Stretched Polymers in Random Environment

We survey recent results and open questions on the ballistic phase of stretched polymers in both annealed and quenched random environments.Comment: Dedicated to Erwin Bolthausen on the occasion of his 65th birthda

Quenched large deviations for multidimensional random walk in random environment with holding times

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and the laws of the holding times are randomly distributed over the integer lattice. Our main result is a quenched large deviation principle for the position of the random walk. The rate function is given by the Legendre transform of the so-called Lyapunov exponents for the Laplace transform of the first passage time. By using this representation, we derive some asymptotics of the rate function in some special cases.Comment: This is the corrected version of the paper. 24 page

Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher

We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment. It is easy to see that the quenched and the averaged rate functions are not identically equal. When the dimension is at least four and Sznitman's transience condition (T) is satisfied, we prove that these rate functions are finite and equal on a closed set whose interior contains every nonzero velocity at which the rate functions vanish.Comment: 17 pages. Minor revision. In particular, note the change in the title of the paper. To appear in Probability Theory and Related Fields

The winking sign is an indicator for increased femorotibial rotation in patients with recurrent patellar instability

Purpose: Rotation of the tibia relative to the femur was recently identified as a contributing risk factor for patellar instability, and correlated with its severity. The hypothesis was that in patellofemoral dysplastic knees, an increase in femorotibial rotation can be reliably detected on anteroposterior (AP) radiographs by an overlap of the lateral femoral condyle over the lateral tibial eminence. Methods: Sixty patients (77 knees) received low-dose computed tomography (CT) of the lower extremity for assessment of torsional malalignment due to recurrent patellofemoral instability. Three-dimensional (3D) surface models were created to assess femorotibial rotation and its relationship to other morphologic risk factors of patellofemoral instability. On weight-bearing AP knee radiographs, a femoral condyle/lateral tibial eminence superimposition was defined as a positive winking sign. Using digitally reconstructed radiographs of the 3D models, susceptibility of the winking sign to vertical/horizontal AP knee radiograph malrotation was investigated. Results: A positive winking sign was present in 30/77 knees (39.0%) and indicated a 6.3 ± 1.4° increase in femorotibial rotation (p 15°) with 43% sensitivity and 90% specificity (AUC = 0.72; p = 0.002). A positive winking sign (with 2 mm overlap) disappeared in case of a 10° horizontally or 15° vertically malrotated radiograph, whereas a 4 mm overlap did not disappear at all, regardless of the quality of the radiograph. In absence of a winking sign, on the other hand, no superimposition resulted within 20° of vertical/horizontal image malrotation. Femorotibial rotation was positively correlated to TT-TG (R2 = 0.40, p = 0.001) and patellar tilt (R2 = 0.30, p = 0.001). Conclusions: The winking sign reliably indicates an increased femorotibial rotation on a weight-bearing AP knee radiograph and could prove useful for day-by-day clinical work. Future research needs to investigate whether femorotibial rotation is not only a prognostic factor but a potential surgical target in patients with patellofemoral disorders. Level of evidence: III. Keywords: Femorotibial rotation; Knee rotation; Patellar instability; Winking sig

Extent of posterolateral tibial plateau impaction fracture correlates with anterolateral complex injury and has an impact on functional outcome after ACL reconstruction

PURPOSE The impact of posterolateral tibial plateau impaction fractures (TPIF) on posttraumatic knee stability in the setting of primary anterior cruciate ligament (ACL) tear is unknown. The main objective was to determine whether increased bone loss of the posterolateral tibial plateau is associated with residual rotational instability and impaired functional outcome after ACL reconstruction. METHODS A cohort was identified in a prospective enrolled study of patients suffering acute ACL injury who underwent preoperative standard radiographic diagnostics and clinical evaluation. Patients were included when scheduled for isolated single-bundle hamstring autograft ACL reconstruction. Exclusion criteria were concurrent anterolateral complex (ALC) reconstruction (anterolateral tenodesis), previous surgery or symptoms in the affected knee, partial ACL tear, multi-ligament injury with an indication for additional surgical intervention, and extensive cartilage wear. On MRI, bony (TPIF, tibial plateau, and femoral condyle morphology) and ligament status (ALC, concomitant collateral ligament, and meniscus injuries) were assessed by a musculoskeletal radiologist. Clinical evaluation consisted of KT-1000, pivot-shift, and Lachman testing, as well as Tegner activity and IKDC scores. RESULTS Fifty-eight patients were included with a minimum follow-up of 12 months. TPIF was identified in 85% of ACL injuries (n = 49). The ALC was found to be injured in 31 of 58 (53.4%) cases. Pearson analysis showed a positive correlation between TPIF and the degree of concomitant ALC injury (p < 0.001). Multiple regression analysis revealed an increased association of high-grade TPIF with increased lateral tibial convexity (p = 0.010). The high-grade TPIF group showed worse postoperative Tegner scores 12 months postoperatively (p = 0.035). CONCLUSION Higher degrees of TPIFs are suggestive of a combined ACL/ALC injury. Moreover, patients with increased posterolateral tibial plateau bone loss showed lower Tegner activity scores 12 months after ACL reconstruction. LEVEL OF EVIDENCE III

Tibial internal rotation in combined anterior cruciate ligament and high-grade anterolateral ligament injury and its influence on ACL length

BACKGROUND Assessment of combined anterolateral ligament (ALL) and anterior cruciate ligament (ACL) injury remains challenging but of high importance as the ALL is a contributing stabilizer of tibial internal rotation. The effect of preoperative static tibial internal rotation on ACL -length remains unknown. The aim of the study was analyze the effect of tibial internal rotation on ACL length in single-bundle ACL reconstructions and to quantify tibial internal rotation in combined ACL and ALL injuries. METHODS The effect of tibial internal rotation on ACL length was computed in a three-dimensional (3D) model of 10 healthy knees with 5° increments of tibial internal rotation from 0 to 30° resulting in 70 simulations. For each step ACL length was measured. ALL injury severity was graded by a blinded musculoskeletal radiologist in a retrospective analysis of 61 patients who underwent single-bundle ACL reconstruction. Preoperative tibial internal rotation was measured in magnetic resonance imaging (MRI) and its diagnostic performance was analyzed. RESULTS ACL length linearly increased 0.7 ± 0.1 mm (2.1 ± 0.5% of initial length) per 5° of tibial internal rotation from 0 to 30° in each patient. Seventeen patients (27.9%) had an intact ALL (grade 0), 10 (16.4%) a grade 1, 21 (34.4%) a grade 2 and 13 (21.3%) a grade 3 injury of the ALL. Patients with a combined ACL and ALL injury grade 3 had a median static tibial internal rotation of 8.8° (interquartile range (IQR): 8.3) compared to 5.6° (IQR: 6.6) in patients with an ALL injury (grade 0-2) (p = 0.03). A cut-off > 13.3° of tibial internal rotation predicted a high-grade ALL injury with a specificity of 92%, a sensitivity of 30%; area under the curve (AUC) 0.70 (95% CI: 0.54-0.85) (p = 0.03) and an accuracy of 79%. CONCLUSION ACL length linearly increases with tibial internal rotation from 0 to 30°. A combined ACL and high-grade ALL injury was associated with greater preoperative tibial internal rotation. This potentially contributes to unintentional graft laxity in ACL reconstructed patients, in particular with concomitant high-grade ALL tears. STUDY DESIGN Cohort study; Level of evidence, 3

Three-dimensional analysis of functional femoral antetorsion and the position of the greater trochanter in high-grade patellofemoral dysplastic knees

BACKGROUND The relationship between functional femoral antetorsion, the greater trochanter (GT) position and anatomical antetorsion has been demonstrated in patients with a primary hip pathology. However, the functional antetorsion and GT position have not been analyzed in patellofemoral dysplastic knees. The aim of this study was to develop a three-dimensional (3D) measurement to quantify the functional femoral antetorsion and position of the GT and to analyze these measurements in a cohort of high-grade patellofemoral dysplastic knees. METHOD A 3D measurement was developed to analyze functional antetorsion and the axial position of the GT and assessed in 100 cadaveric femora. For validity and repeatability testing, inter- and intra-observer reliability were determined using intraclass correlation coefficients (ICCs). These measurements were then evaluated in a cohort of 19 high-grade patellofemoral dysplastic knees (Dejour type C, D). The relationship between anatomical antetorsion, functional antetorsion and GT position were reported. RESULTS Inter- and intra-reader reliability for 3D functional antetorsion and axial position of the GT demonstrated a minimum ICC of 0.96 (P < 0.001). Anatomical and functional antetorsion demonstrated a highly linear relationship (R$^{2}$ = 0.878; P < 0.001) in high-grade patellofemoral dysplastic knees. The mean difference between anatomical and functional antetorsion decreased with increasing anatomical antetorsion (R$^{2}$ = 0.25; P = 0.031, indicating a more anterior position of the GT relative to the femoral neck axis. CONCLUSION In high-grade patellofemoral dysplastic knees, the GT is located more anteriorly, relative to the femoral neck axis, with increasing anatomical antetorsion and correction osteotomy may result in an excessively anterior position of the GT

Influence of Bone Morphology on In Vivo Tibio-Femoral Kinematics in Healthy Knees during Gait Activities

An improved understanding of the relationships between bone morphology and in vivo tibio-femoral kinematics potentially enhances functional outcomes in patients with knee disorders. The aim of this study was to quantify the influence of femoral and tibial bony morphology on tibio-femoral kinematics throughout complete gait cycles in healthy subjects. Twenty-six volunteers underwent clinical examination, radiographic assessment, and dynamic video-fluoroscopy during level walking, downhill walking, and stair descent. Femoral computer-tomography (CT) measurements included medial condylar (MC) and lateral condylar (LC) width, MC and LC flexion circle, and lateral femoral condyle index (LFCI). Tibial CT measurements included both medial (MTP) and lateral tibial plateau (LTP) slopes, depths, lengths, and widths. The influence of bony morphology on tibial internal/external rotation and anteroposterior (AP)-translation of the lateral and medial compartments were analyzed in a multiple regression model. An increase in tibial internal/external rotation could be demonstrated with decreasing MC width β: -0.30 (95% CI: -0.58 to -0.03) (p = 0.03) during the loaded stance phase of level walking. An increased lateral AP-translation occurred with both a smaller LC flexion circle β: -0.16 (95% CI: -0.28 to -0.05) (p = 0.007) and a deeper MTP β: 0.90 (95% CI: 0.23 to 1.56) (p = 0.01) during the loaded stance phase of level walking. The identified relationship between in vivo tibio-femoral kinematics and bone morphology supports a customized approach and individual assessment of these factors in patients with knee disorders and potentially enhances functional outcomes in anterior cruciate ligament injuries and total knee arthroplasty

Tibial tunnel enlargement is affected by the tunnel diameter-screw ratio in tibial hybrid fixation for hamstring ACL reconstruction

INTRODUCTION There is no evidence on screw diameter with regards to tunnel size in anterior cruciate ligament reconstruction (ACLR) using hybrid fixation devices. The hypothesis was that an undersized tunnel coverage by the tibial screw leads to subsequent tunnel enlargement in ACLR in hybrid fixation technique. METHODS In a retrospective case series, radiographs and clinical scores of 103 patients who underwent primary hamstring tendon ACLR with a hybrid fixation technique at the tibial site (interference screw and suspensory fixation) were obtained. Tunnel diameters in the frontal and sagittal planes were measured on radiographs 6 weeks and 12 months postoperatively. Tunnel enlargement of more than 10% between the two periods was defined as tunnel widening. Tunnel coverage ratio was calculated as the tunnel diameter covered by the screw in percentage. RESULTS Overall, tunnel widening 12 months postoperatively was 23.1 ± 17.1% and 24.2 ± 18.2% in the frontal and sagittal plane, respectively. Linear regression analysis revealed the tunnel coverage ratio to be a negative predicting risk factor for tunnel widening (p = 0.001). The ROC curve analysis provided an ideal cut-off for tunnel enlargement of > 10% at a tunnel coverage ratio of 70% (sensitivity 60%, specificity 81%, AUC 75%, p  10% in the frontal plane if the tunnel coverage ratio was < 70% (sagittal plane: OR 14.7, p = 0.001). Clinical scores did not correlate to tunnel widening. CONCLUSION Tibial tunnel widening was affected by the tunnel diameter coverage ratio. To minimize the likelihood of disadvantageous tunnel expansion-which is of importance in case of revision surgery-an interference screw should not undercut the tunnel diameter by more than 1 mm

Excessive femoral torsion is not associated with patellofemoral pain or instability if TKA is functionally aligned and the patella denervated

PURPOSE Recent data suggest that individual morphologic factors should be respected to restore preoperative patellofemoral alignment and thus reduce the likelihood of anterior knee pain. The goal of this study was to investigate the effect of excessive femoral torsion (FT) on clinical outcome of TKA. METHODS Patients who underwent TKA and complete preoperative radiographic evaluation including a long-leg radiograph and CT scan were included. 51 patients showed increased FT of > 20° and were matched for age/sex to 51 controls (FT < 20°). Thirteen patients were lost to follow-up. Thirty-eight matched pairs were compared after a 2 year follow-up clinically (Kujala and patellofemoral score for TKA) and radiographically (FT, frontal leg axis, TT-TG, patellar thickness, patellar tilt, and lateral displacement of patella). Functional alignment of TKA was performed (hybrid-technique). All patellae were denervated but no patella was resurfaced. RESULTS There was no significant difference between clinical scores two years after surgery between patients with normal and excessive FT (n.s.). Kujala score was 64.3 ± 16.7 versus 64.8 ± 14.4 (n.s.), and patellofemoral score for TKA was 74.3 ± 21 versus 78.5 ± 20.7 (n.s.) for increased FT group and control group, respectively. There was no correlation between preoperative FT and clinical scores. Other radiographic parameters were similar between both groups. No correlations between clinical outcomes and preoperative/postoperative frontal leg axis or total leg axis correction were found (n.s.). CONCLUSION If the leg axis deformity is corrected to a roughly neutral alignment during cemented TKA, including patellar denervation, then excessive FT was not associated with patellofemoral pain or instability. LEVEL OF EVIDENCE Prospective comparative study, level II