Aleksander S. Popel

Large deformation of red blood cell ghosts in a simple shear flow

Red blood cells are known to change shape in response to local flow conditions. Deformability affects red blood cell physiological function and the hydrodynamic properties of blood. The immersed boundary method is used to simulate three-dimensional membrane-fluid flow interactions for cells with the same internal and external fluid viscosities. The method has been validated for small deformations of an initially spherical capsule in simple shear flow for both neo-Hookean and the Evans-Skalak membrane models. Initially oblate spheroidal capsules are simulated and it is shown that the red blood cell membrane exhibits asymptotic behavior as the ratio of the dilation modulus to the extensional modulus is increased and a good approximation of local area conservation is obtained. Tank treading behavior is observed and its period calculated.

A theoretical analysis of the effect of the particulate nature of blood on oxygen release in capillaries

A theoretical model is developed to investigate the role played by the particulate (two-phase) nature of blood on oxygen (O2) release in capillary-size vessels. Red cells flowing in single-file suspension through capillaries are modelled as evenly spaced, hemoglobin (Hb)-containing circular particles in a rectangular channel (two-dimensional case) or axisymmetric spheres in a circular tube (three-dimensional case). The model includes the free and Hb-facilitated transport of O2 and Hb-O2 kinetics inside the particles, diffusion of free O2 in the suspending phase, and a specified O2 tension at the capillary wall that drives the release of O2 from the particles as they traverse the capillary. The results are expressed in the form of a capillary mass transfer coefficient, an inverse resistance, that relates the spatial average flux of O2 out of the capillary to a driving force for O2 release. The results indicate that this coefficient depends significantly on particle spacing and clearance (channel size relative to particle size) but not significantly on the O2 tension at the capillary wall nor the eccentricity of the particles in the channel. It is also found that the capillary mass transfer coefficient can be several times smaller (more resistance) than that for a continuous Hb solution releasing O2. As a physiological application of the coefficients obtained, they are combined with a Krogh-type model for tissue, and the resulting analysis suggests that the fraction of total O2 transport resistance that resides inside the capillary is influenced significantly by the discrete nature of blood and can account for 30 to 70% of the total resistance to O2 transport from blood to tissue.

Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows

Concentrated erythrocyte (i.e., red blood cell) suspensions flowing in microchannels have been simulated with an immersed-boundary lattice Boltzmann algorithm, to examine the cell layer development process and the effects of cell deformability and aggregation on hemodynamic and hemorheological behaviors. The cells are modeled as two-dimensional deformable biconcave capsules and experimentally measured cell properties have been utilized. The aggregation among cells is modeled by a Morse potential. The flow development process demonstrates how red blood cells migrate away from the boundary toward the channel center, while the suspending plasma fluid is displaced to the cell free layer regions left by the migrating cells. Several important characteristics of microscopic blood flows observed experimentally have been well reproduced in our model, including the cell free layer, blunt velocity profile, changes in apparent viscosity, and the Fahraeus effect. We found that the cell free layer thickness increases with both cell deformability and aggregation strength. Due to the opposing effects of the cell free layer lubrication and the high viscosity of cell-concentrated core, the influence of aggregation is complex but the lubrication effect appears to dominate, causing the relative apparent viscosity to decrease with aggregation. It appears therefore that the immersed-boundary lattice Boltzmann numerical model may be useful in providing valuable information on microscopic blood flows in various microcirculation situations.

Where is VEGF in the body? A meta-analysis of VEGF distribution in cancer

Vascular endothelial growth factor (VEGF) is a major target for the inhibition of tumour vascularisation and the treatment of human cancer. Many tumours produce large quantities of VEGF, and as a result, diagnosis and prognosis of cancer may be predicted by measuring changes in VEGF concentrations in blood. In blood, the VEGF may be located in the plasma, or in the blood-borne cells and formed elements, in particular, platelets and leukocytes. In this study, we collate the measurements of VEGF in platelets, leukocytes, plasma and serum for breast, prostate, colorectal and other cancers. In addition, we analysed the concentration of VEGF in tumour tissue itself, as well as for other tissues in the human body. Although the concentration of VEGF in tumours is high, the size of tumours is small compared to other tissues, in particular, skeletal muscle. Thus, the total quantity of VEGF in tumours and in blood is small compared to the quantity in muscles. This large reservoir of VEGF may have important implications for the treatment of cancer.

A systems biology perspective on sVEGFR1: its biological function, pathogenic role and therapeutic use

•  Introduction ‐  Angiogenesis in physiology and pathology ‐  Angiogenesis in current medicine ‐  VEGF ligand and receptor system: where does sVEGFR1 fit? ‐  Ligands: the human VEGF family ‐  Membrane‐bound signalling receptors: VEGFRs ‐  Non‐signalling co‐receptors and matrix proteins: HSPGs and NRPs ‐  Soluble receptors: sVEGFR1, sVEGFR2, sNRP1 •  Molecular biology of sVEGFR1 •  Physiological and pathophysiological roles of sVEGFR1 •  Molecular mechanism of sVEGFR1’s anti‐angiogenic potential •  sVEGFR1 as a clinical marker for disease •  Plasma VEGF and sVEGFR1: non‐uniform predictors of angiogenic status across all diseases •  Systems biology perspective: unifying interpretation of plasma angiogenic markers ‐  Baseline heterogeneity in clinical measurements of healthy VEGF and sVEGFR1 levels in plasma ‐  Effect of sVEGFR1 on VEGF bioavailability: VEGF‐sVEGFR1 complexes ‐  Compartmental analysis: biotransport and biodistribution ‐  Pathogenic phenomenon versus compensatory response •  Concluding remarks

Computational Fluid Dynamic Simulation of Aggregation of Deformable Cells in a Shear Flow

We present computational fluid dynamic (CFD) simulation of aggregation of two deformable cells in a shearflow. This work is motivated by an attempt to develop computational models of aggregation of red blood cells (RBCs). Aggregation of RBCs is a major determinant of blood viscosity in microcirculation under physiological and pathological conditions. Deformability of the RBCs plays a major role in determining their aggregability. Deformability depends on the viscosity of the cytoplasmic fluid and on the rigidity of the cell membrane, in a macroscopic sense. This paper presents a computational study of RBC aggregation that takes into account the rheology of the cells as well as cell-cell adhesion kinetics. The simulation technique considered here is two dimensional and based on the front tracking/immersed boundary method for multiple fluids. Results presented here are on the dynamic events of aggregate formation between two cells, and its subsequent motion, rolling, deformation, and breakage. We show that the rheological properties of the cells have significant effects on the dynamics of the aggregate. A stable aggregate is formed at higher cytoplasmic viscosity and membrane rigidity. We also show that the bonds formed between the cells change in a cyclic manner as the aggregate rolls in a shearflow. The cyclic behavior is related to the rolling orientation of the aggregate. The frequency and amplitude of oscillation in the number of bonds also depend on the rheological properties.

Impaired Angiogenesis After Hindlimb Ischemia in Type 2 Diabetes Mellitus Differential Regulation of Vascular Endothelial Growth Factor Receptor 1 and Soluble Vascular Endothelial Growth Factor Receptor 1

Deficient angiogenesis after ischemia may contribute to worse outcomes of peripheral arterial disease in patients with diabetes mellitus (DM). Vascular endothelial growth factor (VEGF) and its receptors promote angiogenesis. We hypothesized that in peripheral arterial disease, maladaptive changes in VEGF ligand/receptor expression could account for impaired angiogenesis in DM. Skeletal muscle from diet-induced, type 2 diabetic (DM) and age-matched normal chow (NC)-fed mice was collected at baseline and 3 and 10 days after hindlimb ischemia and analyzed for expression of VEGF (n=10 per group), full-length VEGF receptor (VEGFR)-1, soluble VEGFR-1, and markers of downstream VEGF signaling (n=20 per group) using ELISA, reverse transcriptase-polymerase chain reaction, and Western blots. In the absence of ischemia, DM mice had increased VEGF (NC versus DM: 26.6±2.6 versus 53.5±8.8 pg/mg protein; P<0.05), decreased soluble and membrane-bound VEGFR-1 (NC versus DM: 1.44±0.30 versus 0.85±0.08 and 1.03±0.10 versus 0.72±0.10, respectively; P<0.05), decreased phospho-AKT/AKT and phospho–endothelial NO synthase/endothelial NO synthase (NC versus DM: 0.76±0.2 versus 0.38±0.1 and 0.36±0.06 versus 0.25±0.04, respectively; P<0.05), and no change in VEGFR-2. After ischemia, both DM and NC had comparable increases in VEGF-A. VEGFR-1 and soluble VEGFR-1 expression increased in both groups, but the fold increase was significantly greater in DM. These data demonstrate that soluble VEGFR-1, an angiogenesis inhibitor, is regulated in skeletal muscle by type 2 DM and ischemia. In the absence of ischemia, despite reductions in both soluble VEGFR-1 and VEGFR-1, VEGF ligand signaling is lower in DM compared with controls. After ischemia, maladaptive upregulation of these receptors further reduces the capacity of VEGF to induce an angiogenic response, which may provide a novel target for therapy.

Systems Biology of Vascular Endothelial Growth Factors

Several cytokine families have roles in the development, maintenance, and remodeling of the microcirculation. Of these, the vascular endothelial growth factor (VEGF) family is one of the best studied and one of the most complex. Five VEGF ligand genes and five cell‐surface receptor genes are known in the human, and each of these may be transcribed as multiple splice isoforms to generate an extensive family of proteins, many of which are subject to further proteolytic processing. Using the VEGF family as an example, we describe the current knowledge of growth‐factor expression, processing, and transport in vivo. Experimental studies and computational simulations are being used to measure and predict the activity of these molecules, and we describe avenues of research that seek to fill the remaining gaps in our understanding of VEGF family behavior.

A Membrane Bending Model of Outer Hair Cell Electromotility

We propose a new mechanism for outer hair cell electromotility based on electrically induced localized changes in the curvature of the plasma membrane (flexoelectricity). Electromechanical coupling in the cells lateral wall is modeled in terms of linear constitutive equations for a flexoelectric membrane and then extended to nonlinear coupling based on the Langevin function. The Langevin function, which describes the fraction of dipoles aligned with an applied electric field, is shown to be capable of predicting the electromotility voltage displacement function. We calculate the electrical and mechanical contributions to the force balance and show that the model is consistent with experimentally measured values for electromechanical properties. The model rationalizes several experimental observations associated with outer hair cell electromotility and provides for constant surface area of the plasma membrane. The model accounts for the isometric force generated by the cell and explains the observation that the disruption of spectrin by diamide reduces force generation in the cell. We discuss the relation of this mechanism to other proposed models of outer hair cell electromotility. Our analysis suggests that rotation of membrane dipoles and the accompanying mechanical deformation may be the molecular mechanism of electromotility.

Blood Flow and Cell-Free Layer in Microvessels

Please cite this paper as: Fedosov, Caswell, Popel and Karniadakis (2010). Blood Flow and Cell‐Free Layer in Microvessels. Microcirculation17(8), 615–628.