Takuji Ishikawa

Hydrodynamic interaction of two swimming model micro-organisms

In order to understand the rheological and transport properties of a suspension of swimming micro-organisms, it is necessary to analyse the fluid-dynamical interaction of pairs of such swimming cells. In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, referred to as a squirmer. The centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). The effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The interaction of two squirmers is calculated analytically for the limits of small and large separations and is also calculated numerically using a boundary-element method. The analytical and the numerical results for the translational–rotational velocities and for the stresslet of two squirmers correspond very well. We sought to generate a database for an interacting pair of squirmers from which one can easily predict the motion of a collection of squirmers. The behaviour of two interacting squirmers is discussed phenomenologically, too. The results for the trajectories of two squirmers show that first the squirmers attract each other, then they change their orientation dramatically when they are in near contact and finally they separate from each other. The effect of bottom-heaviness is considerable. Restricting the trajectories to two dimensions is shown to give misleading results. Some movies of interacting squirmers are available with the online version of the paper.

Can temporal fluctuation in spatial wall shear stress gradient initiate a cerebral aneurysm? A proposed novel hemodynamic index, the gradient oscillatory number (GON).

We propose a new hemodynamic index for the initiation of a cerebral aneurysm, defined by the temporal fluctuations of tension/compression forces acting on endothelial cells. We employed a patient-specific geometry of a human internal carotid artery (ICA) with an aneurysm, and reconstructed the geometry of the ICA before aneurysm formation by artificially removing the aneurysm. We calculated the proposed hemodynamic index and five other hemodynamic indices (wall shear stress (WSS) at peak systole, time-averaged WSS, time-averaged spatial WSS gradient, oscillatory shear index (OSI), and potential aneurysm formation indicator (AFI)) for the geometry before aneurysm formation using a computational fluid dynamics technique. By comparing the distribution of each index at the location of aneurysm formation, we discussed the validity of each. The results showed that only the proposed hemodynamic index had a significant correlation with the location of aneurysm formation. Our findings suggest that the proposed index may be useful as a hemodynamic index for the initiation of cerebral aneurysms.

Red blood cell motions in high-hematocrit blood flowing through a stenosed microchannel

We investigated the behavior of red blood cells (RBCs) in a microchannel with stenosis using a confocal micro-PTV system. Individual trajectories of RBCs in a concentrated suspension of up to 20% hematocrit (Hct) were measured successfully. Results indicated that the trajectories of healthy RBCs became asymmetric before and after the stenosis, while the trajectories of tracer particles in pure water were almost symmetric. The asymmetry was greater in 10% Hct than in 20% Hct. We also investigated the effect of deformability of RBCs on the cell-free layer thickness by hardening RBCs using a glutaraldehyde treatment. The results indicated that deformability is the key factor in the asymmetry of cell-free layer thickness. Therefore, the motions of RBCs are influenced strongly by the Hct, the deformability, and the channel geometry. These results give fundamental knowledge for a better understanding of blood flow in microcirculation and biomedical microdevices.

Measurement of individual red blood cell motions under high hematocrit conditions using a confocal micro-PTV system.

Developments in optical experimental techniques have helped in elucidating how blood flows through microvessels. Although initial developments were encouraging, studies on the flow properties of blood in microcirculation have been limited by several technical factors, such as poor spatial resolution and difficulty obtaining quantitative detailed measurements at such small scales. Recent advances in computing, microscopy, and digital image processing techniques have made it possible to combine a particle tracking velocimetry (PTV) system with a confocal microscope. We document the development of a confocal micro-PTV measurement system for capturing the dynamic flow behavior of red blood cells (RBCs) in concentrated suspensions. Measurements were performed at several depths through 100-μm glass capillaries. The confocal micro-PTV system was able to detect both translational and rotational motions of individual RBCs flowing in concentrated suspensions. Our results provide evidence that RBCs in dilute suspensions (3% hematocrit) tended to follow approximately linear trajectories, whereas RBCs in concentrated suspensions (20% hematocrit) exhibited transversal displacements of about 2% from the original path. Direct and quantitative measurements indicated that the plasma layer appeared to enhance the fluctuations in RBC trajectories owing to decreased obstruction in transversal movements caused by other RBCs. Using optical sectioning and subsequent image contrast and resolution enhancement, the system provides previously unobtainable information on the motion of RBCs, including the trajectories of two or more RBCs interacting in the same focal plane and RBC dispersion coefficients in different focal planes.

Interaction of two swimming Paramecia

SUMMARY The interaction between two swimming Paramecium caudatum was investigated experimentally. Cell motion was restricted between flat plates, and avoiding and escape reactions were observed, as well as hydrodynamic interactions. The results showed that changes in direction between two swimming cells were induced mainly by hydrodynamic forces and that the biological reaction was a minor factor. Numerical simulations were also performed using a boundary element method. P. caudatum was modelled as a rigid spheroid with surface tangential velocity measured by a particle image velocimetry (PIV) technique. Hydrodynamic interactions observed in the experiment agreed well with the numerical simulations, so we can conclude that the present cell model is appropriate for describing the motion of P. caudatum.

The rheology of a semi-dilute suspension of swimming model micro-organisms

The rheological properties of a cell suspension may play an important role in the flow field generated by populations of swimming micro-organisms (e.g. in bioconvection). In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). Effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The three-dimensional movement of 64 identical squirmers in a simple shear flow field, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The computation utilizes a database of pairwise interactions that has been constructed by the boundary element method. The restriction to pairwise additivity of forces is expected to be justified if the suspension is semi-dilute. The results for non-bottom-heavy squirmers show that the squirming does not have a direct influence on the apparent viscosity. However, it does change the probability density in configuration space, and thereby causes a slight decrease in the apparent viscosity at O(c 2 ), where c is the volume fraction of spheres. In the case of bottom-heavy squirmers, on the other hand, the stresslet generated by the squirming motion directly contributes to the bulk stress at O(c), and the suspension shows strong non-Newtonian properties. When the background simple shear flow is directed vertically, the apparent viscosity of the semi-dilute suspension of bottom-heavy squirmers becomes smaller than that of inert spheres. When the shear flow is horizontal and varies with the vertical coordinate, on the other hand, the apparent viscosity becomes larger than that of inert spheres. In addition, significant normal stress differences appear for all relative orientations of gravity and the shear flow, in the case of bottom-heavy squirmers.

Modeling of hemodynamics arising from malaria infection

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.

Asymmetry of red blood cell motions in a microchannel with a diverging and converging bifurcation

In microcirculation, red blood cells (RBCs) flowing through bifurcations may deform considerably due to combination of different phenomena that happen at the micro-scale level, such as: attraction effect, high shear, and extensional stress, all of which may influence the rheological properties and flow behavior of blood. Thus, it is important to investigate in detail the behavior of blood flow occurring at both bifurcations and confluences. In the present paper, by using a micro-PTV system, we investigated the variations of velocity profiles of two working fluids flowing through diverging and converging bifurcations, human red blood cells suspended in dextran 40 with about 14% of hematocrit level (14 Hct) and pure water seeded with fluorescent trace particles. All the measurements were performed in the center plane of rectangular microchannels using a constant flow rate of about 3.0 × 10(-12) m(3)/s. Moreover, the experimental data was compared with numerical results obtained for Newtonian incompressible fluid. The behavior of RBCs was asymmetric at the divergent and convergent side of the geometry, whereas the velocities of tracer particles suspended in pure water were symmetric and well described by numerical simulation. The formation of a red cell-depleted zone immediately downstream of the apex of the converging bifurcation was observed and its effect on velocity profiles of RBCs flow has been investigated. Conversely, a cell-depleted region was not formed around the apex of the diverging bifurcation and as a result the adhesion of RBCs to the wall surface was enhanced in this region.

Radial dispersion of red blood cells in blood flowing through glass capillaries: the role of hematocrit and geometry

The flow properties of blood in the microcirculation depend strongly on the hematocrit (Hct), microvessel geometry, and cell properties. Previous in vitro studies have measured the radial displacement of red blood cells (RBCs) at concentrated suspensions using conventional microscopes. However, to measure the RBCs motion they used transparent suspensions of ghost red cells, which may have different physical properties than normal RBCs. The present study introduces a new approach (confocal micro-PTV) to measure the motion of labeled RBCs flowing in concentrated suspensions of normal RBCs. The ability of confocal systems to obtain thin in-focus planes allowed us to measure the radial position of individual RBCs accurately and to consequently measure the interaction between multiple labeled RBCs. All the measurements were performed in the center plane of both 50 and 100 microm glass capillaries at Reynolds numbers (Re) from 0.003 to 0.005 using Hcts from 2% to 35%. To quantify the motion and interaction of multiple RBCs, we used the RBC radial dispersion (D(yy)). Our results clearly demonstrate that D(yy) strongly depends on the Hct. The RBCs exhibited higher D(yy) at radial positions between 0.4 and 0.8R and lower D(yy) at locations adjacent to the wall (0.8-1R) and around the middle of the capillary (0-0.2R). The present work also demonstrates that D(yy) tends to decrease with a decrease in the diameter. The information provided by this study not only complements previous investigations on microhemorheology of both dilute and concentrated suspensions of RBCs, but also shows the influence of both Hct and geometry on the radial dispersion of RBCs. This information is important for a better understanding of blood mass transport mechanisms under both physiological and pathological conditions.

Suspension biomechanics of swimming microbes

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.