A general axisymmetric contact mechanics model for layered surfaces, with particular reference to artificial hip joint replacements

A general axisymmetric contact mechanics model for layered surfaces is considered in this study, with particular reference to artificial hip joint replacements. The indenting surface, which represents the femoral head, was modelled as an elastic solid with or without coating, while the other contacting surface, which represents the acetabular cup, was modelled as a two-layered solid. It is shown that this model is applicable to current total hip joint prostheses employing ultra-high molecular weight polyethylene (UHMWPE) acetabular cups against metallic, metallic with coating or ceramic femoral heads as well as metal-on-metal combinations. The effect of cement is also investigated for these prostheses using this model. The use of a metallic bearing surface bonded to a UHMWPE substrate for acetabular cups is particularly examined for metal-on-metal hip joint replacements. Both the contact radius and the contact pressure distribution are predicted for examples of these total hip joint replacements, under typical conditions. Application of contact mechanics to the design of artificial hip joint replacements employing various material combinations is discussed.     

A simple fully integrated contact-coupled wear prediction for ultra-high molecular weight polyethylene hip implants

A fully coupled contact and wear model was developed in the present study for hip implants employing an ultra-high molecular weight polyethylene (UHMWPE) cup in combination with a metallic or ceramic femoral head. A simple elasticity equation based on the concept of constrained column model was employed to solve the contact mechanics between the acetabular cup and the femoral head under the three-dimensional physiological loading condition. The wear model was based on the classical Archard-Lancaster equation in common with all other studies reported in the literature. The fully coupled contact and wear model was applied to both conventional and cross-linked UHMWPE cups under a wide range of design parameters such as the clearance and the femoral head radius. The predicted linear and volumetric wear as well as their rates for conventional UHMWPE cups were found to be in good agreement with those obtained from a similar analysis by Maxian but using the finite element method for the contact mechanics analysis. The predicted maximum contact pressure was found to decrease rapidly within the first 10(6) cycles, and below the limit to cause plastic deformation within the UHMWPE cup with a nominal radial clearance of 0.2 mm. The effect of the clearance between the head and the cup on the predicted wear was found to be negligible. For the cross-linked UHMWPE cup with relatively large diameters up to 48 mm and a fixed outside diameter of 50 mm, the predicted wear, which was found to increase with increasing femoral head radius, remained small owing to the small wear factor associated with these materials. Furthermore, if the head diameter increases beyond 42 mm, a rapid increase in the contact pressure was predicted, owing to the decrease in the wall thickness of the cross-linked UHMWPE cup.     

Analysis of contact mechanics in ceramic-on-ceramic hip joint replacements

The contact mechanics in ceramic-on-ceramic hip implants has been analysed in this study using the finite element method. Only the ideal conditions where the contact occurs within the acetabular cup were considered. It has been shown that the contact pressure distribution and the contact area at the main articulating bearing surfaces depend largely on design parameters such as the radial clearance between the femoral head and the acetabular cup, as well as the thickness of the ceramic insert. For the ceramic-on-ceramic hip implants used in clinics today, with a minimum 5-mm-thick ceramic insert, it has been shown that the radius of the contact area between the femoral head and the acetabular cup is relatively small compared with that of the femoral head and the ceramic insert thickness. Consequently, Hertz contact theory can be used to estimate the contact parameters such as the maximum contact pressure and the contact area.     

Elastohydrodynamic lubrication analysis of ultra-high molecular weight polyethylene hip joint replacements under squeeze-film motion

Elastohydrodynamic lubrication was analysed under squeeze-film or normal approach motion for artificial hip joint replacements consisting of an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup and a metallic or ceramic femoral head. A simple ball-in-socket configuration was adopted to represent the hip prosthesis for the lubrication analysis. Both the Reynolds equation and the elasticity equations were solved simultaneously for the lubricant film thickness and hydrodynamic pressure distribution as a function of the squeeze-film time was solved using the Newton-Raphson method. The elastic deformation of the UHMWPE cup was calculated by both the finite element method and a simple equation based upon the constrained column model. Good agreement of the predicted film thickness and pressure distribution was found between these two methods. A simple analytical method based upon the Grubin-Ertel-type approximation developed by Higginson in 1978 [1] was also applied to the present squeeze-film lubrication problem. The predicted squeeze-film thickness from this simple method was found to be remarkably close to that from the full numerical solution. The main design parameters were the femoral head radius, the radial clearance between the femoral head and the acetabular cup, and the thickness and elastic modulus for the UHMWPE cup; the effects of these parameters on the squeeze-film thickness generated in current hip prostheses were investigated.     

Contact mechanics of a novel metal-on-metal total hip replacement

The contact mechanics of a novel metal-on-metal total hip replacement (THR) were investigated in this study. The metal-on-metal prosthesis considered consists of a cobalt-chrome acetabular insert connected to a titanium shell through a taper contact, articulating against a cobalt-chrome femoral head. Both the experimental measurement of the displacement of the acetabular insert and the contact area between the two bearing surfaces, and the corresponding numerical predictions using the finite element method have been conducted. Excellent agreement has been demonstrated between the experimental measurement and the finite element prediction under various loads up to 3 kN. The maximum contact pressure at the articulating surfaces has been predicted to be about 31 MPa from a simple axisymmetric finite element model, significantly lower than that of a similar cup but with a monoblock construct. This has been mainly attributed to the flexibility of the insert, leading to an increase in the conformity between the femoral head and the acetabular insert. In addition, the predicted maximum contact pressure is only slightly increased to 37 MPa, from a more realistic three-dimensional anatomical finite element model. The design features on metal-on-metal THRs have been shown to reduce contact stresses and may improve tribological performances of these hard-on-hard bearing couples.     

Effect of microseparation on contact mechanics in ceramic-on-ceramic hip joint replacements

The contact mechanics in ceramic-on-ceramic hip implants are investigated in this study under the microseparation condition where the edge contact occurs between the superolateral rim of the acetabular cup and the femoral head. A three-dimensional finite element model is developed to examine the effect of the microseparation distance between the femoral head and the acetabular cup on the contact area and contact stresses between the bearing surfaces. It is shown that microseparation leads to edge contact and elevated contact stresses, and these are mainly dependent on the magnitude of separation, the radial clearance between the femoral head and the acetabular cup, and the cup inclination angle. For a small microseparation distance (less than the diametrical clearance), the contact occurs within the acetabular cup, and consequently an excellent agreement of the predicted contact pressure distribution is obtained between the present three-dimensional anatomical model and a simple two-dimensional axisymmetric model adopted in a previous study [5]. However, as microsegregation is increased further, edge contact between the superolateral rim and the femoral head occurs. Consequently, the predicted contact pressure is significantly increased. The corresponding contact area resembles closely the stripe wear pattern observed on both clinically retrieved and simulator-tested ceramic femoral heads [8, 9, 11]. Furthermore, introducing a fillet radius of 2.5 mm at the mouth of the acetabular cup is shown to reduce the contact stress due to edge contact, but only under relatively large microseparation distances.     

Analysis of elastohydrodynamic lubrication in McKee-Farrar metal-on-metal hip joint replacement

An elastohydrodynamic lubrication (EHL) analysis was carried out in this study for a typical McKee-Farrar metal-on-metal hip prosthesis under a simple steady state rotation. The finite element method was used initially to investigate the effect of the cement and bone on the predicted contact pressure distribution between the two articulating surfaces under dry conditions, and subsequently to determine the elastic deformation of both the femoral and the acetabular components required for the lubrication analysis. Both Reynolds equation and the elasticity equation were coupled and solved numerically using the finite difference method. Important features in reducing contact stresses and promoting fluid-film lubrication associated with the McKee-Farrar metal-on-metal hip implant were identified as the large femoral head and the thin acetabular cup. For the typical McKee-Farrar metal-on-metal hip prosthesis considered under typical walking conditions, an increase in the femoral head radius from 14 to 17.4 mm (for a fixed radial clearance of 79 microm) was shown to result in a 25 per cent decrease in the maximum dry contact pressure and a 60 per cent increase in the predicted minimum film thickness. Furthermore, the predicted maximum contact pressure considering both the cement and the bone was found to be decreased by about 80 per cent, while the minimum film thickness was predicted to be increased by 50 per cent. Despite a significant increase in the predicted minimum lubricating film thickness due to the large femoral head and the thin acetabular cup, a mixed lubrication regime was predicted for the McKee-Farrar metal-on-metal hip implant under estimated in vivo steady state walking conditions, depending on the surface roughness of the bearing surfaces. This clearly demonstrated the important influences of the material, design and manufacturing parameters on the tribological performance of these hard-on-hard hip prostheses. Furthermore, in the present contact mechanics analysis, the significant increase in the elasticity due to the relatively thin acetabular cup was not found to cause equatorial contact and gripping of the ball.     

Contact mechanics of metal-on-metal hip implants employing a metallic cup with a UHMWPE backing

The contact mechanics in metal-on-metal hip implants employing a cobalt chromium acetabular cup with an ultra-high molecular weight polyethylene (UHMWPE) backing were analysed in the present study using the finite element method. A general modelling methodology was developed to examine the effects of the interfacial boundary conditions between the UHMWPE backing and a titanium shell for cementless fixation, the coefficient of friction and the loading angle on the predicted contact pressure distribution at the articulating surfaces. It was found that the contact mechanics at the bearing surfaces were significantly affected by the UHMWPE backing. Consequently, a relatively constant pressure distribution was predicted within the contact conjunction, and the maximum contact pressure occurred towards the edge of the contact. On the other hand, the interfacial boundary condition between the UHMWPE backing and the titanium shell, the coefficient of friction and the loading angle were found to have a negligible effect on the contact mechanics at the bearing surfaces. Overall, the magnitude of the contact pressure was significantly reduced, compared with a similar cup without the UHMWPE backing. The importance of the UHMWPE backing on the tribological performance of metal-on-metal hip implants is discussed.     

Contact mechanics analysis of metal-on-metal hip resurfacing prostheses

Finite-element method was employed to study the contact mechanics in metal-on-metal hip resurfacing prostheses, with particular reference to the effects of bone quality, the fixation condition between the acetabular cup and bone, and the clearance between the femoral head and the acetabular cup. Simple finite-element bone models were developed to simulate the contact between the articulating surfaces of the femoral head and the acetabular cup. The stresses within the bone structure were also studied. It was shown that a decrease in the clearance between the acetabular cup and femoral head had the largest effect on reducing the predicted contact-pressure distribution among all the factors considered in this study. It was found that as the clearance was reduced, the influence of the underlying materials, such as bone and cement, became increasingly important. Stress shielding was determined to occur in the bone tissue surrounding the hip resurfacing prosthesis considered in this study. However, the stress-shielding effects predicted were less than those observed in conventional total hip replacements. Both the effects of bone quality (reduction in elastic modulus) and the fixation condition between the cup and the bone were found to have a negligible effect on the predicted contact mechanics at the bearing surface. The loading was found to have a relatively small effect on the predicted maximum contact pressure at the bearing surface; this was attributed to an increase in contact area as the load was increased.     

Analysis of contact mechanics in McKee-farrar metal-on-metal hip implants

Contact mechanics analysis for a typical McKee-Farrar metal-on-metal hip implant was carried out in this study. The finite element method was used to predict the contact area and the contact pressure distribution at the bearing surfaces. The study investigated the effects of the cement and underlying bone, the geometrical parameters such as the radial clearance between the acetabular cup and the femoral head, and the acetabular cup thickness, as well as other geometrical features on the acetabular cup such as lip and studs. For all the cases considered, the predicted contact pressure distribution was found to be significantly different from that based upon the classical Hertz contact theory, with the maximum value being away from the centre of the contact region. The lip on the cup was found to have a negligible effect on the predicted contact pressure distribution. The presence of the studs on the outside of the cup caused a significant increase in the local contact pressure distribution, and a slight decrease in the contact region. Reasonably good agreement of the predicted contact pressure distribution was found between a three-dimensional anatomical model and a simple two-dimensional axisymmetric model. The interfacial boundary condition between the acetabular cup and the underlying cement, modelled as perfectly fixed or perfectly unbonded, had a negligible effect on the predicted contact parameters. For a given radial clearance of 0.079 mm, the decrease in the thickness of the acetabular cup from 4.5 to 1.5 mm resulted in an increase in the contact half angle from 15 degrees to 26 degrees, and a decrease in the maximum contact pressure from 55 to 20 MPa. For a given acetabular cup thickness of 1.5 mm, a decrease in the radial clearance from 0.158 to 0.0395 mm led to an increase in the contact half-angle from 20 degrees to 30 degrees, and a decrease in the maximum contact pressure from 30 to 10 MPa. For zero clearance, although the contact pressure was significantly reduced over most of the contact area, the whole acetabular cup came into contact with the femoral head, leading to stress concentration at the edge of the cup. Design optimization of the geometrical parameters, in terms of the acetabular cup thickness and the radial clearance, is important, not only to minimize the contact stress at the bearing surfaces, but also to avoid equatorial and edge contact.     

Steady-state elastohydrodynamic lubrication analysis of a metal-on-metal hip implant employing a metallic cup with an ultra-high molecular weight polyethylene backing

The elastohydrodynamic lubrication (EHL) analysis was carried out in this study for a 28 mm diameter metal-on-metal hip prosthesis employing a metallic cup with an ultra-high molecular weight polyethylene (UHMWPE) backing under a simple steady state rotation representing the flexion/extension during walking. Both Reynolds and elasticity equations were coupled and solved numerically by the finite difference method. The elastic deformation was determined by means of the fast Fourier transform (FFT) technique using the displacement coefficients obtained from the finite element method. Excellent agreement of the predicted elastic deformation was obtained between the FFT technique and the conventional direct summation method. The number of grid points used in the lubrication analysis was found to be important in predicting accurate film thicknesses, particularly at low viscosities representative of physiological lubricants. The effect of the clearance between the femoral head and the acetabular cup on the predicted lubricant film thickness was shown to be significant, while the effect of load was found to be negligible. Overall, the UHMWPE backing was found not only to reduce the contact pressure as identified in a previous study by the authors (Liu et al., 2003) but also significantly to increase the lubricant film thickness for the 28 mm diameter metal-on-metal hip implant, as compared with a metallic mono-block cup.     

Prediction of scratch resistance of cobalt chromium alloy bearing surface, articulating against ultra-high molecular weight polyethylene, due to third-body wear particles

The entrapment of abrasive particles within the articulation between a cobalt chromium alloy (CoCrMo) femoral component and an ultra-high molecular weight polyethylene (UHMWPE) cup of artificial hip joints or tibial inserts of artificial knee joints usually scratches the metallic bearing surface and consequently increases the surface roughness. This has been recognized as one of the main causes of excessive polyethylene wear, leading to osteolysis and loosening of the prosthetic components. The purpose of this study was to use the finite element method to investigate the resistance of the cobalt chromium alloy bearing surface to plastic deformation, as a first approximation to causing scratches, due to various entrapped debris such as bone, CoCrMo and ZrO2 (contained in radiopaque polymethyl methacrylate cement). A simple axisymmetric micro contact mechanics model was developed, where a spherical third-body wear particle was indented between the two bearing surfaces, modelled as two solid cylinders of a given diameter, under the contact pressure determined from macro-models representing either hip or knee implants. The deformation of both the wear particle and the bearing surfaces was modelled and was treated as elastic-plastic. The indented peak-to-valley height on the CoCrMo bearing surface from the finite element model was found to be in good agreement with that reported in a previous study when the third-body wear particle was assumed to be rigid. Under the physiological contact pressure experienced in both hip and knee implants, ZrO2 wear particles were found to be fully embedded within the UHMWPE bearing surface, and the maximum von Mises stresses within the CoCrMo bearing surface reached the corresponding yield strength. Consequently, the CoCrMo bearing surface was deformed plastically and the corresponding peak-to-valley height (surface roughness) was found to increase with both the hardness and the size of the wear particle. Even in the case of CoCrMo wear particles, with similar mechanical properties to those of the CoCrMo bearing surface, a significant plastic deformation of the bearing surface was also noted; this highlighted the importance of considering the deformation of the wear particles. These findings support the hypotheses made by clinical studies on the contribution of entrapped debris to increased surface roughness of CoCrMo femoral bearing surfaces.     

A new formulation for the prediction of polyethylene wear in artificial hip joints

Artificial joints employing ultra-high molecular weight polyethylene (UHMWPE) are widely used to treat joint diseases and trauma. Wear of the polymer bearing surface largely limits the use of these joints in younger and more active patients. Previous studies have shown the wear factor used in Archard's law for the conventional polyethylene to be highly dependent on contact pressure and this has produced variability in experimental data and has constrained the reliability and applicability of previous computational predictions. A new wear law is proposed, based on wear volume being dependent on, and proportional to, the product of the sliding distance and contact area. The dimensionless proportional constant, wear coefficient, which was independent of contact pressure, was determined from a multi-directional pin on plate study. This was used in computational predictions of the wear of the conventional UHMWPE hip joints. The wear of the polyethylene cup was independently experimentally determined in physiological full hip joint simulator studies. The predicted wear rate from the new computational model was generally increased, with an improved agreement with the experimental measurement compared with the previous computational model. It was shown that wear in the UHMWPE hip joints increased as head size and contact area increased. This resulted in a much larger increase in the wear rate as the head size increased, compared with the previous computational model, and is consistent with clinical observations. This new understanding of the wear mechanism in artificial joints using the UHMWPE bearing surfaces, and the improved ability to predict wear independently and to address previously described discrepancies offer new opportunities to optimize design parameters.     

An elastohydrodynamic lubrication (EHL) model of wear particle migration in an artificial hip joint

A full fluid ball-in-socket elastohydrodynamic lubrication (EHL) analysis of an artificial hip joint made of a metallic femoral head and ultra-high molecular weight polyethylene (UHMWPE) acetabular cup was considered. Since artificial hips operate in a mixed lubrication mode, wear occurs and wear particles lead to reduced hip lifetimes. This study involves simulating these particles within the lubrication regime. Hip deformation was compared to models employing finite element analysis and the spherical fast-Fourier transform technique. Particle modeling results were compared to suspension modeling experiments by other researchers. Results show a strong influence of lubricant fluid velocity on that of the wear particles.     

The influence of bone and bone cement debris on counterface roughness in sliding wear tests of ultra-high molecular weight polyethylene on stainless steel

Studies of explanted hip prostheses have shown high wear rates of ultra-high molecular weight polyethylene (UHMWPE) acetabular cups and roughening of the surface of the metallic femoral head. Bone and bone cement particles have also been found in the articulating surfaces of some joints. It has been proposed that bone or bone cement particles may cause scratching and deterioration in the surface finish of metallic femoral heads, thus producing increased wear rates and excessive amounts of wear debris. Sliding wear tests of UHMWPE pins on stainless steel have been performed with particles of different types of bone and bone cement added. Damage to the stainless steel counterface and the motion of particles through the interface have been studied. Particles of bone cement with zirconium and barium sulphate additives and particles of cortical bone scratched the stainless steel counterface. The cement particles with zirconium additive produced significantly greater surface damage. The number of particles entering the contact and embedding in the UHMWPE pin was dependent on particle size and geometry, surface roughness and contact stress. Particles are likely to cause surface roughening and increased wear rates in artificial joints.     

The effect of stem structure on stress distribution of a custom-made hip prosthesis

A custom-made hip is essential for the initial stability and longevity which correspond to an optimal stress distribution, since a standard hip cannot always satisfy every patient's need. In order to find out the designing principles of a custom-made hip, a patient's personal features on which the design was based were acquired. In this study, an integrated finite element model of the hip (including ilium, acetabular cup, femoral head, femoral stem, and femur) was created based on the computed tomography (CT) images of this patient. A series model with different stem length, cross-section, and collodiaphyseal angle were analysed under both static and quasi-static loading conditions. Comparing the stress distribution on each part of the hip prosthesis with that of the natural hip before replacement, the optimal stem structure for this patient was found. In addition, the changes of interspace between acetabular cup and femoral head were measured according to dynamic CT images on the healthy side of this patient during a gait cycle. Results correspond to the trail of the maximum contact stress sites, which were mainly located on the superolateral surface of the acetabular cup. This custom-design method can also be adopted for other patients.     

Wear and deformation of ceramic-on-polyethylene total hip replacements with joint laxity and swing phase microseparation

Wear of polyethylene and the resulting wear debris-induced osteolysis remains a major cause of long-term failure in artificial hip joints. There is interest in understanding engineering and clinical conditions that influence wear rates. Fluoroscopic studies have shown separation of the head and the cup during the swing phase of walking due to joint laxity. In ceramic-on-ceramic hips, joint laxity and microseparation, which leads to contact of the head on the superior rim of the cup, has led to localized damage and increased wear in vivo and in vitro. The aim of this study was to investigate the influence of joint laxity and microseparation on the wear of ceramic on polyethylene artificial hip joints in an in vitro simulator. Microseparation during the swing phase of the walking cycle produced contact of the ceramic head on the rim of the polyethylene acetabular cup that deformed the softer polyethylene cup. No damage to the alumina ceramic femoral head was found. Under standard simulator conditions the volume change of the moderately crosslinked polyethylene cups was 25.6 +/- 5.3 mm3/million cycles and this reduced to 5.6 +/- 4.2 mm3/million cycles under microseparation conditions. Testing under microseparation conditions caused the rim of the polyethylene cup to deform locally, possibly due to creep, and the volume change of the polyethylene cup when the head relocated was substantially reduced, possibly due to improved lubrication. Joint laxity may be caused by poor soft tissue tension or migration and subsidence of components. In ceramic-on-polyethylene acetabular cups wear was decreased with a small degree of joint laxity, while in contrast in hard-on-hard alumina bearings, microseparation accelerated wear. These findings may have significant implications for the choice of fixation systems to be used for different types of bearing couples.     

Analysis of elastohydrodynamic lubrication in a novel metal-on-metal hip joint replacement

Elastohydrodynamic lubrication (EHL) analysis was carried out in this study for a novel metal-on-metal hip prosthesis, which consists of a cobalt-chrome alloy femoral head articulating against a cobalt-chrome alloy acetabular insert connected to a titanium fixation shell through a taper. Finite element models were developed to investigate the effect of the pelvic bone and the load on the predicted contact pressure distribution between the two bearing surfaces under dry conditions. The finite element method was used to develop elasticity models for both the femoral and the acetabular components; it was found that the elastic deformation of the acetabular insert was mainly dependent on the load, rather than the detailed pressure distribution. A modified solution methodology was accordingly developed to couple the elasticity models for both the femoral and the acetabular surfaces with the Reynolds equation and to solve these numerically by the finite difference method. It was found that a load increase from 500 to 2500 N had a negligible effect on the predicted maximum contact pressure and the minimum film thickness, due to the relatively flexible and accommodating structure of the acetabular insert. Furthermore, the predicted minimum film thickness was shown to be significantly greater than the simple estimation based on the assumption of semi-infinite solids (mono-block design) using the Hamrock and Dowson formula. The effects of the viscosity of the lubricant and the radial clearance between the femoral and the acetabular components on the predicted lubricating film thickness were investigated under both in vitro simulator testing and in vivo walking conditions.     

A New Approach Using Palm Olein,Palm Kernel Oil,and Palm Fatty Acid Distillate as Alternative Biolubricants: Improving Tribology in Metal-on-Metal Contact

Metal-on-metal (MoM) hip replacements are commonly used hip implants. However, one of the issues under debate is the interference of friction and wear. The purpose of this feasibility study is to elucidate the performance of palm lubrication between the femoral head and the acetabular cup. In the tribology of hip implants, the use of palm olein, palm kernel oil, and palm fatty acid distillate as synthetic lubricants for human joints has shown tremendous potential. A modified pin-on-disc as hip screening has been used to evaluate the friction and wear on an acetabular cup with an inner diameter of 28 mm. The wear debris was then observed with microscopy image analysis. This study revealed that the physical and unique chemical properties in palm oil can optimize the rate of friction and wear on the metal acetabular cup and thus allow for a stable implant of MoM.     

Frictional resistance of new and explanted artificial hip joints

The frictional resistance of 54 explanted Charnley joints and 32 new joints (various types) has been measured in a hip function simulator in dry and lubricated environments.

The friction factors (torque/(normal load × radius) ) for new prostheses were remarkably similar no matter what material or head size was used provided the acetabular component was made of ultra high molecular weight polyethylene (UHMWPE).

Charnley joints, implanted for up to 17 years, were removed from the patients at revision operations and showed that most had a friction factor similar to that of new joints. However, 30% had a friction factor greater than 0.16 when dry and 39% showed friction factors in excess of 0.07 when lubricated (cf 0.1 and 0.04 respectively when new).

All the joints operated under a mixed lubrication regimen.

When the acetabular component was made from UHMWPE, the friction factors were hardly affected by the material of the femoral component. 30% of explanted joints had friction almost twice as great as new joints, but loosening of the prostheses also occurred in some joints whose friction remained low.