Blood flow in capillaries

A computational framework for investigating bacteria transport in microvasculature

Blood-borne bacteria disseminate in tissue through microvasculature or capillaries. Capillary size, presence of red blood cells (RBCs), and bacteria motility affect bacteria intracapillary transport, an important yet largely unexplored phenomenon. Computational description of the system comprising interactions between plasma, RBCs, and motile bacteria in 5-10 μm diameter capillaries pose several challenges. The Immersed Boundary Method (IBM) was used to resolve the capillary, deformed RBCs, and bacteria. The challenge of disparate coupled time scales of flow and bacteria motion are reconciled by a temporal multiscale simulation method. Bacterium-wall and bacterium-RBC collisions were detected using a hierarchical contact- detection algorithm. Motile bacteria showed a net outward radial velocity of 2.8 µm/s compared to -0.5 µm/s inward for non-motile bacteria; thus, exhibiting a greater propensity to escape the bolus flow region between RBCs and marginate for potential extravasation, suggesting motility enhances extravasation of bacteria from capillaries.

A geometrical model of dermal capillary clearance

A new microscopic model is developed to describe the dermal capillary clearance process of skin permeants. The physiological structure is represented in terms of a doubly periodic array of absorbing capillaries. Convection-dominated transport in the blood flow within the capillaries is coupled with interstitial diffusion, the latter process being quantified via a slender-body-theory approach. Convection across the capillary wall and in the interstitial phase is treated as a perturbation which may be added to the diffusive transport. The model accounts for the finite permeability of the capillary wall as well as for the geometry of the capillary array, based on realistic values of physiological parameters. Calculated dermal concentration profiles for permeants having the size and lipophilicity of salicylic acid and glucose illustrate the power and general applicability of the model. Furthermore, validation of the model with published in vivo experimental results pertaining to human skin permeation of hydrocortisone is presented. The model offers the possibility for in-depth theoretical understanding and prediction of subsurface drug distribution in the human skin following topical application, as well as rates of capillary clearance into the systemic circulation. A simpler approach that treats the capillary bed as a homogeneously absorbing zone is also employed. The latter may be used in conjunction with the capillary exchange model to estimate measurable dermal transport and clearance parameters in a straightforward manner.

Dermal capillary clearance: physiology and modeling

Substances applied to the skin surface may permeate deeper tissue layers and pass into the body's systemic circulation by entering blood or lymphatic vessels in the dermis. The purpose of this review is an in-depth analysis of the dermal clearance/exchange process and its constituents: transport through the interstitium, permeability of the microvascular barrier and removal via the circulation. We adapt an 'engineering' viewpoint with emphasis on quantifying the dermal microcirculatory physiology, providing the theoretical framework for the physics of key transport processes and reviewing the available computational clearance models in a comparative manner. Selected experimental data which may serve as valuable input to modeling attempts are also reported.

A model for the nutritional transport in capillary-tissue exchange system

By introducing the lubrication theory to the squeezing flow of the plasma between the cell and the vessel wall, an analysis of the flow and the nutritional transport within the tissue has been presented in this paper. Cells are assumed to flow in a single file, with axi-symmetric shapes. The concentration profiles of the dissolved nutrients within the tissue have been drawn under the assumption of the uniform distribution in the capillary due to continuous mixing in bolus flows between the 2 adjacent cells in the capillary. The analysis concludes that, in diseased state, the penetration depth for the substance in the tissue decreases and the cells in the deeper region do not get sufficient nutrition for their survival and they die out.

Red blood cell mechanics and capillary blood rheology

Blood contains a high vol fraction of erythrocytes (red blood cells), which strongly influence its flow properties. Much is known about the mechanical properties of red cells, providing a basis for understanding and predicting the rheological behavior of blood in terms of the behavior of individual red cells. This review describes quantitative theoretical models that relate red cell mechanics to flow properties of blood in capillaries. Red cells often flow in single file in capillaries, and rheological parameters can then be estimated by analyzing the motion and deformation of an individual red cell and the surrounding plasma in a capillary. The analysis may be simplified by using lubrication theory to approximate the plasma flow in the narrow gaps between the cells and the vessels walls. If red cell shapes are assumed to be axisymmetric, apparent viscosities are predicted that agree with determinations in glass capillaries. Red cells flowing in microvessels typically assume nonaxisymmetric shapes, with cyclic "tank-treading" motion of the membrane around the interior. Several analyses have been carried out that take these effects into account. These analyses indicate that nonaxisymmetry and tank-treading do not significantly influence the flow resistance in single-file or two-file flow.

Flow-dependent rheological properties of blood in capillaries

Velocity-dependent flow of human red blood cells in capillaries with inside diameters of 4 to 8 micron is described theoretically. Cells are assumed to flow in single file, with axisymmetric shapes. Plasma flow in the gaps between cells and vessel walls is described by lubrication theory. The model takes into account the elastic properties of red cell membrane, including its responses to shear and bending. Cell shape is computed numerically as a function of tube diameter and cell velocity over the range 0.001 to 10 cm/sec. Relative apparent viscosity and dynamic hematocrit reduction (Fahraeus effect) are also computed. Since effects of interactions between cells are neglected, the Fahraeus effect is independent of hematocrit, while viscosity varies linearly with hematocrit. At moderate or high cell velocities, about 0.1 cm/sec or more, cell shapes and rheological parameters approach flow-independent limits. At lower velocities, cells broaden as a result of membrane shear and bending resistance and approach the walls more closely. Consequently, apparent viscosity increases with decreasing flow rate. Predicted values are in agreement with in vitro experimental determinations. Flow cessation is not predicted to occur in uniform tubes at positive driving pressures. Elastic deformational energies associated with red cell shapes are computed, leading to estimates of the pressure difference required to drive red cells past typical irregularities in capillary lumen cross sections. The hindrance to flow resulting from such structural irregularities represents a potential rheological mechanism for cessation of capillary flow at very low driving pressures.

The clinical impact of the newer research in blood rheology: an overview

Over the last two decades concepts of hemorheology became established and required methods and techniques developed. Progress was made in the formation of a field of clinical hemorheology. The role of viscosity factors in various disorders has been established, especially in heart disease and diabetes. It has been recognized that hyperviscosity can be present if any one of the blood viscosity factors is increased, even if the viscosity of whole blood appears normal or even subnormal. While hyperviscosity may result in ischemic and thromboembolic episodes, the causes of hyperviscosity may include cancer, genetic abnormality, infection, metabolic disorders, and many others. The basic causes can be, in their turn, affected and reinforced by hyperviscosity. Superimposition of an added hyperviscosity factor onto already elevated blood viscosity might lead to precipitation of ischemic episodes. This review deals with the correlations between hyperviscosity and heat disease and among diabetes, cancer, and chronic anxiety. The predictive value of hyperviscosity with respect to ischemic episodes and cancer metastases is discussed.

Concentration polarization in an ultrafiltering capillary

Concentration polarization, the accumulation of retained solute next to an ultrafiltering membrane, elevates osmotic pressure above that which would exist in the absence of polarization. For ultrafiltration in a cylindrical tube, use of the radially averaged solute concentration results in an underestimate of osmotic pressure, yielding an effective hydraulic permeability (k) less than the actual membrane hydraulic permeability (k(m)). The extent to which k and k(m) might differ in an ultrafiltering capillary has been examined theoretically by solution of the momentum and species transport equations for idealized capillaries with and without erythrocytes. For diameters, flow velocities, protein concentrations and diffusivities, and ultrafiltration pressures representative of the rat glomerular capillary network, results indicate that the effects of polarization are substantial without erythrocytes (k/k(m) = 0.7) and persist, but to a lesser extent, with erythrocytes (k/k(m) = 0.9), the reduction in polarization in the latter case being due to enhanced plasma mixing. In accord with recent experimental findings in rats, k is found to be relatively insensitive to changes in glomerular plasma flow rate.