Session GL: Biofluids: Physiological Circulatory I

Stability of two-dimensional collapsible-channel flow to inviscid perturbations

We consider the linear stability of two-dimensional inviscid but vortical flow in a rigid, parallel-sided channel, of which part of one wall has been replaced by a flexible membrane under longitudinal tension $T$. Far upstream the flow is parallel Poiseuille flow; the width of the channel is $a$ and the length of the membrane is $\lambda a$, where $\lambda \gg 1$. Steady flow at high Reynolds number $Re$ was studied using interactive boundary-layer theory by Guneratne \& Pedley (J. Fluid Mech. \textbf{569}, 151-184, 2006) for various values of the pressure difference $P_e$ across the membrane at its upstream end. Here we study small-amplitude, unsteady perturbations to the trivial steady solution for $P_e = 0$. An unexpected finding is that the flow is always unstable, with a growth rate that increases with $T$. In other words, the stability problem is ill-posed. However, when the pressure difference is held fixed (= 0) at the downstream end of the membrane, the problem is well-posed and all solutions are stable. The physical mechanisms underlying these findings are explored; the crucial factor in the fluid dynamics is the vorticity gradient across the incoming Poiseuille flow. Similar results are found for the viscous problem at high $Re$.   

Non-homogeneous concentration of suspensions in micro-capillary networks: particles in a bifurcation

We investigate the distribution of particles in flows of dilute suspensions in bifurcating channels. In studies relevant to blood flow in the microcirculation, an increase of the volume fraction of particles (hematocrit) in the high flow rate branch is usually observed, leading to non-uniform concentrations in a network of channels, with possible consequences on oxygen transport and pressure distribution. In the literature, this phenomenon is often wrongly interpreted as the result of some attraction of the particles towards this high flow rate branch. We show thanks to experiments and numerical simulations that the concentration phenomenon, often referred to as Zweifach-Fung effect, is mainly due to the non-homogeneous spatial distribution of particles in the mother branch, while a weak attraction towards the low flow rate branch occurs in the bifurcation.   

A dynamic model of human physiology

To study the systems-level transport in the human body, we develop the Computational Man (CMAN): a set of one-dimensional unsteady elastic flow simulations created to model a variety of coupled physiological systems including the circulatory, respiratory, excretory, and lymphatic systems. The model systems are collapsed from three spatial dimensions and time to one spatial dimension and time by assuming axisymmetric vessel geometry and a parabolic velocity profile across the cylindrical vessels. To model the actions of a beating heart or expanding lungs, the flow is driven by user-defined changes to the equilibrium areas of the elastic vessels. The equations are then iteratively solved for pressure, area, and average velocity. The model is augmented with valves and contractions to resemble the biological structure of the different systems. CMAN will be used to track material transport throughout the human body for diagnostic and predictive purposes. Parameters will be adjustable to match those of individual patients. Validation of CMAN has used both higher-dimensional simulations of similar geometries and benchmark measurement from medical literature.   

Optimization of a BT-Shunt Geometry for the Norwood Operation

In this study, we present initial results of BT-shunt shape- parameterization and optimization using an automated approach that links optimization to a 3-D custom finite element flow solver. Shape optimization is performed using an efficient derivative-free optimization method called the surrogate management framework (SMF). Two objective functions are developed and tested: first to minimize energy-dissipation, and second to combine oxygen delivery and energy dissipation. Preliminary results suggest that a smooth bifurcation at the BA end with a shunt perpendicular to the PA is the best geometry to minimize energy dissipation, and that the inclusion of an oxygen delivery term in the objective function improved the ratio of systemic to pulmonary blood flow. To better account for global changes in the heart and circulatory system due to changes in shunt geometry, we have implemented a multiscale modeling approach that couples a 0-D lumped parameter network to the 3D flow solver. Initial results of this coupling using idealized geometries demonstrate its stability. Application to the BT shunt problem and design implications will be discussed.   

Particulate Tracer Sensors for X-ray Flow Imaging

Monitoring opaque biological fluid flows is essential to understand the biophysics of biofluids explaining dynamic life phenomenon and basic metabolic mechanisms. Quantitative information on fluid flows also enables to detect and treat the circulatory diseases related with abnormal blood/body fluid flows. In this study, to enhance the imaging efficiency in biological system, various biocompatible micro-/nano-scale tracer particles are developed as X-ray contrast-enhancing flow sensors. The size and shape of the designed flow sensors are optimized in terms of the delivery efficiency and the contrast enhancement in synchrotron X-ray imaging. The controlled physical properties are observed to significantly influence on the flow tracing ability and the contrast enhancement depending on the systems to be studied.   

Magnetic Localization of Maghemite Nanoparticles in Simulated Blood Vessels for Focused Therapy

Magnetic nanoparticles (MNPs) can easily be administered to patients intravenously for use in therapies such as hyperthermia or localized drug delivery. The MNPs are collected within the blood vessel by an externally applied magnet. The capture of maghemite nanoparticles was studied in blood vessels as a function of fluid velocity, vessel diameter, magnetic field strength and fluid viscosity. Nanoparticles were captured most easily in small blood vessels with applications of higher magnetic fields. Higher viscosity fluids cause a reduction in the effective capture of nanoparticles. By studying localization in water and simulated blood plasma, the importance of studying flow behavior in complex fluids for further development of medical therapies is evident.   

Numerical simulation of the motion of superparamagnetic nanoparticle clusters in a pressure-driven channel flow with an external magnet

The motion of a superparamagnetic hydrophobic ferrofluid cluster suspended in a viscous fluid undergoing pressure-driven channel flow is addressed, as a model for magnetic drug targeting through blood vessels. An external magnetic field is applied in order to attract the cluster toward a prescribed target. The transit time is obtained numerically and assessed for the influence of the background flow, cluster size, magnetic field strength and Brownian motion. We derive simplified estimates for the achievement of optimal capture rates in terms of the properties of the magnet and cluster size.   

Blood flow and blood cell interactions and migration in microvessels

Blood flow in microcirculation plays a fundamental role in a wide range of physiological processes and pathologies in the organism. To understand and, if necessary, manipulate the course of these processes it is essential to investigate blood flow under realistic conditions including deformability of blood cells, their interactions, and behavior in the complex microvascular network which is characteristic for the microcirculation. We employ the Dissipative Particle Dynamics method to model blood as a suspension of deformable cells represented by a viscoelastic spring-network which incorporates appropriate mechanical and rheological cell-membrane properties. Blood flow is investigated in idealized (e.g., channels, tubes) and complex (e.g., expansions, bifurcations) geometries. In particular, migration of blood cells and their distribution in blood flow are studied with respect to various conditions such as hematocrit, flow rate, red blood cell aggregation, and vessel geometry. Physical mechanisms which govern cell migration in microcirculation and, in particular, margination of white blood cells towards the vessel wall, will be discussed. In addition, we characterize blood flow dynamics and quantify hemodynamic resistance in the microvascular network.   

Hydrodynamic forces on a wall-bound leukocyte in small vessels due to red cells

As part of the inflammation response, white blood cells (leukocytes) bind to the vessel wall before they transmigrate across the endothelium. The interactions between the wall-adhered leukocyte and flowing red blood cells (erythrocytes) play a critical role in this process. We provide a quantitative investigation of the forces exerted on a wall-bound leukocyte using a simulation tool that is based on a fast $O(N \log N)$ boundary integral formulation. This permits simulations of red cells that are both realistically flexible and can approach to very close separation distances. The elastic membranes deform substantially but strongly resist surface dilatation. The no-slip condition is enforced both on the leukocyte and the round vessel walls. Vessel diameters from 10 to 20 microns are studied. At these scales the cellular-particulate nature of blood significantly affects the magnitude of the forces that the leukocyte experiences. For a tube hematocrit (cell volume fraction) of 25$\%$ and a spherical protrusion with a diameter 0.75 times that of the tube, the average forces are increased by about 40$\%$ and the local forces by more than 100$\%$ relative to those expected for a blood model homogenized by its effective viscosity. For a constant pressure gradient, the wall-bound leukocyte causes a blockage in the vessel. Different contact angles for the leukocyte as well as different mechanical properties for the erythrocytes are examined.   

Evaluation of RBC aggregation using synchrotron X-ray speckles

When a coherent beam illuminates spatially-disordered particles, speckles are usually generated by the inference of the scattered light waves. The speckle has been known to contain the information of the objects under near-field condition. In this study, we hypothesized that the speckle patterns of the red blood cells are related to the aggregation shape and the size of RBCs in the medium. The speckle patterns of RBCs in static condition were investigated by transmitting the monochromatic synchrotron X-ray beam to the sample with varying hematocrit(10-80 {\%}) and medium type(phosphate buffered saline, autologous plasma and 0.75 {\%} polyvinylpyrrolidone 360 in phosphate buffered saline). The temporal variation of speckle patterns after sudden removal of shear rate was observed by stopping the blood flow in a tube. The size of aggregated RBCs is closely correlated with the characteristic features of the speckle patterns.