Numerical Differentiation of Approximated Functions with Limited Order-of-Accuracy Deterioration

We consider the problem of numerical differentiation of a function f from approximate or noisy values of f on a discrete set of points; such discrete approximate data may result from a numerical calculation (such as a finite element or finite difference solution of a partial differential equation), from experimental measurements, or, generally, from an estimate of some sort. In some such cases it is useful to guarantee that orders of accuracy are not degraded: assuming the approximating values of the function are known with an accuracy of order O(h^r), where h is the mesh size, an accuracy of O(h^r) is desired in the value of the derivatives of f. Differentiation of interpolating polynomials does not achieve this goal since, as shown in this text, n-fold differentiation of an interpolating polynomial of any degree ≥ (r − 1) obtained from function values containing errors of order O(h^r) generally gives rise to derivative errors of order O(h^(r−n)); other existing differentiation algorithms suffer from similar degradations in the order of accuracy. In this paper we present a new algorithm, the LDC method (low degree Chebyshev), which, using noisy function values of a function f on a (possibly irregular) grid, produces approximate values of derivatives f^((n)) (n = 1, 2 . . .) with limited loss in the order of accuracy. For example, for (possibly nonsmooth) O(h^r) errors in the values of an underlying infinitely differentiable function, the LDC loss in the order of accuracy is “vanishingly small”: derivatives of smooth functions are approximated by the LDC algorithm with an accuracy of order O(h^r) for all r' < r. The algorithm is very fast and simple; a variety of numerical results we present illustrate the theory and demonstrate the efficiency of the proposed methodology

Somatosensory Deficits in Post-ACL Reconstruction Patients: A Case-Control Study

Introduction: Diminished cutaneous detection thresholds have been identified in patients with multiple orthopedic conditions, and these phenomena may occur in postanterior cruciate ligament reconstructed (ACLR) patients. The purpose of this study was to determine if differences in lower extremity cutaneous detection thresholds exist in post-ACLR patients when compared with healthy controls. Methods: Fifteen individuals who were post-ACLR and 15 individuals who had no history of knee injury participated. Light touch cutaneous detection thresholds were assessed at 4 locations on the foot and ankle (first metatarsal, fifth metatarsal, medial malleolus, and lateral malleolus). Nonparametric statistics examined group differences between the sites. Results: ACLR subjects had decreased cutaneous sensation at the first metatarsal and medial malleolus compared with healthy controls. Conclusions: Somatosensory deficits are present in post-ACLR patients. Future research should investigate these phenomena longitudinally in post-ACLR individuals along with somatosensory targeted interventions

Morphogenesis at criticality

Spatial patterns in the early fruit fly embryo emerge from a network of interactions among transcription factors, the gap genes, driven by maternal inputs. Such networks can exhibit many qualitatively different behaviors, separated by critical surfaces. At criticality, we should observe strong correlations in the fluctuations of different genes around their mean expression levels, a slowing of the dynamics along some but not all directions in the space of possible expression levels, correlations of expression fluctuations over long distances in the embryo, and departures from a Gaussian distribution of these fluctuations. Analysis of recent experiments on the gap gene network shows that all these signatures are observed, and that the different signatures are related in ways predicted by theory. Although there might be other explanations for these individual phenomena, the confluence of evidence suggests that this genetic network is tuned to criticality

Peroneal Reaction Time After Ankle Sprain: A Systematic Review and Meta-Analysis

Background: Many studies have examined the temporal response of the peroneal muscles to sudden inversion perturbation in patients with a previous ankle sprain. The purpose of this systematic review with meta-analysis was to synthesize the evidence and determine whether peroneal reaction time (PRT) impairments are present after ankle sprain. Methods: An electronic search was conducted using PubMed Central and EBSCOhost (1965-January 2013). Articles were included if they 1) examined the PRT to sudden inversion perturbation in patients with a history of ankle sprain using a mechanical tilt platform, 2) made comparisons with a control group or contralateral limb with no history of ankle sprain, and 3) provided data for the calculation of effect sizes (ES). In addition to examining the overall effect of sustaining an ankle sprain on PRT, the effects of study design and subject characteristics on PRT were evaluated. Bias-corrected Hedges g ES and 95% confidence intervals (CI) were calculated to make comparisons across studies. Results: A total of 23 studies met the inclusion criteria. The overall ES was 0.67 (95% CI = 0.37-0.95, P \u3c 0.001), indicating that a previous ankle sprain, regardless of study design or subject characteristics, resulted in moderate-to-strong PRT deficits. Further analyses determined studies with patients classified as having chronic ankle instability demonstrated large magnitude PRT deficits in between groups (ES = 0.72, 95% CI = 0.29-1.14, P = 0.001) and side-to-side (ES = 1.24, 95% CI = 0.70-1.79, P \u3c 0.001) comparisons, whereas patients with all other ankle sprain histories demonstrated weak PRT alterations in between groups (ES = -0.21, 95% CI = -1.01 to 0.59, P = 0.61) and side-to-side (ES = 0.21, 95% CI = -0.19 to 0.60, P = 0.31) comparisons. Conclusions: Overall, this meta-analysis determined that individuals with a previous ankle sprain exhibit delayed PRT. Further analyses determined that these deficits are more evident in patients with chronic ankle instability when compared with the contralateral uninvolved limb or a healthy control group

Plantar Vibrotactile Detection Deficits in Adults with Chronic Ankle Instability

Purpose: The purpose of this study was to investigate the vibrotactile detection thresholds of the plantar cutaneous afferents in subjects with chronic ankle instability compared with healthy control subjects. Methods: Eight adults with chronic ankle instability and eight adults with no ankle sprain history participated. Vibrotactile detection thresholds were assessed using a mechanical stimulus generator system, mounted onto an articulated microscope arm, which delivered sinusoidal vibrotactile inputs to the foot sole at three different sites: head of the first metatarsal, base of the fifth metatarsal, and the heel. Vibrotactile stimulation was delivered at a range of test frequencies that corresponded to the known responsiveness of cutaneous mechanoreceptors in the glabrous skin of the foot sole (10, 25, and 50 Hz). Probe displacement measures (dB) from the last eight displacement trials that contained 50% positive detection responses were averaged to obtain a single threshold estimate for each test frequency and site combination. Results: The results of this study indicate that no significant group-by-site interactions were found for any test frequencies (P \u3e 0.29). However, group main effects were present at the 10-Hz (P \u3c 0.0001), 25-Hz (P = 0.03), and 50-Hz (P = 0.04) test frequencies, indicating that subjects with chronic ankle instability had significantly higher detection thresholds or less sensitivity when stimulation sites were pooled. Conclusions: The results of this study indicate that subjects with chronic ankle instability may demonstrate decreased sensitivity on the plantar surface of the foot. These alterations in plantar cutaneous somatosensation may help explain the underlying mechanisms associated with the prolonged sensorimotor system impairments in postural control and gait commonly exhibited by people with chronic ankle instability

Gluteus maximus tendon transfer as a salvage option for painful chronic hip abductor insufficiency: clinical and MRI results with a minimum follow-up of 24 months

INTRODUCTION: Chronic hip abductor insufficiency is a rare debilitating condition. In cases refractory to conservative treatment and not amenable to direct repair an augmentation becomes necessary. The preferred salvage method at our institution is augmentation with the anterior third of the gluteus maximus tendon. The aim of this study is to describe the results of 8 patients, treated for painful chronic hip abductor insufficiency with gluteus maximus muscle transfer, after a minimal follow-up of 24 months including a full clinical and MRI evaluation of the hip abductors pre- and postoperatively. METHODS: We retrospectively reviewed a consecutive series of 8 patients who were surgically managed for painful chronic hip abductor insufficiency. All patients had a Trendelenburg sign, impaired muscle strength (M ⩽ 3) as well as a complete avulsion of the hip abductors with marked fatty degeneration (⩾3). Pain levels, muscle strength, functional scores as well as a postoperative MRI was obtained after a minimal follow-up of 24 months. RESULTS: The mean age of the patients was 69 years, mean follow-up was 35 (26-54) months. Pain was significantly reduced postoperatively to VAS 2.5 from VAS 5 (p = 0.046). Trendelenburg sign remained positive in all patients and hip abductor strength did not improve significantly from 2.4 to 3.1 (p = 0.19). Complete healing of the transferred tendon was confirmed by MRI in all patients at last follow-up. CONCLUSIONS: In the setting of painful chronic hip abductor insufficiency refractory to conservative treatment with advanced muscle degeneration without the possibility of a direct reconstruction the gluteus maximus tendon transfer significantly decreased pain. The effect on hip abductor strength and patient-reported functional outcome scores is limited. Despite the modest results it remains our preferred salvage treatment option for lack of better alternatives. Larger studies are necessary to confirm these findings

Two-week joint mobilization intervention improves self-reported function, range of motion, and dynamic balance in those with chronic ankle instability

We examined the effect of a 2-week anterior-to-posterior ankle joint mobilization intervention on weight-bearing dorsiflexion range of motion (ROM), dynamic balance, and self-reported function in subjects with chronic ankle instability (CAI). In this prospective cohort study, subjects received six Maitland Grade III anterior-to-posterior joint mobilization treatments over 2 weeks. Weightbearing dorsiflexion ROM, the anterior, posteromedial, and posterolateral reach directions of the Star Excursion Balance Test (SEBT), and self-reported function on the Foot and Ankle Ability Measure (FAAM) were assessed 1 week before the intervention (baseline), prior to the first treatment (pre-intervention), 24–48 h following the final treatment (post-intervention), and 1 week later (1-week follow-up) in 12 adults (6 males and 6 females) with CAI. The results indicate that dorsiflexion ROM, reach distance in all directions of the SEBT, and the FAAM improved (p < 0.05 for all) in all measures following the intervention compared to those prior to the intervention. No differences were observed in any assessments between the baseline and pre-intervention measures or between the postintervention and 1-week follow-up measures (p > 0.05). These results indicate that the joint mobilization intervention that targeted posterior talar glide was able to improve measures of function in adults with CAI for at least 1 week

Subtrochanteric osteotomy in the management of femoral maltorsion results in anteroposterior malcorrection of the greater trochanter: computed simulations of 3D surface models of 100 cadavers

Aim: The purpose of this study was to investigate the greater trochanter's (GT) behaviour in simulated subtrochanteric osteotomy. Materials and methods: Measurement of functional and anatomical femoral torsion, and position of the GT and lesser trochanter was performed using 3-dimensional (3D) surface models of 100 cadaveric femora. Femoral torsion between 2° and 22° was defined as normal, femora with 22° of femoral torsion were assigned to the low- and high-torsion group. Subtrochanteric osteotomy was simulated to normalise torsional deformities to 12°. Results: With subtrochanteric osteotomy, functional torsion was simultaneously corrected while adjusting anatomical torsion (R2 = 0.866, p < 0.001). Compared to the normal-torsion group, an anteroposterior (AP) overcorrection of ±0.5 centimetres (range 0.02-1.1 cm) of the GT resulted in the high- and low-torsion group, respectively (p < 0.001): Mean AP GT distance to a standardised coronal plane was 2.1 ± 0.3 cm (range 12-30 cm) in the normal-torsion group compared to 1.61 ± 0.1 cm (range 1.4-1.71 cm) and 2.6 ± 0.6 cm (range 1.8-3.6 cm) for the corrected high and low-torsion groups, respectively. The extent of the GT shift in AP direction correlated strongly with the extent to which anatomical femoral torsion was corrected (R2 = 0.946; p < 0.001). Conclusions: Subtrochanteric osteotomy for femoral maltorsion reliably adjusts anatomical and functional torsion, but also results in a ±1 cm AP shift of the GT per 10° of torsional correction. However, this effect of the procedure is most likely not clinically relevant in relation to hip abductor performance. Keywords: Femoral anteversion; maltorsion; subtrochanteric osteotomy; torsional correctio

Hip arthroscopy versus total hip arthroplasty-A study on patients with obesity above 40 years of age

Patients older than 40 years with a body-mass-index (BMI) >30 kg/m$^{2}$ , a femoroacetabular-impingement (FAI) and little cartilage damage are a challenge for hip surgeons. Hip-arthroscopy (HAS) or conservative therapy until a total hip arthroplasty (THA) is needed are possible treatments. Our research purpose was to compare the clinical results and complication/reoperation rate after HAS and THA in patients with obesity over 40 years. This retrospective study includes a consecutive series of patients with obesity (BMI >30 kg/m$^{2}$ ) who underwent HAS (19 hips) and THA (37 hips) over 40 years of age between 2007 and 2013 at our institution with a minimum of 12-months follow-up. Outcome measures were WOMAC (Western Ontario und McMaster Universities Arthritis Index), subjective-hip-value (SHV), residual complaints and the reoperation rate. Patient data and scores were collected pre-operative, 12 months post-operatively and at the last follow-up. Both groups showed a comparable age (mean 48 years). Regarding SHV-Scores the THA-group shows continuous significant improvements. Reaching 87% (range 50%-100%), the HAS-group showed in case of the SHV no significant change after 1 year and an improvement from preoperative to the last follow-up reaching 72% (range 30%-100%) at the last follow-up. Residual groin pain was significant higher in the HAS-group. Two deep infections (5.4%) requiring reoperations were reported in the THA-group. The conversion rate to THA after a mean time of 60 months was 26% (5 of 19). Patients with obesity over 40 years demonstrated inferior SHV, more often residual pain and revision surgery after HAS, when compared to THA at short-term, with conversions rate of one fourth. However, THA in this patient group showed high infection rate of 5%. This information is relevant for counselling above-mentioned patients