Red blood cells and other non-spherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition

We consider the motion of red blood cells and other non-spherical microcapsules dilutely suspended in a simple shear flow. Our analysis indicates that depending on the viscosity, membrane elasticity, geometry and shear rate, the particle exhibits either tumbling, tank-treading of the membrane about the viscous interior with periodic oscillations of the orientation angle, or intermittent behavior in which the two modes occur alternately. For red blood cells, we compute the complete phase diagram and identify a novel tank-treading-to-tumbling transition at low shear rates. Observations of such motions coupled with our theoretical framework may provide a sensitive means of assessing capsule properties.Comment: 11 pages, 4 figure

A simplified particulate model for coarse-grained hemodynamics simulations

Human blood flow is a multi-scale problem: in first approximation, blood is a dense suspension of plasma and deformable red cells. Physiological vessel diameters range from about one to thousands of cell radii. Current computational models either involve a homogeneous fluid and cannot track particulate effects or describe a relatively small number of cells with high resolution, but are incapable to reach relevant time and length scales. Our approach is to simplify much further than existing particulate models. We combine well established methods from other areas of physics in order to find the essential ingredients for a minimalist description that still recovers hemorheology. These ingredients are a lattice Boltzmann method describing rigid particle suspensions to account for hydrodynamic long range interactions and---in order to describe the more complex short-range behavior of cells---anisotropic model potentials known from molecular dynamics simulations. Paying detailedness, we achieve an efficient and scalable implementation which is crucial for our ultimate goal: establishing a link between the collective behavior of millions of cells and the macroscopic properties of blood in realistic flow situations. In this paper we present our model and demonstrate its applicability to conditions typical for the microvasculature.Comment: 12 pages, 11 figure

Soft lubrication: the elastohydrodynamics of non-conforming and conforming contacts

We study the lubrication of fluid-immersed soft interfaces and show that elastic deformation couples tangential and normal forces and thus generates lift. We consider materials that deform easily, due to either geometry (e.g. a shell) or constitutive properties (e.g. a gel or a rubber), so that the effects of pressure and temperature on the fluid properties may be neglected. Four different system geometries are considered: a rigid cylinder moving parallel to a soft layer coating a rigid substrate; a soft cylinder moving parallel to a rigid substrate; a cylindrical shell moving parallel to a rigid substrate; and finally a cylindrical conforming journal bearing coated with a thin soft layer. In addition, for the particular case of a soft layer coating a rigid substrate we consider both elastic and poroelastic material responses. For all these cases we find the same generic behavior: there is an optimal combination of geometric and material parameters that maximizes the dimensionless normal force as a function of the softness parameter = hydrodynamic pressure/elastic stiffness = surface deflection/gap thickness which characterizes the fluid-induced deformation of the interface. The corresponding cases for a spherical slider are treated using scaling concepts.Comment: 61 pages, 20 figures, 2 tables, submitted to Physics of Fluid

Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour

Structural Adaptation and Heterogeneity of Normal and Tumor Microvascular Networks

Relative to normal tissues, tumor microcirculation exhibits high structural and functional heterogeneity leading to hypoxic regions and impairing treatment efficacy. Here, computational simulations of blood vessel structural adaptation are used to explore the hypothesis that abnormal adaptive responses to local hemodynamic and metabolic stimuli contribute to aberrant morphological and hemodynamic characteristics of tumor microcirculation. Topology, vascular diameter, length, and red blood cell velocity of normal mesenteric and tumor vascular networks were recorded by intravital microscopy. Computational models were used to estimate hemodynamics and oxygen distribution and to simulate vascular diameter adaptation in response to hemodynamic, metabolic and conducted stimuli. The assumed sensitivity to hemodynamic and conducted signals, the vascular growth tendency, and the random variability of vascular responses were altered to simulate ‘normal’ and ‘tumor’ adaptation modes. The heterogeneous properties of vascular networks were characterized by diameter mismatch at vascular branch points (d3var) and deficit of oxygen delivery relative to demand (O2def). In the tumor, d3var and O2def were higher (0.404 and 0.182) than in normal networks (0.278 and 0.099). Simulated remodeling of the tumor network with ‘normal’ parameters gave low values (0.288 and 0.099). Conversely, normal networks attained tumor-like characteristics (0.41 and 0.179) upon adaptation with ‘tumor’ parameters, including low conducted sensitivity, increased growth tendency, and elevated random biological variability. It is concluded that the deviant properties of tumor microcirculation may result largely from defective structural adaptation, including strongly reduced responses to conducted stimuli

Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

Uptake Rate of Cationic Mitochondrial Inhibitor MKT-077 Determines Cellular Oxygen Consumption Change in Carcinoma Cells

<div><h3>Objective</h3><p>Since tumor radiation response is oxygen-dependent, radiosensitivity can be enhanced by increasing tumor oxygenation. Theoretically, inhibiting cellular oxygen consumption is the most efficient way to increase oxygen levels. The cationic, rhodacyanine dye-analog MKT-077 inhibits mitochondrial respiration and could be an effective metabolic inhibitor. However, the relationship between cellular MKT-077 uptake and metabolic inhibition is unknown. We hypothesized that rat and human mammary carcinoma cells would take up MKT-077, causing a decrease in oxygen metabolism related to drug uptake.</p> <h3>Methods</h3><p>R3230Ac rat breast adenocarcinoma cells were exposed to MKT-077. Cellular MKT-077 concentration was quantified using spectroscopy, and oxygen consumption was measured using polarographic electrodes. MKT-077 uptake kinetics were modeled by accounting for uptake due to both the concentration and potential gradients across the plasma and mitochondrial membranes. These kinetic parameters were used to model the relationship between MKT-077 uptake and metabolic inhibition. MKT-077-induced changes in oxygen consumption were also characterized in MDA-MB231 human breast carcinoma cells.</p> <h3>Results</h3><p>Cells took up MKT-077 with a time constant of ∼1 hr, and modeling showed that over 90% of intracellular MKT-077 was bound or sequestered, likely by the mitochondria. The uptake resulted in a rapid decrease in oxygen consumption, with a time constant of ∼30 minutes. Surprisingly the change in oxygen consumption was proportional to uptake rate, not cellular concentration. MKT-077 proved a potent metabolic inhibitor, with dose-dependent decreases of 45–73% (p = 0.003).</p> <h3>Conclusions</h3><p>MKT-077 caused an uptake rate-dependent decrease in cellular metabolism, suggesting potential efficacy for increasing tumor oxygen levels and radiosensitivity <em>in vivo</em>.</p> </div

Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids

Toward an Ising Model of Cancer and Beyond

Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must account for the complex mechanisms involved in tumor growth. Here we review resarch work that we have done toward the development of an "Ising model" of cancer. The review begins with a description of a minimalist four-dimensional (three in space and one in time) cellular automaton (CA) model of cancer in which healthy cells transition between states (proliferative, hypoxic, and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to model the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment is then described. How angiogenesis as well as the heterogeneous and confined environment in which a tumor grows is incorporated in the CA model is discussed. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently described. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. The need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented.Comment: 55 pages, 21 figures and 3 tables. To appear in Physical Biology. Added reference