Gait alterations can reduce the risk of edge loading

Following metal‐on‐metal hip arthroplasty, edge loading (i.e., loading near the edge of a prosthesis cup) can increase wear and lead to early revision. The position and coverage angle of the prosthesis cup influence the risk of edge loading. This study investigates the effect of altered gait patterns, more specific hip, and pelvis kinematics, on the orientation of hip contact force and the consequent risk of antero‐superior edge loading using muscle driven simulations of gait. With a cup orientation of 25° anteversion and 50° inclination and a coverage angle of 168°, many gait patterns presented risk of edge loading. Specifically at terminal double support, 189 out of 405 gait patterns indicated a risk of edge loading. At this time instant, the high hip contact forces and the proximity of the hip contact force to the edge of the cup indicated the likelihood of the occurrence of edge loading. Although the cup position contributed most to edge loading, altering kinematics considerably influenced the risk of edge loading. Increased hip abduction, resulting in decreasing hip contact force magnitude, and decreased hip extension, resulting in decreased risk on edge loading, are gait strategies that could prevent edge loading. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1069–1076, 2016.     

Spectral characterization of squeaking in ceramic‐on‐ceramic total hip arthroplasty: Comparison of in vitro and in vivo values

Squeaking is a cause for concern in total hip arthroplasty (THA). However, the definition of this sound remains vague. Our goals were to characterize spectrally the squeaking in vitro under lubricated conditions and to compare the in vitro frequencies to in vivo frequencies. Four patients, who presented with a squeaking after ceramic‐on‐ceramic THA were investigated. In addition, 3 alumina ceramic 32 mm diameter components were tested in vitro under edge loading conditions using a friction simulator. Tests were conducted under lubricated conditions without and with the addition of a third body alumina particle. In vitro, no squeaking occurred under edge loading conditions. However, with the addition of a third body particle in the contact region, squeaking was obtained; the dominant frequency was 2.6 kHz. In vivo, the main recorded sound frequencies were: 2.3, 2.24, and 2.46 kHz for squeakers during walking and 1.45 kHz for a squeaker rising from a bent position. The in vivo recordings had a dominant frequency similar to, but slightly lower than, the in vitro values. Two types of squeaking were found in vivo and characterized spectrally. The rising squeaker had intermittent squeaking corresponding to a lower fundamental frequency compared to the walking squeakers. This finding suggests two different mechanism of squeaking. © 2011 Orthopaedic Research Society Published by Wiley Periodicals, Inc. J Orthop Res 30:185–189, 2012     

Hip abduction can prevent posterior edge loading of hip replacements

Edge loading causes clinical problems for hard‐on‐hard hip replacements, and edge loading wear scars are present on the majority of retrieved components. We asked the question: are the lines of action of hip joint muscles such that edge loading can occur in a well‐designed, well‐positioned acetabular cup? A musculoskeletal model, based on cadaveric lower limb geometry, was used to calculate for each muscle, in every position within the complete range of motion, whether its contraction would safely pull the femoral head into the cup or contribute to edge loading. The results show that all the muscles that insert into the distal femur, patella, or tibia could cause edge loading of a well‐positioned cup when the hip is in deep flexion. Patients frequently use distally inserting muscles for movements requiring deep hip flexion, such as sit‐to‐stand. Importantly, the results, which are supported by in vivo data and clinical findings, also show that risk of edge loading is dramatically reduced by combining deep hip flexion with hip abduction. Patients, including those with sub‐optimally positioned cups, may be able to reduce the prevalence of edge loading by rising from chairs or stooping with the hip abducted. © 2013 Orthopaedic Research Society Published by Wiley Periodicals, Inc. J Orthop Res 31:1172–1179, 2013

     

Edge‐loading severity as a function of cup lip radius in metal‐on‐metal total hips—A finite element analysis

While favorable tribological properties and allowance for larger femoral head sizes have made metal‐on‐metal (MoM) bearings an increasingly popular choice for total hip arthroplasty, concerns have mounted regarding adverse reactions to metal wear debris and ions. MoM cups differ from conventional polyethylene cups in terms of edge profile design and reductions from full hemisphericity, suggesting differences in loading at or near the cup edge, especially during subluxation events. Finite element analysis was used to investigate the effects of cup orientation and lip edge curvature on damage propensity for edge or near‐edge loading during subluxation. Increased cup lip radius (resulting in reduced articular arc) had a detrimental effect upon subluxation‐free hip range of motion and upon dislocation resistance. Contact stresses near the cup edge demonstrated complex relationships between edge radius and cup orientation, with peak stresses being influenced by both variables. The tendency for scraping wear at the egress site demonstrated similarly complex dependencies. These data indicate that acetabular cup design is an important determinant of edge and near‐edge loading damage propensity. © 2011 Orthopaedic Research Society Published by Wiley Periodicals, Inc. J Orthop Res 30:169–177, 2012     

Concomitant evolution of wear and squeaking in dual‐severity,lubricated wear testing of ceramic‐on‐ceramic hip prostheses

Ceramic‐on‐ceramic (CoC) hip bearings were tested in short‐term wear tests with a systematically varied contact force. Continuous vibration and intermittent surface roughness measurements were obtained to elucidate potential causes of in vivo hip joint squeaking. The three‐phase test comprised alternating cycles of edge loading (EL) and concentric articulation (CA), always using ample serum lubricant. A 50,000‐cycle wear trial in which the contact force during CA was distant from the head's wear patch yielded no squeaking and practically no liner roughening. In 10‐cycle trials of an edge‐worn head coupled with a pristine liner, the contact force was varied in magnitude and point of application; immediate, recurrent squeaking occurred only when the contact force exceeded a critical threshold value and was centered upon the head's wear patch. In a 27,000‐cycle wear trial with the contact force applied near the margin of the head's wear patch, recurrent squeaking emerged progressively as the liner's inner surface was roughened via its articulation with the worn portion of the head. The results reveal key conditions that yield recurrent squeaking in vitro in various scenarios without resorting to implausible dry conditions. A fundamental theory explains that hip squeaking is induced by myriad stress waves emanating from asperity collisions; yet, the root cause is edge loading. © 2012 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 30:1377–1383, 2012     

Influence of Acetabular Cup Rim Design on the Contact Stress During Edge Loading in Ceramic-on-Ceramic Hip Prostheses

The purpose of the study was to investigate the contact stresses in 3 different acetabular cup rim designs (new, worn, chamfer) during edge loading, after microseparation of ceramic on ceramic hip prostheses. A 3-dimensional finite element analysis was conducted for a 28-mm diameter alumina ceramic bearing with a radial clearance of 40 μm using a normal load of 2500 N under edge loading. At a separation distance of 250 μm, the maximum tensile stress in the “new” design was of similar magnitude to the flexural strength of the alumina material that supports the localized breakdown (stripe wear) of the acetabular cup surface observed clinically. Introducing a 2.5-mm radius chamfer should reduce the maximum tensile stress in the region of 60%.     

High friction moments in large hard‐on‐hard hip replacement bearings in conditions of poor lubrication

Disappointing clinical results for large diameter metal replacement bearings for the hip are related to compromised lubrication due to poor cup placement, which increases wear as well as friction moments. The latter can cause overload of the implant–bone interfaces and the taper junction between head and stem. We investigated the influence of lubrication conditions on friction moments in modern hip bearings. Friction moments for large diameter metal and ceramic bearings were measured in a hip simulator with cup angles varying from 0° to 60°. Two diameters were tested for each bearing material, and measurements were made in serum and in dry conditions, representing severely compromised lubrication. Moments were lower for the ceramic bearings than for the metal bearings in lubricated conditions, but approached those for metal bearings at high cup inclination. In dry conditions, friction moments increased twofold to 12 Nm for metal bearings. For ceramic bearings, the increase was more than fivefold to over 25 Nm. Although large diameter ceramic bearings demonstrate an improvement in friction characteristics in the lubricated condition, they could potentially replicate problems currently experienced due to high friction moments in metal bearings once lubrication is compromised. © 2012 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 31: 807–813, 2013     

Bony impingement affects range of motion after total hip arthroplasty: A subject‐specific approach

Hip range of motion after total hip arthroplasty has been shown to be dependent on prosthetic design and component placement. We hypothesized that bony anatomy would significantly affect range of motion. Computer models of a current generation hip arthroplasty design were virtually implanted in a model of pelvis and femur in various orientations ranging from 35° to 55° cup abduction, 0° to 30° cup anteversion, and 0° to 30° femoral anteversion. Four head sizes ranging from 22.2 to 32 mm and two neck sizes ranging from 10‐mm and 12‐mm diameter were tested. Range of motion was recorded as maximum flexion–extension, abduction–adduction, and axial rotation of the femur before any contact between prosthetic components or bone was detected. Bony impingement preceded component impingement in about 44% of all conditions tested, ranging from 66% in adduction to 22% in extension. Range of motion increased as head size increased. However, increasing head size also increased the propensity for bony impingement, which tended to reduce the beneficial effect of increased head size on range of motion. Reducing neck diameter had a greater effect on prosthetic impingement (mean, 3.5° increase in range of motion) compared to bone impingement (mean, 1.9°). This model allowed for a clinically relevant assessment of range of motion after total hip arthroplasty and may also be used with patient‐specific geometry [such as that obtained from preoperative computed tomography (CT) scans] for more accurate preoperative planning. © 2007 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 26:443–452, 2008     

A forty millimetre head significantly improves range of motion compared with a twenty eight millimetre head in total hip arthroplasty using a computed tomography-based navigation system

Purpose

Larger-diameter (≥40 mm) femoral heads decrease the incidence of post-operative dislocation in total hip arthroplasty (THA). This study was conducted to discover whether larger-diameter femoral heads result in greater range of motion of the hip with the use of a computed tomography (CT)-based navigation system.

Methods

Thirty-nine primary THAs were performed via a posterolateral approach using a CT-based navigation system. The stem was inserted in the femur in line with the original femoral neck anteversion. Considering the range of motion during various daily activities which could occur without impingement, the cup anteversion was decided at 10 ° increments according to the stem anteversion. While the cup inclination was set at 40 ° in order to avoid a high inclination angle to prevent the edge roading between the HXLPE liner and ceramic head. After implantation, trial liners and femoral heads were used with either 28 or 40 mm diameter. Maximal hip flexion, extension, abduction, external rotation in extension at 0° and internal rotation angles in flexion at 90 ° were measured. The differences between the ranges of motion with the 40-mm and 28-mm heads were tested. The results were assessed with paired Student t-tests.

Results

The ranges of motion in flexion, extension, abduction and internal rotation angles improved significantly with the 40-mm heads compared with the 28-mm heads. The ranges of motion of cases where maximal flexion angle was 90° or less were excluded, improved significantly with the 40 mm heads.

Conclusions

We concluded that the larger-diameter 40-mm femoral prosthetic heads result in greater ranges of motion in flexion, extension, abduction and internal rotation.

     

Dynamical analysis of dislocation‐associated factors in total hip replacements by hardware‐in‐the‐loop simulation

Since dislocation of total hip replacements (THR) remains a clinical problem, its mechanisms are still in the focus of research. Previous studies ignored the impact of soft tissue structures and dynamic processes or relied on simplified joint contact mechanics, thus, hindered a thorough understanding. Therefore, the purpose of the present study was to use hardware‐in‐the‐loop (HiL) simulation to analyze systematically the impact of varying implant positions and designs as well as gluteal and posterior muscle function on THR instability under physiological‐like loading conditions during dynamic movements. A musculoskeletal multibody model emulated the in situ environment of the lower extremity during deep sit‐to‐stand with femoral adduction maneuver while a six‐axis robot moved and loaded a THR accordingly to feed physical measurements back to the multibody model. Commercial THRs with hard‐soft bearings were used in the simulation with three different head diameters (28, 36, 44 mm) and two offsets (M, XL). Cup inclination of 45°, cup anteversion of 20°, and stem anteversion of 10° revealed to be outstandingly robust against any instability‐related parameter variation. For the flexion motion, higher combined anteversion angles of cup and stem seemed generally favorable. Total hip instability was either deferred or even avoided even in the presence of higher cup inclination. Larger head diameters (>36 mm) and femoral head offsets (8 mm) deferred occurrence of prosthetic and bone impingement associated with increasing resisting torques. In summary, implant positioning had a much higher impact on total hip stability than gluteal insufficiency and impaired muscle function. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2557–2566, 2017.

     

Fracture of the alumina-bearing couple delta ceramic liner

The fracture rate of third-generation ceramic liners is greatly reduced compared with first- and second-generation liners because of improvements in the design and manufacturing process. Fractures of the alumina-bearing couple are rare for the same reason.This article describes a case of a fracture of an alumina-bearing couple delta ceramic liner without trauma history that was treated with ceramic-on-polyethylene revision total hip arthroplasty. A 57-year-old man was admitted to the hip ward because of an alumina-bearing couple delta ceramic liner fracture. He underwent hip replacement by anterior approach 18 months previously in the same center because of left hip primary osteoarthritis. He received a 54×36-mm modular press-fit cup ceramic alumina-bearing couple delta insert. Probable causes of such fractures are manufacture production failure and edge loading based on cup inclination, but in our patient, inacceptable range of motion, failure of the locking mechanism during implantation insertion, or cracking were possible causes of fracture.Although the fracture rate of third-generation alumina-bearing couples is low, we believe that it may not be possible to eliminate the actual risk of alumina head fracture. Patients should be informed about the potential for this complication before receiving an alumina-bearing couple.     

Component positioning and ceramic damage in cementless ceramic-on-ceramic total hip arthroplasty

BackgroundIn ceramic-on-ceramic (CoC) total hip arthroplasty (THA), component positioning demonstrated to influence the bearing damage: however the connection between angles and clinical outcomes at long-term follow-ups is currently lacking. Aims of this study were: the computer tomography (CT) assessment of component positioning in CoC THAs; the correlation analysis between positioning and ceramic damage; the identification of safe zones.Methods91 consecutive post-operative CT scans including two types of CoC implants, with a mean follow-up of 12 ± 4.4 years, were evaluated. III generation (74.2%) and IV generation (25.8%) CoC surfaces were included. The angle measurements (cup abduction, anteversion, cup tilt, stem antetorsion, sacral slope) were automated using a CT-based software. The combined anteversion was assessed as well as the cup-neck position at −15°, 0°, 45° and 90° of flexion. Ceramic damage was diagnosed using synovial fluid analyses and radiological criteria.Results63.7% of THAs was inside the cup abduction target 30°–45° and 68.1% was inside the cup anteversion target 5°–25°. 19 patients (20.9%) showed signs of ceramic damage. High cup abduction and high cup-neck 45° minimum angle (which stood for high abduction and extreme combined version) significantly correlated with ceramic damage. No demographical features apart III generation ceramic bearings influenced the results. No safe zones could be detected.ConclusionsIn CoC THA, no safe zones can be described. However it is important to avoid cup inclination over 45° and a combination of steep cup and extreme combined version.     

Primary stability of a cementless acetabular cup in a cohort of patient‐specific finite element models

The primary stability achieved during total hip arthroplasty determines the long‐term success of cementless acetabular cups. Pre‐clinical finite element testing of cups typically use a model of a single patient and assume the results can be extrapolated to the general population. This study explored the variability in predicted primary stability of a Pinnacle^® cementless acetabular cup in 103 patient‐specific finite element models of the hemipelvis and examined the association between patient‐related factors and the observed variability. Cups were inserted by displacement‐control into the FE models and then a loading configuration simulating a complete level gait cycle was applied. The cohort showed a range of polar gap of 284–1112 μm and 95th percentile composite peak micromotion (CPM) of 18–624 μm. Regression analysis was not conclusive on the relationship between patient‐related factors and primary stability. No relationship was found between polar gap and micromotion. However, when the patient‐related factors were categorised into quartile groups, trends suggested higher polar gaps occurred in subjects with small and shallow acetabular geometries and cup motion during gait was affected most by low elastic modulus and high bodyweight. The variation in primary stability in the cohort for an acetabular cup with a proven clinical track record may provide benchmark data when evaluating new cup designs. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:1012–1023, 2018.

     

全髋关节置换术中的髋臼外展角和磨损的关系

目的研究人工全髋关节置换术中的髋臼外展角与磨损的关系,及其对人工全髋关节稳定性的影响。方法对30例32髋进行平均4.2年的随访。测量髋臼杯的外展角,并通过测量在随访期间股骨头中心相对于髋臼中心的矢量位移,来确定关节面磨损的大小和方向,并进行统计学分析。结果最近随访时,30例患者的32个髋关节假体均未发现临床松动和失败征象,假体柄轴线与股骨纵轴成角均在3°以内。聚乙烯平均线性磨损量为0.81mm,磨损速度为0.18mm/年,髋臼外展角平均54.5°。磨损方向平均为?6.93°,指向上方稍偏外侧。线性回归分析显示磨损方向与髋臼假体外展角度存在负相关关系。随着外展角度的增加,磨损方向由内上方转为外上方,外展角55°以上的假体磨损方向基本指向外上方。未发现线性磨损速度与外展角及磨损方向之间的相关关系。结论过大的外展角使股骨头中心向外上方迁移,可能会造成应力分布不均和假体磨损增加,因此临床上应该避免髋臼假体植入的外展角超过55°,以维持髋关节的活动度和稳定性。     

Optimized design for a novel acetabular component with three wings. A study of finite element analysis

BackgroundA novel acetabular component with three wings has earlier been explored for reconstructing extensive acetabular bone defects in hip revision arthroplasty with a satisfying clinical result. However, the periacetabular stress patterns and mechanisms by which the acetabular cup obtains initial stability are not clear.PurposesThe purpose of this study was to evaluate the stress patterns of the novel cup using finite element method and possible effects of joint loading postoperatively, and to analyze its optimized design for the structural parameters of the cup.MethodsThree-dimensional finite-element (FE) models of the cup with three wings and the hemispherical cup were created to calculate the stress patterns during a normal gait cycle using FE formulations. The stresses of these acetabular components were analyzed and compared.ResultsFE analysis demonstrated that the cup with three wings and the hemispherical cup had the same trend for stress and strain. The stress of the wings increased gradually from rim to root. Its peak stress was significantly lower than the yield force of the Co-Cr-Mo alloy at the joint between the wing and the shell. The graft portion near the acetabular component was subjected to higher stress conditions. The contact stresses were found to be decreased with a reduced abduction angle of wings and not affected by changed eversion angle of wings. The cup with wings of abduction angle of 15° had lower stresses compared with other cups.ConclusionsThe cup with wings is a reliable option for the reconstruction of the acetabulum with extensive bone socket defects. The reduced abduction angle of wings helps to decrease the stress of the cup with wings. However, removing the eversion angle of wings may be the most prudent choice to avoid the introduction of adverse variables, which may contribute to the loosening of the acetabular component. FE analysis is a useful tool with which to address these issues.     

Acetabular Cup Stiffness and Implant Orientation Change Acetabular Loading Patterns

Acetabular cup orientation has been shown to influence dislocation, impingement, edge loading, contact stress, and polyethylene wear in total hip arthroplasty. Acetabular implant stiffness has been suggested as a factor in pelvic stress shielding and osseous integration. This study was designed to examine the combined effects of acetabular cup orientation and stiffness and on pelvic osseous loading. Four implant designs of varying stiffness were implanted into a composite hemipelvis in 35° or 50° of abduction. Specimens were dynamically loaded to simulate gait and pelvic strains were quantified with a grid of rosette strain gages and digital image correlation techniques. Changes in the joint reaction force orientation significantly altered mean acetabular bone strain values up to 67%. Increased cup abduction resulted in a 12% increase along the medial acetabular wall and an 18% decrease in strain in inferior lateral regions. Imbalanced loading distributions were observed with the stiffer components, resulting in higher, more variable, and localized surface strains. This study illustrates the effects of cup stiffness, gait, and implant orientation on loading distributions across the implanted pelvis.     

Relation between vertical orientation and stability of acetabular component in the dysplastic hip simulated by nonlinear three-dimensional finite element method

In acetabular dysplasia, more vertical orientation of the acetabular component is often used to minimize the superolateral bone grafting. This study was designed to determine the effects of vertical orientation of the cup on the stability and polyethylene wear of the acetabular component in uncemented total hip arthroplasty (THA). Three-dimensional finite element models of the hemipelvis with dysplastic acetabulum were developed. Metal-backed hemispherical cups were placed in the true acetabulum with abduction angles of 35, 45, 55, and 65 degrees. It was found that more vertical orientation of the cup was associated with larger relative motion of the metal shell between the acetabulum and metal shell. Furthermore, tilting and torsional shear stresses in the model of the cup abduction angle of 65 degrees were found to be 1.7 times larger than that in the model with 35 degrees at the bone-metal shell interface. More vertically oriented cups caused larger contact stresses at the articulating surfaces of the polyethylene liners. The results suggest that the abduction angle of the acetabular component significantly influences cup loosening and polyethylene wear in THA.     

Reduction in variability of acetabular cup abduction using computer assisted surgery: a prospective and randomized study.

Optimal orientation of the acetabular component of a total hip prosthesis is an important factor in determining the early and long-term result of a total hip arthroplasty (THA). Conventional positioning of the cup component is usually done using a free-hand method, or with the help of a mechanical acetabular alignment guide. However, these methods have proven to be inaccurate, and a great variation in orientation of the cup is found postoperatively. In this study, we wished to determine if the variability of the abduction angle of acetabular cups could be reduced with the use of computer navigation. The abduction angles of the acetabular components of three groups of 50 THAs were assessed. In the first group, a free-hand method was used to position the cup component. This group was operated in the period before we started using computer navigation for hip surgery. In the second group, CT-based computer navigation was used to plan and help position the cup. The third group consisted of 50 THA cases in which a free-hand method was used to position the cup, although these procedures were performed in the period after we had begun using the Computer Assisted Surgery (CAS) system. The variability in cup abduction angle was assessed in all three groups and compared. There was a significant reduction in variability in the CAS group compared to the first group. There was also a reduction in variability in the CAS group compared to the third group, although this was not statistically significant. It is concluded that the use of computer navigation helped the surgeon to place the cup component with less variability of the abduction angle, and, more importantly, we found that no cups were placed in the more extreme positions (outliers).     

An early follow-up of the mecring cup in total hip arthroplasty

41 non-cement total hip arthroplasties with the Mecring cup are reported in this paper. The follow-up results in an average of 14 months showed that this operation relieved the hip pain and improved the functional capacity and the motion of the hip. 80.5% of the reported hips gained excellent or good results. Because the cup was firm on the acetabulum with the thread, the defect of bone was smaller and the cup revision was easier than others, it is applicable not only for the elderly but also for younger patients. The relationship between the hip function and cup position was observed and it suggested that the correct abduction angle of the cup should be 40-50 degrees and the anteversion angle 5-20 degrees. The postoperative complications were dislocation and ectopic ossification.     

Serum ion levels after ceramic‐on‐ceramic and metal‐on‐metal total hip arthroplasty: 8‐year minimum follow‐up

Alternative bearing surfaces for total hip arthroplasty, such as metal‐on‐metal and ceramic‐on‐ceramic, offer the potential to reduce mechanical wear and osteolysis. In the short and medium term, the second generation of metal‐on‐metal bearings demonstrated high systemic metal ion levels, whereas ceramic‐on‐ceramic bearings showed the lowest ones. We aimed to verify whether the long‐term ion release in metal‐on‐metal subjects was still relevant at a median 10‐year follow‐up, and whether a fretting process at the modular junctions occurred in ceramic‐on‐ceramic patients and induced an ion dissemination. Serum levels were measured in 32 patients with alumina‐on‐alumina implants (group A), in 16 subjects with metal‐on‐metal implants (group B), and in 47 healthy subjects (group C). Group B results were compared with medium‐term findings. Cobalt and chromium levels were significantly higher in metal‐on‐metal implants than in ceramic‐on‐ceramic ones and controls. Nevertheless, ion levels showed a tendency to decrease in comparison with medium‐term content. In ceramic‐on‐ceramic implants, ion values were not significantly different from controls. Both in groups A and B, aluminum and titanium release were not significantly different from controls. In conclusion, negligible serum metal ion content was revealed in ceramic‐on‐ceramic patients. On the contrary, due to the higher ion release, metal‐on‐metal coupling must be prudently considered, especially in young patients, in order to obtain definitive conclusions. © 2008 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res