Proposal Number: 0625936 Principal Investigator: Bagchi, Prosenjit Affiliation: Rutgers University New Brunswick Proposal Title: Mechanics of Blood Flow in Microvessels
Intellectual Merit:
The proposed modeling work includes the impacts of cell aggregation, white blood cell interactions, complex flow geometry and multi-particle hydrodynamics. The focus will be on modeling red blood cell aggregation and solid-liquid suspensions to include other physics of interest in red blood cell transport. The work will address an issue of significant interdisciplinary interest in modeling multiple physical forces on cells treated as membrane encapsulated viscous liquids, with red blood cells being the cell of interest. The application of existing immersed boundary methods combined with direct numerical simulation has been done but the application to the problem of red blood cell transport in capillaries is novel. The simulations will be multi-scale, fully three dimensional, unsteady and their dynamic deformation will be accurately resolved. Molecular interaction between adjacent cells and between cell and vessel wall will also be modeled by a kinetic approach, and be coupled to the hydrodynamics.
Broader Impact:
The proposal has the potential to increase the understanding of human physiology, microfluidic transport of cells and biotechnology applications involving cell transport, and as such could broadly impact society. A program of educational integration of the research is provided including interaction with an undergraduate research program and undergraduate and graduate courses. The research will be disseminated through publication in journals and conferences and underrepresented minorities will be recruited into the research.
We have a developed high-fidelity three-dimensional computational methodology to study various aspects of cellular transport in microcirculation. Of particular interest is the understanding of the flow-induced deformation and dynamics of red blood cells, and their variants, namely, the capsules and vesicles, and the dynamics and rheology of cellular suspension. It has been well known that the red blood cells are highly deformable particles. The deformability arises due to liquid-like nature of the fluid interior to the cell, and the elasticity of the membrane. The intellectual merit of this project is the development of a 3D computational method to solve the complex non-linear equations of motion govering the flow of cytoskeletal fluid interior of the cells, and the suspending fluid, and coupling the flow field with the deformation of the cell membrane via an immersed-boundary method. The flow field is solved using finite-difference/Fourier transform method, and the membrane deformation is solved using a finite-element method. A continuum scale model for the cell membrane has been implemented: it includes the resistance to shear deformation, area dilatation, and bending. The code is parallelized to run on multiple processors. Using the code we have addressed a range of problems: from the dynamics of individual capsules and red blood cell to rheology of cell suspension under dense conditions. As our first topic, we have studied the coupling between deformation and orientation dynamics of nonspherical capsules (Bagchi and Kalluri, PRE 2009). We have simulated tank-treading, tumbling, and swinging dynamics of capsules in shear flow. Here we found that the deformation oscillates with time along with the angular oscillation, and becomes maximum at an intermediate shear rate and viscosity ratio. This result suggests that for a red blood cell the deformation oscillation is expected to be maximum for intermediate shear rate and viscosity raito, i.e., at the border between the transition between tank-treading and tumbling. We then extend this work to cosider rheology of dense suspension of capsules (Bagchi and Kalluri, PRE, 2010), and found that the suspension exhibits a shear viscosity minimum at an intermediate viscosity ratio. We also found that the shear viscosity minimu is independent of whether the capsule is in the tank-treading or tumbling mode. We investigated the origin of the shear viscosity monimum, and found that it is due to the opposite trend of the rheological contributions of the membrane elasticity and the viscisity difference between the internal and external fluids (Bagchi and Kalluri, JFM, 2011). We also extended our simulation technique to consider dense suspension of multiple deformable capsules in shear flow (Kalluri and Bagchi, JFM, submitted). We found that the shear viscosity minimu gradually diminishes as the capsule volume fraction increases. This trend is explained by decomposing the particle stress tension in to contributions coming from the membrane and from the viscosity difference. We find that the contribution from the membrane increases with increasing capsule volume fraction due to increases interparticle interaction, but that due to the viscosity difference is independent of the volume fraciton. We have also studied the effect of flow oscillation on the time-dependent dynamics of capsules (Zhao and Bagchi, Physics of Fluids, 2011). Here we found that the deformation and angular response of an initially non-spherical capsule is non-identical in the accelerating and decelerating phases of the shear flow. We further found that the capsule exhibits a swinging behavior at both high and low values of shear rates and oscillation frequencies, but a tumbling behavior at intermediate values. Further, the dynamics appears to be strongly dependent on the initial capsule orientation. This result underscores the importance of deformation, and the coupling between deformation and orientation dynamics in the study of cellular motion. The broader impact of the project lies in the fact that it encompasses multiple areas of science and engineering -- from transport phenomena to biomedical sciences to computational sciences. The methodology developed here can be used to study the rheology of deformable particulate suspension; it could be used to study the blood flow in microcirculation for normal and pathological red blood cells (e.g., sickle cell); it could also be used to study the process of leukocyte rolling on a blood vessel which is the first event during the body's response to inflammation. Further, the methodology can be easily adopted to consider transport of micro- and nano-particles in blood flow, which can be used as a model for targeted drug delivery.
