Efficiency considerations for the purely tapered interference fit (TIF) abutments used in dental implants

A tapered interference fit provides a mechanically reliable retention mechanism for the implant-abutment interface in a dental implant. Understanding the mechanical properties of the tapered interface with or without a screw at the bottom has been the subject of a considerable amount of studies involving experiments and finite element (FE) analysis. In this paper, approximate closed-form formulas are developed to analyze the mechanics of a tapered interference fit. In particular, the insertion force, the efficiency, defined as the ratio of the pull-out force to insertion force, and the critical insertion depth, which causes the onset of plastic deformation, are analyzed. It is shown that the insertion force is a function of the taper angle, the contact length, the inner and outer radii of the implant, the static and the kinetic coefficients of friction, and the elastic modulii of the implant/abutment materials. The efficiency of the tapered interference fit, which is defined as the ratio of the pull-out force to insertion force, is found to be greater than one, for taper angles that are less than 6 deg when the friction coefficient is 0.3. A safe range of insertion forces has been shown to exist. The lower end of this range depends on the maximum pull-out force that may occur due to occlusion in the multiple tooth restorations and the efficiency of the system; and the upper end of this range depends on the plastic deformation of the abutment and the implant due to interference fit. It has been shown that using a small taper angle and a long contact length widens the safe range of insertion forces.     

Mechanics of the tapered interference fit in dental implants

In evaluation of the long-term success of a dental implant, the reliability and the stability of the implant-abutment interface plays a great role. Tapered interference fits provide a reliable connection method between the abutment and the implant. In this work, the mechanics of the tapered interference fits were analyzed using a closed-form formula and the finite element (FE) method. An analytical solution, which is used to predict the contact pressure in a straight interference, was modified to predict the contact pressure in the tapered implant-abutment interface. Elastic-plastic FE analysis was used to simulate the implant and abutment material behavior. The validity and the applicability of the analytical solution were investigated by comparisons with the FE model for a range of problem parameters. It was shown that the analytical solution could be used to determine the pull-out force and loosening-torque with 5-10% error. Detailed analysis of the stress distribution due to tapered interference fit, in a commercially available, abutment-implant system was carried out. This analysis shows that plastic deformation in the implant limits the increase in the pull-out force that would have been otherwise predicted by higher interference values.     

Theoretical analysis of pressure pulse propagation in arterial vessels.

An original mathematical model of viscous fluid motion in a tapered and distensible tube is presented. The model equations are deduced by assuming a two-dimensional flow and taking into account the nonlinear terms in the fluid motion equations, as well as the nonlinear deformation of the tube wall. One distinctive feature of the model is the formal integration with respect to the radial coordinate of the Navier-Stokes equations by power series expansion. The consequent computational frame allows an easy, accurate evaluation of the effects produced by changing the values of all physical and geometrical tube parameters. The model is employed to study the propagation along an arterial vessel of a pressure pulse produced by a single flow pulse applied at the proximal vessel extremity. In particular, the effects of the natural taper angle of the arterial wall on pulse propagation are investigated. The simulation results show that tapering considerably influences wave attenuation but not wave velocity. The substantially different behavior of pulse propagation, depending upon whether it travels towards the distal extremity or in the opposite direction, is observed: natural tapering causes a continuous increase in the pulse amplitude as it moves towards the distal extremity; on the contrary, the reflected pulse, running in the opposite direction, is greatly damped. For a vessel with physical and geometrical properties similar to those of a canine femoral artery and 0.1 degree taper angle, the forward amplification is about 0.9 m-1 and the backward attenuation is 1.4 m-1, so that the overall tapering effect gives a remarkably damped pressure response. For a natural taper angle of 0.14 degrees the perturbation is almost extinct when the pulse wave returns to the proximal extremity.     

The Advantages of a Tapered Whisker

The role of facial vibrissae (whiskers) in the behavior of terrestrial mammals is principally as a supplement or substitute for short-distance vision. Each whisker in the array functions as a mechanical transducer, conveying forces applied along the shaft to mechanoreceptors in the follicle at the whisker base. Subsequent processing of mechanoreceptor output in the trigeminal nucleus and somatosensory cortex allows high accuracy discriminations of object distance, direction, and surface texture. The whiskers of terrestrial mammals are tapered and approximately circular in cross section. We characterize the taper of whiskers in nine mammal species, measure the mechanical deflection of isolated felid whiskers, and discuss the mechanics of a single whisker under static and oscillatory deflections. We argue that a tapered whisker provides some advantages for tactile perception (as compared to a hypothetical untapered whisker), and that this may explain why the taper has been preserved during the evolution of terrestrial mammals.     

Stem surface roughness alters creep induced subsidence and 'taper-lock' in a cemented femoral hip prosthesis

The clinical success of polished tapered stems has been widely reported in numerous long term studies. The mechanical environment that exists for polished tapered stems, however, is not fully understood. In this investigation, a collarless, tapered femoral total hip stem with an unsupported distal tip was evaluated using a 'physiological' three-dimensional (3D) finite element analysis. It was hypothesized that stem-cement interface friction, which alters the magnitude and orientation of the cement mantle stress, would subsequently influence stem 'taper-lock' and viscoelastic relaxation of bone cement stresses. The hypothesis that creep-induced subsidence would result in increases to stem-cement normal (radial) interface stresses was also examined. Utilizing a viscoelastic material model for the bone cement in the analysis, three different stem-cement interface conditions were considered: debonded stem with zero friction coefficient (mu=0) (frictionless), debonded stem with stem-cement interface friction (mu=0.22) ('smooth' or polished) and a completely bonded stem ('rough'). Stem roughness had a profound influence on cement mantle stress, stem subsidence and cement mantle stress relaxation over the 24-h test period. The frictionless and smooth tapered stems generated compressive normal stress at the stem-cement interface creating a mechanical environment indicative of 'taper-lock'. The normal stress increased with decreasing stem-cement interface friction but decreased proximally with time and stem subsidence. Stem subsidence also increased with decreasing stem-cement interface friction. We conclude that polished stems have a greater potential to develop 'taper-lock' fixation than do rough stems. However, subsidence is not an important determinant of the maintenance of 'taper-lock'. Rather subsidence is a function of stem-cement interface friction and bone cement creep.     

Temporal changes in the physical properties of healing fractures in rabbits

Temporal changes in the physical properties of healing fractures in rabbits were studied. The mechanical environment at the fracture site was measured and monitored during healing. Animals were sacrificed after 3 to 8 weeks. The results of healing were quantified by whole bone dynamic torsional strength tests. Torque-angle curves were recorded by computer. At maximum torque four parameters were calculated: torque, angle, energy absorbed and stiffness. Torque and stiffness increased while energy remained constant and angle decreased with time. However, values calculated by a constant deformation criteria showed the three strength parameters to increase with time. The rate of increase was highest for stiffness followed by torque and energy.     

Numerical simulation of the insertion process of an uncemented hip prosthesis in order to evaluate the influence of residual stress and contact distribution on the stem initial stability

The long-term success of a cementless total hip arthroplasty depends on the implant geometry and interface bonding characteristics (fit, coating and ingrowth) and on stem stiffness. This study evaluates the influence of stem geometry and fitting conditions on the evolution and distribution of the bone–stem contact, stress and strain during and after the hip stem insertion, by means of dynamic finite element techniques. Next, the influence of the mechanical state (bone–stem contact, stress and strain) resulted from the insertion process on the stem initial resistance to subsidence is investigated. In addition, a study on the influence of bone–stem interface conditions (friction) on the insertion process and on the initial stem stability under physiological loading is performed. The results indicate that for a stem with tapered shape the contact in the proximal part of the stem was improved, but contact in the calcar region was achieved only when extra press-fit conditions were considered. Changes in stem geometry towards a more tapered shape and extra press fit and variation in the bone–stem interface conditions (contact amount and high friction) led to a raise in the total insertion force. A direct positive relationship was found between the stem resistance to subsidence and stem geometry (tapering and press fit), bone–stem interface conditions (bone–stem contact and friction interface) and the mechanical status at the end of the insertion (residual stress and strain). Therefore, further studies on evaluating the initial performance of different stem types should consider the parameters describing the bone–stem interface conditions and the mechanical state resulted from the insertion process.     

Convection-diffusion interaction for oscillatory flow in a tapered tube

Transport of soluble material is analyzed for volume-cycle oscillatory flow in a tapered tube. The equations of motion are solved using a regular perturbation method for small taper angle and order unity amplitude over a range of the Womersley parameter. The transport equation is also solved by a regular perturbation method where uniform end concentrations and no wall flux are assumed. The time-averaged axial transport of solute is calculated for several tapered tubes. There is substantial modification of transport compared to the straight tube case and the results are interpreted with respect to pulmonary gas exchange.     

Amylose content and chemical modification effects on the extrusion of thermoplastic starch from maize

The effects of starch structural properties and starch modification on extruder operation were monitored via die pressure, motor torque, mean residence time and specific mechanical energy (SME). The structural properties studied involved variations in the ratios of amylose and amylopectin as well as the effect of a hydroxypropylated starch on the fore mentioned extruder properties. A full factorial design of experiments (DOE) was used to then determine the influence of starch type (unmodified starches with 0%, 28%, 50% and 80% amylose; 80% amylose hydroxypropylated starch) and screw speed (250, 300 and 350 rpm) on these processing parameters. The effects of starch type and screw speed on extrusion operation that were systematically investigated using the DOE and have provided valuable insight into the relationships between starch structure and processing. The design of experiments showed that starch type for both unmodified and modified maize had a statistically significant effect on parameters such as torque, die pressure and specific mechanical energy and that screw speed also significantly effected specific mechanical energy. Residence time distributions differed according to starch type (amylose content, hydroxypropylation) and screw speed. The additional study of residence time distribution also gave an indication of the degree of mixing in the extruder. Starch type variations were apparent at low screw speed however at higher screw speed the influence of starch type decreased significantly.     

A morphological model of vertebral trabecular bone

In their micro-structures, typical natural cellular materials such as vertebral trabecular bone have a network of doubly tapered struts, thickening near the strut joints. However, past analytical models for vertebral trabecular bone do not take account of the effect of strut taper on the mechanical properties.This paper presents an analytical cell model comprised of doubly tapered struts to predict the global mechanical properties of vertebral trabecular bone. The predicted results for male, female, and both sexes fit the experimental data well. By considering several strut taper geometries, it is shown that the horizontal Young's modulus and the horizontal uniaxial collapse stress are, in some cases, approximately 1.8- and 2.2-fold higher, respectively, than those of the uniform strut model. This finding illustrates the importance of increased trabecular thickening near the strut joints (i) for improving the accuracy of calculating the mechanical properties and (ii) for the effective treatment of aged bone using drug therapy. It also highlights the need to combine trabecular architecture measurements with information about the morphology near the strut joints.     

Relevance of the insertion force for the taper lock reliability of a hip stem and a ceramic femoral head]

In endoprosthetics alumina ceramic femoral heads have been established for many years and their outstanding wear characteristics are scientifically proven. The taper connection between the hard but brittle ceramic head and the metallic stem must be performed by the operating surgeon intraoperatively. Thereby it is left to the surgeon to interpret imprecise and strongly deviating instructions given from manufacturer to manufacturer. This study clarifies the enormously large variations of interpretation in the clinical everyday life based on interviews and force measurements during handling when assembling. In comparable situations the axial cone setting forces, applied by a total of 39 operating surgeons from German hospitals, varied between 273 N and 7848 N. An additional coupling strength examination in the laboratory shows that torque loadings necessary for loosening several cone connection designs are in the range of those occurring under usual in vivo situations. This leads to the conclusion that for low-force-connected cone tapers joint friction of the artificial hip joint can cause a rotation and thus a loosening of the ceramic head of the implant neck during everyday activities. The authors proclaim the urgent necessity for clear handling references and the supply of a reproducibly safe taper lock method.     

Does screw–bone interface modelling matter in finite element analyses?

The effect of screw-bone interface modelling strategies was evaluated in the setting of a tibial mid-shaft fracture stabilised using locking plates. Three interface models were examined: fully bonded interface; screw with sliding contact with bone; and screw with sliding contact with bone in an undersized pilot hole. For the simulation of the last interface condition we used a novel thermal expansion approach to generate the pre-stress that the bone would be exposed to during screw insertion. The study finds that the global load-deformation response is not influenced by the interface modelling approach employed; the deformation varied by less than 1% between different interaction models. However, interface modelling is found to have a considerable impact on the local stress-strain environment within the bone in the vicinity of the screws. Frictional and tied representations did not have significantly different peak strain values (<5% difference); the frictional interface had higher peak compressive strains while the tied interface had higher tensile strains. The undersized pilot hole simulation produced the largest strains. The peak minimum principal strains for the frictional interface were 26% of those for the undersized pilot hole simulation at a load of 770 N. It is concluded that the commonly used tie constraint can be used effectively when the only interest is the global load-deformation behaviour. Different contact interface models, however, alter the mechanical response around screw holes leading to different predictions for screw loosening, bone damage and stress shielding.     

Tensile strength of bone fixation of hydroxyapatite coated Schanz screws of the Heidelberg External Fixation System (HEFS)--comparative torque measurements in clinical use and in cadaver tibia]

It is claimed in the literature that hydroxyapatite(HA)-coated screws of external fixators have superior fixation strength in bone, which is postulated to lead to a substantial decrease in loosening and infection rates. We report on a study of the maximum torque values developed while inserting and removing 30 HA-coated Schanz screws of 8 Heidelberg external fixation systems applied to the tibia to correct leg length differences and axial deformities. The infection rate was determined in accordance with defined criteria, and was found to be about 20% for the HA-coated screws. Screws without infection showed an extraction torque above insertion torque, screws with infection an extraction torque below. A significant correlation (p = 0.05) was seen between infection and decrease in fixation strength (quotient: loosening torque/tightening torque). To exclude the impact of such biological processes as osteointegration and bone remodelling, the clinical results were compared with the torques measured for coated and uncoated Schanz screws in a human cadaveric tibia. A significantly higher fixation strength in bone was found for HA-coated screws in comparison with uncoated screws (p = 0.002). These data warrant a clinical study directly comparing HA-coated and uncoated Schanz screws.     

Evaluating the bending response of two osseointegrated transfemoral implant systems using 3D digital image correlation

Osseointegrated transfemoral implants have been introduced as a prosthetic solution for above knee amputees. They have shown great promise, providing an alternative for individuals who could not be accommodated by conventional, socket-based prostheses; however, the occurrence of device failures is of concern. In an effort to improve the strength and longevity of the device, a new design has been proposed. This study investigates the mechanical behavior of the new taper-based assembly in comparison to the current hex-based connection for osseointegrated transfemoral implant systems. This was done to better understand the behavior of components under loading, in order to optimize the assembly specifications and improve the useful life of the system. Digital image correlation was used to measure surface strains on two assemblies during static loading in bending. This provided a means to measure deformation over the entire sample and identify critical locations as the assembly was subjected to a series of loading conditions. It provided a means to determine the effects of tightening specifications and connection geometry on the material response and mechanical behavior of the assemblies. Both osseoinegrated assemblies exhibited improved strength and mechanical performance when tightened to a level beyond the current specified tightening torque of 12 N?m. This was shown by decreased strain concentration values and improved distribution of tensile strain. Increased tightening torque provides an improved connection between components regardless of design, leading to increased torque retention, decreased peak tensile strain values, and a more gradual, primarily compressive distribution of strains throughout the assembly.     

Simulation of impact test for determining "health" of percutaneous bone anchored implants

There is an ongoing requirement for a clinically relevant, noninvasive technique to monitor the integrity of percutaneous implants used for dental restorations, bone-anchored hearing aids, and to retain extra-oral prostheses (ear, eye, nose, etc). Because of the limitations of conventional diagnostic techniques (CT, MRI), mechanical techniques that measure the dynamic response of the implant-abutment system are being developed. This paper documents a finite element analysis that simulates a transient response to mechanical impact testing using contact elements. The detailed model allows for a specific interface between the implant and bone and characterizes potential clinical situations including loss of bone margin height, loss of osseointegration, and development of a soft connective tissue layer at the bone-implant interface. The results also show that the expected difference in interface stiffness between soft connective tissue and osseointegrated bone will cause easily measurable changes in the response of the implant/abutment system. With respect to the loss of bone margin height, changes in the order of 0.2 mm should be detectable, suggesting that this technique is at least as sensitive as radiography. A partial loss of osseointegration, while not being as readily evident as a bone margin loss, would still be detectable for losses as small as 0.5 mm.     

Comparison of pressure losses in steady non-Newtonian flow through experimental tapered and cylindrical arterial prostheses

The use of an arterial prosthesis with a tapered lumen has several important advantages; for example, improved stability of flow, increased wall shear and better matching of its size with that of the host vessel. Tapering may, however, lead to increased energy losses, particularly if the angle of taper is large and the flow is high. This study is concerned with the determination of pressure drop for steady and laminar converging flow through rigid wall models of tapered arterial grafts. The angles of taper examined ranged from 0.5° to 1.0°. Aqueous solutions of polyacrylamide, with non-Newtonian viscous properties similar to those of blood, were used. The pressure drops across the tapered tubes were measured and the data were measured and the data were related to the pressure loss in cylindrical tubes of equivalent dimensions. Expressions for the ratio of the pressure drop in a tapered tube to that in a cylindrical tube for steady flow of a power law fluid were derived; there was good agreement between the predicted and the measured pressure drop ratios over a wide range of flows. The results of this study may be applied to the design of tapered arterial grafts. The pressure losses to be expected in tapered bypass grafts having various dimensions can easily be computed.     

Design and testing of external fixator bone screws

In external fixation, bone screw loosening still presents a major clinical problem. For this study, the design factors influencing the mechanics of the bone-screw interface were analysed and various experimental screws designed with the intention of maximizing the strength and stiffness of the inserted screw. Push-in, pull-out and bending tests were then carried out on the three experimental screws, and on two commercially available screws in both a synthetic material and in cadaveric bone; photoelastic tests on different screw threadforms were also performed. The results of the push-in and pull-out tests indicate that both the screw threadform and cutting head have a significant effect on the holding strength of the screw. The photoelastic tests show that most of the applied load is distributed over the first few threads closest to the load, and that the area between the thread crests is subjected to high shear stresses.     

Attenuation of flow disturbances in tapered arterial grafts

Flow disturbances in tapered arterial grafts of angles of taper between 0.5 and 1.0 deg were measured in vitro using a pulsed ultrasound Doppler velocimeter. The increase in transition Reynolds numbers with angle of taper and axial distance was determined for steady flow. The instantaneous centerline velocities were measured distal to a 50 percent area stenosis (as a model of a proximal anastomosis), in steady and pulsatile flow, from which the disturbance intensities were calculated. A significant reduction in post-stenotic disturbance intensity was recorded in the tapered grafts, relative to a conventional cylindrical graft. In pulsatile flow with a large backflow component, however, there was an increase in disturbance intensity due to diverging flow during flow reversal. This was observed only in the 1.0 deg tapered graft. These findings indicate that taper is an important consideration in the design of vascular prostheses.     

Evidence for IHA migration during axial rotation of a lumbar spine segment by using a novel high-resolution 6D kinematic tracking system

The biomechanical properties of the lumbar spine have long been studied. However, despite its enormous importance, basic functional and morphological properties have been not well understood and require further experimental analysis since data concerning the spatial instantaneous segmental motions are hardly available. This study describes the theoretical background and the technical properties of an innovative method for tracking the instantaneous 3D motion of human spinal segments in vitro at high spatial resolution. This new acquisition system allows to scrutinise closely the location and alignment of the segmental instantaneous helical axis (IHA) and the respective screw pitch as functions of the absolute rotational angle. The required precision of the measuring device was attained (a) by six highly resolving linear inductive displacement sensors in a special spatially configuration (3-2-1), (b) by a method to apply torque and force independently of each other without counteraction, and (c) by suppression of vibrations. The validity and reliability of the experimental set-up and the numerical method of data analysis were tested by subjects of known mechanical properties. In vitro experiments with a human lumbar segment (L3/L4, autopsy material) demonstrated that (a) the IHA migrated during axial rotation from one segmental articulatio zygapophysialis to the other joint, (b) the IHA tilted medial-laterally, and (c) the pitch of the screw altered linearly as a function of the rotational angle. This phenomenon is traced back to the guidance of the articluationes zygapophysiales. The validation of the method allows to map segments of the entire vertebral column. The results can be used as benchmarks for future models of the human spine.     

Finite Element Analysis of Tibial Implants - Effect of Fixation Design and Friction Model

A three dimensional nonlinear finite element model was developed to investigate tibial fixation designs and friction models (Coulomb's vs nonlinear) in total knee arthroplasty in the immediate postoperative period with no biological attachment. Bi-directional measurement-based nonlinear friction constitutive equations were used for the bone-porous coated implant interface. Friction properties between the polyethylene and femoral components were measured for this study. Linear elastic isotropic but heterogeneous mechanical properties taken from literature were considered for the bone. The Tensile behaviour of polyethylene was measured and subsequently modeled by an elasto-plastic model. Based on the earlier finite element and experimental pull-out studies, pegs and screws were also realistically modeled. The geometry of every component was obtained through measurement. The PCA tibial baseplate with three different configurations was considered; one with three screws, one with one screw and two short inclined porous-coated pegs, and a third one with no fixation for the sake of comparison. The axial load of 2000N was applied through the femoral component on the medial plateau of articular insert. It was found that Coulomb's friction significantly underestimates the relative micromotion at the bone-implant interface. The lowest micromotion and lift-off were found for the design with screws. Relative micromotion and stress transfer at the bone-implant interface depended significantly on the friction model and on the baseplate anchorage configuration. Cortical and cancellous bones carried, respectively, 10-13% and 65-86% of the axial load depending on the fixation configuration used. The remaining portion was transmitted as shear force by screws and pegs. Normal and Mises stresses as well as contact area in the polyethylene insert were nearly independent of the baseplate fixation design. The Maximum Mises stress in the polyethylene exceeded yield and was found 1-2 mm below the contact surface for all designs.