Session EA: Biofluid Dynamics V: Pumps and Capillary Flows

Properties of the microcirculation in capillary bundles of rat spinotrapezius muscle fascia

Properties of the microcirculation in capillary bundles of rat spinotrapezius muscle fascia are investigated using microscope observations, empirical modeling, and numerical simulations. Capillary bundles consist of a network of feeding arterioles, draining venules, and capillary vessels. A dozen samples of muscle fascia tissue were prepared for microscope observation. The chosen method of preparation allows for the long-term preservation of the tissue samples for future studies. Capillary bundles are photographed under a microscope with 40x magnification. From the images, the microvasculature of the tissue samples is reconstructed. It was found, for example, that the distribution of vessel length in a capillary bundle follows a log-normal law. In addition to a statistical analysis of the vessel data, the network topology is used for numerical simulations of the flow in the capillary bundles. The numerical approach uses a sparse-matrix solver and it considers vessel elasticity and blood rheology. The numerical simulations show, for example, a strong pressure drop across the capillary vessels of the bundle.   

Characterization of the Cell-Free Layer in a Microvessel by Computer Simulation

The cell-free layer between the erythrocyte-rich core of a micro-vessel and the vessel wall is a significant component of the hydrodynamics of the microcirculation. To investigate the mechanics of the cell-free layer, we simulate a two-dimensional periodic blood flow in a microvessel containing numerous erythrocytes, modeled as capsules with elastic shell membranes using the boundary integral method. Cell-cell interactions are mediated with an interaction potential which represents aggregation forces. Our model successfully recreates in-vivo hemodynamic properties such as blunt velocity profile and Fahraeus effect. The cell-free layer has a thickness of order one erythrocyte radius which is consistent with experimental results. To investigate the mechanics of the cell-free layer a number of numerical experiments were conducted, in which the effects of aggregation forces, and lubrication forces are investigated, by varying the aggregation potential, introducing artificial body forces and changing boundary condition.   

Mesoscale simulation of blood flow in microvessels

Computational modeling of blood flow in microvessels (20--500 micron) is a major challenge. Blood in such vessels behaves as a multiphase suspension of deformable particles. Individual red blood cell (RBC), which is highly deformable, must be considered in the model. Multiple cells, often a few thousands in number, must also be considered. We present two dimensional computational simulation of blood flow in 20--300 micron vessels at discharge hematocrit of 10--60 percent taking into consideration the particulate nature of blood and cell deformation. The numerical model is based on the immersed boundary method, and the red blood cells are modeled as liquid capsules. A large RBC population of up to 2500 cells is simulated. Migration of the cells normal to the wall of the vessel and the formation of the cell- free layer are studied. Results on the trajectory and velocity traces of the RBCs are presented. Also presented are the plug flow velocity profile of blood, the apparent viscosity, and the Fahraeus-Lindqvist effect. The computational results are in good agreement with the experimental results of Bishop et al (2001, 2002) and Pries et al (1992).   

Inside Flow of Mosquito's Proboscis

Mosquito has a magnificent pump mechanism which has been never achieved by technology. We want to apply this high performance mechanism to a micro-TAS system which is designed for a daily check of blood to keep a human health. We need a high powered pump similar to a mosquito's sucking blood mechanism and a low-resistance micro channel mimicked a surface of proboscis. The details of mosquito's pump mechanism, however, have not been ascertained yet. Therefore we tried to investigate the mosquito's pump mechanism by measuring the flow due to suction. A visualization of flow was done by a confocal micro-PIV system. We could analyze the velocity vector profile in the proboscis. The velocity distribution in the proboscis is necessary to estimate the friction drag. In the experiment, a live mosquito was fixed on the glass plate and fed nano-particles near the tip of proboscis. We found that the inside flow of proboscis deviate from Hargen-Poisueuille Flow. It indicates that the surface of inside proboscis has unknown fact for the friction drag reduction.   

Reynolds number effects on gill pumping mechanics in mayfly nymphs

Mayfly nymphs have an entirely aquatic life stage in which they frequently inhabit stagnant water. Nymphs have the capability to generate a ventilation current to compensate for the low oxygen level of the water by beating two linear arrays of plate-like gills that typically line the lateral edge of the abdomen. The characteristic Reynolds number associated with the gill motion changes with animal size, varying over a span of Re = 5 to 100 depending on age and species. The assumption that the system maintains optimal energetic efficiency leads to the prediction that animals transition from rowing to flapping mechanisms with increasing Re, while possibly utilizing a squeeze mechanism to a greater extent at lower Re. To investigate this hypothesis, we capture the motion of the gills through 3D imaging to investigate the effect of Reynolds number on the stroke patterns. PIV is utilized to assess flow rates and viscous dissipation. The effectiveness of the ventilation mechanism at each size has important consequences for the range of oxygen levels, and hence the habitat range, that can be tolerated by that size.   

Effects of Chaos in Peristaltic Flows: Towards Biological Applications

One in seven couples in the Western World will have problems conceiving naturally and with the cost of state provided fertility treatment in the United Kingdom being over USD 3Million per annum and a round of treatment paid for privately costing around USD 6000, the desire to understand the mechanisms of infertility is leading to a renewed interest in collaborations between mathematicians and reproductive biologists. Hydrosalpinx is a condition in which the oviduct becomes blocked, fluid filled and dilated. Many women with this condition are infertile and the primary method of treatment is \textit{in vitro fertilisation}, however, it is found that despite the embryo being implanted into the uterus, the hydrosalpinx adversely affects the implantation rate. We shall consider a mathematical model for peristaltic flow with an emphasis towards modelling the fluid flow in the oviducts and the uterus of humans. We shall consider the effects of chaotic behavior on the system and demonstrate that under certain initial conditions trapping regions can be formed and discuss our results with a view towards understanding the effects of hydrosalpinx.   

Large-Amplitude Peristaltic Pumping of a Viscoelastic Fluid

Peristaltic pumping by wave-like musculuar contractions is a fundamental biomechanical mechanism for fluid and material transport, and is used in the esophagus, intestine, oviduct and ureter. ~ While peristaltic pumping of a Newtonian fluid is well understood, in many important applications (as in the fluid dynamics of reproduction) the fluids have non-Newtonian responses. ~Recent work has focused on large wave-length peristalsis of Oldroyd fluids. To study the problem more generally, we have developed a numerical method for simulating an Oldroyd-B fluid coupled to a deforming elastic membrane. ~A MAC grid-based projection method is used for the fluid equations and an immersed boundary method is used for coupling to a Lagrangian elastic representation of the deforming walls. We examine numerically the peristaltic transport of a viscous Oldroyd-B fluid over a range of Weissenberg numbers and peristalsis wave-lengths, and demonstrate fundamentally different and important behavior in the presence of large amplitude, short-wavelength peristalsis. ~We also demonstrate the loss of flow reversibility, and its consequences, due to fluid visco-elasticity.   

Capillary feeding in shorebirds

Certain shorebirds rely on surface tension to draw fluid along their beaks and into their mouths. We here present the results of a combined experimental and theoretical examination of this capillary feeding technique. Particular attention is paid to the importance of beak geometry and chatter. The possible relevance of related capillary transport mechanisms for smaller scale creatures (e.g. insects) is discussed.