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Biomedical subjects

R Skalak

Publications and source records attributed to R Skalak.

At least 91 records · Page 5Linked to original sources
PubMed1983

Theoretical modeling of filtration of blood cell suspensions.

A theoretical model of filtration of suspensions containing red blood cells (RBCs) and white blood cells (WBCs) has been developed. Equations are written for the pressure drop, the filtration flow and the fractions of filter pores containing RBCs (alpha) and WBCs (alpha*). Because the relative resistances (ratios of resistance of cell to resistance of suspending fluid) of RBCs (beta) and WBCs (beta*) through the filter pore are greater than one, the transit of these cells (especially WBCs) through the filter is slower than that of suspending fluid; this leads to values of alpha and alpha* higher than those simply expected from the hematocrit and leukocrit, respectively, in the entering and exiting suspensions. In the absence of pore plugging by the cells (steady flow), the pressure drop can be computed from alpha, alpha*, beta and beta*. In order to model unsteady flow, differential equations are written to include pore plugging and the subsequent unplugging by the rising filtration pressure at a constant flow. By specifying the fractions of entering RBCs (epsilon) and WBCs (epsilon*) which would plug the pores and the rate at which the plugged pores would unplug in response to pressure rise (epsilon u), as well as the fractions of entering RBCs (epsilon p) and WBCs (epsilon p*) that would plug the pores permanently, theoretical pressure-time curves can be generated by numerical integration, and the results fit the experimental data well. From such fitting of theoretical curve to experimental data, information can be deduced for epsilon, epsilon*, epsilon u, epsilon p and epsilon* p.

Erythrocytes↗
PubMed1983

The motion of close-packed red blood cells in shear flow.

Experimental and theoretical results are presented concerning the motion of close-packed red blood cell suspensions subjected to steady simple shear flow. The behavior of the suspension was observed microscopically using a cone-and-plate rheoscope. At moderate and high shear rates the cells show a fairly orderly arrangement, each appearing polygonal in the field of view. An idealized theoretical model for the suspension is developed, in which each cell is a 14-sided polyhedron of varying shape, but with constant surface area and volume. Tank-treading motion of the membrane is predicted, and an approximation to the motion is calculated which is consistent with the known mechanical properties of the membrane. It is shown that considerably more energy is dissipated in the membrane than in the cytoplasm during tank-treading.

Erythrocyte Membrane↗
PubMed1983

The bulk rheology of close-packed red blood cells in shear flow.

A theoretical analysis is made of the dynamical behavior and bulk rheology of close-packed red blood cell suspensions subjected to simple shear flow. The model for the polyhedral cell shapes and tank-treading membrane motion developed in the companion paper (1) is used. The flow in the thin lubricating plasma layers between cells is analyzed taking into account the mechanical properties of the membrane at the corner regions of sharp membrane curvature. This leads to predictions for the apparent viscosity as a function of hematocrit and shear rate. Good agreement with experimental results is obtained at moderate and high shear rates (above 20 s-1). At lower shear rates, a rapid rise in apparent viscosity has been found experimentally, and the mechanisms leading to this behavior are examined.

Blood Viscosity↗
PubMed1983

Indices of filterability of red blood cell suspensions.

A number of different experimental techniques have been devised in recent years to use microsieving as a test of the filterability of suspensions of red blood cells. Various indices have been proposed to express the results of these tests. In the present paper a correlation is made of the intrinsic increase in resistance at the level of a single pore in the filter to the macroscopically observed pressure and flow through the entire filter. Further it is shown how a number of different tests may be used to derive the same index. The results apply only to situations in which there is no plugging of pores.

Erythrocytes↗
PubMed1983

Determination of erythrocytes transit times through a 5 mu "nuclepore" filter.

Filtration experiments through 5 or 3 mu Nuclepore membranes are often performed in order to assess the so-called erythrocyte deformability. The relation between this parameter and the RBC filterability is not straightforward. A simple theoretical treatment relating filtration index (as determined by the initial flow rate method) to the average RBC flow resistance through an average pore is presented. In order to deduce the average RBC transit time through the membrane from the initial flow rate data, the suspension hematocrit change after filtration has been determined. The calculated average transit time is comparable to experimental values, as determined by KIESEWETTER et al. with the single pore technique.

Erythrocytes↗
PubMed1982

Viscoelastic behavior of erythrocyte membrane.

A nonlinear viscoelastic relation is developed to describe the viscoelastic properties of erythrocyte membrane. This constitutive equation is used in the analysis of the time-dependent aspiration of an erythrocyte membrane into a micropipette. Equations governing this motion are reduced to a nonlinear integral equation of the Volterra type. A numerical procedure based on a finite difference scheme is used to solve the integral equation and to match the experimental data. The data, aspiration length vs. time, is used to determine the relaxation function at each time step. The inverse problem of obtaining the time dependence of the aspiration length from a given relaxation function is also solved. Analytical results obtained are applied to the experimental data of Chien et al. 1978. Biophys. J. 24:463-487. A relaxation function similar to that of a four-parameter solid with a shear-thinning viscous term is proposed.

Animals↗
PubMed1982

Influence of physicochemical factors on rheology of human neutrophils.

The effects of variations in temperature, pH, and osmolality on the rheological properties of human neutrophils were determined by studying the cell deformation in response to aspirational pressure applied via a micropipette. The time history of the deformation was analyzed by the use of a standard solid viscoelastic model consisting of an elastic element K1 in parallel with a Maxwell element (an elastic element K2 in series with a viscous element mu). With changes in temperature over a range of 9-40 degrees C, only mu varied inversely with temperature, while K1 and K2 did not show significant alterations. Variations in pH over the range of 5.4-7.8 did not significantly affect the viscoelastic coefficients, but K1 and mu rose at pH 8.4. An increase in osmolality caused all three coefficients to rise, but a decrease in osmolality had relatively little effect on the coefficients. These changes in response to physicochemical variations serve to provide insights into the viscoelastic properties of neutrophils and their possible roles in health and disease.

Adult↗
PubMed1982

Rheology of blood cells as soft tissues.

Erythrocytes are unusual in that the cell membrane plays a large and direct role in observed rheological properties. The cell membrane is not a three dimensional material or tissue in the usual sense but being only two molecules thick. It behaves like a liquid sheet of constant thickness and surface area with some elastic properties due in part to protein networks of spectrin and actin on the interior face of the cell membrane. Packed red cells form a viscoelastic fluid which can be sheared, but exhibits a considerable elastic response. The elastic component decreases as the hematocrit is reduced, but is present at all hematocrits. Leukocytes also exhibit viscoelasticity but the properties are primarily dependent on the cell cytoplasm. The cell membrane plays a role only when it is stretched taut. The normal white cell properties have been explored over a wide range of osmolarities, becoming much less viscous and less elastic as the fluid content of the cell increases. White cells also may show spontaneous deformation during which the rheological properties become much stiffer than in the normal passive state.

Biomechanical Phenomena↗
PubMed1982

Theoretical models of capillary flow.

Mathematical models of capillary blood flow are described consisting of axisymmetric particles in cylindrical tubes. The blood cells are modelled by elastic sphere, rigid red blood cells and normal flexible red blood cells. The results show that the deformability of red blood cells is important in reducing the apparent viscosity in capillary blood flow.

Anemia, Sickle Cell↗
PubMed1981

Space-time presentations of the shell of the bivalved mollusk Cardium edule.

In a recent article the concept of studying craniofacial growth in space-time was introduced. The possibilities of carrying out such studies were demonstrated with the aid of some generalized shell of a bivalved mollusk. In this study presentations of space-time models of a real biologic model, the shell of the bivalved mollusk Cardium edule, have been constructed. Quantitative expressions of paths in space-time of anatomic and material points have been elaborated. A further analysis has shown that a number of the space-time presentations may represent biologic reality. They may be used for comparisons with presentations of skull models and may represent a tool for the better understanding of results from other studies.

Animals↗
PubMed1981

Passive mechanical properties of human leukocytes.

Micropipette experiments are used to determine the rheological properties of human leukocytes. Individual cells in EDTA are subjected to a known aspiration pressure via a micropipette, and their surface deformation from the undeformed spherical shape is recorded on a television monitor. The cells are mathematically modeled as homogeneous spheres, and a standard solid viscoelastic model is found to describe accurately the deformation of the cell for small strains. These experimental and theoretical studies provide the basis for further investigations of leukocyte rheology in health and disease.

Adult↗
PubMed1981

Mechanics of Rouleau formation.

The formation of rouleau of red blood cells is considered from the standpoint of adhesion theory. With the use of the elastic properties of the red blood cell membrane obtained from previous work, the strain energy of the red blood cell in rouleau formation has been computed. The surface energy of adhesion for the bonding of two red blood cells is then computed from the variation of this strain energy. Computed cell shapes agree well with experiments.

Cell Adhesion↗
PubMed1981

The stress-free shape of the red blood cell membrane.

The two main proposals found in the literature for the stress-free shape of the red cell membrane are (a) the bioconcave shape and (b) the sphere of the same surface area. These possibilities are evaluated in this paper using theoretical modeling of equilibrium membrane shapes according to Zarda et al. (1977. J. Biomech. 10:211-221) and by comparison to experiments on red cells whose membrane shear modulus has been increased by treatment with diamide. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. To account for this discrepancy we propose that either the shear modulus of the native membrane is dependent on the membrane strain or that the bending stiffness is higher than estimated by Evans (1980. Biophys. J. 30:265-286). These studies suggest that the bioconcave disk is the more likely possibility for the stress-free shape.

Diamide↗
PubMed1981

Mechanics of blood flow.

The historical development of the mechanics of blood flow can be traced from ancient times, to Leonardo da Vinci and Leonhard Euler and up to the present times with increasing biological knowledge and mathematical analysis. In the last two decades, quantitative and numerical methods have steadily given more complete and precise understanding. In the arterial system wave propagation computations based on nonlinear one-dimensional modeling have given the best representation of pulse wave propagation. In the veins, the theory of unsteady flow in collapsible tubes has recently been extensively developed. In the last decade, progress has been made in describing the blood flow at junctions, through stenoses, in bends and in capillary blood vessels. The rheological behavior of individual red blood cells has been explored. A working model consists of an elastic membrane filled with viscous fluid. This model forms a basis for understanding the viscous and viscoelastic behavior of blood.

Animals↗