Dependence of stem stress in total hip replacement on prosthesis and cement stiffness

Two dimensional finite element analyses were used to determine the direct tensile stress distributions along the lateral edge of the stem of the femoral component of a total hip replacement. The efficacy of using two-dimensional analysis for three-dimensional composite structures was assessed, and the two-dimensional model was found to be suitable for parametric studies. Various combinations of stem and cement stiffnesses were investigated. In particular the influence of stem taper, cement stiffness, prosthesis stiffness and the effect of a plateau on the prosthesis stresses, were examined and compared. The most significant factor was found to be the modulus of elasticity of the stem material. The tensile stresses decrease with decreasing modulus. Cement stiffness and stem shape appeared to have for less effect on stem stress.     

Residual stresses at the stem-cement interface of an idealized cemented hip stem

During the operation of total hip arthroplasty, when the cement polymerizes between the stem implant and the bone, residual stresses are generated in the cement. The purpose of this study was to determine whether including residual stresses at the stem-cement interface of cemented hip implants affected the cement stress distributions due to externally applied loads. An idealized cemented hip implant subjected to bending was numerically investigated for an early post-operative situation. The finite element analysis was three-dimensional and used non-linear contact elements to represent the debonded stem-cement interface. The results showed that the inclusion of the residual stresses at the interface had up to a 4-fold increase in the von Mises cement stresses compared to the case without residual stresses.     

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.     

Evaluation of cement stresses in finite element analyses of cemented orthopaedic implants.

Stress analysis of the cement fixation of orthopaedic implants to bone is frequently carried out using finite element analysis. However the stress distribution in the cement layer is usually intricate, and it is difficult to report it in a way that facilitates comparison of implants for pre-clinical testing. To study this problem, and make recommendations for stress reporting, a finite element analysis of a hip prosthesis implanted into a synthetic composite femur is developed. Three cases are analyzed: a fully bonded implant, a debonded implant, and a debonded implant where the cement is removed distal to the stem tip. In addition to peak stresses, and contour and vector plots, a stressed volume and probability-of-failure analysis is reported. It is predicted that the peak stress is highest for the debonded stem, and that removal of the distal cement more than halves this peak stress. This would suggest that omission of the distal cement is good for polished prostheses (as practiced for the Exeter design). However, if the percentage of cement stressed above a certain threshold (say 3 MPa) is considered, then the removal of distal cement is shown to be disadvantageous because a higher volume of cement is stressed to above the threshold. Vector plots clearly demonstrate the different load transfer for bonded and debonded prostheses: A bonded stem generates maximum tensile stresses in the longitudinal direction, whereas a debonded stem generates most tensile stresses in the hoop direction, except near the tip where tensile longitudinal stresses occur due to subsidence of the stem. Removal of the cement distal to the tip allows greater subsidence but alleviates these large stresses at the tip, albeit at the expense of increased hoop stresses throughout the mantle. It is concluded that a thorough analysis of cemented implants should not report peak stress, which can be misleading, but rather stressed volume, and that vector plots should be reported if a precise analysis of the load transfer mechanism is required.     

A finite element analysis of hollow stemmed hip prostheses as a means of reducing stress shielding of the femur.

Stress shielding of the femur is known to be a principal factor in aseptic loosening of hip replacements. This paper considers the use of a hollow stemmed hip implant for reducing the effects of stress shielding, while maintaining acceptably low levels of stress in the cement. Using finite element modelling, the stresses in the proximal femur using different shapes of hollow stem were compared with those produced using comparable sizes of solid stem with different values of elastic modulus. A reduction in stress shielding could be achieved with a hollow stem. A cylindrical hollow stem design was then optimised in order to control the maximum allowable stress in the cement, the minimum allowable stresses in the bone, and a combination of the two. The resulting stems achieved an increase in proximal bone stress of about 15% for the first case and 32% for a model using high strength cement, compared with solid stems of the same nominal outside diameter. The gains of these theoretically optimised designs dropped off rapidly further down the stem. Linearly tapered hollow stems reached a 22% gain, which could be a good compromise between acceptable cement stresses and ease of manufacture.     

Measurement of transient and residual stresses during polymerization of bone cement for cemented hip implants

The initial fixation of a cemented hip implant relies on the strength of the interface between the stem, bone cement and adjacent bone. Bone cement is used as grouting material to fix the prosthesis to the bone. The curing process of bone cement is an exothermic reaction where bone cement undergoes volumetric changes that will generate transient stresses resulting in residual stresses once polymerization is completed. However, the precise magnitude of these stresses is still not well documented in the literature. The objective of this study is to develop an experiment for the direct measurement of the transient and residual radial stresses at the stem-cement interface generated during cement polymerization. The idealized femoral-cemented implant consists of a stem placed inside a hollow cylindrical bone filled with bone cement. A sub-miniature load cell is inserted inside the stem to make a direct measurement of the radial compressive forces at the stem-cement interface, which are then converted to radial stresses. A thermocouple measures the temperature evolution during the polymerization process. The results show the evolution of stress generation corresponding to volumetric changes in the cement. The effect of initial temperature of the stem and bone as well as the cement-bone interface condition (adhesion or no adhesion) on residual radial stresses is investigated. A maximum peak temperature of 70 degrees C corresponds to a peak in transient stress during cement curing. Maximum radial residual stresses of 0.6MPa in compression are measured for the preheated stem.     

Pre-clinical validation of a new partially cemented femoral prosthesis by synergetic use of numerical and experimental methods

The present work reports the pre-clinical validation of an innovative partially cemented femoral prosthesis called cement-locked uncemented (CLU) prosthesis. The inventors of the device under investigation claimed that, when compared to a comparable fully cemented stem, the new stem would present various advantages. Two previous experimental studies confirmed that primary stability and stress shielding were comparable to those of cemented stems. Aim of the present study was to investigate if the remaining claims were confirmed as well. A complete finite element model of the bone-implant complex was created from CT data. The model was validated against in vitro measurements of bone surface strains as well as against primary stability measurements. The peak stresses predicted in the CLU cement mantle were not found significantly lower than those reported in other studies on fully cemented stems. However, once the cement inlet geometry is optimised and the associated stress risers are eliminated, the CLU cement mantle should be subjected to much lower stresses. The stress induced in the stems by both load cases was well below the fatigue limit of the Ti6Al4V alloy. Finite element models predicted for all load cases relative motion between cement and metal lower than 60 microm. This amplitude may be fully accommodated by elastic deformations of the cement micro-ridges. The experimental and numerical results showed the validity of the new fixation concept, although a further optimisation of the geometry of the cement pockets is needed in order to further reduce the stresses in the cement.     

Influence of the change in stem length on the load transfer and bone remodelling for a cemented resurfaced femur

The effect of a short-stem femoral resurfacing component on load transfer and potential failure mechanisms has rarely been studied. The stem length has been reduced by approximately 50% as compared to the current long-stem design. Using 3-D FE models of natural and resurfaced femurs, the study is aimed at investigating the influence of a short-stem resurfacing component on load transfer and bone remodelling. Applied loading conditions include normal walking and stair climbing. The mechanical role of the stem along with implant–cement and stem–bone contact conditions was observed to be crucial. Shortening the stem length to half of the current length (long-stem) led to several favourable effects, even though the stress distributions in the implant and the cement were similar in both the cases. The short-stem implant led not only to a more physiological stress distribution but also to bone apposition (increase of 20–70% bone density) in the superior resurfaced head, when the stem–bone contact prevailed. This also led to a reduction in strain concentration in the cancellous bone around the femoral neck–component junction. The normalised peak strain in this region was lower for the short-stem design as compared to that of the long-stem one, thereby reducing the initial risk of neck fracture. The effect of strain shielding (50–75% reduction) was restricted to a small bone volume underlying the cement, which was approximately half of that of the long-stem design. Consequently, bone resorption was considerably less for the short-stem design. The short-stem design offers better prospects than the long-stem resurfacing component.     

Three-dimensional finite element analysis of the composite and compomer onlays in primary molars

Resin onlay restoration is an esthetic alternative technique used for restoring extensively damaged primary molars. Understanding the behavior of materials under repeated functional stress and how the stress is transmitted to the remaining tooth structure is important. The aim of this study was to compare stresses in primary molars restored with indirect composite and compomer onlay. 3D frame models of the right mandibular and maxillary primary molars and the alveolar bone were created using computerized tomography images of a six-year-old girl. The enamel and dentine layers above the cement layer were unified to generate onlay restoration, and composite and compomer were used as restorative materials. The vertical occlusal load (100?N) was applied to the teeth in the occlusal contact areas. The von Mises stress distributions and normal stress distributions of the y-axis (parallel to the long axis of tooth) were evaluated. The occlusal stress is transmitted to the cervical part of healthy teeth by spreading it through the enamel layer. The composite and compomer restorative materials exhibited similar stress distribution patterns. An indirect technique creates a structure similar to the original morphological form, and it allows restorations to distribute high occlusal stresses and to minimize possible breakages.     

Mathematical shape optimization of hip prosthesis design

The long-term success of artificial-joint replacement depends partly on the chances for acrylic cement failure and interface disruption. These chances can be diminished by an optimal load-transfer mechanism, whereby stress concentrations are avoided. The present paper introduces a method for numerical shape optimization, whereby the finite element method is used iteratively to determine optimal prosthetic designs, which minimize interface stresses. The method is first applied in a simplified one-dimensional model of a cemented femoral stem fixation, using acrylic cement. The results show that 30-70% cement and interface stress reductions can be obtained in principle with an optimized design. Although the actual optimal shape is susceptible to the characteristics of the joint load, the stem length, stem modulus, cement modulus and bone properties, its general geometrical characteristics are consistent, featuring proximal and distal tapers, and a belly-shaped middle region. These general characteristics are confirmed in a more realistic two-dimensional FEM model. It is concluded that this method of shape optimization can provide a meaningful basis for prosthetic design and analysis activities in general.     

Hip-joint and abductor-muscle forces adequately represent in vivo loading of a cemented total hip reconstruction.

Using finite element analyses, we investigated which muscle groups acting around the hip-joint most prominently affected the load distributions in cemented total hip reconstructions with a bonded and debonded femoral stem. The purpose was to determine which muscle groups should be included in pre-clinical tests, predicting bone adaptation and mechanical failure of cemented reconstructions, ensuring an adequate representation of in vivo loading of the reconstruction. Loads were applied as occurring during heel-strike, mid-stance and push-off phases of gait. The stress/strain distributions within the reconstruction, produced by the hip-joint contact force, were compared to ones produced after sequentially including the abductors, the iliotibial tract and the adductors and vastii. Inclusion of the abductors had the most pronounced effect. They neutralized lateral bending of the reconstruction at heel-strike and increased medial bending at mid-stance and push-off. Bone strains and stem stresses were changed accordingly. Peak tensile cement stresses were reduced during all gait phases by amounts up to 50% around a bonded stem and 11% around a debonded one. Additional inclusion of the iliotibial tract, the adductors and the vastii produced relatively small effects during all gait phases. Their most prominent effect was a slight reduction of bone strains at the level of the stem tip during heel-strike. These results suggest that a loading configuration including the hip-joint contact force and the abductor forces can adequately reproduce in vivo loading of cemented total hip reconstructions in pre-clinical tests.     

Experimentally tested computer modeling of stress fractures in rats

The objective of this study was to develop a finite-element (FE) modeling methodology for studying the etiology of a stress fracture (SF). Several variants of three-dimensional FE models of a rat hindlimb, which differed in length or stiffness of tissues, enabling the analyses of mechanical strains and stress in the tibia, were created. We compared the occurrence of SFs in an animal model to validate locations of peak strains/stresses in the FE models. Four Sprague-Dawley male rats, age ~7 wk, were subjected to mechanical cyclic loads of 1.2 Hz and ~6 N, which were delivered to their hindlimb for 30 min, 3 times/wk, up to 12 wk, by using a specially designed apparatus. The results showed that 1) FE modeling predicted the maximal strains/stresses (~220,0 με and ~29 MPa, respectively) between the mid- and proximal thirds of the tibia; 2) in a longer shin, greater and more inhomogeneous tensile strains/stresses were evident, at the same location; 3) anatomical variants in shin length influenced the strain/stress distributions to a greater extent with respect to changes in mechanical properties of tissues; and 4) bone stiffness was more dominant than muscle stiffness in affecting the strain/stress distributions. In the animal study, 35,000 loading cycles were associated with the formation of a SF. The location of the identified SF in the rat limb verified the FE model. We find the suggested model a valuable tool in studying various aspects of SFs.     

Prevention of mesh-dependent damage growth in finite element simulations of crack formation in acrylic bone cement

Peak stress levels predicted in finite element analysis (FEA) usually depend on mesh density, due to singular points in the model. In an earlier study, an FEA algorithm was developed to simulate the damage accumulation process in the cement mantle around total hip replacement (THR) implants. It allows cement crack formation to be predicted, as a function of the local cement stress levels. As the simulation is driven by mesh-dependent peak stresses, predicted crack formation rates are also likely to be mesh dependent. The aim of this study was to evaluate the mesh dependence of the predicted crack formation process, and to present a method to reduce the mesh dependence. Crack-propagation experiments were simulated. Experimental specimens, representing transverse slices of cemented THR reconstructions, were subjected to cyclic torsional loading. Crack development around the corners of the stem was monitored. The experiments were simulated using three meshes with increasing levels of mesh refinement. Crack locations and orientations were accurately predicted, and were virtually independent of the level of mesh refinement. However, the experimental crack propagation rates were overestimated considerably, increasing with mesh refinement. To eliminate the effect of stress singularities around the corners of the stem, a stress averaging algorithm was applied in the simulation. This algorithm redistributed the stresses by weighted spatial averaging. When damage accumulation was computed based on averaged stresses, the crack propagation rates predicted were independent of the level of mesh refinement. The critical distance, a parameter governing the effect of the averaging algorithm, was optimized such that the predicted crack propagation rates accurately corresponded to the experimental ones. These results are important for the validity and standardization of pre-clinical testing methods for orthopaedic implants.     

Residual stress due to curing can initiate damage in porous bone cement: experimental and theoretical evidence

Residual stress due to shrinkage of polymethylmethacrylate bone cement after polymerisation is possibly one factor capable of initiating cracks in the mantle of cemented hip replacements. No relationship between residual stress and observed cracking of cement has yet been demonstrated. To investigate if any relationship exists, a physical model has been developed which allows direct observation of damage in the cement layer on the femoral side of total hip replacement. The model contains medial and lateral cement layers between a bony surface and a metal stem; the tubular nature of the cement mantle is ignored. Five specimens were prepared and examined for cracking using manual tracing of stained cracks, observed by transmission microscopy; cracks were located and measured using image analysis. A mathematical approach for the prediction of residual stress due to shrinkage was developed which uses the thermal history of the material to predict when stress-locking occurs, and estimates subsequent thermal stress. The residual stress distribution of the cement layer in the physical model was then calculated using finite element analysis. Results show maximum tensile stresses normal to the observed crack directions, suggesting a link between residual stress and pre-load cracking. The residual stress predicted depends strongly on the definition of the reference temperature for stress-locking. The highest residual stresses (4-7 MPa) are predicted for shrinkage from maximum temperature; in this case, magnitudes are sufficiently high to initiate cracks when the influence of stress raisers such as pores or interdigitation at the bone/cement interface are taken into account (up to 24 MPa when calculating stress around a pore according to the method of Harrigan and Harris (J. Biomech. 24(11) (1991) 1047-1058). We conclude that the damage accumulation failure scenario begins before weight-bearing due to cracking induced by residual stress around pores or stress raisers.     

Mechanical variables affecting balloon kyphoplasty outcome--a finite element study

It is still unclear how a vertebral fracture should be stabilised and strengthened without endangering the remaining intact bone of the augmented vertebra or the adjacent vertebrae. Numerical modelling may provide insight. To date, however, few finite element (FE) spine models have been developed which are both multi-segmental and capture a more complete anatomy of the vertebrae. A 3-D, two-functional unit, CT-based, lumbar spine, FE model was developed and used to predict load transfer and likelihood of fracture following balloon kyphoplasty. The fractured anterior wall and injected cement were modelled in a two-functional spinal unit model with osteoporotic bone properties. Parameters investigated included: cement stiffness, cement volume and height restoration. Models were assessed based on stresses and a user-defined fracture-predicting field. Augmentation altered the stress distribution; shielding was dependent on positioning of the cement; and fracture algorithm found incomplete height restoration to increase the likelihood of fracture, particularly in adjacent vertebrae.     

Three-dimensional finite element analysis of glenoid replacement prostheses: a comparison of keeled and pegged anchorage systems

Glenoid component loosening is the dominant cause of failure in total shoulder arthroplasty. It is presumed that loosening in the glenoid is caused by high stresses in the cement layer. Several anchorage systems have been designed with the aim of reducing the loosening rate, the two major categories being "keeled" fixation and "pegged" fixation. However, no three-dimensional finite element analysis has been performed to quantify the stresses in the cement or to compare the different glenoid prosthesis anchorage systems. The objective of this study was to determine the stresses in the cement layer and surrounding bone for glenoid replacement components. A three-dimensional model of the scapula was generated using CT data for geometry and material property definition. Keeled and pegged designs were inserted into the glenoid, surrounded by a 1-mm layer of bone cement. A 90 deg arm abduction load with a full muscle and joint load was applied, following van der Helm (1994). Deformations of the prosthesis, stresses in the cement, and stresses in the bone were calculated. Stresses were also calculated for a simulated case of rheumatoid arthritis (RA) in which bone properties were modified to reflect that condition. A maximum principal stress-based failure model was used to predict what quantity of the cement is at risk of failure at the levels of stress computed. The prediction is that 94 percent (pegged prosthesis) and 68 percent (keeled prosthesis) of the cement has a greater than 95 percent probability of survival in normal bone. In RA bone, however, the situation is reversed where 86 percent (pegged prosthesis) and 99 percent (keeled prosthesis) of the cement has a greater than 95 percent probability of survival. Bone stresses are shown to be not much affected by the prosthesis design, except at the tip of the central peg or keel. It is concluded that a "pegged" anchorage system is superior for normal bone, whereas a "keeled" anchorage system is superior for RA bone.     

The behavior of the micro-mechanical cement-bone interface affects the cement failure in total hip replacement

In the current study, the effects of different ways to implement the complex micro-mechanical behavior of the cement-bone interface on the fatigue failure of the cement mantle were investigated. In an FEA-model of a cemented hip reconstruction the cement-bone interface was modeled and numerically implemented in four different ways: (I) as infinitely stiff, (II) as infinitely strong with a constant stiffness, (III) a mixed-mode failure response with failure in tension and shear, and (IV) realistic mixed mode behavior obtained from micro-FEA models. Case II, III, and IV were analyzed using data from a stiff and a compliant micro-FEA model and their effects on cement failure were analyzed. The data used for Case IV was derived from experimental specimens that were tested previously. Although the total number of cement cracks was low for all cases, the compliant Case II resulted in twice as many cracks as Case I. All cases caused similar stress distributions at the interface. In all cases, the interface did not display interfacial softening; all stayed the elastic zone. Fatigue failure of the cement mantle resulted in a more favorable stress distribution at the cement-bone interface in terms of less tension and lower shear tractions. We conclude that immediate cement-bone interface failure is not likely to occur, but its local compliancy does affect the formation of cement cracks. This means that at a macro-level the cement-bone interface should be modeled as a compliant layer. However, implementation of interfacial post-yield softening does seems to be necessary.     

Mineral heterogeneity affects predictions of intratrabecular stress and strain

Knowledge of the influence of mineral variations (i.e., mineral heterogeneity) on biomechanical bone behavior at the trabecular level is limited. The aim of this study is to investigate how this material property affects the intratrabecular distributions of stress and strain in human adult trabecular bone. Two different sets of finite element (FE) models of trabecular samples were constructed; tissue stiffness was either scaled to the local degree of mineralization of bone as measured with microCT (heterogeneous) or tissue stiffness was assumed to be homogeneous. The influence of intratrabecular mineral heterogeneity was analyzed by comparing both models. Interesting effects were seen regarding intratrabecular stress and strain distributions. In the homogeneous model, the highest stresses were found at the surface with a significant decrease towards the core. Higher superficial stresses could indicate a higher predicted fracture risk in the trabeculae. In the heterogeneous model this pattern was different. A significant increase in stress with increasing distance from the trabecular surface was found followed by a significant decrease towards the core. This suggests trabecular bending during a compression. In both models a decrease in strain values from surface to core was predicted, which is consistent with trabecular bending. When mineral heterogeneity was taken into account, the predicted intratrabecular patterns of stress and strain are more consistent with the expected biomechanical behavior as based on mineral variations in trabeculae. Our findings indicate that mineral heterogeneity should not be neglected when performing biomechanical studies on topics such as the (long-term or dose dependent) effects of antiresorptive treatments.     

Epiphyseal-based designs for tibial plateau components--II. Stress analysis in the sagittal plane

A two-dimensional, finite element study was undertaken to establish the stresses in the proximal tibia before and after total knee arthroplasty. Equivalent-thickness models in a sagittal plane were created for the natural, proximal tibia and for the proximal tibia with two different types of tibial plateau components. All components simulated bony ingrowth fixation, i.e. no cement layer existed between component and bone. In addition, the interface between component and bone was assumed to be intimately connected, representing complete bony ingrowth and a rigid state of fixation. Two load cases were considered: a joint reaction force acting in conjunction with a patellar ligament force, simulating the knee at 40 degrees of flexion; and a joint reaction force directed along the long axis of the tibia. For the natural tibia model, the pattern of principal stresses for loadcase 1 more closely corresponds to the epiphyseal plate geometry and trabecular morphology than do the principal stress patterns for loadcase 2. Judging from the distribution of principal stresses, loadcase 1 represents a more severe test of implant design than does loadcase 2. The model of the component with a peg predicted that the trabecular bone near the tip of the peg will experience higher than normal stresses, while the bone stresses near the posterior aspect adjacent to the metal tray will be reduced. A component without pegs that incorporates a posterior chamfer and an anterior lip lead to stress distributions closer to those existing in the natural tibia. The interface geometry for this design is based upon the contour of the epiphyseal plate.     

The role of the epidermis as a stiffening agent in Tulipa (Liliaceae) stems

We investigated the hypothesis that the epidermis is a tension-stressed "skin' whose contribution to stem stiffness depends on the turgor pressure exerted on it by an hydrostatically inflated inner "core' of tissues. This hypothesis was tested by relying on the intensities of bending stresses due to stem flexure, which must reach their maximum levels at the outer surface of epidermis such that damage to the surface of the stem should produce the most significant decrease in overall flexural stiffness. We discerned whether the principal tension supporting members at the stem surface (cellulosic microfibrils) were oriented parallel or normal to stem length by comparing the bending stiffness of stems before and after their surface cells first received three parallel longitudinal incisions followed by one helical incision, and by comparing the bending stiffness of stems for which the sequence of cuts was reversed. The same protocol was also applied to stems with various water potentials to determine the effect of hydrostatic pressure on stem stiffness contributed by the surface. Based on the behavior of 82 turgid Tulipa stems, parallel cuts reduced, on average, stem stiffness by 8%, whereas a subsequent helical incision further reduced stiffness by 42%. In contrast, an initial helical incision reduced stem stiffness by 50%, while three subsequent parallel cuts through the same stems did not significantly further reduce stiffness. These results suggested that the net orientation of cellulose microfibrils in the outer epidermal walls was parallel to stem length. This was confirmed by microscopic observations of cells with dichroic staining and polarized light. The responses to surgical damage were directly proportional to stem water potential. We thus conclude that the epidermis, probably in conjunction with a single layer of subepidermal collenchyma cells, acts as a tension-stiffening agent that can contribute as much as 50% to overall stem stiffness We present a simple mechanical model that can account for all our observations.