Richard Skalak

Biomechanical considerations in osseointegrated prostheses

On the basis of the previous discussions, several conclusions may be drawn. 1. The close apposition of bone to the titanium implant is the essential feature that allows a transmission of stress from the implant to the bone without any appreciable relative motion or abrasion. The absence of any intermediate fibrotic layer allows stress to be transmitted without any progressive change in the bond or contact between the bone and implant. 2. The use of a threaded screw provides a form of interlocking with the bone on a macroscopic scale that allows full development of the strength of the bone in shear or compression. A smooth, cylindrical implant may require an adhesive bond for satisfactory performance, but a screw shape is able to work as long as the apposition of bone and implant is close, whether or not a true adhesive bond is developed. 3. The distribution of a vertical or lateral load applied to a fixed partial denture depends on the number, arrangement, and stiffness of abutment fixtures used, as well as the form and stiffness of the fixed prosthesis itself. In general a stiff fixed partial denture will distribute loads to several fixtures more effectively. A flexible prosthesis may be adequate if the strength developed by each fixture is able to carry the full load that is applied. Cantilevered ends of a fixed partial denture increases the loading on the first screw nearest the cantilevered end. Moderate overhangs may be tolerated if the fixtures are sufficiently strong. 4. A tight connection of the fixed partial denture to fixtures provides a combined structure that can act in concert with the bone to provide a greater strength than that of the fixture or the jaw bone alone. 5. The osseointegrated implant provides a direct contact with bone and therefore will transmit any stress waves or shocks applied to the fixtures. For this reason it is advisable to use a shock-absorbing material such as acrylic resin in the form of acrylic resin artificial teeth in the fixed partial denture. This arrangement allows for the development of a stiff and strong substructure with adequate shock protection on its outer surface.

Strain Energy Function of Red Blood Cell Membranes

The several widely different values of the elastic modulus of the human red blood cell membrane which have been reported in the literature are incorporated into a single strain energy function consisting of two terms. One term gives the small stresses and low elastic modulus which is observed when the red cell membrane is deformed at constant area. The second term contributes a large isotropic stress dependent on the change of area. The strain energy function is applied to the process of sphering of red blood cells in a hypotonic solution. It is shown that a nearly perfect sphere can result even though the red blood cell membrane is homogeneous in all areas of the cell. Results pertinent to sieving and micropipette experiments are also explored.

The interface zone of inorganic implantsIn vivo: Titanium implants in bone

The interface zone between titanium implants and bone is considered at the macroscopic, microscopic, and molecular levels. A high rate of successful dental implants of pure titanium is associated with a very close apposition of the bone to the titanium surface, called osseointegration. At the macroscopic level, osseointegration allows efficient stress transfer from the implant to the bone without abrasion or progressive movement that can take place if a fibrous layer intervenes. At the microscopic level, surface roughness and porosity provide interlocking of the implant and bone tissue which grows into direct contact with titanium. Sections studied in the electron microscope show that calcified tissue can be identified within 50 Å of the implant surface. The interface zone includes a tightly adherent titanium oxide layer on the surface of the implant which may be similar to a ceramic material in relation to tissue response. The five year success rate of 90% in 2895 implants in clinical trials since 1965 is associated with the favorable behavior of bone tissue at the interface zone with pure titanium.

Passive mechanical properties of human leukocytes

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

The interaction of leukocytes and erythrocytes in capillary and postcapillary vessels

Abstract In capillaries white blood cells tend to flow with a lower velocity than red blood cells. This is due to the larger volume of the white cells and their spherical shape as compared to that of the red cells with their biconcave disk shape, as well as to the smaller deformation of the white cell during flow in narrow blood vessels. As a result, red blood cells often accumulate upstream of a white cell in a capillary with a single file of cells, whereas downstream of the white cell a red cell depleted region is formed. When the white cell enters a postcapillary vessel with increased diameter, the following red cells will pass the slower white cell and thereby displace it away from the vessel axis toward the wall. Then interaction between the white cell and the endothelium leads to adhesion, and the white cell starts rolling along the endothelium. We have investigated the detailed flow field in these small vessels with a large-scale hydrodynamic model of a capillary and a postcapillary vessel based on geometric and kinematic similarity. The capillary is simulated by a straight or divergent rigid axisymmetric tube, and white cells are simulated by spheres, red cells by flexible disks, and plasma by a Newtonian fluid. The experiments show that, under the proper circumstances, hydrodynamic collision of a disk and a sphere in a narrow tube results in the disks passing the sphere, leading to the displacement of the sphere toward the tube wall. The model reproduces qualitatively the in vivo flow field, and the results indicate that the attachment of white blood cells in postcapillaries is augmented as a result of hydrodynamic interaction with red cells.

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.

Motion of a tank-treading ellipsoidal particle in a shear flow

A theoretical model is developed for the motion of a human red blood cell in a shear field. The model consists of a tank-treading ellipsoidal membrane encapsulating an incompressible Newtonian liquid immersed in a plane shear flow of another incom- pressible Newtonian liquid. Equilibrium and energy considerations lead to a solution for the motion of the particle that depends on the ellipsoidal-axis ratios and the ratio of the inner- to outer-liquid viscosities. The effect of variation in these parameters is explored and it is shown that, depending on their values, one of two types of overall motion is exhibited: a steady stationary-orientation motion or an unsteady flipping motion. A qualitative agreement of the predicted behaviour of the model with experi- mental observations on red blood cells is found.

Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane

The deformation of a portion of erythrocyte during aspirational entry into a micropipette has been analyzed on the basis of a constant area deformation of an infinite plane membrane into a cylindrical tube. Consideration of the equilibrium of the membrane at the tip of the pipette has generated the relation between the aspirated length and the dimensionless time during deformational entry as well as during relaxation after the removal of aspiration pressure. Experimental studies on deformation and relaxation of normal human erythrocytes were performed with the use of micropipettes and a video dimension analyzer which allowed the continuous recording of the time-courses. The deformation consisted of an initial rapid phase with a membrane viscosity (range 0.6 x 10(-4) to 4 x 10(-4) dyn.s/cm) varying inversely with the degree of deformation and a later slow phase with a high membrane viscosity (mean 2.06 x 10(-2) dyn.s/cm) which was not correlated with the degree of deformation. The membrane viscosity of the recovery phase after 20 s of deformation (mean 5.44 x 10(-4) dyn.s/cm) was also independent of the degree of deformation. When determined after a short period of deformation (e.g., 2 s), however, membrane viscosity of the recovery phase became lower and agreed with that of the deformation phase. These results suggest that the rheological properties of the membrane can undergo dynamic changes depending on the extent and duration of deformation, reflecting molecular rearrangement in response to membrane strain.

Analytical description of growth

Abstract Methods for the mathematical description of growth are reviewed and extended. The main mode of description is that of identifying the material point paths (in space-time) of the mass points which make up the animal or plant. The spatial location and mass of the elementary particles of the animal are considered to be continuous in space-time. Discontinuities are allowed in displacement functions to allow for slip, as in a knee joint; discontinuities are also allowed in material properties in the sense of sudden adhesion or non-adhesion of surfaces and in the topology, such as the completion or opening of a ring. When cells proliferate or atrophy throughout the tissue growth is considered as distributed sources or sinks in space-time. Deposition or resorption on the surface of a bone is considered to be a surface distribution of mass sources or sinks in space-time. The theoretical framework is illustrated by idealized examples of mathematical descriptions involved.

Cell distribution in capillary networks

Abstract The distribution of red and white blood cells at diverging capillary branches in the rabbit ear chamber has been studied by means of high-speed microcinephotography. The experimental results are summarized in the form of a cell distribution function which is defined as the flux of cells as a function of the bulk flow into the daughter vessels. In capillaries the cell distribution function is nonlinear and strongly dependent on the eccentric position of the blood cells at the upstream entrance to the branch. If one daughter vessel carries the majority of the entering flow, all red blood cells are collected into the same channel. The cell distribution function is readily incorporated into a numerical network analysis to simulate the path velocity, pressure drop, and concentrations of red and white cells as a function of time throughout a capillary bed. The computational results show that, due to nonlinear cell distribution functions and nonuniform flow rates, the concentration of blood cells in a capillary network will be generally nonuniform. The flow fluctuations are the consequence of the particle nature of blood in capillaries without active changes in their diameters. Vasomotion would alter the hemodynamic conditions in upstream vessels and the influx of cells into the capillary network; therefore its effect would be superimposed on the flow fluctuations considered here.