid flow in the node cavity and plays an important role in left-right determination. The leftward unidirectional flow results from tilting of the rotational axis of the cilium to the posterior side. By combining computational fluid dynamics with experimental observations, we demonstrate that the leftward stroke can be more effective than expected for cases in which cilia tilting alone is considered with the no-slip condition under constant driving torque. Our results suggest that the driving torque is asymmetric.

Flow-induced membrane tension contributes to the release of molecules by red blood cells (RBCs), and extremely high tension may cause haemolysis. Here, we investigated the membrane tension of RBCs during pairwise interactions in simple shear flow, given that pairwise interactions form the basis of many-body interactions. RBCs were modelled as capsules with a two-dimensional hyperelastic membrane, and large deformations were solved by the finite element method. Due to the small size of the RBCs, surrounding fluid motion was estimated as a Stokes flow and solved by the boundary element method. The results showed that the maximum isotropic tension appeared around the dimple of the biconcave surface and not around the rim. A comparison of the results with solitary cases indicated that the maximum principal tension and isotropic tension were significantly increased by cell-cell interaction effects. As the volume fraction of RBCs is large under physiological conditions, as well as in blood flow in vitro, cell-cell interactions must be analysed carefully when considering mechanotransduction and haemolysis in blood flow., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Previous studies investigating thrombus formation have not focused on the physical interaction between red blood cells (RBCs) and thrombus, although they have been speculated that some pathological conditions such as microangiopathic hemolytic anemia (MAHA) stem from interactions between RBCs and thrombi. In this study, we investigated the mechanical influence of RBCs on primary thrombi during hemostasis. We also explored the mechanics and aggravating factors of intravascular hemolysis. Computer simulations of primary thrombogenesis in the presence and the absence of RBCs demonstrated that RBCs are unlikely to affect the thrombus height and coverage, although their presence may change microvessel hemodynamics and platelet transportation to the injured wall. Our results suggest that intravascular hemolysis owing to RBC membrane damage would be promoted by three hemodynamic factors: (1) dispersibility of platelet thrombi, because more frequent spatial thrombus formation decreases the time available for an RBC to recover its shape and enforces more severe deformation; (2) platelet thrombus stiffness, because a stiffer thrombus increases the degree of RBC deformation upon collision; and (3) vessel size and hemocyte density, because a smaller vessel diameter and higher hemocyte density decrease the room for RBCs to escape as they come closer to a thrombus, thereby enhancing thrombus-RBC interactions., (Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.)

We investigated how breath holding increases the deposition of micrometer particles in pulmonary airways, compared with the deposition during inhalation period. A subject-specific airway model with up to thirteenth generation airways was constructed from multi-slice CT images. Airflow and particle transport were simulated by using GPU computing. Results indicate that breath holding effectively increases the deposition of 5μm particles for third to sixth generation (G3-G6) airways. After 10s of breath holding, the particle deposition fraction increased more than 5 times for 5μm particles. Due to a small terminal velocity, 1μm particles only showed a 50% increase in the most efficient case. On the other hand, 10μm particles showed almost complete deposition due to high inertia and high terminal velocity, leading to an increase of 2 times for G3-G6 airways. An effective breath holding time for 5μm particle deposition in G3-G6 airways was estimated to be 4-6s, for which the deposition amount reached 75% of the final deposition amount after 10s of breath holding., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

The study of pair-wise interactions between swimming microorganisms is fundamental to the understanding of the rheological and transport properties of semi-dilute suspensions. In this paper, the hydrodynamic interaction of two ciliated microorganisms is investigated numerically using a boundary-element method, and the microorganisms are modeled as spherical squirmers that swim by time-dependent surface deformations. The results show that the inclusion of the unsteady terms in the ciliary propulsion model has a large impact on the trajectories of the interacting cells, and causes a significant change in scattering angles with potential important consequences on the diffusion properties of semi-dilute suspensions. Furthermore, the analysis of the shear stress acting on the surface of the microorganisms revealed that the duration and the intensity of the near-field interaction are significantly modified by the presence of unsteadiness. This observation may account for the hydrodynamic nature of randomness in some biological reactions, and supersedes the distinction between intrinsic randomness and hydrodynamic interactions, adding a further element to the understanding and modeling of interacting microorganisms., (Copyright © 2010 Elsevier Ltd. All rights reserved.)

The near-surface motility of bacteria is important in the initial formation of biofilms and in many biomedical applications. The swimming motion of Escherichia coli near a solid surface is investigated both numerically and experimentally. A boundary element method is used to predict the hydrodynamic entrapment of E. coli bacteria, their trajectories, and the minimum separation of the cell from the surface. The numerical results show the existence of a stable swimming distance from the boundary that depends only on the shape of the cell body and the flagellum. The experimental validation of the numerical approach allows one to use the numerical method as a predictive tool to estimate with reasonable accuracy the near-wall motility of swimming bacteria of known geometry. The analysis of the numerical database demonstrated the existence of a correlation between the radius of curvature of the near-wall circular trajectory and the separation gap. Such correlation allows an indirect estimation of either of the two quantities by a direct measure of the other without prior knowledge of the cell geometry. This result may prove extremely important in those biomedical and technical applications in which the near-wall behavior of bacteria is of fundamental importance.

We calculate non-Brownian fluid particle diffusion in a semidilute suspension of swimming micro-organisms. Each micro-organism is modeled as a spherical squirmer, and their motions in an infinite suspension otherwise at rest are computed by the Stokesian-dynamics method. In calculating the fluid particle motions, we propose a numerical method based on a combination of the boundary element technique and Stokesian dynamics. We present details of the numerical method and examine its accuracy. The limitation of semidiluteness is required to ensure accuracy of the fluid particle velocity calculation. In the case of a suspension of non-bottom-heavy squirmers the spreading of fluid particles becomes diffusive in a shorter time than that of the squirmers, and the diffusivity of fluid particles is smaller than that of squirmers. It is confirmed that the probability density distribution of fluid particles also shows diffusive properties. The effect of tracer particle size is investigated by inserting some inert spheres of the same radius as the squirmers, instead of fluid particles, into the suspension. The diffusivity for inert spheres is not less than one tenth of that for fluid particles, even though the particle size is totally different. Scaling analysis indicates that the diffusivity of fluid particles and inert spheres becomes proportional to the volume fraction of squirmers in the semidilute regime provided that there is no more than a small recirculation region around a squirmer, which is confirmed numerically. In the case of a suspension of bottom-heavy squirmers, horizontal diffusivity decreases considerably even with small values of the bottom heaviness, which indicates the importance of bottom heaviness in the diffusion phenomena. We believe that these fundamental findings will enhance our understanding of the basic mechanics of a suspension of swimming micro-organisms.

We propose a numerical model of hemodynamics arising from malaria infection. This model is based on a particle method, where all the components of blood are represented by the finite number of particles. A two-dimensional spring network of membrane particles is employed for expressing the deformation of malaria infected red blood cells (IRBCs). Malaria parasite within the IRBC is modeled as a rigid object. This model is applied to the stretching of IRBCs by optical tweezers, the deformation of IRBCs in shear flow, and the occlusion of narrow channels by IRBCs. We also investigate the effects of IRBCs on the rheological property of blood in micro-channels. Our results indicate that apparent viscosity is drastically increased for the period from the ring stage and the trophozoite stage, whereas it is not altered in the early stage of infection., (Copyright 2010 Elsevier Ltd. All rights reserved.)

Micro-organisms play a vital role in many biological, medical and engineering phenomena. Some recent research efforts have demonstrated the importance of biomechanics in understanding certain aspects of micro-organism behaviours such as locomotion and collective motions of cells. In particular, spatio-temporal coherent structures found in a bacterial suspension have been the focus of many research studies over the last few years. Recent studies have shown that macroscopic properties of a suspension, such as rheology and diffusion, are strongly affected by meso-scale flow structures generated by swimming microbes. Since the meso-scale flow structures are strongly affected by the interactions between microbes, a bottom-up strategy, i.e. from a cellular level to a continuum suspension level, represents the natural approach to the study of a suspension of swimming microbes. In this paper, we first provide a summary of existing biomechanical research on interactions between a pair of swimming micro-organisms, as a two-body interaction is the simplest many-body interaction. We show that interactions between two nearby swimming micro-organisms are described well by existing mathematical models. Then, collective motions formed by a group of swimming micro-organisms are discussed. We show that some collective motions of micro-organisms, such as coherent structures of bacterial suspensions, are satisfactorily explained by fluid dynamics. Lastly, we discuss how macroscopic suspension properties are changed by the microscopic characteristics of the cell suspension. The fundamental knowledge we present will be useful in obtaining a better understanding of the behaviour of micro-organisms.