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Biomedical subjects

R Skalak

Publications and source records attributed to R Skalak.

At least 55 records · Page 3Linked to original sources
PubMed1989

One-dimensional steady continuum model of retraction of pseudopod in leukocytes.

A one-dimensional steady state continuum mechanics model of retraction of pseudopod in leukocytes is developed. The retracting pseudopod is assumed to move bodily toward the main cell body, the bulk motion of which can be represented by cytoplasmic flow within a typical stream tube through the leukocyte. The stream tube is approximated by a frictionless tube with prescribed geometry. The passive rheological properties of cytoplasm in the main cell body and in the pseudopod are modeled, respectively, by Maxwell fluid and Hookean solid. The two regions are assumed to be separated by a sharp interface at which actin gel solates and thereby changes its rheological properties as it flows from the pseudopod to the main cell body. The driving mechanism responsible for the active retraction motion is hypothesized to be a spontaneous deformation of the actin gel, analogous but not necessarily equal to the well known actin-myosin interaction. This results in an active contractile stress being developed in the pseudopod as well as in the cell cortex. The transverse traction pulls against the inclined wall of the stream tube and is transduced into an axial stress gradient, which in turn drives the flow. The tension on the tube wall is picked up by the prestressed cortical shell. Governing equations and boundary conditions are derived. A solution is obtained. Sample data are computed. Comparison of the theory with experiments shows that the model is compatible to the observations.

Cell Movement↗
PubMed1989

Stability of particle motions in a narrow channel flow.

Single rows or two rows of identical circular cylinders spaced regularly in a narrow channel flow have been shown to be capable of steady flow provided the cylinders are located at equal lateral positions and with equal spacings in the flow direction. The stability of such steady flows of circular cylinders is studied for periodic perturbations of the particle positions, assuming that every other cylinder is equally perturbed in lateral position and spacing along the channel. This results in two rows which are not symmetrically placed. The suspending fluid is assumed to be an incompressible Newtonian fluid. It is assumed that no external forces or moments act on the cylinders and the effects of inertia forces on the motion of the fluid and the cylinders are negligible. The velocity field of the suspending fluid and the instantaneous velocities of the cylinders are computed by the finite element method. The translational velocities of the cylinders are obtained for a large number of particle positions, from which the trajectories of their relative motion are determined for various initial positions near the regular single-file and two-file arrangements. It is shown that when the initial arrangements of the cylinders are slightly perturbed from the regular (alternating) two-file flows, the trajectories of their relative motions become small closed loops around the regular two-file arrangements. In contrast, such small closed trajectories are not obtained when they start from the arrangements near the regular single-file flows or regular (symmetric) double-file flows, suggesting that these flows are unstable under the conditions examined.

Mathematics↗
PubMed1988

Interaction of stress and growth in a fibrous tissue.

The influence of stress on the growth and remodeling of a soft biological tissue is considered. For this purpose, the soft tissue is idealized as a fiber network. The stress-free lengths of the fibers composing the network are not fixed as in an inert elastic solid, but are assumed to evolve as a result of growth and stress adaptation. Similarly, the topology of the fiber network may also evolve under the application of stress. A set of constitutive equations are proposed which relate the tissue stress to the deformation of the tissue as well as to its growth and microstructure. It is shown that distinctly different growth patterns which may arise during initial growth or wound healing can be modeled by the proposed mathematical analysis.

Connective Tissue↗
PubMed1988

Numerical study of asymmetric flows of red blood cells in capillaries.

Experimental studies have shown that red blood cells in capillaries may flow in single-file or multifile arrangements. To model multifile rheological behavior, the asymmetric flows of rigid circular cylinders in a two-dimensional channel are studied by numerical analysis. The rigid circular cylinders are arranged off-center in a channel in a row or two rows with equal spacings. The motion of the suspending fluid is analyzed by the finite element method applied to the Stokes equation, and the motions of the particles are simultaneously determined under the zero force and zero moment conditions appropriate to neutorally buoyant particles. The velocity difference between the particles and the bulk flow is significantly affected by the arrangement of the particles. The particle velocity is reduced as the particles are moved away from the centerline of the channel. At a constant concentration of the particles, the relative apparent viscosity of an off-center arrangement is considerably higher than that of a single-file flow of the particles located on the centerline of the channel. The present results suggest that changes of the radial distribution of red cells flowing through narrow vessels may lead to alterations of the Fahraeus and Fahraeus-Lindqvist effects.

Blood Flow Velocity↗
PubMed1988

Leukocyte relaxation properties.

Study of the mechanical properties of leukocytes is useful to understand their passage through narrow capillaries and interaction with other cells. Leukocytes are known to be viscoelastic and their properties have been established by micropipette aspiration techniques. Here, the recovery of leukocytes to their normal spherical form is studied after prolonged deformation in a pipette which is large enough to permit complete entry of the leukocyte. The recovery history is characterized by the time history of the major diameter (d1) and minor diameter (d2). When the cell is removed from the pipette, it shows initially a small rapid recoil followed by a slower asymptotic recovery to the spherical shape. In the presence of cell activation and formation of pseudopods, the time history for recovery is prolonged compared with passive cell recovery. If a protopod pre-existed during the holding period, the recovery only begins when the protopod starts to retract.

Cell Movement↗
PubMed1988

A continuum model of protrusion of pseudopod in leukocytes.

The morphology of human leukocytes, the biochemistry of actin polymerization, and the theory of continuum mechanics are used to model the pseudopod protrusion process of leukocytes. In the proposed model, the pseudopod is considered as a porous solid of F-actin network, the pores of which are full of aqueous solution. G-actin is considered as a "solute" transported by convection and diffusion in the fluid phase. The pseudopod grows as actin filaments elongate at their barbed ends at the tip of the pseudopod. The driving force of extension is hypothesized as being provided by the actin polymerization. It is assumed that elongation of actin filaments, powered by chemical energy liberated from the polymerization reaction, does mechanical work against opposing pressure on the membrane. This also gives rise to a pressure drop in the fluid phase at the tip of the pseudopod, which is formulated by an equation relating the work done by actin polymerization to the local state of pressure. The pressure gradient along the pseudopod drives the fluid filtration through the porous pseudopod according to Darcy's Law, which in turn brings more actin monomers to the growing tip. The main cell body serves as a reservoir of G-actin. A modified first-order equation is used to describe the kinetics of polymerization. The rate of pseudopod growth is modulated by regulatory proteins. A one-dimensional moving boundary problem based on the proposed mechanism has been constructed and approximate solutions have been obtained. Comparison of the solutions with experimental data shows that the model is compatible with available observations. The model is also applicable to growth of other cellular systems such as elongation of acrosomal process in sperm cells.

Acrosome↗
PubMed1988

Passive deformation analysis of human leukocytes.

The following analysis presents an experimental and theoretical study of the passive viscoelastic behavior of human leukocytes. Individual neutrophils in EDTA were observed both during their partial aspiration into a small micropipette and after expulsion from a large micropipette where the cell had been totally aspirated and deformed into a sausage shape. To analyze the data, a passive model of leukocyte rheology has been developed consisting of a cortical shell containing a Maxwell fluid which describes the average properties of the cell cytoplasm. The cortical shell represents a crosslinked actin layer near the surface of the cell and is assumed to be under pre-stressed tension. This model can reproduce the results of experiments using micropipette for both short-time small deformation and slow recovery data after large deformation. In addition, a finite element scheme has been established for the same model which shows close agreement with the analytical solution.

Blood Viscosity↗
PubMed1988

Transient relative motion of two cells in a channel flow.

The hydrodynamic interaction of a red blood cell and a white blood cell in microvessels is studied, by use of a two-dimensional numerical model. The red blood cell, modeled as a small rigid circular cylinder, and the white blood cell, modeled as a larger rigid circular cylinder, are immersed in an incompressible Newtonian fluid in a two-dimensional channel. It is assumed that no external force or moment acts on the model cells, and the effect of inertia forces on the motion of the fluid and the cells is neglected. The velocity field of the suspending fluid and the instantaneous velocities of the two model cells are computed by the finite element method. Using the translational velocities of the model cells obtained, the trajectories of their relative motion are determined, for various initial positions. It is shown that the cells may or may not pass each other or separate, depending on the initial positions. The present results compare well to the experimental results.

Animals↗
PubMed1987

Studies on orthocephalization: growth behavior of the rat skull in the period 13-49 days as described by the finite element method.

Rat cranial skeletal growth was studied, using a cross-sectional data set, for the period 13-49 days by the application of the concepts of continuum mechanics and the numerical techniques of the finite element method (FEM). In contrast to the methods of conventional craniometry (CM) and roentgenographic cephalometry (RCM) the FEM permits fine scale, reference frame invariant descriptions and analysis of growth behavior. This advantage was demonstrated by a numerical example of the use of FEM. The skull was discretized into a number of two-dimensional, triangular elements, whose enclosed areas corresponded closely to both specific skeletal structures and to related functional matrices. Since it was assumed presently that the growth behavior of all of the points enclosed within a given element was similar, the application of the functional matrix hypothesis permitted an integrated description of the growth of the skeletal structure and functional matrix related to each element. The principal locus of rotation of the facial skull, relative to the cranial base, is the inferior frontoethmoidal articulation, a motion that includes a rigid body rotation. Other active and passive skeletal and visceral growth events associated with orthocephalization were located and described. Finally it was shown that the morphogenetically important growth behavior of other portions of the rat head were not directly involved in orthocephalization.

Aging↗
PubMed1987

Rheology of leukocytes.

The rheological properties of human leukocytes (WBCs) have been studied by micropipette aspiration and filtration tests. A small aspiration pressure applied via a micropipette (diameter approximately equal to 3 micron) causes the WBC to undergo a rapid elastic deformation followed by a slow creep. The data can be analyzed with a viscoelastic model: an elastic element K1 in parallel with a Maxwell element (elastic element K2 in series with viscous element mu). Neutrophils and B lymphocytes are similar in K1, K2, and mu, but these values are higher for T lymphocytes. Treatment of neutrophils with colchicine decreases K2 and mu without changing K1, whereas cytochalasin B decreases all three coefficients; these results indicate the importance of cytoskeletal microtubules and microfilaments in WBC rheology. In the presence of Ca2+, WBCs form protopods which have increased viscoelastic coefficients. Inhibition of protopod formation with pentoxifylline is associated with an increase in WBC deformability. The ruffled surface of the apparently round WBC provides an area about twice that needed to enclose a smooth sphere of the same volume; this geometric feature plays an important role in whole WBC deformability tested through 4-5 micron filter pores or micropipettes. Because of its larger volume and higher cellular viscosity, each WBC is equivalent to approximately 700 erythrocytes in its tendency to block 5-micron channels. The rheology of WBCs has significant implications in their functional behavior, including flow through the microcirculation and interaction with endothelial cells.

Capillaries↗
PubMed1987

Theory of filtration of mixed blood suspensions.

A theory is developed for the flow of suspensions of blood cells through filters in which the properties of the cells are defined by statistical distributions. It is shown that conditions are generally transient, and computational procedures are developed to compute the pressure drop and the fraction of the pores of the filter containing cells of various types as a function of time. The computations show a large influence of very small concentrations of stiff cells which gradually collect in the filter and effectively plug the filter during the time of a typical test. It is also shown that the mean value of the resistance offered by a cell population with a limited distribution of resistances is more important than dispersion of resistances about the mean in determining the observable pressure curve. Experimental data are presented demonstrating that the drug pentoxifylline reduces the stiffness of leukocytes.

Blood Flow Velocity↗
PubMed1987

Effects of pre-weaning undernutrition on 21 day-old male rat skull form as described by the finite element method.

Conventional Roentgenographic Cephalometric Methods (RCM) have certain conceptual and geometric constraints that ensure that their descriptions of cephalic growth and comparisons of cephalic form are reference-frame-dependent; and it is impossible to determine which, if any, RCM reference frame provides a biologically more correct description or comparison. The use of the concepts of continuum mechanics and of the numerical techniques of the Finite Element Method (FEM) overcomes these constraints and provides reference-frame-independent (invariant) growth descriptions and form comparisons. In the FEM, the structure of the head is subdivided (discretized) into a number of smaller, finite, elements. The FEM then describes the growth behavior, or compares the form, of the entire continuum of points enclosed with each element independently; in RCM only the behaviors, or comparisons, of the landmark points are described. The FEM is described and its use illustrated by a comparison of the cephalic forms of 4 groups of weanling (21 d old) rats. The 1st (control) group is derived from normally nourished dams, while the other 3 groups are derived from dams who were malnourished throughout the weaning period in 3 group specific manners. The FEM permitted reference-frame-independent comparisons of the 4 different, and group specific, head forms. These differences were reflected in the forms of each of the finite elements. The differences in element forms between the 4 groups were shown to be related primarily to nutritionally produced alterations of either neurocranial or splanchocranial viscera. These differences were expressed in the alterations of the forms of the continua enclosed within the boundaries of the several finite elements, and secondarily in the form of the cranial skeleton.

Animals↗
PubMed1987

Morphological analysis and computer-aided, three dimensional reconstruction of chondrocytic columns in rabbit growth plates.

Proximal tibial growth plates of New Zealand white rabbits were serially sectioned in parasagittal and horizontal planes for three dimensional, light microscopic analysis of the chondrocytic columns. A total of 431 columns was analysed. Of these, 258 columns extended through the full height of the growth plate. The remaining columns were considerably shorter, being located either predominantly in the epiphyseal half of the growth plate (100) or in the metaphyseal half of the growth plate (73). The epiphyseal and metaphyseal columns were found in clusters in the plate. Some columns in all three groups had interruptions along their length, while others had duplications. Computer-aided, three dimensional graphic reconstructions were prepared of a selected group of columns. The reconstructions illustrated the variability in the morphology and the dimensions of the neighbouring chondrocytic columns. The observations suggest that chondrocytic columns in rabbit growth plates are replaced regularly and that the small cell zone may play an important role as the cellular source for column renewal.

Animals↗
PubMed1985

Finite element method modeling of craniofacial growth.

The application of the concepts of continuum mechanics and of the numerical techniques of the finite element method permits the development of a new and potentially clinically useful method of describing craniofacial skeletal growth. This new method differs from those associated with customary roentgenographic cephalometry in that its descriptions and analyses are invariant; that is, they are independent of any method of registration and superimposition. Such invariance avoids the principal geometric constraint explicit in all analytical methods associated with conventional roentgenographic cephalometry. The conceptual and mathematical bases of the finite element method (FEM) are presented and illustrated by the numerical and graphic descriptions of the two-dimensional growth of the rat skull, for which two sets of longitudinal growth data are used. In practice, the FEM permits analysis of the skull at a scale significantly finer than previously possible, by considering cranial structure as consisting of a relatively large number of contiguous finite elements. For each such element, independently, it is then possible to describe and depict both the magnitude and the direction of temporal size and shape changes occurring in that element relative to itself at some initial time. It is emphasized that such descriptions are completely independent of any local reference frame.

Aging↗