Leukocyte rolling in rat mesentery venules: distribution of adhesion bonds and the effects of cytoactive agents

A new method of analyzing in vivo measurements of leukocyte WBC rolling along venular endothelium (EC) has been developed to extract insightful information on the dynamics of WBC-EC bond formation and disruption. The rolling velocity of WBCs was obtained by intravital microscopy of rat mesenteric venules. For the "spontaneous" rolling observed following exteriorization of the mesentery, we estimated that the average distance between clusters of adhesion bonds which tether a rolling cell to the venular wall was about 2 microm, and that the average lifetime of a bond cluster at the trailing edge of the rolling cell, from its exposure to the tensile force to its release, was on the order of 0.05 s. Both the inter-cluster distance and the lifetime were significantly reduced by treatments with the chemoattractant N-formyl-methionyl-leucyl-phenylalanine and the cytokine interleukin-1, while the average lifetime of the stretched bond clusters was not significantly changed by treatment with the cytoskeleton-modifying agents cytochalasin B and colchicine. Each of the four treatments significantly reduced the heterogeneity in the cell rolling velocity, presumably by the selective recruitment of WBC subsets from the circulating WBC population or by a reduction in the heterogeneity of endothelial adhesiveness. These results were analyzed in the context of in vitro data in the literature on molecular bonds of cell adhesion. The findings suggest that, in the case of "spontaneous" rolling, there are on average approximately 2-3 clusters of adhesion bonds between a rolling cell and the vessel wall, and approximately five bonds in each cluster.

Interaction of Force-Fitting and Surface Roughness of Implants

BACKGROUND

Increased surface roughness may increase installation torque and thus appear to increase the initial stability of an implant. However, it is not immediately clear if the increased torque is attributable to an increase in the effective diameter of the implant or to increased resistance of the bone because of the greater roughness.

PURPOSE

Force-fitting stresses arise when an implant is placed into a predrilled hole of smaller-diameter in bone. The purpose of this report is to discuss the interaction of force-fitting stresses and surface roughness effects and to develop some general guidelines as to clinical procedures based on this theory.

MATERIALS AND METHODS

Solutions for the force-fitting stresses are derived from well-known equations of elasticity.

RESULTS

Substantial force-fitting stresses on the order of several tens of MPa can be generated when a titanium cylinder is placed into a hole in bone, the diameter of which is only 100 microns smaller.

CONCLUSION

When a hole slightly smaller than the implant diameter is prepared for implant placement, force-fitting stress increases installation torque and stability can be induced. Thus, large surface roughness of implants should not be viewed as an exclusive mechanism for providing a desirable level of initial fixity. Smaller roughness with the same mean diameter is equally effective.

Similarity of Stress Distribution in Bone for Various Implant Surface Roughness Heights of Similar Form

BACKGROUND

Surface roughness effects on osseointegration can be considered from two viewpoints: purely mechanical effects of stresses attributable to roughness and cell and molecular response to surface roughness.

PURPOSE

The goal of this study is to provide a theoretical basis to understand the effects of surface roughness size on the osseointegration of implants. The emphasis is primarily on the purely mechanical effects.

METHODS

Mathematical proofs of some similarity principles are provided.

RESULTS

The main result is that if the geometric form of the roughness or thread cross-section is held constant, then the peak elastic stress depends on the form but not on the size of the roughness or thread height.

CONCLUSION

The purely mechanical effects of surface roughness are well understood on a theoretical basis. The interpretation for clinical procedures, however, needs careful attention. Considering the present state of knowledge and clinical experience, no change in the roughness height of current practice is recommended.

Shear stress induces spatial reorganization of the endothelial cell cytoskeleton

The morphology of endothelial cells in vivo depends on the local hemodynamic forces. Cells are polygonal and randomly oriented in areas of low shear stress, but they are elongated and aligned in the direction of fluid flow in regions of high shear stress. Endothelial cells in vitro also have a polygonal shape, but the application of shear stress orients and elongates the cells in the direction of fluid flow. The corresponding spatial reorganization of the cytoskeleton in response to the applied hemodynamic forces is unknown. In this study, we determined the spatial reorganization of the cytoskeleton throughout the volume of cultured bovine aortic endothelial cells after the cells had been exposed to a physiological level of shear stress for 0, 1.5, 3, 6, 12, or 24 h. The response of the monolayer to shear stress was not monotonic; it had three distinct phases. The first phase occurred within 3 h. The cells elongated and had more stress fibers, thicker intercellular junctions, and more apical microfilaments. After 6 h of exposure, the monolayer entered the second phase, where the cells exhibited characteristics of motility. The cells lost their dense peripheral bands and had more of their microtubule organizing centers and nuclei located in the upstream region of the cell. The third phase began after 12 h of exposure and was characterized by elongated cells oriented in the direction of fluid flow. The stress fibers in these cells were thicker and longer, and the heights of the intercellular junctions and microfilaments were increased. These results suggest that endothelial cells initially respond to shear stress by enhancing their attachments to the substrate and neighboring cells. The cells then demonstrate characteristics of motility as they realign. The cells eventually thicken their intercellular junctions and increase the amount of apical microfilaments. The time course of rearrangement can be described as a constrained motility that produces a new cytoskeletal organization that alters how the forces produced by fluid flow act on the cell and how the forces are transmitted to the cell interior and substrate.

Strain distribution in the layered wall of the esophagus

The function of the esophagus is to move food by peristaltic motion, which is the result of the interaction of the tissue forces in the esophageal wall and the hydrodynamic forces in the food bolus. To understand the tissue forces in the esophagus, it is necessary to know the zero-stress state of the esophagus, and the stress-strain relationships of the tissues. This article is addressed to the first topic: the representation of zero-stress state of the esophagus by the states of zero stress-resultant and zero bending moment of the mucosa-submucosa and the muscle layers. It is shown that at the states of zero stress-resultant and zero bending moment, these two layers are not tubes of smaller radii but are open sectors whose shapes are approximately cylindrical and more or less circular. When the sectors are approximated by circular sectors, we measured their radii, opening angles, and average thickness around the circumference. Data on the radii, thickness-to-radius ratios, and the opening angles of these sectors are presented. Knowing the zero-stress state of these two layers, we can compute the strain distribution in the wall at any in vivo state, as well as the residual strain in the esophageal wall at the no-load state. The results of the in vivo states are compared to those obtained by a conventional approach, which treats the esophageal wall as a homogeneous material, and to another popular simplification, which ignores the residual strains completely. It is shown that the errors caused by the homogeneous wall assumption are relatively minor, but those caused by ignoring the residual strains completely are severe.

Chained vesicles in vascular endothelial cells

There is extensive ultrastructural evidence in endothelium for the presence of chained vesicles or clusters of attached vesicles, and they are considered to be involved in specific transport mechanisms, such as the formation of trans-endothelial channels. However, few details are known about their mechanical characteristics. In this study, the formation mechanism and mechanical aspects of vascular endothelial chained vesicles are investigated theoretically, based on membrane bending strain energy analysis. The shape of the axisymmetric vesicles was computed on the assumption that the cytoplasmic side of the vesicle has a molecular layer or cytoskeleton attached to the lipid bilayer, which induces a spontaneous curvature in the resting state. The bending strain energy is the only elasticity involved, while the shear elasticity is assumed to be negligible. The surface area of the membrane is assumed to be constant due to constant lipid bilayer thickness. Mechanically stable shapes of chained vesicles are revealed, in addition to a cylindrical tube shape. Unfolding of vesicles into a more flattened shape is associated with increase in bending energy without a significant increase in membrane tension. These results provide insights into the formation mechanism and mechanics of the chained vesicle.

A mechanism for erythrocyte-mediated elevation of apparent viscosity by leukocytes in vivo without adhesion to the endothelium

In spite of the relatively small number of leukocytes in the circulation, they have a significant influence on the perfusion of such organs as skeletal muscle or kidney. However, the underlying mechanisms are incompletely understood. In the current study a combined in vivo and computational approach is presented in which the interaction of individual freely flowing leukocytes with erythrocytes and its effect on apparent blood viscosity are explored. The skeletal muscle microcirculation was perfused with different cell suspensions with and without leukocytes or erythrocytes. We examined a three-dimensional numerical model of low Reynolds number flow in a capillary with a train of erythrocytes (small spheres) in off-axis positions and single larger leukocytes in axisymmetric positions. The results indicate that in order to match the slower axial velocity of leukocytes in capillaries, erythrocytes need to position themselves into an off-axis position in the capillary. In such off-axis positions at constant mean capillary velocity, erythrocyte axial velocity matches on average the axial velocity of the leukocytes, but the apparent viscosity is elevated, in agreement with the whole organ perfusion observations. Thus, leukocytes influence the whole organ resistance in skeletal muscle to a significant degree only in the presence of erythrocytes.

An in-vivo method for biomechanical characterization of bone-anchored implants

Experimental equipment for in-vivo registrations of pull-out load vs displacement, applied torque vs angle of rotation, and lateral load vs lateral displacement has been developed. The set-up is designed for testing three implants inserted in a row and osseointegrated in, for instance, the proximal tibia of the beagle dog. The details of the set-up are described and considerations of the stress distributions are reported.

Effects of disturbed flow on endothelial cells

Atherosclerotic lesions tend to localize at curvatures and branches of the arterial system, where the local flow is often disturbed and irregular (e.g., flow separation, recirculation, complex flow patterns, and nonuniform shear stress distributions). The effects of such flow conditions on cultured human umbilical vein endothelial cells (HUVECs) were studied in vitro by using a vertical-step flow channel (VSF). Detailed shear stress distributions and flow structures have been computed by using the finite volume method in a general curvilinear coordinate system. HUVECs in the reattachment areas with low shear stresses were generally rounded in shape. In contrast, the cells under higher shear stresses were significantly elongated and aligned with the flow direction, even for those in the area with reversed flow. When HUVECs were subjected to shearing in VSF, their actin stress fibers reorganized in association with the morphological changes. The rate of DNA synthesis in the vicinity of the flow reattachment area was higher than that in the laminar flow area. These in vitro experiments have provided data for the understanding of the in vivo responses of endothelial cells under complex flow environments found in regions of prevalence of atherosclerotic lesions.

Biomechanical characterization of osseointegration: an experimental in vivo investigation in the beagle dog

This study reports the results of torsion tests, pull-out tests, and lateral loading tests on osseointegrated commercially pure titanium fixtures. The tests were performed in vivo on six beagle dogs. Three fixtures, each with a diameter of 3.7 mm, were installed bilaterally in the tibia of each animal. The mean maximal pull-out load was 1.55 kN (n = 4), the mean maximal lateral transverse load was 0.21 kN (n = 2), the mean maximal lateral axial load was 0.18 kN (n = 2), the mean breakpoint torque was 0.31 Nm (n = 3), and the mean maximal torque was 0.43 Nm (n = 3). The torsion test revealed an almost immediate plastic deformation of the interface between the implant and bone; this indicates that although the contact between the bone and the implant is close, there is no strong bond, at least not in shear. The major transfer of load from the implant to the surrounding bone tissue must therefore depend on the design of the implant. A histological evaluation with measurements of the amount of bone in contact with the fixtures was performed. By the use of the histological and mechanical data, it is possible to estimate shear stresses in bone tissue (pull-out test) and in the interface (torque test). The mean maximal shear stress in bone tissue in the pull-out tests was 100 MPa (n = 4); the mean shear stress in the interface was 4.3 MPa (n = 3) in the torsion tests at the breakpoint torque and was 6.0 MPa (n = 3) at the maximal torque. It was also possible to estimate the shear modulus of elasticity in the pull-out and torque tests. The mean shear modulus in pull-out was 119 MPa (n = 4), and the mean apparent shear modulus in torsion was 9 kPa (n = 3) for an assumed interface thickness of 100 nm and was 86 kPa (n = 3) for an assumed interface thickness of 1,000 nm.

Mechanisms for increased blood flow resistance due to leukocytes

Despite the small number of leukocytes relative to erythrocytes in the circulation, leukocytes contribute significantly to organ blood flow resistance. The present study was designed to investigate whether interactions between leukocytes and erythrocytes affect the pressure-flow relationship in a hemodynamically isolated rat gracilis muscle. At constant arterial flow rate, arterial pressure was increased significantly when relatively few physiological counts of leukocytes were added to a suspension containing erythrocytes at physiological hematocrits. However, the arterial pressure after perfusion of similar numbers of isolated leukocytes without erythrocytes was only slightly increased. An increase in resistance was also observed when leukocytes were replaced with 6-micron microspheres. We propose a new mechanism for increasing the hemodynamic resistance that involves hydrodynamic interactions between leukocytes and erythrocytes. In the presence of larger and less deformable leukocytes, erythrocytes move through capillaries more slowly than without leukocytes. Therefore erythrocytes are displaced from their axial positions. Slowing and radial displacement of erythrocytes serve to increase the relative apparent viscosity attributable to erythrocytes, thereby causing a significant elevation of organ blood flow resistance.

Morphometry and strain distribution in guinea pig duodenum with reference to the zero-stress state

The aim of the present study is to determine the distribution of residual circumferential strains along the duodenum in anesthetized guinea pigs. A silicone elastomer was allowed to harden in the duodenal lumen under a pressure of 0.7 kPa. The duodenum was excised with the cast and photographed. The zero-stress state was obtained by cutting rings of duodenum radially. The geometric configuration at the zero-stress state is of fundamental importance, because it is the basic state with respect to which the physical stresses and strains are defined. A basic piece of information is the way the tangent vector rotates from one end of the circumference to the other. In the duodenum at zero-stress state, the total rotation of the tangent from one tip to the other is -500 to -850 , with the lowest absolute value in the proximal duodenum. In other words, the duodenum usually turns itself inside out on changing from a loaded state to the zero-stress state. The serosal circumference, the duodenal wall thickness, and the ratio of wall thickness to mucosal circumference decreased in the distal direction. In the pressurized state, the serosal Cauchy strain was tensile and increased in the distal direction; the mucosal Cauchy strain was compressive in the proximal half of the duodenum and tensile in the distal half. The large circumferential residual strains must be taken into account in a study of physiological problems in which the stresses and strains are important, e.g., the bolus transport function.

Kinematics of surface growth

In this paper a general mathematical framework is developed to describe cases of fixed and moving growth surfaces. This formulation has the mathematical structure suggested by Skalak (1981), but is extended herein to include discussion of possible singularities, incompatibilities, residual stresses and moving growth surfaces. Further, the general theoretical equations necessary for the computation of the final form of a structure from the distribution of growth velocities on a growth surface are presented and applied in a number of examples. It is shown that although assuming growth is always in a direction normal to the current growth surface is generally sufficient, growth at an angle to the growth surface may represent the biological reality more fully in some respects. From a theoretical viewpoint, growth at an angle to a growth surface is necessary in some situations to avoid postulating singularities in the growth velocity field. Examples of growth on fixed and moving surfaces are developed to simulate the generation of horns, seashells, antlers, teeth and similar biological structures.

Spectrin properties and the elasticity of the red blood cell membrane skeleton

Two models of spectrin elasticity are developed and compared to experimental measurements of the red blood cell (RBC) membrane shear modulus through the use of an elastic finite element model of the RBC membrane skeleton. The two molecular models of spectrin are: (i) An entropic spring model of spectrin as a flexible chain. This is a model proposed by several previous authors. (ii) An elastic model of a helical coiled-coil which expands by increasing helical pitch. In previous papers, we have computed the relationship between the stiffness of a single spectrin molecule (K) and the shear modulus of a network (mu), and have shown that this behavior is strongly dependent upon network topology. For realistic network models of the RBC membrane skeleton, we equate mu to micropipette measurements of RBCs and predict K for spectrin that is consistent with the coiled-coli molecular model. The value of spectrin stiffness derived from the entropic molecular model would need to be at least 30 times greater to match the experimental results. Thus, the conclusion of this study is that a helical coiled-coil model for spectrin is more realistic than a purely entropic model.

Force acting on spheres adhered to a vessel wall

To evaluate the force and torque acting on leukocytes attached to the vessel wall, we numerically study the flow field around the leukocytes by using rigid spherical particles adhered to the wall of a circular cylindrical tube as a model of adherent leukocytes. The adherent particles are assumed to be placed regularly in the flow direction with equal spacings, in one row or two rows. The flow field of the suspending fluid is analyzed by a finite element method applied to the Stokes equations, and the drag force and torque acting on each particle, as well as the apparent viscosity, are evaluated as a function of the particle to tube diameter ratio and the particle arrangements. For two-row arrangements of adhered particles where neighboring particles are placed alternately on opposite sides of the vessel, the drag and the torque exerted on each particle are higher than those for single-row arrangements, for constant particle to tube diameter ratio and axial spacing between neighboring particles. This is enhanced for larger particles and smaller axial spacings. The apparent viscosity of the flow through vessels with adhered particles is found to be significantly higher than that without adhered particles or when the particles are freely floating through the vessels.

Influence of network topology on the elasticity of the red blood cell membrane skeleton

A finite-element network model is used to investigate the influence of the topology of the red blood cell membrane skeleton on its macroscopic mechanical properties. Network topology is characterized by the number of spectrin oligomers per actin junction (phi a) and the number of spectrin dimers per self-association junction (phi s). If it is assumed that all associated spectrin is in tetrameric form, with six tetramers per actin junction (i.e., phi a = 6.0 and phi s = 2.0), then the topology of the skeleton may be modeled by a random Delaunay triangular network. Recent images of the RBC membrane skeleton suggest that the values for these topological parameters are in the range of 4.2 < phi a < 5.5 and 2.1 < phi s < 2.3. Model networks that simulate these realistic topologies exhibit values of the shear modulus that vary by more than an order of magnitude relative to triangular networks. This indicates that networks with relatively sparse nontriangular topologies may be needed to model the RBC membrane skeleton accurately. The model is also used to simulate skeletal alterations associated with hereditary spherocytosis and Southeast Asian ovalocytosis.

Asymmetric flows of spherical particles in a cylindrical tube

To study the rheological behavior of blood cells in various flow patterns through narrow vessels, we analyzed numerically the motion of blood cells arranged in one row or two rows in tube flow, at low Reynolds numbers. The particles are assumed to be identical rigid spheres placed periodically along the vessel axis at off-axis positions with equal spacings. The flow field of the suspending fluid in a circular cylindrical tube is analyzed by a finite element method applied to the Stokes equations, and the motion of each particle is simultaneously determined by a force-free and torque-free condition. In both cases of single- and two-file arrangements of the particles, their longitudinal and angular velocities are largely affected by the radial position and the axial spacing between neighboring particles. The apparent viscosity of the asymmetric flows in higher than that of the symmetric flow where particles are located on the tube centerline, and this is more pronounced when particles are placed farther from the tube centerline and when the axial distance between neighboring particles is reduced.

Compatibility and the genesis of residual stress by volumetric growth

The equations of compatibility which are pertinant for growth strain fields are collected and examples are given in simply-connected and multiply-connected regions. Compatibility conditions for infinitesimal strains are well known and the possibilities of Volterra dislocations in multiply-connected regions are enumerated. For finite growth strains in a multiply-connected regions, each case must be examined individually and no generalizations in terms of Volterra dislocations are available. Any incompatible growth strains give rise to residual stresses which are known to occur in many tissues such as the heart, arterial wall, and solid tumors.

A model of the hydrostatic skeleton of the leech

A mathematical model of the hydrostatic skeleton of the leech has been developed to predict the shape of and internal pressure within the animal in response to a given pattern of motor neuron activity in different behaviors. The model incorporates experimental data on: the dimensions of the animal at behavioral extremes, the passive properties of the tissues, the active length-tension behavior of the muscles in response to neural activation, the relations between firing frequencies and forces developed by the muscles. The model is based on three general assumptions: (i) the cross-sectional geometry of each segment is elliptical, (ii) the volume of each segment remains constant during movement, (iii) the shape of the animal reflects dimensions that minimize the total potential energy. Presently the model is implemented to simulate the vermiform elongation of the leech, predicting the shape and the pressure changes during behavior. The results are in good agreement with the experimental measurements. The pattern of motor neuronal activity was determined by the known intersegmental travel time and estimated delay time between relaxation of the longitudinal muscles and the activation of the circular muscles. The anesthetized state of the leech was taken as the reference state for the model in which the active and passive stresses are zero.

Mapping motor neurone activity to overt behaviour in the leech: internal pressures produced during locomotion

Several behaviour patterns have been studied in the leech at both the kinematic and neuronal levels. However, very little is known about how patterns of motor neurone activity map to actual movements. Internal pressure is an essential biomechanical property in this process, being responsible for producing the rigidity and posture that allow the directed delivery of forces produced by muscle contraction. To obtain a better understanding of the biomechanical processes involved in movement of the leech, we have measured the internal pressure of the animal by placing catheters through the body wall and into the gut of intact animals showing normal patterns of behaviour. Each type of behaviour had a characteristic pressure waveform. The elongation phase of crawling produced a rapid increase in pressure that peaked when midbody segments were maximally elongated. The pressure produced during the contraction phase of crawling depended on the type of crawl, only inchworm crawling producing a second peak. Whole-body shortening in response to a head poke also produced a pressure peak, but it had a faster rise time. Swimming produced the largest pressure, which was marked by a large sustained increase that fluctuated phasically with undulations of the body. Dual pressure recordings using two catheters demonstrated that pressure was not uniform along the length of the leech, indicating that the body cavity is functionally compartmentalised. Injecting fluid into the gut via a recording catheter allowed us to determine the effects of increasing internal volume on pressure. In line with previous predictions made using an abstract biomechanical model of the leech hydroskeleton, we found that an increase in the volume caused a reduction in the pressure. We are in the process of constructing a more realistic biomechanical model of the leech, based on actual data reported elsewhere. The results in this paper will provide key tests for refining these models.

Mapping motor neuron activity to overt behavior in the leech. I. Passive biomechanical properties of the body wall

As an initial step in constructing a quantitative biomechanical model of the medicinal leech (Hirudo medicinalis), we determined the passive properties of its body wall over the physiological range of dimensions. The major results of this study were: 1. The ellipsoidal cross section of resting leeches is maintained by tonic muscle activation as well as forces inherent in the structure of the body wall (i.e., residual stress). 2. The forces required for longitudinal and circumferential stretch to maximum physiological dimensions were similar in magnitude. Cutting out pieces of body wall did not affect the passive longitudinal or circumferential properties of body wall away from the edges of the cut. 3. The strain (i.e., the percentage change in dimension of different body segments when subject to the same force was identical, despite differences in muscle cross-sections. 4. Serotonin, a known modulator of tension in leech muscles, affected passive forces at all physiological muscle lengths. This suggests that the longitudinal muscle is responsible for at least part of the passive tension of the body wall. 5. We propose a simple viscoelastic model of the body wall. This model captures the dynamics of the passive responses of the leech body wall to imposed step changes in length. Using steady-state passive tensions predicted by the viscoelastic model we estimate the forces required to maintain the leech at any given length over the physiological range.

An elastic network model based on the structure of the red blood cell membrane skeleton

A finite element network model has been developed to predict the macroscopic elastic shear modulus and the area expansion modulus of the red blood cell (RBC) membrane skeleton on the basis of its microstructure. The topological organization of connections between spectrin molecules is represented by the edges of a random Delaunay triangulation, and the elasticity of an individual spectrin molecule is represented by the spring constant, K, for a linear spring element. The model network is subjected to deformations by prescribing nodal displacements on the boundary. The positions of internal nodes are computed by the finite element program. The average response of the network is used to compute the shear modulus (mu) and area expansion modulus (kappa) for the corresponding effective continuum. For networks with a moderate degree of randomness, this model predicts mu/K = 0.45 and kappa/K = 0.90 in small deformations. These results are consistent with previous computational models and experimental estimates of the ratio mu/kappa. This model also predicts that the elastic moduli vary by 20% or more in networks with varying degrees of randomness. In large deformations, mu increases as a cubic function of the extension ratio lambda 1, with mu/K = 0.62 when lambda 1 = 1.5.

Time-dependent behavior of interstitial fluid pressure in solid tumors: implications for drug delivery

Elevated interstitial fluid pressure (IFP) may constitute a significant physiological barrier to drug delivery in solid tumors. Strategies for overcoming this barrier have not been developed to date. To identify and characterize various mechanisms regulating IFP and to develop strategies for overcoming the IFP barrier, we modeled the tumor as a poroelastic solid. We used this model to simulate the effect of changes in microvascular pressure and tumor blood flow (TBF) on IFP. To test model predictions, the effects of changes in arterial pressure and TBF on IFP were measured using a tissue-isolated tumor preparation. IFP in the center of an isolated tumor was predicted to follow variation of the arterial pressure with a time delay of the order of magnitude of 10 s, and this delay was found to be 11 +/- 6 s experimentally. Following a cessation of TBF, the time constant of the drop in IFP was predicted to be of the order of 1000 s and was found to be 1500 +/- 900 s experimentally. The former time scale is characteristic of transcapillary fluid exchange, and the latter of percolation of fluid through the interstitial matrix. Relying on the good agreement between theoretical predictions and experimental data, we estimated the effect of blood pressure modulation on macromolecular uptake in solid tumors. Our results show that no appreciable increase of macromolecular uptake should occur either by an acute or by a chronic increase of blood pressure. On the other hand, higher uptake would result from periodic modulation of blood pressure. Therefore, the effectiveness of a vasoconstrictor such as angiotensin II to increase macromolecular delivery should be significantly enhanced by periodic rather than bolus or continuous administration of the vasoactive agent.

A stochastic model of leukocyte rolling

Selectin-mediated leukocyte rolling under flow is an important process in leukocyte recruitment during inflammation. The rolling motion of individual cells has been observed to fluctuate randomly both in vivo and in vitro. This paper presents a stochastic model of the micromechanics of cell rolling and provides an analytical method of treating experimental data. For a homogeneous cell population, the velocity distribution is obtained in an analytical form, which is in good agreement with experimentally determined velocity histograms obtained previously. For a heterogeneous cell population, the model provides a simple, analytical method of separating the contributions of temporal fluctuations and population heterogeneity to the variance of measured rolling velocities. The model also links the mean and variance of rolling velocities to the molecular events underlying the observed cellular motion, allowing characterization of the distribution and release rate of the clusters of molecular bonds that tether the cell to substratum. Applying the model to the analysis of data obtained for neutrophils rolling on an E-selectin-coated surface at a wall shear stress of 1.2 dyn/cm2 yields estimations of the average distance between bond clusters (approximately micron) and the average time duration of a bond cluster resisting the applied fluid force (approximately 0.5 s).

Modeling of molecular mechanisms of cell adhesion

Cellular adhesion is a process of great importance in biology. We present a simple model of the adhesion process in which the molecular mechanisms involve a receptor, a ligand, and the cytoskeleton of the cell. Based on the energetic consideration of the process, we propose a molecular interpretation of the existing experimental data. The model suggests that the interaction of the receptor and (or) receptor-ligand with the cytoskeleton can have important influence on the formation and strength of the adhesion complex as well as on the subsequent interaction with different ligands. When conformational changes take place during the adhesion process, the characterization of the adhesion bonds based on chemical kinetics alone seems to be incomplete and must be supplemented by parameters, describing the functionality of the complex, i.e., change of the affinity for different ligands, as in the signal transduction, or the strength of the bond, as in the adhesion process.

Membrane model of endothelial cells and leukocytes. A proposal for the origin of a cortical stress

Previous models of the erythrocyte membrane have been based on the assumption that the resting curvature of the membrane is either flat or has a small curvature relative to the overall cell dimension. In contrast, several recent experimental observations, both in leukocytes and in endothelial cells, suggest that local regions of the membrane may have high membrane curvature in the resting state. The resting curvature may be of the order of plasmalemmal vesicles in endothelial cells or surface membrane folds on leukocytes. A tension is required to unfold the membrane with strain energy which depends largely on mean curvature. It is proposed that the tendency of endothelial or leukocyte membranes to wrinkle in the unstressed state may provide a restoring force, i.e. a cortical tension.

Active motion of polymorphonuclear leukocytes in response to chemoattractant in a micropipette

A novel experimental method of producing and observing the active motion of polymorphonuclear leukocytes (PMNs) using a micropipette technique has been recently developed (Usami et al., 1992). The present paper develops a quantitative theory for the chemoattractant gradients and cell locomotion observed in these experiments. In previous experimental methods (e.g., the Boyden chamber, the Zygmond chamber and the Dunn chamber) for study chemotaxis of leukocytes, fibroblasts, and PMNs, the exact nature of the concentration gradient of the chemoattractant is unknown. The cells may themselves modify the local gradient of the chemoattractant. In experiments using the micropipette, an internal source of chemoattractant provides well-defined boundary and initial conditions which allow the computation of the chemoattractant concentration gradient during the active locomotion of the PMNs. Since the cell completely fills the pipette lumen, convection is limited to the motion of the cells themselves. In coordinates moving with cell, it is assumed that diffusion is the only mechanism of mass transport of the chemoattractant (fMLP). Computations of the fMLP concentration during locomotion of the cell were carried out for a range of rates of fMLP binding by the receptors expressed on the front face of the cell membrane. The results show that the front face of the cell is subjected to increasing fMLP concentration during the cell motion. The sequence of events involve receptor binding of fMLP, signal transduction, polymerization of the cell cytoskeleton at the membrane of the front face, spatially dependent adhesion to the pipette wall, and localized contraction of the cytoskeleton. This sequence of events leads to the steady locomotion of the leukocytes in the micropipette. The computation of the distribution of the fMLP concentration during cell locomotion with constant velocity in micropipette experiments shows that the cell is exposed to increasing concentration of fMLP. This suggests that chemotaxis maybe induced by temporal gradient of an attractant.

Development of a device for measuring adherence of skin grafts to the wound surface

Adherence of a biological graft to the wound surface is the most important factor influencing the ultimate success of graft viability. A machine has been developed to test the adherence of biological graft materials to a substrate such as a wound surface. The peeling mode, which yields reproducible quantitative measurements of adherence, is a standard method for testing adhesives. The device is designed to continuously measure the force required to peel the graft from the substrate at a constant rate. This force is a function of the energy of adhesion per unit area of adhered surface. This device has been used to measure the peeling force of (2 x 2 cm) skin grafts which are applied to full-thickness wounds on mice. Results of tests on adherence of autografts on mice show that the peeling force increases significantly with time over the first 9 days of healing. Thus, this device is useful in quantitative comparison of various skin grafting techniques and artificial grafts.

Design and construction of a linear shear stress flow chamber

A new parallel plate flow chamber that has a linear variation of shear stress, starting from a predetermined maximum value at the entrance and falling to zero at the exit, has been designed and tested. This is in contrast to the usual rectangular channel plan which produces a constant shear stress over the entire length. The new design is based on the theory of Hele-Shaw flow between parallel plates. To verify the efficacy of the flow channel, the effect of fluid shear stress on platelet adhesion to a fibrinogen-coated glass surface was tested. The percentage of attached platelets after 5 min of shear stress is shown to be a function of shear stress. With this new flow chamber, cell-cell interactions can be studied efficiently over a wide range of shear stress using a single run at constant discharge.

Locomotion forces generated by a polymorphonuclear leukocyte

There have been very few studies which have measured the physical forces generated by cells during active movements. A special micropipette system has been designed to make it possible to observe cell motion within the pipette and to apply a pressure to counter the chemotactic migration of the cell. This provides a direct measure of the locomotion force generated by the cell. The average velocity of forward motion is 0.33 microns/s in the absence of counter-pressure. The application of a positive counter-pressure (C-P) causes a decrease in the velocity of the forward motion of the cell. At 17 cm H2O of C-P, the cell velocity drops to zero and even moves backward with a higher C-P. The results show that the decrement of velocity is linearly related to the magnitude of the C-P with a complete stoppage at a pressure of 17 cm H2O which corresponds to a force of 0.003 dyn. The maximum work rate of the cell is approximately 2.5 x 10(-8) erg/s.

Leukocyte deformability: finite element modeling of large viscoelastic deformation

An axisymmetric deformation of a viscoelastic sphere bounded by a prestressed elastic thin shell in response to external pressure is studied by a finite element method. The research is motivated by the need for understanding the passive behavior of human leukocytes (white blood cells) and interpreting extensive experimental data in terms of the mechanical properties. The cell at rest is modeled as a sphere consisting of a cortical prestressed shell with incompressible Maxwell fluid interior. A large-strain deformation theory is developed based on the proposed model. General non-linear, large strain constitutive relations for the cortical shell are derived by neglecting the bending stiffness. A representation of the constitutive equations in the form of an integral of strain history for the incompressible Maxwell interior is used in the formulation of numerical scheme. A finite element program is developed, in which a sliding boundary condition is imposed on all contact surfaces. The mathematical model developed is applied to evaluate experimental data of pipette tests and observations of blood flow.

Red cell membrane elasticity as determined by flow channel technique

The elasticity of red cell membrane was determined in a rectangular flow channel under controlled shear flow. The relation between shear stress and cell extension ratio (lambda) has been analyzed with the use of Evans' two-dimensional model. The deformed cell shapes observed experimentally agreed well with the model with lambda up to 1.4. The best correlation was found at lambda = 1.2. The analysis suggests a nonlinear extensional membrane modulus in the low stress range encountered in the flow channel. In terms of an appropriate strain parameter, the elastic modulus is shown to rise toward the level encountered in micropipette aspiration experiments. The implications of the present findings in modeling of cell mechanics and in cell hemolysis are discussed.

An interpretation of partial plug flow of concentrated suspensions

The partial plug flow of a concentrated suspension of rigid particles in a circular tube has been previously studied experimentally. It has been shown that a central core may exist in which the mean velocities of the particles and the suspending fluid are equal and constant within a cylindrical core of the flow. This behavior has been attributed to hydrodynamic interaction of the particles within the core. In the present analysis this interaction is interpreted in terms of passing vs. non-passing motions of adjacent particles. A hypothesis of a critical parameter alpha c involving the shear stress and the pressure gradient is explored and a new form of the relation of core diameter to particle size and concentration is developed based on alpha c.

Cytoplasmic rheology of passive neutrophils

The rheological properties of leukocytes are important to their effectiveness in the microcirculation. Previous studies based on in vitro data from micropipette experiments suggest that a Maxwell fluid bounded by a cortical shell with persistent tension is a realistic model for non-activated neutrophils in both the rapid and slow deformation phases. However, various viscoelastic coefficients have been obtained depending on the degree of cell deformation. In the present paper it is demonstrated that the cytoplasmic apparent viscosity and elasticity vary continuously, depending on the degree of deformation. These apparent variations are due to the inhomogeneous nature of the neutrophil internal structure. It is shown that the nucleus is much stiffer than the cytoplasm. The composite structure of the cell results in the deformation-dependent properties.

Folding of red blood cells in capillaries and narrow pores

The geometric features of red blood cells in narrow channels in vivo and in vitro were studied by electron microscopy. In rabbit myocardial capillaries about half of the red cells were folded. In polycarbonate filters with pore diameters of 2.2-4.5 microns approximately one third of the trapped red blood cells were folded. The frequency of folding did not depend on the applied pressure, which ranged from 0.1 to 8.0 cm H2O. The folding of the red blood cells in filter pores was used to estimate the bending stiffness of the membrane. An analysis based on the large deformation theory of bending of an elastic sheet was developed. Using pressures of 0.2 and 1.0 cm H2O, the bending stiffness of human red cell membranes was estimated to be approximately 2.4 - 11.6 x 10(-12) dyn-cm, which is in good agreement with other methods. A limiting radius of curvature of about 85 nm was found at higher pressures.

TEM immunogold staining of C3 from plasma onto titanium oxides

Immunogold staining in conjunction with TEM was used to observe C3 adsorption from plasma in relation to the underlying titanium structure of thermal, anodic, and electropolished oxides. Heat treatments and oxide thickness were found to have no significant effect on the adsorption behavior of C3, while surface oxide type possibly has. Surface concentration of C3 was found to be time- and plasma concentration-dependent. Evidence is given for the possible involvement of C3 in protein exchange, i.e., the Vroman effect. Diluted plasma resulted in a random distribution of gold colloids, whereas clustering occurred with undiluted plasma. Although C3 concentrations present on grain boundaries followed the same trend as that found on the surface, C3 was found to have a higher grain boundary than bulk concentration for 0.1% plasma.

Two-dimensional analysis of two-file flow of red cells along capillaries

The effect of a tank-treading motion of the red cell membrane on a staggered "zipper"-type red cell flow in capillaries is examined, using a two-dimensional theoretical model. An approximately triangular cell with a thin flexible membrane enclosing a viscous fluid is adopted as a model of the red cell. The motion of model red cells arranged periodically along a two-dimensional channel in an idealized zipper-type arrangement is analyzed numerically by a finite element method applied to the Stokes equations for the flow both inside and outside the model cells. It is shown that, if the viscosity ratio of the internal fluid to the suspending fluid is lower than a critical value, there exists a stable zipper-type arrangement of cells. In that arrangement, the cells remain stationary relative to each other with the membrane tank-treading. In contrast, inhibiting tank-treading by increasing the viscosity ratio above the critical value induces a cyclic oscillatory motion of red cells. The critical viscosity ratio increases if the channel is narrowed or if the spacing between cells is reduced. The present results suggest that the membrane tank-treading tends to stabilize zipper-type arrangements of red cells in capillaries at high hematocrit.

Passive deformations and active motions of leukocytes

The purpose of this paper is to review the development of continuum mechanics models of single leukocytes in both passive deformations and active motions and to indicate some future directions. Models of passive deformations describe the overall rheological behavior of single leukocytes under externally applied forces and predict the average mechanical properties from experimental data. Various "apparent" viscoelastic coefficients are obtained depending on the models assumed and the types of test used. Models of spontaneous motions postulate active driving mechanisms which must be derived internally from the cell itself and probably have different bases for different kind of motions. For pseudopod protrusion on leukocytes, energy transduction from chemical potential to mechanical work associated with actin polymerization at the tip of the projection is assumed to supply the motive power. For pseudopod retraction, active contraction due to actin-myosin interaction is assumed to be the driving force. The feasibility of the hypotheses are tested via numerical examples and comparison of the theoretical results with experimental measurements.

Rheological aspects of red blood cell aggregation

The rheological aspects of red blood cell aggregation include molecular phenomena, cell viscoelasticity, and bulk flow rheology. At the molecular level, rates at which bonds are formed and broken, the chemical energy liberation from bond formation, the elasticity of the cross-bridges and lateral mobility of cross-linking molecules must all be considered for a complete description of bond formation and distribution. Lateral migration of binding molecules occurs due to diffusion in the surface of the membrane but may also be influenced by the stresses in the membrane during separation of adhering cells. In red blood cell disaggregation, fluorescent probes have shown concentration of ligands in the region of contact close to the line of separation. The chemical potential decrement that occurs when a bond is formed provides the energy source that may deform red blood cells in the process of aggregation. The degree of aggregation and the extent of cell deformation depends on the viscoelastic properties of the cell as well as the dynamics of bond formation and repulsive potential of surface charges present, which is governed by an equation representing a balance of these energies. In flowing blood, the hydrodynamic forces applied by the plasma and surrounding cells must be added to the bond forces and elastic response of the cell. Under sufficiently strong aggregation, plug flow or large aggregates may result. At high shear rates, aggregation may be prevented due to the small contact time and high shear stresses so that no effects of aggregation may be observed. At intermediate shear stresses, transitory contact, adhesion and disaggregation may occur between neighboring cells. Such phenomena have not been analyzed in detail, but simplified models suggest that plug-like flow can occur due to hydrodynamic cell-cell interaction even when cells are not aggregated.

The dynamics of shear disaggregation of red blood cells in a flow channel

Red blood cell (RBC) rouleaux were formed in a flow channel in the presence of 2 g/dl dextran (molecular weight 76,000). The partial separation of RBC rouleau doublets adhering to the floor of the flow channel in response to small oscillatory shear stresses was observed experimentally. Theoretical analyses on displacement and drag force were performed to determine whether the motion of the cell involves membrane rotation (i.e., rolling) or sliding. From the experimental data and the results of theoretical analyses, it is concluded that, under the conditions of the experiments, the RBCs in a doublet separate from each other by rolling, rather than sliding of the sheared cell.

Velocity distribution on the membrane of a tank-treading red blood cell

The kinematics of an area-conserving tank-treading disk-shaped red blood cell membrane is studied using the stream function method suggested by Secomb and Skalak (Q. Jl Mech. appl. Math. 35, Pt 2, 233-247, 1982). Two simple area-conserving velocity fields are superimposed to satisfy the continuity condition at the curved edges of the disk. A differential equation for the trajectory of any material point of the membrane is derived. The requirement of synchrony of the cycle for all membrane points leads to an integral equation which determines a magnitude function. An approximate solution is made possible by assuming small trajectory deflections.

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.

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.

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.