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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.