Proximal Convergence Research Articles

Femoral and tibial phenotypes of varus alignment in a Southeast Asian arthritic population: a descriptive study.

Knowledge of femoral and tibial morphology is important for patient-specific surgery in both joint reconstruction and preservation procedures. Studies evaluating morphological variance in femoral and tibial alignments in Asian populations are scarce. This is the first descriptive study evaluating the femoral and tibial phenotypes of varus alignment in a Southeast Asian population. Long-leg coronal standing radiographs of 2021 limbs were obtained, and the hip-knee-ankle angle, mechanical lateral distal femoral angle, medial proximal tibial angle and joint line convergence angle were measured. Joint line obliquity was calculated, and the knees were classified according to the Coronal Plane Alignment of Knee (CPAK) classification. Descriptive analyses on alignment parameters and demographic data (age, gender, ethnicity and body mass index [BMI]) were performed and entered into a linear regression model. The highest frequency of limb alignment in the population was found to be CPAK type I (52.71%, n = 1003). Tibial varus was the largest contributor of varus malignment. Of the varus knees (n = 1247), varus deformity was found solely in the tibia (68.60%), solely in the femur (2.07%) and was contributed by both the femur and the tibia (4.97%). In the linear regression model, BMI was found to be a strong determinant for femoral varus (P = 0.004) and joint line incongruence (P < 0.001). The findings of this study will be important to surgeons during planning for joint preservation procedures (such as corrective osteotomies) and joint arthroplasties to restore alignment.

How a Subclinical Unilateral Vestibular Signal Improves Binocular Vision.

The present study aimed to determine if an infra-liminal asymmetric vestibular signal could account for some of the visual complaints commonly encountered in chronic vestibular patients. We used infra-liminal galvanic vestibular stimulation (GVS) to investigate its potential effects on visuo-oculomotor behavior. A total of 78 healthy volunteers, 34 aged from 20 to 25 years old and 44 aged from 40 to 60 years old, were included in a crossover study to assess the impact of infra-liminal stimulation on convergence, divergence, proximal convergence point, and stereopsis. Under GVS stimulation, a repeated measures ANOVA showed a significant variation in near convergence (p < 0.001), far convergence (p < 0.001), and far divergence (p = 0.052). We also observed an unexpected effect of instantaneous blocking of the retest effect on the far divergence measurement. Further investigations are necessary to establish causal relationships, but GVS could be considered a behavioral modulator in non-pharmacological vestibular therapies.

A fast proximal gradient method and convergence analysis for dynamic mean field planning

In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial projection step becomes solving an elliptic equation whose solution can be obtained by conventional methods efficiently. By induction on iterations used in the algorithm, we theoretically show that the proposed discrete solution converges to the underlying continuous solution as the grid becomes finer. Furthermore, we generalize our algorithm to mean-field game problems and accelerate it using multilevel and multigrid strategies. We conduct comprehensive numerical experiments to confirm the convergence analysis of the proposed algorithm, to show its efficiency and mass preservation property by comparing it with state-of-the-art methods, and to illustrate its flexibility for handling various mean-field variational problems.

Normative Value of Accommodative Convergence to Accommodation in Indian Population Measured by Heterophoria Method

Abstract Introduction: Near response is a complex synkinesis required for a good binocular vision. accommodative convergence per diopter of accommodation (AC/A ratio) is a value of significance in this synkinetic movement. In addition, the value is used to classify and treat ocular movement abnormalities. The two commonly used methods for determining the AC/A ratio are Gradient Method and Heterophoria method. The normative data for Indian population by gradient method was described in two studies. However, the normative data for heterophoria method is lacking in Indian population. Objective: The purpose of this cross-sectional study is to generate the normative value for AC/A ratio for the Indian population by heterophoria method. One hundred healthy ophthalmologically normal adults with no presbyopia or refractive error were chosen consecutively among the attendants of patients visiting the center. Materials and Methods: After thorough ophthalmic evaluation, the participants were subjected to AC/A ratio calculation by heterophoria method using 6/9 fixation target and PMMA Prism bar. Results: One hundred healthy adults with no refractive error or ocular abnormality were selected with a mean age of 25.70 years (standard deviation [SD] = 4.92) and equal gender distribution. The mean Inter Pupillary Distance (IPD) was found to be 62.88 mm with a SD of 3.91 mm. The average phoria at distance was 1.82 prism diopters (SD = 2.03pd) of exophoria and for near at 33 cm was 4.20pd (SD = 1.92pd). The mean AC/A ratio by heterophoria method was found to be 5.49PD/D with an SD of 0.54PD/D. The highest being 6.90PD/D and the lowest being 4.27PD/D with no statistically significant difference between genders. Conclusion and Relevance: According to the previous studies, the normative data arrived is lesser than the value reached in the current study for similar population groups when considering both methodologies of testing. This variation between the gradient method and heterophoria method accounted for by the involvement of proximal convergence during the heterophoria method.

Postoperative full leg radiographs exhibit less residual coronal varus deformity compared to intraoperative measurements in robotic arm-assisted total knee arthroplasty with the MAKO™ system

PurposeRobotic arm-assisted total knee arthroplasty (raTKA), currently a major trend in knee arthroplasty, aims to improve the accuracy of implant positioning and limb alignment. However, it is unclear whether and to what extent manual radiographic and navigation measurements with the MAKO™ system correlate. Nonetheless, a high agreement would be crucial to reliably achieve the desired limb alignment.MethodsThirty-six consecutive patients with osteoarthritis and a slight-to-moderate varus deformity undergoing raTKA were prospectively included in this study. Prior to surgery and at follow-up, a full leg radiograph (FLR) under weight-bearing conditions was performed. In addition, a computed tomography (CT) scan was conducted for preoperative planning. The hip–knee–ankle angle (HKA), mechanical lateral distal femur angle (mLDFA), mechanical medial proximal tibial angle (mMPTA) and joint line convergence angle (JLCA) were measured in the preoperative and follow-up FLR as well as in the CT scout (without weight-bearing) by three independent raters. Furthermore, the HKA was intraoperatively assessed with the MAKO™ system before and after raTKA.ResultsSignificantly higher HKA values were identified for intraoperative deformity assessment using the MAKO system compared to the preoperative FLR and CT scouts (p = 0.006; p = 0.05). Intraoperative assessment of the HKA with final implants showed a mean residual varus deformity of 3.2° ± 1.9°, whereas a significantly lower residual varus deformity of 1.4° ± 1.9° was identified in the postoperative FLR (p < 0.001). The mMPTA was significantly higher in the preoperative FLR than in the CT scouts (p < 0.001). Intraoperatively, the mMPTA was adjusted to a mean of 87.5° ± 0.9° with final implants, while significantly higher values were measured in postoperative FLRs (p < 0.001). Concerning the mLDFA, no significant differences could be identified.ConclusionThe clinical importance of this study lies in the finding that there is a difference between residual varus deformity measured intraoperatively with the MAKO™ system and those measured in postoperative FLRs. This has implications for preoperative planning as well as intraoperative fine-tuning of the implant position during raTKA to avoid overcorrection of knees with slight-to-moderate varus osteoarthritis.Level of evidenceLevel IV.

Case Report of Modified Sauvé-Kapandji Technique Using Endobutton Suture in Secondary Treatment of Madelung Deformity

The Sauvé-Kapandji technique is considered a useful treatment option for distal radioulnar joint instability encountered in many conditions, such as Madelung deformity or in post-traumatic entities. However, post-operative instability of the proximal ulnar stump and radioulnar convergence may be symptomatic and is still a major concern. Despite proximal ulnar stump stabilization with various techniques, many patients still complain of pain and limitation of wrist movement. We report a case of a patient with Madelung disease treated initially by corrective radial and ulnar osteotomy, and then encountered a post-traumatic distal radioulnar joint instability. This condition was treated with a modified Sauvé-Kapandji procedure using a single endobutton suture, leading to good clinical and radiological results.

Functional magnetic resonance imaging activation for different vergence eye movement subtypes.

Maddox suggested that there were four convergence subtypes, each driven by a different stimulus. The purpose of this study was to assess the neural correlates for accommodative convergence, proximal convergence (convergence stimulus provided), disparity convergence and voluntary convergence (no specific convergence stimulus provided) using functional magnetic resonance imaging (fMRI). Ten subjects (mean age=24.4 years) with normal binocular vision participated. The blood oxygenation level-dependent (BOLD) signals of the brain from fMRI scans were measured when subjects made vergence eye movements while: (1) alternately viewing letters monocularly where one eye viewed through a -2.00 D lens, (2) alternately viewing Difference of Gaussian targets monocularly at distance and near, (3) viewing random dot stereograms with increasing disparity and (4) voluntarily converging the eyes with binocular viewing. The accommodative convergence paradigm resulted in activation on the right side in the right fusiform cortex and the right middle occipital cortex. The proximal convergence stimulus mainly activated areas in the right occipital lobe. The disparity stimulus activated areas in the left occipital cortex and the left frontal cortex. Finally, the voluntary convergence paradigm resulted in activation primarily in the occipital lobe and mostly bilaterally. The accommodative, proximal, disparity and voluntary convergence paradigms resulted in activation in unique areas in the brain with functional MRI. Activation was found in more areas in the proximal and voluntary conditions compared with the accommodative and disparity conditions.

The outcome of Sauve Kapandji procedure on patient with DRUJ arthritis: A case report

BackgroundThe distal radioulnar joint (DRUJ) is frequently involved in inflammatory diseases, both de-generative and notably traumatic, resulting in pain, wrist motion and strength loss, and severe functional impairment. DRUJ dysfunction can be highly incapacitating. The Sauve-Kapandji (SK) procedure can be indicated to address multiple etiologies of DRUJ dysfunction.Case presentationA 54-year-old woman presented with pain and difficulty moving the left wrist. X-ray imaging revealed the union of the distal radius with the plate still in there with subluxation of the distal radioulnar joint after surgery in 2005. Afterwards, she underwent the Sauve-Kapandji procedure. Follow-ups were done at periodic intervals, and wrist physiotherapy was instituted. We evaluated the range of motion and the VAS score as well. The patient had acceptable motion after four weeks of evaluation.DiscussionThe SK method has been advocated as a treatment for DRUJ derangement because, un-like the Darrach surgery, it preserves the ulnar head at the wrist. As with the Darrach opera-tion, postoperative instability of the proximal ulnar stump or radioulnar convergence may occur despite the favourable clinical prognosis.ConclusionThe Sauve-Kapandji procedure could treat wrist pain and deformity in DRUJ arthritis. It gives a good result in two weeks, four weeks, twelve weeks, and twenty after the procedure. The peak time of recovery is four weeks after the procedure.

Impact of leaflet-tethering angle correction on the assessment of tricuspid regurgitation severity using the PISA method

Abstract Funding Acknowledgements Type of funding sources: None. Background Severe tricuspid regurgitation (TR) is associated with excess mortality and morbidity. Therefore, assessment of TR severity is pivotal. Calculation of the effective regurgitant orifice area (EROA) and the regurgitant volume (RVol) using flow convergence method (PISA) by echocardiography are still the recommended parameters to define TR severity. However, the distortion of the proximal convergence zone related to the extent of valve leaflet tethering may result in smaller PISA radius and in underestimation of TR severity. Correcting for the angle of the leaflet tethering could reduce errors due to geometric assumption of a flat valvular plane and improve the accuracy of the calculations. Purpose: The aims of our study were (1) to evaluate whether taking into account the extent of leaflet tethering by applying the angle correction (AC) in the PISA formula improves the accuracy of the quantitative assessment of TR severity; (2) to assess the potential clinical impact of AC. Methods Forty-one patients with functional TR (73.5 ± 11.8 years,51% men,36% sinus rhythm,17% severe), underwent 2D and 3D echocardiography. We compared the RVol obtained by volumetric method (as reference) with the RVol by PISA with and without AC. TR RVol by volumetric method was calculated as: total RV stroke volume (RVSV) – left ventricular forward SV (LVSV), where RVSV was obtained by subtracting the end-systolic from end-diastolic RV volume measured by 3D echocardiography and LV SV was calculated by multiplying LV outflow area by velocity time integral (VTI) (Fig. 1). TR RVol by PISA was calculated as EROA x VTITR. Uncorrected EROA was calculated using the formula: 6.28 r2 xVa/ PeakVTR (r - PISA radius, Va, aliasing velocity, PeakVTR – TR peak velocity). The corrected EROA accounting for the PISA geometric distortion by leaflet tethering angle (α) was calculated as: 6.28 r2 x Va (α/180)/ PeakV TR (PISAac), where α was measured using a protractor generated by dedicated software. Results Application of AC to PISA method resulted in larger EROA and RVol (0.34± 0.38 cm2 vs 0.24± 0.24cm2 and, 25.2± 19.3 mL vs 18.6 ± 13.1mL, respectively). The percentage change in EROAac was over 40%. When compared to the volumetric method, RVol by corrected PISA method was significantly closer and correlated (bias -3.95mL, LOA ± 6.41 mL, r= .987; p&amp;lt; .001) than the conventional PISA without AC (bias -10.5 mL, LOA ± 15 mL, r= .975). Angle correction resulted in a change of TR severity in 32% of cases (Fig. 2) and in a greater concordance of TR severity grade with the volumetric method (75%, 31/41 with AC vs 52%, 22/41 without AC). Conclusions Angle-corrected PISA method that accounts for the extent of the leaflet tethering in TR provided significantly larger TR RVol that were closely correlated with the volumetric RVol by 3D echocardiography. A simple geometric angle correction of the proximal flow with PISA method reclassified up to 1/3 of patients with functional TR. Abstract Figure. Representation of study method Abstract Figure. Reclassification of TR severity

Comparing proximal convergence ratio in myopes.

Aim: To determine if there is a difference at all in proximal convergence to accommodation ratio (PC/ A) between 2 myopic groups. Group A: -0.50D < SE < 3.00D, SE: spherical equivalent, D: Diopter) and Group B (-3.00D SE and above). Patients and methods: In this prospective observational study, 24 consecutive patients with myopia between -0.50D < SE < 3.00D were included in group A and 27 consecutive patients with myopia > -3.00 D SE were included in group B. Patients with pathological myopia, strabismus or heterophoria anomalies were excluded. The PC/ A ratio for both the groups were calculated by measuring the difference between value of accommodative convergence to accommodation ratio (AC/ A) derived from heterophoria and gradient method using a prism bar method. Statistical analysis was performed by analyzing descriptive statistics and the independent sample t-test using SPSS ver. 22.0 software.Results: The average calculated PC/ A ratio was 3.24∆/ D (SD = +0.68/ D) in group B (n=27) and 2.6∆/ D (SD = 0.86/ D) in group A (n=24) (p value <0.05).Conclusion: An evident high AC/ A ratio in group B patients with myopia more than -3.00 D was the predominant cause for high PC/ A ratio in group B patients.

181 Impact of leaflet-tethering angle correction on the assessment of tricuspid regurgitation severity using the PISA method

Abstract Aims Severe tricuspid regurgitation (TR) is associated with excess mortality and morbidity. Therefore, accurate assessment of TR severity is pivotal. In clinical routine, the calculation of the effective regurgitant orifice area (EROA) and the regurgitant volume (RVol) using flow convergence method (PISA) by echocardiography are among the recommended parameters to define TR severity. However, the distortion of the proximal convergence zone related to the extent of valve leaflet tethering may result in smaller PISA radius and in underestimation of TR severity. Correcting for the angle of the leaflet tethering could reduce errors due to geometric assumption of a flat valvular plane and improve the accuracy of the calculations. The aims of our study were: (1) to evaluate whether taking into account the extent of leaflet tethering by applying the angle correction (AC) in the PISA formula improves the accuracy of the quantitative assessment of TR severity; (2) to assess the potential clinical impact of AC. Methods and results Forty-one patients with functional TR (73.5 ± 11.8 years, 51% men, 36% sinus rhythm, 17% severe), underwent 2D and 3D echocardiography. We compared the RVol obtained by volumetric method (as reference) with the RVol by PISA with and without AC. TR RVol by volumetric method was calculated as: total RV stroke volume (RV SV)–left ventricular forward SV (LV SV), where RV SV was obtained by subtracting the end-systolic from end-diastolic RV volume measured by 3D echocardiography and LV SV was calculated by multiplying LV outflow area by velocity time integral (VTI). TR RVol by PISA was calculated as EROA × VTI TR. Uncorrected EROA was calculated using the formula: 6.28 r2 × Va/PeakV TR (r—PISA radius, Va, aliasing velocity, PeakV TR—TR peak velocity). The corrected EROA accounting for the PISA geometric distortion by leaflet tethering angle (α) was calculated as: 6.28 r2 × Va (α/180)/PeakV TR (PISAAC), where α was measured using a protractor generated by dedicated software. PISA radius and angle were 5.5 ± 1.97 mm and 211.2° ± 13.6°, respectively. Application of AC to PISA method resulted in larger EROA and RVol (0.34 ± 0.38 cm2 vs. 0.24 ± 0.24 cm2 and, 25.2 ± 19.3 ml vs. 18.6 ± 13.1 ml, respectively). The percentage change in EROAAC was over 40%. When compared to the volumetric method, RVol by corrected PISA method was significantly closer and correlated (bias −3.95 ml, LOA ± 6.41 ml, r = 0.987; P &amp;lt; 0.001) than the conventional PISA without AC (bias −10.5 ml, LOA ± 15 ml, r = 0.975). Angle correction resulted in a change of TR severity in 32% of cases and in a greater concordance of TR severity grade with the volumetric method (75%, 31/41 with AC vs. 52%, 22/41 without AC). Conclusions Angle-corrected PISA method that accounts for the extent of the leaflet tethering in TR provided significantly larger TR RVol that were closely correlated with the volumetric RVol by 3D echocardiography. A simple geometric angle correction of the proximal flow with PISA method reclassified up to one-third of patients with functional TR.

Some Results on Iterative Proximal Convergence and Chebyshev Center

In this paper, we prove a sufficient condition that every nonempty closed convex bounded pair M , N in a reflexive Banach space B satisfying Opial’s condition has proximal normal structure. We analyze the relatively nonexpansive self-mapping T on M ∪ N satisfying T M ⊆ M and T N ⊆ N , to show that Ishikawa’s and Halpern’s iteration converges to the best proximity point. Also, we prove that under relatively isometry self-mapping T on M ∪ N satisfying T N ⊆ N and T M ⊆ M , Ishikawa’s iteration converges to the best proximity point in the collection of all Chebyshev centers of N relative to M . Some illustrative examples are provided to support our results.

Quantification of tricuspid regurgitation area by 3-dimensional color Doppler echocardiography considering different clinical settings.

The precise assessment of tricuspid regurgitation (TR) using 2D imaging techniques may be associated with significant difficulties due to the nonround regurgitation area. Direct analysis of the regurgitation area by 3D color Doppler echocardiography at the vena contracta (3D VCA) has the potential to adequately quantify even complex TR. This study compared 3D VCA for quantification of the TR with the regurgitant area determined by proximal isovolumetric convergence method (PISA-EROA) considering different clinical settings. In 95 patients with TR of different severity, the regurgitant orifice area was determined by 3D color Doppler echocardiography and by PISA-EROA. Using 3D color Doppler echocardiography, the regurgitant orifice area was determined three times in each patient considering 3 datasets. Mean 3D VCA was 0.27±0.14, 0.27±0.13, and 0.29±0.14cm2 , respectively, as determined by three separate measurements in each of the 95 patients. There was a mean relative deviation between the three measurements in each patient of 12.4±14.9%. The regurgitant orifice area using the PISA method was 0.28±0.14cm2 . There was a mean difference of 0.07cm2 (95% CI -0.124 to 0.138cm2 ) between 3D VCA and PISA-EROA. The correlation between 3D VCA and PISA-EROA was r=.88 (P<.001). Considering a grading of TR severity in grade I (regurgitant area<0.2cm2 ), grade II (area 0.2-0.4cm2 ), and grade III (area>0.4cm2 ), there was a good agreement between severity grade determined by 3D VCA and severity grade determined by PISA-EROA (kappa 0.71). The analysis of the VCA of a TR using 3D color Doppler echocardiography is an alternative method to determine the regurgitant severity with good agreement to the PISA method.

P1779Quantitation of severe degenerative mitral regurgitation by echocardiography and CMR with acetate PET for external reference for left ventricular volumes

Abstract Background Quantitative echocardiographic assessment of severity of primary mitral regurgitation (MR) is challenging. CMR is recommended if MR severity cannot be clearly determined, since quantitation of regurgitation as well as of left ventricular (LV) volumes and function is crucial for the indication for surgery especially in asymptomatic patients. Purpose We aimed to compare volumetric measurements obtained from transthoracic echo (TTE) and cardiovascular magnetic resonance (CMR) using ECG-gated [(11)C]acetate PET as reference for assessment of LV volumes. Methods A total of 51 asymptomatic patients with severe primary mitral regurgitation underwent TTE, CMR and PET on the same day. Mitral regurgitant volumes (RVol) were measured by TTE using proximal convergence (PISA) method and by CMR, subtracting aortic forward flow volume from LV stroke volume. LV volumes were measured by TTE, CMR and PET. Results Despite a fair correlation between regurgitant volumes measured by TTE and CMR (r=0.53, p&lt;0.001), PISA method heavily overestimated regurgitant volumes on TTE as compared to CMR (103±60ml vs. 78±35ml, p&lt;0.001). TTE systematically underestimated LV volumes as compared to CMR (see table) despite a good correlation (r=0.81, 0.67 and 0.76 respective for LV EDV, ESV and SV, p&lt;0.001 for all). There was no difference in LV EF between the methods. LV volumes obtained by CMR and PET showed a strong correlation (r=0.92, 0.79 and 0.89 respective for LV EDV, ESV and SV, p&lt;0.001 for all) and agreement (see table). Comparison of TTE, CMR and PET TTE CMR PET PET TTEvs.CMR PET CMRvs.PET F-test LV EDV, ml 145±34 241±57 234±51 &lt;0.001 0.004 &lt;0.001 LV ESV, ml 47±11 76±22 81±23 &lt;0.001 0.067 &lt;0.001L LV SV, ml 99±26 164±38 152±34 &lt;0.001 &lt;0.001 &lt;0.001 LV EF, % 68±5 69±5 65±6 0.236 &lt;0.001 &lt;0.001 Conclusions As compared to CMR, PISA method used by TTE substantially overestimates regurgitant volumes in patients with asymptomatic primary mitral regurgitation. Conversely, LV volumes in spite of good correlation are heavily underestimated by TTE in comparison with CMR. A strong correlation and agreement between LV volumes measured by CMR and PET confirms the accuracy of the former method which is considered as a golden standard for assessment of ventricular function and volumes. Thus, even so-called quantitative echo measures should be understoas essentially semi-quantitative indicators of severity.

A residual intra-articular varus after medial opening wedge high tibial osteotomy (HTO) for varus osteoarthritis of the knee.

Varus deformity of knee osteoarthritis was formed by both intra-articular and extra-articular pathologies. Such intra-articular deformities could not be fully corrected by a medial open-wedge high tibial osteotomy (HTO), which was performed as an extra-articular procedure. Therefore, the purpose of this study was to investigate whether any residual varus was left inside the joint after HTO in the patients with knee osteoarthritis, and a correlation of the residual varus could be traced. This study involved 66 patients (66 knees) undergoing HTO for medial knee osteoarthritis. The percentage of mechanical axis (%MA), mechanical femorotibial angle (mFTA), mechanical lateral distal femoral angle (mLDFA), mechanical medial proximal tibial angle (mMPTA) and joint line convergence angle (JLCA) were measured on radiographs of the full-length legs preoperatively and 6 months postoperatively. The relationship between changes in the JLCA and alignment correction was assessed. The postoperative residual JLCA was categorized as the optimal (postoperative JLCA ≤ 2°), the acceptable (2° < postoperative JLCA ≤ 5°), and the unacceptable (postoperative JLCA > 5°) to analyze its correlation with pre- or intra-operative factors. Average %MA and mFTA were improved from 5.5 to 60% and from 190.2° to 176.4°, respectively. There was no change in mLDFA, whereas mMPTA changed from 80.3° to 91.8°. JLCA changed from 4.2° to 2.7°. The analyses of multiple linear regression showed that the preoperative JLCA and postoperative changes in mechanical alignment (%MA, mFTA and mMPTA) were two important variables dependently associated with differences in JLCAs postoperatively. However, postoperative JLCAs showed a stronger correlation to preoperative JLCAs than to changes in mechanical alignment postoperatively. A Chi-square analysis showed a significantly higher percentage of patients achieved acceptable postoperative JLCAs in the preoperative JLCA ≤ 6° group (78.8%) compared to the preoperative JLCA > 6° group (6.1%). Therefore, 6° of JLCA was suggested to be a tipping point. The capability of HTO to correct intra-articular varus deformities, which was represented by JLCAs, is limited. Postoperative residual JLCAs were correlated primarily to preoperative JLCA values and total alignment correction, while the former accounted for most. A preoperative JLCA of 6° was suggested to be a tipping point, and a larger value indicated more than 5° residual JLCA after the HTO.

Hybrid Moreau’s Proximal Algorithms and Convergence Theorems for Minimization Problems in Hilbert Spaces with Applications

In this paper, motivated by Moreau’s proximal algorithm, we give several algorithms and related weak and strong convergence theorems for minimization problems under suitable conditions. These algorithms and convergence theorems are different from the results in the literatures. Besides, we also study algorithms and convergence theorems for the split feasibility problem in real Hilbert spaces. Finally, we give numerical results for our main results.

Modified Sauvé-Kapandji procedure for the distal radioulnar joint disorders of osteoarthritis and rheumatoid arthritis.

The Sauvé-Kapandji (SK) procedure is one of several surgical options in the treatment of distal radioulnar disorders by osteoarthritis (OA) and rheumatoid arthritis (RA). While satisfactory postoperative clinical results were obtained in most cases, instability of the proximal ulnar stump and radioulnar convergence are the most common complications. Minami etal. have developed a modification of the SK procedure that maintains the transverse diameter of the distal radioulnar joint and stabilizes the proximal ulnar stump, using a half-slip of the extensor carpi ulnaris tendon. In this study, the modified SK procedure was performed on 83 patients with distal radioulnar disorders, due to OA and RA. We evaluated the clinical and radiographical postoperative results with an average follow-up period of 82.3 months. Post-operative extension of the wrist and pronation/supination of the forearm had significantly improved with the exception of wrist flexion. Postoperative x-rays showed no instability of the proximal ulnar stump in both coronal and lateral planes. However, breakage of the drilled hole at the proximal ulnar stump occurred in 10 cases, and of these, there was instability of the proximal ulnar stump in 5 cases. This modification is very simple and does not require extension of the surgical field. This paper concludes that the modified SK procedure is a safe and effective surgical intervention of distal radioulnar disorders from OA and RA.

Radial Shaft Convergence in Distal Radius Fractures: Diagnosis and Treatment.

Radial shaft convergence in distal radius fractures is often misdiagnosed. This common deformation is often associated with a radial translation of the distal fragment. This parameter has to be corrected because of the increased risk of distal radioulnar joint instability due to detensioning of the distal interosseous membrane if there is an associated triangular fibrocartilage complex lesion. A new radiologic sign for diagnosis of proximal radius convergence during distal radius fracture is presented as well as technical tips for correction of this deformity.

Risk factors for consecutive esotropia

Purpose The aim of this retrospective study was to investigate the different factors predisposing to consecutive esotropia (CET) after surgical management of intermittent exotropia (IXT). Patients and methods This study included the medical records of patients who had surgery for IXT from March 2016 to March 2017. Postoperatively, the patients were divided into two groups: A group who developed CET and another group who became orthotropic within 6 months of follow-up. Possible risk factors for the development of CET were recorded and analyzed. Results Eighteen patients developed CET, while the orthotropic group consisted of 78 cases. CET occurred in 61% of patients of less than 6 years old. There was no significant correlation between preoperative angle of IXT and development of CET, but there was significant correlation with the angle of initial CET (postoperatively). CET was found in 16.7% of preoperative tenacious proximal convergence exotropia. CET was developed in 66.7% of cases of asymmetrical surgery (recession–resection), and more common with the development of lateral incomitance (27.8%). Amblyopia, suppression, and absence of stereopsis were considered risk factors in 50% of the cases. No correlation between errors of refraction and development of CET. Conclusion This study concluded that many risk factors may predispose to CET, the more significant factors were the age of the patients (<6 years old), large angle of initial postoperative CET, type of IXT, asymmetric surgery (recession–resection procedure), development of lateral incomitance, and presence of amblyopia or suppression.

Inverse of the Sum of Set-Valued Mappings and Applications

ABSTRACTIn this article, we develop results on the behavior of fixed points sets of set-valued pseudo-contraction mappings. Then, we investigate the notions related to the Aubin property and make use of connections between the two involved set-valued nonnecessarily Lipschitzian mappings to obtain results on the inverse of their sum similar to those in the literature generalizing Lyusternik and Graves theorems. By proximal convergence, we apply our results to the sensitivity analysis of variational inclusions.