Cortical bone viscoelasticity and fixation strength of press-fit femoral stems: an in-vitro model

Cementless total hip femoral components rely on press-fit for initial stability and bone healing and remodeling for secondary fixation. However, the determinants of satisfactory press-fit are not well understood. In previous studies, human cortical bone loaded circumferentially to simulate press-fit exhibited viscoelastic, or time dependent, behavior. The effect of bone viscoelastic behavior on the initial stability of press-fit stems is not known. Therefore, in the current study, push-out loads of cylindrical stems press-fit into reamed cadaver diaphyseal femoral specimens were measured immediately after assembly and 24 h with stem-bone diametral interference and stem surface treatment as independent variables. It was hypothesized that stem-bone interference would result in a viscoelastic response of bone that would decrease push-out load thereby impairing initial press-fit stability. Results showed that push-out load significantly decreased over a 24 h period due to bone viscoelasticity. It was also found that high and low push-out loads occurred at relatively small amounts of stem-bone interference, but a relationship between stem-bone interference and push-out load could not be determined due to variability among specimens. On the basis of this model, it was concluded that press-fit fixation can occur at relatively low levels of diametral interference and that stem-bone interference elicits viscoelastic response that reduces stem stability over time. From a clinical perspective, these results suggest that there could be large variations in initial press-fit fixation among patients.     

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.     

A nonlinear homogenized finite element analysis of the primary stability of the bone–implant interface

Stability of an implant is defined by its ability to undergo physiological loading–unloading cycles without showing excessive tissue damage and micromotions at the interface. Distinction is usually made between the immediate primary stability and the long-term, secondary stability resulting from the biological healing process. The aim of this research is to numerically investigate the effect of initial implantation press-fit, bone yielding, densification and friction at the interface on the primary stability of a simple bone–implant system subjected to loading–unloading cycles. In order to achieve this goal, human trabecular bone was modeled as a continuous, elasto-plastic tissue with damage and densification, which material constants depend on bone volume fraction and fabric. Implantation press-fit related damage in the bone was simulated by expanding the drilled hole to the outer contour of the implant. The bone–implant interface was then modeled with unilateral contact with friction. The implant was modeled as a rigid body and was subjected to increasing off-axis loading cycles. This modeling approach is able to capture the experimentally observed primary stability in terms of initial stiffness, ultimate force and progression of damage. In addition, it is able to quantify the micromotions around the implant relevant for bone healing and osseointegration. In conclusion, the computationally efficient modeling approach used in this study provides a realistic structural response of the bone–implant interface and represents a powerful tool to explore implant design, implantation press-fit and the resulting risk of implant failure under physiological loading.     

The influence of friction and interference on the seating of a hemispherical press-fit cup: a finite element investigation.

The formation of gaps in the polar region of acetabular cups is seen as a drawback of press-fit fixation of non-cemented acetabular cups. Recent findings indicate a link between long-term polar gaps and the gaps present directly after implantation. In this study the process of press-fitting is simulated with a linear-elastic two-dimensional axisymmetric finite-element model. The aim of this paper is to investigate the possible importance of friction and interference on the formation of these gaps. A range of cup-bone friction coefficients (mu = 0.1-0.5) is assigned to the cup-bone interface in order to represent the unknown amount of friction occurring during press-fitting. The cup is modeled with a radius of 27 mm, whereas the radius of the cavity is varied between 26.50 and 26.75 mm, thus, creating 0.50 and 0.25 mm radial interference fits. The difference in cavity radius represents the discrepancy between the radius of the last-reamer-used and radius of the cavity it creates. The subchondral plate is considered as being completely removed during reaming. The effects of impact blows via the surgeon's mallet during surgery are modeled as a series of four load pulses, in which peak force is gradually increased from 0.5 to 4.0 kN. The effects of load removal as well as those of load application are investigated. On load application, the cup penetrates into the cavity, and on load removal, the cup rebounds. Depending on the friction, interference and load applied, the position of the cup after the load pulse is somewhere between its position at peak force and its position at the beginning of the pulse. Although the simplifications and conditions involved in the creation of the model necessitate caution when interpreting the results for all clinical cases, it is found that the seating of hemispherical cups in trabecular bone could be more satisfactory for intermediate values of friction (mu = 0.2-0.3) and smaller interference fits (0.25 mm).     

Primary Rotational Stability of Various Megaprostheses in a Biomechanical Sawbone Model with Proximal Femoral Defects Extending to the Isthmus

Purpose

Fixation of proximal femoral megaprostheses is achieved in the diaphyseal isthmus. We hypothesized that after extended bone resection including the proximal part of the isthmus a reduced length of fixation will affect the stability and fixation characteristics of these megaprostheses. The aim of this study was to analyze in a validated sawbone model with extended proximal femoral defects which types of implants have sufficient primary stability to allow osteointegration and to describe their fixation characteristics.

Methods

Four different cementless megaprostheses were implanted into 16 Sawbones with an AAOS type III defect after resection 11cm below the lesser trochanter involving the proximal isthmus. To determine the primary implant stability relative micromotions between bone and implant were measured in relation to a cyclic torque of 7Nm applied on the longitudinal axis of the implant. We determined the fixation characteristics of the different implant designs by comparing these relative micromotions along the longitudinal stem axis.

Results

In the tested sawbones all studied implants showed sufficient primary stability to admit bone integration with relative micromotions below 150µm after adapting our results to physiologic hip joint loadings. Different fixation characteristics of the megaprostheses were determined, which could be explained by their differing design and fixation concepts.

Conclusions

Cementless megaprostheses of different designs seem to provide sufficient primary stability to bridge proximal femoral defects if the diaphyseal isthmus is partially preserved. In our sawbone model the different implant fixation patterns can be related to their stem designs. No evidence can be provided to favor one of the studied implants in this setting. However, femoral morphology is variable and in different isthmus configurations specific implant designs might be appropriate to achieve the most favorable primary stability, which enables bone integration and consequently long term implant stability.     

Characterization of bone-implant fixation using modal analysis: Application to a press-fit implant model

Orthopaedic implant fixation is strongly dependant upon the effective mechanical properties of newly formed tissue. In this study, we evaluated the potential of modal analysis to derive viscoelastic properties of periprosthetic tissue. We hypothesized that Young's modulus and loss factor could be obtained by a combined theoretical, computational and experimental modal analysis approach. This procedure was applied to ex vivo specimens from a cylindrical experimental implant placed in cancellous bone in an unloaded press-fit configuration, obtained after a four week observation period. Four sections each from seven textured titanium implants were investigated. The first resonant frequency and loss factor were measured. Average experimentally determined loss factor was 2% (SD 0.4%) and average first resonant frequency was 2.1 KHz (SD: 50). A 2D axisymmetric finite element (FE) model identified effective Young's modulus of tissue using experimental resonant frequencies as input. Average value was 42 MPa (SD: 2.4) and no significant difference between specimens was observed.In this pilot study, the non-destructive method allowed accurate measure of dynamic loss factor and resonant frequency and derivation of effective Young's modulus. Prior to implementing this dynamic protocol for broader mechanical evaluation of experimental implant fixation, further work is needed to determine if this affects results from subsequent destructive shear push-out tests.     

Primary stability of uncemented femoral resurfacing implants for varying interface parameters and material formulations during walking and stair climbing

Primary stability of uncemented resurfacing prosthesis is provided by an interference fit between the undersized implant and the reamed bone. Dependent on the magnitude of interference, the implantation process causes high shear forces and large strains which can exceed the elastic limit of cancellous bone. Plastification of the bone causes reduced stiffness and could lead to bone damage and implant loosening. The purpose in this study was to determine press-fit conditions which allow implantation without excessive plastic bone deformation and sufficient primary stability to achieve bone ingrowth. In particular, the influence of interference, bone quality and friction on the micromotion during walking and stair-climbing was investigated. Therefore elastic and plastic finite element (FE) models of the proximal femur were developed. Implantation was realized by displacing the prosthesis onto the femur while monitoring the contact pressure, plastic bone deformation as well as implantation forces. Subsequently a physiologic gait and stair-climbing cycle was simulated calculating the micromotion at the bone-implant interface. Results indicate that plastic deformation starts at an interference of 30 μm and the amount of plastified bone at the interface increases up to 90% at 150 μm interference. This effect did not reduce the contact pressure if interference was below 80 μm. The micromotion during walking was similar for the elastic and plastic FE models. A stable situation allowing bony ingrowth was achieved for both constitutive laws (elastic, plastic) for walking and stair climbing with at least 60 μm press-fit, which is feasible with clinically used implantation forces of 4 kN.     

Finite element stress analysis of a push-out test. Part II: Free interface with nonlinear friction properties.

In this second part of a two-part paper, nonlinear frictional properties measured at the bone/porous-surfaced metal interface are used to perform the stress analysis of a push-out test assuming free interface. In this case, the friction at the interface is the only mechanism to resist the externally applied load. Similar to the part I, the model is axisymmetric and consists of two cylinders in contact with each other through the interface. Various relative material properties and boundary conditions are simulated in order to examine their effects on the interface stresses and overall push-out resistance. The role of the force-fit and the load direction (push-out versus pull-out) on the results is also investigated. The computed radial and shear stresses are found to markedly vary both with location along the interface and with the testing configuration. The ultimate push-out resistance is also found to significantly alter as the material arrangement and boundary conditions change. The predicted push-out load augments with an increase in the force-fit and diminishes to nil in the absence of a press-fit. For the cases studied here, there is a relative difference of as large as 13 percent between the push-out response and the pull-out response so far as the interface stresses and the maximum resistance are concerned. Therefore, any comparison between the results of push-out (or pull-out) tests performed with different design configurations appears to be invalid.     

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.     

Strain shielding in proximal tibia of stemmed knee prosthesis: experimental study

Theoretical concerns about the use of cemented or press-fit stems in revision total knee arthroplasty (TKA) include stress shielding with adverse effects on prosthesis fixation. Revision TKA components are commonly stemmed to protect the limited autogenous bone stock remaining. Revision procedures with the use of stems can place abnormal stresses through even normal bone by their constrained design, type of materials and fixation method and may contribute for bone loss. Experimental quantification of strain shielding in the proximal synthetic tibia following TKA is the main purpose of the present study. In this study, cortical bone strains were measured experimentally with tri-axial strain gauges in synthetic tibias before and after in vitro knee surgery. Three tibias were implanted with cemented and press-fit stem augments and solely with a tibial tray (short monobloc stem) of the P.F.C. Sigma Modular Knee System. The difference between principal strains of the implanted and the intact tibia was calculated for each strain gauge position. The results demonstrated a pronounced strain-shielding effect in the proximal level, close to tibial tray with the cemented stem augment. The press-fit stem presented a minor effect of strain shielding but was more extensively throughout the stem. An increase of strains closely to the distal tip of the cemented and the press-fit stem augment was observed. This suggests for a physiological condition, a potential effect of bone resorption at the proximal region for the cemented stem augment. The localized increase of strains in stems tip can be related with the clinical finding of the pain, at the end of stem after revision TKA.     

Bone ingrowth simulation for a concept glenoid component design

Glenoid component loosening is the major problem of total shoulder arthroplasty. It is possible that uncemented component may be able to achieve superior fixation relative to cemented component. One option for uncemented glenoid is to use porous tantalum backing. Bone ingrowth into the porous backing requires a degree of stability to be achieved directly post-operatively. This paper investigates the feasibility of bone ingrowth with respect to the influence of primary fixation, elastic properties of the backing and friction at the bone prosthesis interface. Finite element models of three glenoid components with different primary fixation configurations are created. Bone ingrowth into the porous backing is modelled based on the magnitude of the relative interface micromotions and mechanoregulation of the mesenchymal stem cells that migrated via the bonded part of the interface. Primary fixation had the most influence on bone ingrowth. The simulation showed that its major role was not to firmly interlock the prosthesis, but rather provide such a distribution of load, that would result in reduction of the peak interface micromotions. Should primary fixation be provided, friction has a secondary importance with respect to bone ingrowth while the influence of stiffness was counter intuitive: a less stiff backing material inhibits bone ingrowth by higher interface micromotions and stimulation of fibrous tissue formation within the backing.     

Bone ingrowth into a porous coated implant predicted by a mechano-regulatory tissue differentiation algorithm

Bone ingrowth into a porous surface is one of the primary methods for fixation of orthopaedic implants. Improved understanding of bone formation and fixation of these devices should improve their performance and longevity. In this study predictions of bone ingrowth into an implant porous coating were investigated using mechano-reculatory models. The mechano-regulatory tissue differentiation algorithm proposed by Lacroix et al., and a modified version that enforces a tissue differentiation pathway by transitioning from differentiation to bone adaptation were investigated. The modified algorithm resulted in nearly the same behavior as the original algorithm when applied to a fracture-healing model. The algorithms were further compared using micromechanical finite element model of a beaded porous scaffold. Predictions of bone and fibrous tissue formation were compared between the two algorithms and to clinically observed phenomena. Under loading conditions corresponding to a press-fit hip stem, the modified algorithm predicted bone ingrowth into approximately 25% of the pore space, which is similar to that reported in experimental studies, while the original algorithm was unstable. When micromotion at the bone-implant interface was simulated, 20 mum of transverse displacement resulted in soft tissue formation at the bone-implant interface and minimal bone ingrowth. In contrast, 10 and 5 mum of micromotion resulted in bone filling 40% of the pore space and a stable interface, again consistent with clinical and experimental observations.     

Finite element modelling of primary hip stem stability: the effect of interference fit

The most commonly reported complications related to cementless hip stems are loosening and thigh pain; both of these have been attributed to high levels of relative micromotion at the bone-implant interface due to insufficient primary fixation. Primary fixation is believed by many to rely on achieving a sufficient interference fit between the implant and the bone. However, attempting to achieve a high interference fit not infrequently leads to femoral canal fracture either intra-operatively or soon after. The appropriate range of diametrical interference fit that ensures primary stability without risking femoral fracture is not well understood. In this study, a finite element model was constructed to predict micromotion and, therefore, instability of femoral stems. The model was correlated with an in vitro micromotion experiment carried out on four cadaver femurs. It was confirmed that interference fit has a very significant effect on micromotion and ignoring this parameter in an analysis of primary stability is likely to underestimate the stability of the stem. Furthermore, it was predicted that the optimal level of interference fit is around 50 microm as this is sufficient to achieve good primary fixation while having a safety factor of 2 against femoral canal fracture. This result is of clinical relevance as it indicates a recommendation for the surgeon to err on the side of a low interference fit rather than risking femoral fracture.     

Primary stability of cementless stem in THA improved with reduced interfacial gaps

Large interfacial gaps between the stem and the bone in cementless total hip arthroplasty may prevent successful bone ingrowth at the sites, and can also be a passage for wear particles. Furthermore, interfacial gaps between the stem and the bone are believed to compromise the primary stability of the implant. Thus, a broaching method that serves to reduce gaps is expected to give clinically preferable results. A modified broach system with a canal guide is introduced to enhance the accuracy of femoral canal shaping in comparison with the conventional broach system for a Versys fibermetal taper stem. The primary stability of the hip systems and the ratios of the stem surface in contact with the femur were measured in a composite femur model. With the conventional method, an average of 67% of the stem surface was shown to be in contact with the bone, and an average stem micromotion/migration of 35 microm 290 microm was observed under 1000 cycles of stair climbing loads. With the modified method, the stem-bone contact ratio significantly increased to 82% (p<0.05), and the average micromotion/migration reduced to 29 microm 49 microm, respectively (p<0.05 for migration). Our finite element models of the hip systems supported that the difference in micromotion could be attributed to the difference in interfacial contact. Interfacial gaps occurring with the conventional broach system were effectively reduced by the proposed method, resulting in improved primary stability.     

Effects of tissue preservation on murine bone mechanical properties

Murine bone specimens are used extensively in skeletal research to assess the effects of environmental, physiologic and pathologic factors on their mechanical properties. Given the destructive nature of mechanical testing, it is normally performed as a terminal procedure, where specimens must be preserved without affecting their mechanical properties. To this end, we aimed to study the effects of tissue preservation (freezing and formalin fixation) on the elastic and viscoelastic mechanical properties of murine femur and vertebrae. A total of 120 femurs and 180 vertebral bodies (L3–L5) underwent non-destructive cyclic loading to assess their viscoelastic properties followed by mono-cyclic loading to failure to assess their elastic properties. All specimens underwent re-hydration in 0.9% saline for 30 min prior to mechanical testing. Analysis indicated that stiffness, modulus of elasticity, yield load, yield strength, ultimate load and ultimate strength of frozen and formalin-fixed femurs and vertebrae were not different from fresh specimens. Cyclic loading of both femurs and vertebrae indicated that loss, storage and dynamic moduli were not affected by freezing. However, formalin fixation altered their viscoelastic properties. Our findings suggest that freezing and formalin fixation over a 2-week period do not alter the elastic mechanical properties of murine femurs and vertebrae, provided that specimens are re-hydrated for at least half an hour prior to testing. However, formalin fixation weakened the viscoelastic properties of murine bone by reducing its ability to dissipate viscous energy. Future studies should address the long-term effects of both formalin fixation and freezing on the mechanical properties of murine bone.     

The effect of damage on the viscoelastic behavior of human vertebral trabecular bone

The present study examines the viscoelastic behavior of cancellous bone at low strains and the effects of damage on this viscoelastic behavior. It provides experimental evidence of interaction between stress relaxation behavior and the effect of accumulated damage. The results suggest that damage is at least orthotropic in trabecular bone specimens under uniaxial loading. Simple linear models of viscoelasticity described the time-dependent stress-strain behavior at low strains before and after specimen damage, although better fits of these models were obtained prior to damage. Modeling the observed changes in relaxation times with damage accumulation appears necessary to successfully predict the post-damage viscoelastic response.     

Loosening of cementless femoral stems: a biomechanical analysis of immediate fixation with loading vertical, femur horizontal

Large joint implants must have immediate fixation to be successful. Unfortunately, the magnitude and consistency of achieving this remains largely unknown. For cementless femoral components it is being increasingly appreciated that torsional loading as occurs during stair climbing or rising from a chair leads to loosening and thigh pain in some cases. A biomechanical test was developed to evaluate fixation in this position. Twelve pairs of human cadaveric femora were press-fit with an AML stem. Each femur was secured in a horizontal position, and the prosthetic head cyclically loaded in a vertically downward direction. The offset of the prosthetic head resulted in a combined torsional and compressive load being applied to the stem within the proximal femur. Loosening was found to consistently occur and rapidly accelerate when the head subsided more than 0.2 mm during 100 cycles. For the AML stem, loosening developed at loads from 62 to 171% of body weight and after as few as 800 cycles. This is within the physiologic range of normal daily activities as measured by others with instrumented prostheses. This poses a challenge to the ability of press-fit stems to tolerate torsional loads in vivo. Patients with a cementless prosthesis should be protected from torsional loading until porous ingrowth and/or bone remodelling have had time to occur. Testing the same stem in paired femora demonstrated no right vs left difference (p greater than 0.6).     

Transformation of the viscoelastic functions of calcified tissues and interfacial biomaterials into a common representation

Since both connective and calcified tissues are markedly viscoelastic in nature, an understanding of the behavior of these tissues intrinsically as materials on their own, as well as in composite formation with synthetic implants, is of prime importance in order to predict and anticipate materials' design and function. Thus considerable interest has developed in recent years with respect to measurements of the viscoelastic properties of biological materials. However, attempts to characterize the viscoelasticity of calcified tissues have involved many different experimental procedures; hence results appear in terms of different functions, e.g. relaxation modulus, creep compliance. Since this diversity precludes a simple useful comparison of the results, the present study was initiated so that measured functions could be cast into a common representation, and thus compared. Linear viscoelasticity theory implies definite exact relationships between the functions. Using these relations, experimental results on bone, dentin and implant materials presently used to interface to the natural tissues, e.g. polymethyl methacrylate and high density linear polyethylene, were transformed into the complex dynamic modulus representation. Analysis shows that the results of experiments on bone are not in agreement as to dispersion (i.e. change of modulus with frequency) and its variation with strain. Further, analysis of the internal consistency of some experiments demonstrates a violation of the Boltzmann integral which indicates that linear viscoelasticity (almost invariably assumed by workers in the field) fails for bone in compression. It is concluded that the dynamic behavior of bone is not as well understood as has been thought heretofore; direction is given for future experiments. Contribution No. 59 from the Laboratory for Crystallographic Biophysics; supported by USPHS through NIDR Grant Number 5T1-DE-117-10.     

Advanced material modelling in numerical simulation of primary acetabular press-fit cup stability

Primary stability of artificial acetabular cups, used for total hip arthroplasty, is required for the subsequent osteointegration and good long-term clinical results of the implant. Although closed-cell polymer foams represent an adequate bone substitute in experimental studies investigating primary stability, correct numerical modelling of this material depends on the parameter selection.

Material parameters necessary for crushable foam plasticity behaviour were originated from numerical simulations matched with experimental tests of the polymethacrylimide raw material. Experimental primary stability tests of acetabular press-fit cups consisting of static shell assembly with consecutively pull-out and lever-out testing were subsequently simulated using finite element analysis.

Identified and optimised parameters allowed the accurate numerical reproduction of the raw material tests. Correlation between experimental tests and the numerical simulation of primary implant stability depended on the value of interference fit. However, the validated material model provides the opportunity for subsequent parametric numerical studies.     

Skin viscoelasticity studied in vitro by microprobe-based techniques

Time-dependent deformation of porcine skin was studied in vitro using specialized microprobe instruments. The deformation behavior of stratum corneum, dermis, and whole skin is examined in the context of results of creep strain, elastic stiffness, and viscoelastic constants obtained in terms of the hold time, loading/unloading rate, and maximum indentation depth (load). Skin time-dependent deformation is significantly influenced by dermis viscoelasticity up to a critical indentation depth (load) beyond which it is controlled by the outermost hard epidermis, particularly stratum corneum. Skin viscoelastic behavior under constant load (creep) and constant displacement (stress relaxation) is interpreted in the light of phenomenological observations and experimental trends.