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Category: Trauma; Ankle Introduction/Purpose: Isolated lateral malleolus fracture is one of the most common fractures. However, there is controversy regarding the rehabilitation protocols used after surgery. In particular, the initiation point for the weight bearing has not been standardized. In the present study, we investigated the prognostic difference between the immediate and delayed weight bearing on isolated lateral malleolus fractures. Methods: Retrospectively, the medical records of matched 50 and 41patients in the immediate and delayed weight-bearing groups were reviewed. All patients were treated with open reduction and internal fixation using an anatomical locking compression plate. In the immediate weight-bearing group (IWB), tolerable weight bearing (i.e., that can be endured immediately after surgery with crutches) was permitted. In the delayed weight-bearing group (DWB), weight bearing was completely restricted for 4 weeks after surgery. Ankle motion exercise were permitted in both groups since postoperative day. Radiographic assessment data and the clinical outcomes were reviewed. Results: There were no significant differences noted in the radiographic assessments and complications between the two groups. Significant differences of shortening the return to work and hospital stays of IWB rehabilitation protocol were confirmed(5.7 vs. 8.0 days, 6.0 vs. 8.0 days in the IBW and DWB groups, respectively). In FAOS, there was a significant difference in the sport factor evaluated at postoperative 3 months(75.5 vs 68.5, respectively). Conclusion: There were no significant differences between the two groups in the postoperative radiological outcome and complications. And benefits of shortening the return to work and hospital stays of IWB rehabilitation protocol were confirmed. Conclusively, immediate weight bearing is recommended in patients with isolated lateral malleolus fracture, following anatomical reduction and firm fixation through surgery.

Abstract Background Incomplete sesamoid reduction is a potential risk factor for the recurrence of hallux valgus. The purpose of this study was to radiologically investigate changes in sesamoid position after chevron osteotomy and the open lateral soft tissue procedure. Methods Sixty-eight feet that underwent operative correction for hallux valgus deformity were reviewed consecutively. The hallux valgus angle (HVA), first to second intermetatarsal angle (IMA), tibial sesamoid position (TSP), distance of the fibular sesamoid (DFS), and translation of the metatarsal head (TMH) were evaluated preoperatively and at final follow-up. Results While most parameters were significantly decreased after surgery, no significant change in DFS (correction − 1.45 mm, p = 0.08) was noted. The difference between preoperative and postoperative TSP values (ΔTSP) has a moderately positive correlation with difference in TMH values (ΔTMH) (Rho 0.475, p = .000). Other parameters were similarly correlated. Conclusions First, metatarsal bone realignment reduced the sesamoid, but its position, relative to the second metatarsal axis (DFS), was unchanged. The sesamoid is reduced by the lateral translation of the first metatarsal but not by medial sesamoid migration.

Background: The morphology and alignment of the patellofemoral joint are crucial risk factors for patellar instability, and the incidence of acute primary patellar dislocation is the highest in women in their second decade of life. The purpose of the study was to analyze age and gender variations of the patellofemoral joint using magnetic resonance imaging (MRI). Methods: A total of 852 patients aged between 4 and 18 years with a history of knee MRI examinations were screened for eligibility and 663 patients (470 males, 193 females) were included. Patients were divided into groups according to age and sex. The age group was divided into five groups (Group 1, 4–6 years; Group 2, 7–9 years; Group 3, 10–12 years; Group 4, 13–15 years; and Group 5, 16–18 years). Three orthopaedic surgeons measured MRI parameters reflecting the patellofemoral morphology (sulcus angle, lateral trochlear inclination, trochlear facet symmetry, and femoral depth) and alignment (tibial tuberosity–trochlear groove distance, percent sulcus location, and percent tibia tuberosity location). Results: Parameters including tibial tuberosity–trochlear groove distance, sulcus angle, percent tibial tuberosity location, trochlear facet symmetry, and femoral depth showed significant differences between the age groups (p < 0.05). The sulcus angle decreased fin Group 2, and the femoral depth showed an increasing trend with aging in male patients. However, the sulcus angle in females decreased first and then increased in Group 3 as the inflection point. The femoral depth showed an opposite pattern. Conclusions: Patellofemoral morphometry showed age and gender variation. Notably, the sulcus angle and femoral depth were significantly different between males and females and changed according to the development. These findings may reflect the sex difference and peak incidence of the patellar instability risk. Understanding the morphological changes and differences of the patellofemoral joint may facilitate the diagnosis of patellofemoral pathologies.

A set S of natural numbers is a Sidon set if all the sums s1 +s2 with s1, s2 2 S and s1 s2 are distinct. Let constant > 0 and 0 << 1 be xed, and let pm = minf1;m1+g for all positive integers m. Generate a random set R N by adding m to R with probability pm, independently for each m. We investigate how dense a Sidon set S contained in R can be. Our results show that the answer is qualitatively very diferent in at least three ranges of . We prove quite accurate results for the range 0 < 2=3, but only obtain partial 1. [ABSTRACT FROM AUTHOR]

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For a family Ƒ of graphs, a graph G is called Ƒ-universal if G contains every graph in Ƒ as a subgraph. Let Ƒn(d) be the family of all graphs on n vertices with maximum degree at most d. Dellamonica, Kohayakawa, Rödl, and Ruciński [An improved upper bound on the density of universal random graphs, Random Structures & Algorithms, doi: 10.1002/rsa.20545] showed that, for d ≥ 3, the random graph G(n,p) is Ƒn(d)-universal with high probability provided p ≥ C(log n/n)1/d for a sufficiently large constant C = C(d). In this paper we prove the missing part of the result, that is, the random graph G(n,p) is Ƒn(2)-universal with high probability provided p ≥ C(log n/n)½ for a sufficiently large constant C. [ABSTRACT FROM AUTHOR]

This paper presents a method for detecting and restoring integer datasets that have been manipulated by operations involving nonintegral real-number multiplication and rounding. As we discuss in the paper, detecting and restoring such manipulated integer datasets is not straightforward, nor are there any known solutions. We introduce the manipulation process, which was motivated by an actual case of fraud, and survey several areas of literature dealing with the possibility that manipulation may have happened or might occur. From our mathematical analysis of the manipulation process, we can prove that the nonintegral real number ( $\alpha $ ) used in the multiplication exists not as a single real number but as an interval containing infinitely many real numbers, any of which could have been used to produce the same manipulation result. Based on these analytic findings, we provide an algorithm that can detect and restore manipulated integer datasets. To validate our algorithm, we applied it to 40,000 test datasets that were randomly generated using controllable parameters that matched the real fraud case. Our results indicated that the algorithm detected and perfectly restored all datasets for which the value of the nonintegral real number was at least 16 ( $\alpha \geq 16$ ) and the number of data entries was at least 40 ( $n\geq 40$ ).